Handbook of Solvents, Volume 1 [3rd ed] 9781927885406, 192788540X, 9781927885383

Table of contents :
Content: Front Cover
Handbook of Solvents: Properties
Copyright Page
Table of Contents
Chapter 1. Introduction
REFERENCES
Chapter 2. Fundamental Principles Governing Solvents Use
2.1 SOLVENT EFFECTS ON CHEMICAL SYSTEMS
2.2 MOLECULAR DESIGN OF SOLVENTS
2.3 BASIC PHYSICAL AND CHEMICAL PROPERTIES OF SOLVENTS
Chapter 3. Production Methods, Properties, and Main Applications
3.1 DEFINITIONS AND SOLVENT CLASSIFICATION
3.2 OVERVIEW OF METHODS OF SOLVENT MANUFACTURE
3.3 SOLVENT PROPERTIES
Chapter 4. General Principles Governing Dissolution of Materials in Solvents 4.1 SIMPLE SOLVENT CHARACTERISTICS4.2 EFFECT OF SYSTEM VARIABLES ON SOLUBILITY
4.3 SOLVATION DYNAMICS: THEORY AND EXPERIMENTS
4.4 METHODS FOR THE MEASUREMENT OF SOLVENT ACTIVITY OF POLYMER SOLUTIONS
Chapter 5. Solubility of Selected Systems and Influence of Solutes
5.1 EXPERIMENTAL METHODS OF EVALUATION AND CALCULATION OF SOLUBILITY PARAMETERS OF POLYMERS AND SOLVENTS. SOLUBILITY PARAMETERS DATA
5.2 PREDICTION OF SOLUBILITY PARAMETERS
5.3 METHODS OF CALCULATION OF SOLUBILITY PARAMETERS OF SOLVENTS AND POLYMERS
Chapter 6. Swelling 6.1 MODERN VIEWS ON KINETICS OF SWELLING OF CROSSLINKED ELASTOMERS IN SOLVENTS6.2 EQUILIBRIUM SWELLING IN BINARY SOLVENTS
6.3 SWELLING DATA ON CROSSLINKED POLYMERS IN SOLVENTS
6.4 INFLUENCE OF STRUCTURE ON EQUILIBRIUM SWELLING
6.5 EFFECT OF STRAIN ON THE SWELLING OF NANO-STRUCTURED ELASTOMERS
6.6 THE EFFECT OF THERMODYNAMIC PARAMETERS OF POLYMER−SOLVENT SYSTEM ON THE SWELLING KINETICS OF CROSSLINKED ELASTOMERS
Chapter 7. Solvent Transport Phenomena
7.1 INTRODUCTION TO SOLVENT TRANSPORT PHENOMENA
7.2 BUBBLES DYNAMICS AND BOILING OF POLYMERIC SOLUTIONS
Chapter 8. Solvent Mixtures 8.1 MIXED SOLVENTS8.2 THE PHENOMENOLOGICAL THEORY OF SOLVENT EFFECTS IN MIXED SOLVENT SYSTEMS
Chapter 9. Acid-base and Other Interactions
9.1 GENERAL CONCEPT OF ACID-BASE INTERACTIONS
9.2 ACIDS AND BASES IN MOLTEN SALTS, OXOACIDITY
9.3 SOLVENT EFFECTS BASED ON PURE SOLVENT SCALES
9.4 MODELING OF ACID-BASE PROPERTIES IN BINARY-SOLVENT SYSTEMS
Chapter 10. Electronic and Electrical Effects of Solvents
10.1 SOLVENT EFFECTS ON ELECTRONIC AND VIBRATIONAL SPECTRA
10.2 DIELECTRIC SOLVENT EFFECTS ON THE INTENSITY OF LIGHT ABSORPTION AND THE RADIATIVE RATE CONSTANT 10.3 SOLVENT EFFECTS ON THE TWO-PHOTON ABSORPTION CROSS-SECTION OF ORGANIC MOLECULESChapter 11. Other Properties of Solvents, Solutions, and Products Obtained from Solutions
11.1 RHEOLOGICAL PROPERTIES
11.2 AGGREGATION
11.3 PERMEABILITY
11.4 MOLECULAR STRUCTURE AND CRYSTALLINITY
11.5 OTHER PROPERTIES AFFECTED BY SOLVENTS
Chapter 12. Effect of Solvents on Chemical Reactions and Reactivity
12.1 SOLVENT EFFECTS ON CHEMICAL REACTIVITY
12.2 SOLVENT EFFECTS ON FREE RADICAL POLYMERIZATION
Index

Citation preview

Handbook of rd

Solvents, 3 Edition Volume 1. Properties

George Wypych, Editor

Toronto 2019

Published by ChemTec Publishing 38 Earswick Drive, Toronto, Ontario M1E 1C6, Canada © ChemTec Publishing, 2000, 2014, 2019 ISBN 978-1-927885-38-3 (hard copy); 978-1-927885-40-6 (epub) Cover: Anita Wypych

All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means without written permission of copyright owner. No responsibility is assumed by the Author and the Publisher for any injury or/and damage to persons or properties as a matter of products liability, negligence, use, or operation of any methods, product ideas, or instructions published or suggested in this book.

Library and Archives Canada Cataloguing in Publication Handbook of solvents / George Wypych, editor. -- 3rd edition. First edition issued in one volume. Includes bibliographical references and index. Contents: Volume 1. Properties. Issued in print and electronic formats. ISBN 978-1-927885-38-3 (v. 1).--ISBN 978-1-927885-40-6 (v. 1) 1. Solvents--Handbooks, manuals, etc. I. Wypych, George, editor TP247.5.H35 2019

661'.807

C2018-904011-4 C2018-904012-2

1

Introduction Christian Reichardt Fachbereich Chemie, Philipps-Universität, Marburg, Germany Chemical transformations can be performed in a gas, liquid, or solid phase, but, with good reasons, the majority of such reactions is carried out in the liquid phase, that is in solution.1,2 In this context, a familiar and often cited quotation of the famous ancient Greek philosopher Aristotle (384 − 322 B.C.) was handed down, which reads in Latin Corpora non agunt nisi fluida (or liquida) seu soluta, and was later translated into English as Compounds do not react unless fluid (or if dissolved), or No reactions in the absence of solvent; for examples see refs.3-5 However, this common version seems to be a misinterpretation of the original text given in Greek as Τά ύγρά μικτά μάλιστα τών σωμάτων (Tá hygrá miktá málista ton somáton), which is probably taken from Aristotle's work De Generatione et Corruptione.6 According to Hedvall,5 this statement should be better read as … it is chiefly the liquid substances which react,5 or … for instance liquids are the type of bodies liable to mixing.6c In this somewhat softened version, Aristotle's statement is obviously less distinct and didactic. With respect to the many solid/solid reactions known today,5,7 it is understandable that solid-state chemists were not entirely happy with the common first version of Aristotle's statement. At the macroscopic level, a liquid is an ideal medium to transport heat to and from endo- and exothermic chemical reactions. From the molecular-microscopic point of view, solvents break the crystal lattices of solid reactants, dissolve gaseous or liquid reactants, and they may exert considerable influence over reaction rates and the positions of chemical equilibria. Because of nonspecific and specific intermolecular forces acting between the ions or molecules of dissolved reactants, activated complexes as well as products and the surrounding solvent molecules (leading to differential solvation of all solutes), the rates, equilibria, and the selectivity of chemical reactions can be strongly influenced by the solvent. Other than the fact that the liquid medium should dissolve the reactants and should be easily separated from the reaction products afterward, the solvent can have a decisive influence on the outcome (i.e., yield and product distribution) of the chemical reaction under study. Therefore, whenever a chemist wishes to perform a certain chemical reaction, she/he has to take into account not only suitable reaction partners and their concentrations, the proper reaction vessel, the appropriate reaction temperature and, if necessary, the selection of the right reaction catalyst, but also, if the planned reaction is to be successful, the selection of an appropriate solvent or solvent mixture. It stands for the reason that the solvent of choice should not chemically react with the reactants and products and, thus, interfere directly with the planned reaction as a new reaction partner.

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Introduction

The solvent influence on chemical reactivity has been studied for more than a century, beginning with the pioneering work of M. Berthelot and L. Péan de Saint Gilles8 in Paris in 1862 on the esterification reaction of acetic acid with ethanol, and with that of N. Menschutkin9-11 in St. Petersburg in 1890 on the quaternization of tertiary amines by haloalkanes to give tetraalkylammonium salts. At this time Menschutkin remarked that “a reaction cannot be separated from the medium in which it is performed … Experience shows that solvents exert considerable influence on reaction rates.” Today, we can suggest a striking example to reinforce this remark, the rate of the unimolecular heterolysis of 2chloro-2-methylpropane observed in water and benzene increases by a factor of approximately 1011 when the nonpolar benzene is replaced by water.1,12 The influence of solvents on the position of chemical equilibria was discovered in 1896 by L. Claisen13 in Aachen, L. Knorr14 in Jena, W. Wislicenus15 in Würzburg, and A. Hantzsch16 in Würzburg, all places in Germany. They investigated almost simultaneously but independently of one another the keto-enol tautomerism of 1,3-dicarbonyl compounds13-15 and the nitro-isonitroso tautomerism of primary and secondary aliphatic nitro compounds.16 For example, the enol content of acetylacetone increases from 62 to 95 mol-% when acetonitrile or dimethyl sulfoxide is substituted with n-hexane as solvent (at 33°C and 0.1 mole fraction of solute).1,17 A first attempt to introduce an empirical parameter of solvent polarity or solvent power was already made in 1914 by K. H. Meyer in Munich18 by means of selected solvent-dependent keto-enol equilibria. He found a proportionality between the tautomeric equilibrium constants KT of various 1,3-dicarbonyl compounds measured in the same set of solvents, and he split these constants into two independent factors according to KT = c(enol)/c(keto) ≡ L • E. E is the so-called enol constant and measures the enolization capability of the diketo form (E = 1 for ethyl acetoacetate by definition), and L is called desmotropic constant as a measure of the enolization power of the solvent. By definition, the values of L are equal to the equilibrium constants of ethyl acetoacetate (E = 1), determined in different solvents. This desmotropic constant L can be considered as the first empirical parameter of solvent polarity, determined by means of a carefully selected standard chemical reaction, and its definition equation as the first linear free-energy (LFE) relationship. An analogous, better-known approach was used in 1937 by L. P. Hammett in New York (at Columbia University),19 using the ionization constants of substituted benzoic acids, measured in water at 25 °C, in order to define his famous equation lg(kx / k0) = σ • ρ , in which kx is the rate or equilibrium constant for meta- and parasubstituted benzoic acids and k0 that of unsubstituted benzoic acid, ρ the reaction constant ( ρ = 1 for the standard reaction by definition), and σ the empirical substituent constant. For reviews of important LFE relationships, dealing among others with solvent effects, see references.1,11,20 The proper solvent or solvent mixture selection is not only important for chemical but also for physical processes such as recrystallization,21 all extraction and partitioning processes,22 chromatographic separations,23 liquid/liquid phase-transfer catalytic reactions,24 etc. Of particular interest in this context is the influence of solvents on all types of light absorption processes, e.g., on UV/Vis/NIR, IR, ESR, and NMR spectra of

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dissolved solutes, caused by differential solvation of the ground and first excited states of the absorbing species.1,25 For example, in 1878, A. Kundt26 in Zürich proposed the rule that increasing dispersion interactions between the absorbing solute and the solvent lead in general to a bathochromic shift of a UV/Vis absorption band. In 1922, A. Hantzsch27 in Würzburg termed the solvent dependence of UV/Vis absorption spectra solvatochromism. Later on, a bathochromic band shift with increasing solvent polarity was called positive solvatochromism, a corresponding hypsochromic band shift negative solvatochromism.1,25,27 UV/Vis absorption spectra of solute chromophores can be influenced not only by the surrounding solvent sphere, but also by other surroundings such as micelles, vesicles, gels, polymers, glasses, solids, and surfaces. Therefore, the use of the more general term perichromism (from Greek peri = around and chrōma = color) has been recommended by E. M. Kosower.28 A typical, more recent example of an extraordinarily large negative solvatochromism is the intramolecular charge-transfer Vis/NIR absorption of 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl)phenolate, a zwitterionic, commercially available betaine dye: its long-wavelength absorption band is shifted from λmax = 810 to 453 nm (Δλ = −357 nm; Δv˜ = +9730 cm-1) when diphenyl ether is replaced by water as solvent.1,25 Such solvatochromic dyes have been used for the introduction of spectroscopically derived empirical parameters of solvent polarity such as the ET(30) and the normalized ETN values.1,20,25 The number of solvents generally available to chemists working in research and industrial laboratories is between 250 and 300,1,29 with an indefinite number of solvent mixtures,30 and this number is increasing. More recently and for obvious reasons, the search for new, less toxic and more sustainable new solvents has been intensified.31 For example, peroxide-forming solvents are being substituted by solvents which are more stable against oxidation (e.g., diethyl ether by t-butyl methyl ether,32 by formaldehyde dialkylacetals,33 or by 2-methyltetrahydrofuran34); toxic solvents are being replaced by nontoxic ones [e.g., the cancerogenic hexamethylphosphoric triamide (HMPT) by N,N'dimethylpropyleneurea (DMPU)35]; and environmentally dangerous solvents by benign ones (e.g., ozone-depleting tetrachloromethane by perfluorohexane36). The further development of modern solvents for organic syntheses is subject of current research, and many reviews and books on this topic are already available.31,37-45 For solvents commonly used in pharmaceuticals production, Pfizer has developed a widely used “traffic light” solvent preference system, which divides these solvents into preferred (green), usable (orange), and undesirable (red) solvents.46 Amongst these modern solvents, also called neoteric solvents (neoteric = recent, new, modern), in contrast to classical molecular solvents, are ionic liquids (i.e., at room-temperature liquid salts such as 1,3-dialkylimidazolium salts),47-55 supercritical fluids, SCF's56 (such as scf carbon dioxide57,58 and scf water59,60), perfluorinated solvents61,62 (such as partially or perfluorinated hydrocarbons as used in socalled “fluorous biphasic catalysis reactions”, making possible mono-phase reactions followed by a two-phase separation of catalyst and reaction products), and biomass-derived solvents (e.g., glycerol and its derivatives, ethyl lactate, fatty acid esters, etc.).31 Even plain water63-65 and liquid ammonia66 have found a magnificent renaissance as solvents for organic reactions. Another class of versatile and benign solvents is gas-expanded liq-

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Introduction

uids (GXL's), which are intermediate in properties between common molecular liquids and supercritical fluids.67,68 GXL's are mixed solvents composed of a compressible gas (such as CO2 or ethane), dissolved in an organic solvent (such as methanol, acetone, or acetonitrile). By varying the gas/solvent composition, the mixture properties can be easily adjusted by tuning the operating pressure. In addition, another class of so-called switchable69 and tunable solvents70 have attracted great attention recently. These solvents are designed in their molecular structure in such a way, that they can be reversibly converted from one form to another, depending on the reaction conditions. The chemical and physical properties of such switchable and tunable solvents can be changed abruptly resp. continuously by application of an external stimulus (change in temperature and/or pressure). For example, when CO2 is bubbled through a 1:1 mixture of the cyclic amidine DBU with an alcohol (e.g., 1-hexanol), an ionic amidinium alkyl carbonate is formed. This change can be easily reversed by mild heating (50-60 °C) or by bubbling nitrogen or argon at room temperature through the ionic liquid formed, and the liquid goes back to its initial state. Recent useful compilations of neoteric solvent-based new green synthetic techniques can be found in reference.71 All these efforts into finding new liquid reaction media have also strengthened the search for completely solvent-free reactions, thus avoiding the use of expensive, toxic, and environmentally problematic solvents.4a,72-75 Solid-state chemical reactions are not quite new. One of the first solvent-free reaction is the rearrangement of solid ammonium cyanate into solid urea, discovered by F. Wöhler in 1828 in Berlin, as a historically important example for the transformation of an inorganic into an organic material.76 However, for good reasons, a majority of chemical reactions cannot be carried out in the absence of solvents. Solvents will still be indispensable in mediating and moderating chemical reactions and books like this handbook will certainly not become superfluous in the foreseeable future.1 With respect to the large and increasing number of valuable solvents useful for organic syntheses, a chemist needs, in addition to his experience and intuition, to have general rules, objective criteria, and the latest information about the solvents' physical, chemical, and toxicological properties for the selection of the proper solvent or solvent mixture for a planned reaction or a technological process. To make this often cumbersome and time-consuming task easier, this third edition of the “Handbook of Solvents” with its twenty-two chapters is designed to provide a comprehensive source of information on solvents over a broad range of applications. It is directed not only to chemists working in research laboratories but also to all industries using solvents for various purposes. A particular advantage is that the printed handbook is accompanied by a compact disc (CDROM) containing additional solvent databases with a hundred forty fields for over sixteen hundred solvents. This makes large datasets available for quick search and retrieval and frees the book text from bulky tables, thus giving more room for a thorough description of the underlying theoretical and practical fundamental concepts. Fundamental principles governing the use of solvents such as chemical structure, molecular design, basic physical and chemical properties, as well as classification of intermolecular solute/solvent interactions, modeling of solvent effects, and solvent influence

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on chemical reactions in solution, are given in Chapter 2. Definitions needed to classify solvents, an overview of methods of solvent manufacture, together with properties of typical solvent classes (i. e., hydrocarbons, halohydrocarbons, alcohols, ketones, etc.) are provided in Chapter 3. Chapters 4, 5, and 6 deal with all aspects of the dissolution of materials in solvents and solvent mixtures as well as with the solubility of selected systems (e.g., polymers and elastomers) and the influence of the solute's molecular structure on its solubility behavior. In particular, the valuable solubility-parameter concept of Hildebrand and its three-dimensional modification by Hansen are extensively treated in these Chapters. The diffusion of organic solvents and binary solvent mixtures into crosslinked elastomers, leading to considerable swelling of these materials, is especially addressed in Chapter 6. All aspects of solvent transport phenomena (i.e., the formation of solutions or films by diffusion or swelling and subsequent removal of the solvents by various drying processes), which are also solute- and solvent-dependent, are described in Chapter 7. Chapter 8 deals with chemical and physical properties of solvent mixtures, which are usually non-additive because of the often found non-ideality of such mixtures, caused by specific intermolecular solvent/solvent interactions, and mostly leading to preferential or even selective solvation of the solute by one component of the solvent mixture.30 Specific solute/solvent interactions, particularly Lewis acid/base interactions between electron-pair donors (EPD) and electron-pair acceptors (EPA), are reviewed in Chapter 9, together with the development of empirical scales of solvent polarity and solvent Lewis acidity/basicity,77 based on suitable, well-selected, solvent-dependent reference processes, and their application for the correlation analysis of solvent effects in the framework of single- or multi-parameter Linear Free-Energy Relationships (LFER's).1,11,20 Properties of solutions and products affected by solvents such as electronic and vibrational spectral properties, dielectric solvent effects, the two-photon absorption cross-section of organic molecules, and solvatochromism are treated in Chapter 10. Other properties of solutions and products affected by solvents such as rheological characteristics, aggregation, permeability, molecular structure, crystallinity, etc. are reviewed in Chapter 11. The solvent influence on solvent reactions and reactivity is given in Chapter 12, along with a detailed discussion of the effect of solvents on free-radical homo- and copolymerization reactions. The second part of this Handbook (Volume 2; Chapters 13-22) is devoted more to the industrial use of solvents. Formulating with solvents applied in a broad range of industrial areas such as biotechnology, coil coating, cosmetics, dry cleaning, electronic industry, food industry, iron and steel industry, paints and coatings, petroleum refining industry, pharmaceutical industry, textile industry, to mention only a few (of over thirty discussed sectors), is extensively described in Chapter 13. At present, large-scale chemical manufacturing is facing serious solvent problems concerning increasing environmental concerns. National and international regulations for the proper use of hazardous solvents are becoming increasingly stringent, and this requires the introduction of environmentally more benign but nevertheless economically acceptable new liquid reaction media. This has enormously stimulated the search for such new solvent systems,37-71 particularly within the framework of Sustainable or Green Chemistry.78 This Handbook includes in Chapters 14-22 all the knowledge necessary for the safe

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Introduction

handling of solvents in research laboratories and in large-scale manufacturing. In Chapter 14, the detection and testing of solvents in an industrial environment, as well as special methods of analysis of solvent absorbed by exposed individuals are discussed. The problem of residual solvents in various products, particularly in pharmaceutical substances is reviewed in Chapter 15. The environmental impact of organic solvents in water, soil, air, and solvent-containing waste, as well as pollution of troposphere, are the main subjects of Chapter 16. Chapter 17 deals with considerations about safe solvent concentrations and the risks of solvent exposure in various industrial environments as well as with corresponding measurements of the emission of the so-called volatile organic compounds (VOC's). Chapter 18 summarizes the relevant legal regulations for the handling of solvents, valid in North America and Europe. Chapter 19 describes the manifold toxic effects of solvent exposure to human beings. Authors specialized in different fields of solvent toxicity give the most current information on the influence of solvent exposure from the point of view of neurotoxicity, reproductive and maternal effects, nephrotoxicity, carcinogenicity, lymphatic leukemia, hepatotoxicity, chromosomal aberrations, and toxicity to brain, lungs, and heart. This information brings both the results of documented studies and an evaluation of risk in different industrial environments in a comprehensive but easy to understand form to engineers and decision-makers in the industry. Chapter 20 is focused on the replacement of harmful solvents by safer ones and the development of corresponding new technological processes. Recommended new solvent systems include amongst others supercritical fluid (scf) solvents,56-60 high-temperature molten salts,50-51 at room temperature fluid ionic liquids,47-55 as well as deep eutectic solvents (DESs). Chapter 21 describes modern methods of solvent recovery, solvent recycling, and solvent removal. Solvent contamination cleanup, in particular, the natural attenuation of solvents in groundwater and advanced remediation technologies as well as management strategies for sites impacted by solvent contamination, is described in Chapter 22. In most cases, the intelligent choice of the proper solvent or solvent mixture is essential for the realization of certain chemical transformations and physical processes. This handbook tries to cover all theoretical and practical information necessary for this often difficult task for both academic and industrial applications. It should be used not only by chemists, but also by physicists, chemical engineers, and technologists as well as environmentally engaged scientists in academic and industrial institutions. It is to be hoped that the present compilation of all relevant aspects connected with the use of solvents will also stimulate further basic and applied research in the still topical research field of the physics and chemistry of liquid media.

REFERENCES 1 2 3 4

C. Reichardt, T. Welton, Solvents and Solvent Effects in Organic Chemistry. 4th ed., Wiley-VCH, Weinheim, Germany, 2011 (Chapter 1: Introduction). C. Reichardt, Solvents and Solvent Effects: An Introduction. Org. Process Res. Dev., 11, 105-113 (2007). E. Buncel, R. A. Stairs, Solvent Effects in Chemistry. 2nd ed., Wiley, Hoboken/NJ, USA, 2016. (a) K. Tanaka, F. Toda, Solvent-Free Organic Synthesis, Chem. Rev., 100, 1025-1074 (2000); (b) D. Bradley, Proving Aristotle Wrong, Chemistry in Britain, 38 (Sept. Issue), 42-45 (2002); (c) W. M. Nelson, Green Solvents for Chemistry − Perspectives and Practice, Oxford University Press, Oxford, New York, 2003, p. 183; (d) L. R. Nassembini, Physicochemical Aspects of Host-Guest

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Compounds. Acc. Chem. Res., 36, 631-637 (2003), p. 635. (a) J. A. Hedvall, Einführung in die Festkörperchemie, Vieweg & Sohn, Braunschweig, Germany, 1952, p. 2; (b) J. A. Hedvall, Solid State Chemistry − Whence, where and whither. Elsevier, Amsterdam, 1966, p. 1-2. (a) H. H. Joachim (Ed.), On Coming-to-Be and Passing Away (De generatione et corruptione), 328b (Original Greek version, p. 36), Clarendon Press, Oxford, U. K., 1922; (b) J. Judycka (Ed.), Aristoteles Latinus IX, 1: De Generatione et Corruptione, 328b (Latin version, p. 50), E. J. Brill, Leiden, 1986; (c) C. J. F. Williams, Aristotle's De Generatione et Corruptione, 328b (English version, p. 35), Clarendon Press, Oxford, U. K., 1982; (d) P. Gohlke, Aristoteles: Vom Werden und Vergehen, (German version, p. 239), Schöningh, Paderborn, Germany, 1958. (a) F. Toda (Ed.), Solid State Reactions. Top. Curr. Chem., 254, 1-305 (2005); (b) K. Tanaka, Solvent-free Organic Synthesis. 2nd ed., Wiley-VCH, Weinheim, Germany, 2009; (c) G. Kaupp, Organic Solid-State Reactions. In Z. Wang, U. Wille, E. Juaristi (Eds.), Encyclopedia of Physical Organic Chemistry. Wiley, Hoboken/NJ, USA, 2017; Vol. 2, Chapter 17, p. 737-815. M. Berthelot, L. Péan de Saint Gilles, Ann. Chim. Phys., 3. Sér., 65, 385 (1862); ibid., 66, 5 (1862); ibid., 68, 255 (1863); translated into German and edited by M. and A. Ladenburg in: Ostwalds Klassiker der exakten Wissenschaften. Nr. 173, Engelmann, Leipzig, 1910; see also N. Menschutkin, Z. Phys. Chem. (Leipzig), 1, 611-630 (1887), particularly p. 627. N. Menschutkin, Z. Phys. Chem. (Leipzig), 5, 589-600 (1890); ibid., 6, 41-57 (1890); ibid., 34, 157-167 (1900). J.-L. M. Abboud, R. Notario, J. Bertrán, M. Solá, One Century of Physical Organic Chemistry: The Menshutkin Reaction, Prog. Phys. Org. Chem., 19, 1-182 (1993). (a) K. J. Laidler, The World of Physical Chemistry. Oxford University Press, Oxford, New York, 1993; particularly Chapter 8.6 on pp. 273 ff.: Reactions in Solution; (b) K. J. Laidler, A century of solution chemistry. Pure Appl. Chem., 62, 2221-2226 (1990). (a) G. F. Dvorko, E. A. Ponomareva, N. I. Kulik, Usp. Khim., 53, 948-970 (1984); Russ. Chem. Rev., 53, 547-560 (1984); (b) M. H. Abraham, Pure Appl. Chem., 57, 1055-1064 (1985); (c) And references cited in both reviews. L. Claisen, Justus Liebigs Ann. Chem., 291, 25-137 (1896). L. Knorr, Justus Liebigs Ann. Chem., 293, 70-101 (1896). W. Wislicenus, Justus Liebigs Ann. Chem., 291, 147-216 (1896). A. Hantzsch, O. W. Schultze, Ber. Dtsch. Chem. Ges., 29, 2251-2267 (1896). M. T. Rogers, J. L. Burdett, Can. J. Chem., 43, 1516-1526 (1965). K. H. Meyer, Ber. Dtsch. Chem. Ges., 47, 826-832 (1914). (a) L. P. Hammett, J. Am. Chem. Soc., 59, 96-103 (1937); (b) L. P. Hammett, Physical Organic Chemistry − Reaction Rates, Equilibria, and Mechanisms. 2nd ed., McGraw-Hill, New York, USA, 1970; (c) J. Shorter, Hammett Memorial Lecture. Prog. Phys. Org. Chem., 17, 1-29 (1990). (a) C. Reichardt, Empirical Parameters of Solvent Polarity as Linear Free-Energy Relationships. Angew. Chem., 91, 119-131 (1979); Angew. Chem., Int. Ed. Engl., 18, 98-110 (1979); (b) A. Williams, Free Energy Relationships in Organic and Bio-Organic Chemistry. Royal Society of Chemistry, Cambridge, U. K., 2003; (c) F. H. Quina, E. L. Bastos, Fundamental Aspects of Quantitative StructureReactivity Relationships. In Z. Wang, U. Wille, E. Juaristi (Eds.), Encyclopedia of Physical Organic Chemistry. Wiley, Hoboken/NJ, USA, 2017; Vol. 1, Chapter 9, p. 437-489. S. Rohani, S. Horne, K. Murthy, Design of the Crystallization Process and the Effect of Solvent. Org. Process Res. Dev., 9, 858-872 (2005). T. C. Lo, M. H. I. Baird, C. Hanson (Eds.), Handbook of Solvent Extraction. Reprint ed., Krieger Publishing Company, Malabar/FL, USA, 1991. C. F. Poole, S. K. Poole, Chromatography today. 5th ed., Elsevier, Amsterdam, 1991. (a) Y. Sasson, R. Neumann (Eds.), Handbook of Phase-Transfer Catalysis. Blackie Academic & Professional, London, 1997; (b) M. Makosza, M. Fedorynski, Phase Transfer Catalysis. Catal. Rev., 45, 321-367 (2003); and further reviews in issues 3-4 of volume 45. (a) C. Reichardt, Solvatochromic Dyes as Solvent Polarity Indicators. Chem. Rev., 94, 2319-2358 (1994); (b) V. G. Machado, R. I. Stock, C. Reichardt, Pyridinium N-Phenolate Betaine Dyes. Chem. Rev., 114, 10429-10475 (2014); (c) A. R. Katritzky, D. C. Fara, H. Yang, K. Tamm, T. Tamm, M. Karelson, Quantitative Measures of Solvent Polarity. Chem. Rev., 104, 175-198 (2004). A. Kundt, Poggendorfs Ann. Phys. Chem. N. F., 4, 34-54 (1878); Chemisches Zentralblatt, 498 (1878); for surveys of older work on solvent effects on UV/Vis spectra see S. E. Sheppard, Rev. Mod. Phys., 14, 303-340 (1942), and M. F. Nicol, Appl. Spectrosc. Rev., 8, 183-227 (1974).

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47 48 49 50

Introduction A. Hantzsch, Ber. Dtsch. Chem. Ges., 55, 953-979 (1922). The present-day meaning of the term solvatochromism differs somewhat from that introduced by Hantzsch; see also P. Suppan, N. Ghoneim, Solvatochromism. Royal Society of Chemistry, Cambridge, U. K., 1997. Prof. E. M. Kosower, Tel Aviv University, Tel Aviv, Israel: private communication to C. R. in 1994. (a) Y. Marcus, The Properties of Solvents. Wiley, Chichester, UK, 1998; (b) Y. Marcus, Ions in Solution and their Solvation. Wiley, Hoboken/NJ, USA, 2015. Y. Marcus, Solvent Mixtures − Properties and Selective Solvation. Dekker, New York, Basel, 2002. (a) See reference 1, Chapter 8, p. 509ff. (Solvents and Green Chemistry), and Appendix, Table A-14, p. 583ff.; (b) P. Pollet, E. A. Davey, E. E. Ureña-Benavides, C. A. Eckert, C. L. Liotta, Solvents for sustainable chemical processes. Green Chem., 16, 1034-1055 (2014); (c) F. Jérôme, R. Luque (Eds.), Bio-based Solvents. Wiley-VCH, Weinheim, Germany, 2017; (d) X.-F. Wu (Ed.), Solvents as Reagents in Organic Synthesis − Reactions and Applications. Wiley-VCH, Weinheim, Germany, 2017; (e) C. J. Clarke, W.-C. Tu, O. Levers, A. Bröhl, J. P. Hallett, Green and Sustainable Solvents in Chemical Processes. Chem. Rev., 118, 747-800 (2018). (f) J. L. Scott, H. F. Sneddon, Green Solvents. In W. Zhang, B. W. Cue (Eds.), Green Techniques for Organic Synthesis and Medicinal Chemistry. 2nd ed., Wiley, Hoboken/NJ, USA, 2018; Part I, Chapter 2, p. 21ff. M. J. O'Neil et al. (Eds.), The Merck Index. 13th ed., Merck & Co, Whitehouse Station/NJ, USA, 2001, p. 1078 (no. 6059). N. Gálvez, M. Moreno-Mañas, R. M. Sebastián, A. Vallribera, Tetrahedron, 52, 1609-1616 (1996). (a) K. Watanabe, N. Yamigawa, Y. Torisawa, Cyclopentyl Methyl Ether as a New and Alternative Process Solvent. Org. Process Res. Dev., 11, 251-258 (2007); (b) A. Kadam, M. Nguyen, M. Kopach, P. Richardson, F. Gallou, Z.-K. Wan, W. Zhang, Comparative performance evaluation and systematic screening of solvents in a range of Grignard reactions. Green Chem., 15, 1880-1888 (2013). (a) T. Mukhopadhyay, D. Seebach, Helv. Chim. Acta, 65, 385-391 (1982); (b) D. Seebach, Chemistry in Britain, 21, 632-633 (1985). S. M. Pereira, G. P. Sauvage, G. W. Simpson, Synth. Commun., 25, 1023-1026 (1995). P. Knochel (Ed.), Modern Solvents in Organic Synthesis. Top. Curr. Chem., 206, 1-152 (1999). W. M. Nelson, Green Solvents for Chemistry − Perspectives and Practice. Oxford University Press, Oxford, New York, 2003. (a) D. J. Adams, P. J. Dyson, S. J. Tavener, Chemistry in Alternative Reaction Media. Wiley, Chichester, U. K., 2004; (b) J. H. Clark, S. J. Tavener, Alternative Solvents: Shades of Green. Org. Process Res. Dev., 11, 149-155 (2007). (a) R. A. Sheldon, Green solvents for sustainable organic chemistry: state of the art. Green Chem., 7, 267-278 (2005); (b) R. A. Sheldon, Biocatalysis and biomass conversion in alternative media. Chem. Eur. J., 22, 12984-12999 (2016). K. Mikami (Ed.), Green Reaction Media in Organic Synthesis. Blackwell Publishing, Oxford, UK, 2005. M. Avalos, R. Babiano, P. Cintas, J. L. Jiménez, J. C. Palacios, Greener Media in Chemical Synthesis and Processing. Angew. Chem., 118, 4008-4012 (2006); Angew. Chem. Int. Ed., 45, 3904-3908 (2006). (a) I. T. Horváth, Solvents from Nature. Green Chem., 10, 1024-1028 (2008); (b) I. T. Horvath, H. Mehdi, V. Fábos, L. Boda, L. T. Mika, Green Chem., 10, 238-242 (2008). F. M. Kerton, Alternative Solvents for Green Chemistry. RSC Publishing, Cambridge, U. K., 2009. M. C. Bubalo, S. Vidović, I. R. Redovniković, S. Jokić, Green solvents for green technologies. J. Chem. Technol. Biotechnol., 90, 1631-1639 (2015). (a) K. Alfonsi et al., Green chemistry tools to influence a medicinal chemistry and research chemistry based organization. Green Chem., 10, 31-36 (2008); see also (b) D. Prat et al., Sanofi's Solvent Selection Guide: A Step Toward More Sustainable Processes. Org. Process Res. Dev., 17, 1517-1525 (2013); (c) C. M. Alder et al., Updating and further expanding GSK's solvent sustainability guide. Green Chem., 18, 3879-3890 (2016); (d) D. Prat, J. Hayler, A. Wells, A survey of solvent selection guides. Green Chem., 16, 4546-4551 (2014). (a) T. Welton, Room-Temperature Ionic Liquids. Solvents for Synthesis and Catalysis. Part 1. Chem. Rev., 99, 2071-2084 (1999); (b) J. P. Hallett, T. Welton, ibid., Part 2. Chem. Rev., 111, 3508-3576 (2011). P. Wasserscheid, T. Welton (Eds.), Ionic Liquids in Synthesis. 2nd ed., Wiley-VCH, Weinheim, Germany, 2008. M. Freemantle, An Introduction to Ionic Liquids. Royal Society of Chemistry, Cambridge, U. K., 2010. (a) M. Gaune-Escard, K. R. Seddon (Eds.), Molten Salts and Ionic Liquids: Never the Twain? Wiley, Hoboken/NJ, USA, 2010; (b) N. V. Plechkova, K. R. Seddon (Eds.), Ionic Liquids UnCOILed − Critical Expert Overviews. Wiley, Hoboken/NJ, USA, 2013; (c) N. V. Plechkova, R. D. Roberts (Eds.), Ionic Liquids further UnCOILed. Wiley-VCH, Weinheim, Germany, 2014; (d) N. V. Plechkova,

Christian Reichardt

51 52 53 54 55 56 57 58 59 60 61 62

63 64 65 66 67

68 69

70 71

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K. R. Seddon (Eds.), Ionic Liquids Completely UnCOILed. Wiley-VCH, Weinheim, Germany, 2016; (e) M. Deetlefs, M. Fanselow, K. R. Seddon, Ionic Liquids: the view from Mount Improbable. RSC Adv., 6, 4280-4288 (2016). D. Freudenmann, S. Wolff, M. Wolff, C. Feldmann, Ionic Liquids: New Perspectives for Inorganic Chemistry? Angew. Chem., 123, 11244-11255 (2011); Angew. Chem. Int. Ed., 50, 11050-11060 (2011). C. D. Hubbard, P. Illner, R. van Eldik, Understanding chemical reaction mechanisms in ionic liquids: success and challenges. Chem. Soc. Rev., 40, 272-290 (2011). P. Domínguez de María (Ed.), Ionic Liquids in Biotransformations and Organocatalysis - Solvents and Beyond. Wiley, Hoboken/N. J., USA, 2012. T. Payagala, D. W. Armstrong, Chiral Ionic Liquids: A Compendium of Syntheses and Applications (2005-2012). Chirality, 24, 17-53 (2012). S. T. Keaveney, R. S. Haines, J. B. Harper, Reactions in Ionic Liquids. In Z. Wang, U. Wille, E. Juaristi (Eds.), Encyclopedia of Physical Organic Chemistry. Wiley, Hoboken/NJ, USA, 2017; Vol. 2, Chapter 27, p. 1411-1464. (a) R. Noyori (Ed.), Supercritical fluids (Special Issue). Chem. Rev., 99, 353-633 (1999); (b) W. Leitner, P. G. Jessop (Eds.): Handbook of Green Chemistry - Green Solvents. Volume 4: Supercritical Solvents. Wiley-VCH, Weinheim, Germany, 2013. (a) W. Leitner, Reactions in Supercritical CO2. Top. Curr. Chem., 206, 107-132 (1999); (b) W. Leitner, Supercritical CO2 as a Green Reaction Medium for Catalysis. Acc. Chem. Res., 35, 746-756 (2002). C. M. Rayner, The Potential of CO2 in Synthetic Organic Chemistry. Org. Process Res. Dev., 11, 121-132 (2007). H. Weingärtner, E. U. Franck, Supercritical Water as a Solvent. Angew. Chem., 117, 2730-2752 (2005); Angew. Chem. Int. Ed., 44, 2672-2692 (2005). Y. Marcus, Supercritical Water − A Green Solvent: Properties and Uses. Wiley, Hoboken/N. J., USA, 2012. (a) B. Betzemeier, P. Knochel, Perfluorinated Solvents - a Novel Reaction Medium in Organic Chemistry. Top. Curr. Chem., 206, 61-78 (1999); (b) T. Mukherjee, J. A. Gladysz, Fluorous Chemistry Meets Green Chemistry: A Concise Primer. Aldrichimica Acta, 48, 25-28 (2015). (a) I. T. Horváth (Ed.), Fluorous Chemistry. Top. Curr. Chem., 308, 1-411 (2012); (b) L. T. Mika, I. T. Horváth, Fluorous Catalysis. In W. Zhang, B. W. Cue (Eds.), Techniques for Organic Synthesis and Medicinal Chemistry. 2nd ed., Wiley, Hoboken/NJ, USA, 2018; Part II, Chapter 10, p. 219ff.; (c) H. Matsubara, Reactions in Fluorous Solvents. In Z. Wang, U. Wille, E. Juaristi (Eds.), Encyclopedia of Physical Organic Chemistry. Wiley, Hoboken/NJ, USA, 2017; Vol. 3, Chapter 28, p. 1467-1526. U. M. Lindström (Ed.), Organic Reactions in Water − Principles, Strategies and Applications. Blackwell Publishing, Oxford, U. K., 2007. H. C. Hailes, Reaction Solvent Selection: The Potential of Water as a Solvent for Organic Transformations. Org. Process Res. Dev., 11, 114-120 (2007). (a) S. Kobayashi, Water in Organic Syntheses (Science of Synthesis Workbench Edition). Thieme, Stuttgart, Germany, 2012; (b) T. Kitanosono, K. Masuda, P. Xu, S. Kobayashi, Catalytic Organic Reactions in Water toward Sustainable Society. Chem. Rev., 118, 679-746 (2018). (a) J. J. Lagowski, Liquid Ammonia. Synthesis and Reactivity in Inorganic, Metal-Organic, and NanoMetal Chemistry, 37, 115-153 (2007); (b) P. Ji, J. H. Atherton, M. I. Page, Organic reactivity in liquid ammonia. Org. Biomol. Chem., 10, 5732-5739 (2012). (a) C. A. Eckert, C. L. Liotta, D. Bush, J. S. Brown, J. P. Hallett, Sustainable Reactions in Tunable Solvents. J. Phys. Chem. B, 108, 18108-18118 (2004); (b) J. P. Hallett, C. L. Kitchens, R. Hernandez, C. L. Liotta, C. A. Eckert, Probing the Cybotactic Region in Gas-Expanded Liquids (GXLs). Acc. Chem. Res., 39, 531-538 (2006). P. G. Jessop, B. Subramaniam, Gas-Expanded Liquids. Chem. Rev., 107, 2666-2694 (2007). (a) D. J. Heldebrant, P. K. Koech, M. T. C. Ang, C. Liang, J. E. Rainbolt, C. R. Yonker, P. G. Jessop, Reversible zwitterionic liquids, the reaction of alkanol guanidines, alkanol amidines, and diamines with CO2. Green Chem., 12, 713-721 (2010); (b) P. G. Jessop, Switchable Solvents as Media for Synthesis and Separations. Aldrichimica Acta, 48, 18-21 (2015). P. Pollet, R. J. Hart, C. A. Eckert, C. L. Liotta, Organic Aqueous Tunable Solvents (OATS): A Vehicle for Coupling Reactions and Separations. Acc. Chem. Res., 43, 1237-1245 (2010). (a) W. Zhang, B. W. Cue (Eds.), Green Techniques for Organic Synthesis and Medicinal Chemistry. 2nd ed., Wiley, Hoboken/NJ, USA, 2018; (b) I. T. Horváth, M. Malacria (Eds.), Advanced Green Chemistry, Part I: Greener Organic Reactions and Processes. World Scientific Publishing Co., Singapore, 2018.

10 72 73 74 75

76 77 78

Introduction J. O. Metzger, Solvent-Free Organic Syntheses. Angew. Chem., 110, 3145-3148 (1998); Angew. Chem. Int. Ed., 37, 2975-2978 (1998). A. Loupy, Solvent-free Reactions. Top. Curr. Chem., 206, 153-207 (1999). K. Tanaka, Solvent-Free Organic Synthesis. 2nd ed., Wiley-VCH, Weinheim, Germany, 2009. (a) M. S. Singh, S. Chowdhury, Recent developments in solvent-free multicomponent reactions: a perfect synergy for eco-compatible organic synthesis. RSC Adv., 2, 4547-4592 (2012); (b) S. L. James et al., Mechanochemistry: Opportunities for new and cleaner synthesis. Chem. Soc. Rev., 41, 413-447 (2012); (c) G. A. Bowmaker, Solvent-assisted mechanochemistry. Chem. Commun., 49, 334-348 (2013); J. G. Hernández (Guest Ed.), Beilstein J. Org. Chem., 13, 2372-2373 (2017): Special Issue on Mechanochemistry. F. Wöhler, Über künstliche Bildung des Harnstoffs. Annalen der Physik und Chemie (Leipzig), 87 (2), 253-256 (1828). (a) C. Laurence, J.-F. Gal, Lewis Basicity and Affinity Scales − Data and Measurement. Wiley, Chichester, U.K., 2010; (b) C. Laurence, J. Graton, J.-F. Gal, J. Chem. Educ., 88, 1651-1657 (2011). (a) P. T. Anastas, J. C. Warner, Green Chemistry: Theory and Practice. Oxford University Press, Oxford, UK, 2000; (b) J. H. Clark, D. J. Macquarrie (Eds.), Handbook of Green Chemistry and Technology. Blackwell Publishing, Oxford, UK, 2002; (c) Various editors, Handbook of Green Chemistry. Wiley-VCH, Weinheim, Germany, 12 Volumes, 2009-2018; above all Volumes 4-6 on Green Solvents: (1) W. Leitner, P. G. Jessop (Eds.), Supercritical Solvents. Vol. 4, 2013; (2) C.-J. Li (Ed.), Reactions in Water. Vol. 5, 2013; (3) P. Wasserscheid, A. Stark (Eds.), Ionic Liquids. Vol. 6, 2013.

2

Fundamental Principles Governing Solvents Use 2.1 SOLVENT EFFECTS ON CHEMICAL SYSTEMS Estanislao Silla, Arturo Arnau, and Iñaki Tuñón Department of Physical Chemistry, University of Valencia, Burjassot (Valencia), Spain 2.1.1 HISTORICAL OUTLINE The chemistry of living beings and that which we practice in laboratories and factories is generally a chemistry in solution, a solution which is generally aqueous. Throughout the history of chemistry, attempts were being made to understand the effects of solvent in chemical transformations, a goal which was not achieved in a precise way until well into the XX century. The development of experimental techniques in vacuo was required to compare the chemical processes in the presence of a solvent and in its absence with the purpose of getting to know its role in the chemical transformations. Although very essential for the later cultural development, Greek philosophy was a work of the imagination, not based on experimentation, and much more than rationalization was needed to explain a process of dissolution. In those distant times, any chemically active liquid was included under the name of “divine water”, bearing in mind that the term “water” was used to refer to anything liquid or dissolved.1 Parallel to the fanciful search for the philosopher's stone, the alchemists embarked on another impossible search, that of universal solvent which some called “alkahest” and others referred to as “menstruum universale”, which term was used by Paracelsus (14931541), which gives an idea of the importance given to solvents during the dark and obscurantist period. Even though the “menstruum universale” proved just as elusive as the philosopher's stone, all the work carried out by the alchemists in search of these illusionary materials opened the way to improving the work in the laboratory, the development of new methods, the discovery of compounds, and the utilization of novel solvents. One of the tangible results of all alchemistry work was the discovery of one of the first experimental rules of chemistry: “similia similibus solvuntur”, which indicates the importance of compatibility in a solution of substances of similar nature. Revisions and updates by G.Wypych, ChemTec Laboratories, Toronto, Canada

12

2.1 Solvent effects on chemical systems

The alchemistry only touched slightly on the subject of the role played by the solvent, with so many conceptual gaps in those pre-scientific times, in which the terms dissolution and solution referred to any process which led to a liquid product, without making any distinction between the fusion of a substance: such as the transformation of ice into liquid water, mere physical dissolution: such as that of a sweetener in water, or the dissolution which takes place with a chemical transformation, for example, dissolution of a metal in an acid. This incomplete definition of the dissolution process led alchemists to equally erroneous pathways which were dominant for a long time. Some examples are worth quoting: Hermann Boerhaave (1688-1738) thought that dissolution and chemical reaction constituted the same process; the solvent, (menstruum), habitually a liquid, was considered to be formed by diminutive particles moving around those of the solute, leaving the interactions of these particles dependent on the mutual affinities of both substances.2 This paved the way for Boerhaave to introduce term affinity in a such a way as was conserved throughout the whole of the following century.3 This approach also enabled Boerhaave to conclude that combustion was accompanied by an increase in weight due to the capturing of “particles” of fire, which he considered to add weight to the substance which was burned. This explanation, supported by the well-known Boyle, paved the way to consider fire, heat, and light as material substances until the XIX century when the modern concept of energy put things in their place.4 Even Berthollet (1748-1822) saw no difference between a dissolution and a chemical reaction, which prevented him from the formulation of the law of definite proportions. It was Proust, an experimenter who was more precise and capable of differentiating between chemical reaction and dissolution, who made his opinion to prevail:

“The dissolution of ammonia in water is not the same as that of hydrogen in azote (nitrogen), which gives rise to ammonia”5 There were some alchemists who defended the idea that substances lose their nature when dissolved. Van Helmont (1577-1644) was one of the first to oppose this mistaken idea by pointing out that the substance dissolved remains in the solution in the same form, which can be recovered from solution. Later, the theories of osmotic pressure of van´t Hoff (1852-1911) and that of electrolytic dissociation of Arrhenius (1859-1927) took this approach even further. Until almost the end of the XIX century, the effects of solvent on different chemical processes did not become the object of systematic study by experimenters. The effect of solvent was simply assumed, without reaching the point of creating the interest among chemists. Some chemists of the XIX century became capable of unraveling the role played by some solvents by carrying out experiments on different solvents, which were classified according to their physical properties; in this way, the influence of solvent both on chemical equilibrium and on the rate of reaction was brought to light. Thus, in 1862, Berthollet and Saint-Gilles, in their studies on the esterification of acetic acid with ethanol, discovered that some solvents, which do not participate in the chemical reaction, are capable of slowing down the process.6 In 1890, Menschutkin, in a now classical study on the reaction of the trialkylamines with haloalcanes in 23 solvents, made it clear how the choice of sol-

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vent could substantially affect the reaction rate.7 It was also Menschutkin who discovered that, in reactions between liquids, one of the reactants could constitute a solvent imprudent for that reaction. Thus, in the reaction between aniline and acetic acid to produce acetanilide, it is better to use an excess of acetic acid than an excess of aniline, since the latter is a solvent which is not very favorable for this reaction. The experimentation with a series of solvents was instrumental in the creation of the first rules regarding the participation of the solvent, such as those discovered by Hughes and Ingold for the rate of the nucleophilic reactions.8 Utilizing a simple electrostatic model of the solute-solvent interactions, Hughes and Ingold concluded that the transition state is more polar than the initial state, thus an increase in the polarity of a solvent will stabilize the transition state as compared to the initial state, thus leading to an increase in the reaction rate. If, on the contrary, the transition state is less polar, then the increase of the polarity of the solvent will lead to a decrease in reaction rate. The rules of HughesIngold for the nucleophilic aliphatic reactions are summarized in Table 2.1.1. Table 2.1.1. Rules of Hughes-Ingold on the effect of the increased polarity of the solvent on the rate of nucleophilic aliphatic reactions Mechanism SN2

Initial state -

-

Effect on the reaction rate

Y + RX

[Y--R--X]

slight decrease

Y + RX

[Y--R--X]

large increase

Y + RX

[Y--R--X]

large increase

Y + RX+

[Y--R--X]+

slight decrease

RX

[R--X]

large increase

RX+

[R--X]+

slight decrease

-

SN1

State of transition

+

In 1896, the first results on a role of solvent in chemical equilibrium were obtained, coinciding with the discovery of the keto-enolic tautomerism.9 Claisen identified the reaction medium as one of the factors which, together with temperature and substituents, influenced reaction equilibrium. Soon systematic studies began on the effect of solvent on the tautomeric equilibrium. Wislicenus studied the keto-enolic equilibrium of ethylformylphenylacetate in eight solvents, concluding that the final proportion between keto and enol forms depended on the polarity of a solvent.10 The effect of solvent also revealed itself in other types of equilibria: acid-base, conformational, isomerization, and electronic transfer. The acid-base equilibrium is of particular interest. The relative scales of basicity and acidity of different organic compounds and homologous families were established on the basis of measurements carried out in solution, mostly aqueous. These scales permitted the establishment of hypotheses regarding the effect of substituents on the acidic and basic centers, but without separating it from the effect of solvent. Thus, the scale obtained in solution for the acidity of the α-substituted methyl alcohols [(CH3)3COH > (CH3)2CHOH > CH3CH2OH > CH3OH]11 came into conflict with the conclusions obtained from the measurements of movements by NMR.12 The irregular order in the basicity of the methylamines in aqueous solution also proved to be confusing [NH3

14

2.1 Solvent effects on chemical systems

(CH3)3N],13 since it did not match any of the existing models concerning the effect of the substituents. These conflicts were only resolved when the scales of acidity-basicity were established in the gas phase. Elimination of solvent contributed to the understanding of its real role in chemical reactivity. The great technological development which arrived with the XX century has brought us a set of techniques capable of giving accurate values in the study of chemical processes in the gas phase. The methods most widely used for these studies were: • high-pressure mass spectrometry, which uses a beam of electron pulses14 • ion cyclotron resonance and its corresponding Fourier Transform (FT-ICR)15 • chemical ionization mass spectrometry, in which the analysis is made of the kinetic energy of the ions, after generating them by collisions16 • techniques of flowing afterglow, where the flow of gases is submitted to ionization by electron bombardment17-19 All of these techniques give absolute values with an accuracy of ±(2-4) kcal/mol and of ±0.2 kcal/mol for the relative values.20 During the last decades of XX century, the importance of the effect of solvent on the behavior of biomacromolecules has also been made clear. To give an example, the influence of solvent on proteins was made evident not only by its effect on their structure and thermodynamics but also on their dynamics (both at local and global levels).21 In the same way, the effect of the medium proves to be indispensable in explaining a large variety of biological processes, such as the rate of interchange of oxygen in myoglobin.22 Therefore, the actual state of chemistry development, as much in its experimental aspect as in its theoretical one, allows us to identify and analyze the influence of solvent on processes increasingly more complex, leaving the subject open for new challenges and investigating the scientific necessity of creating models with which we can interpret a wide range of phenomena. 2.1.2 CLASSIFICATION OF SOLUTE-SOLVENT INTERACTIONS Fixing the limits of the different interactions between the solute and the solvent which envelopes it is not a trivial task. In the first place, the liquid state, which is predominant in the majority of solutions in use, is more difficult to comprehend than the solid state (which has its constitutive particles, atoms, molecules or ions, in fixed positions) or the gaseous state (in which the interactions between the constitutive particles are not so intense). Moreover, the solute-solvent interactions, which happen in a liquid phase, are half a way between the predominant interactions in the solid phase and those which happen in the gas phase; too weak to be linked with the physics of the solid state but too strong to fit into the kinetic theory of gases. Dissecting the solute-solvent interaction into different sub-interactions gives us an approximate idea of reality because the solute-solvent interaction is not the sum of both partners. The world of solvents is very different from molecules which have a very strong internal structure, as in the case of water compared with hydrocarbons as their molecules interact only superficially. If we mix a solute and a solvent, both being constituted by chemically saturated molecules, their molecules attract one another as they approach each other. This interaction can only be electrical in its nature, given that other known interactions are much more

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intense and of a much shorter range of action (such as those which can be explained by means of nuclear forces) or much lighter and of the longer range of action (such as the gravitational force). These intermolecular forces usually receive the name of van der Waals forces, from the fact that it was this Dutch physicist, Johannes D. van der Waals (1837-1923), who recognized them as being the cause of the non-perfect behavior of the real gases, in a period in which the modern concept of the molecule still had to be consolidated. The intermolecular forces not only permit the interactions between solutes and solvents to be explained but also determine the properties of gases, liquids, and solids; they are essential in the chemical transformations and are responsible for organizing the structure of biological molecules. The analysis of solute-solvent interactions is usually based on the following partition scheme: ΔE = ΔE i + ΔE ij + ΔE jj

[2.1.1]

where i stands for the solute and j for the solvent. This approach can be maintained if the identities of the solute and solvent molecules are preserved. In some special cases (see about specific interactions below), it will be necessary to include some solvent molecules in the solute definition. The first term in the above expression is the energy change of the solute due to the electronic and nuclear distortion induced by the solvent molecule and is usually given the name of solute polarization. ΔEij is the interaction energy between the solute and solvent molecules. The last term is the energy difference between the solvent after and before the introduction of the solute. This term reflects the changes induced by the solute to the solvent structure. It is usually called cavitation energy in the framework of continuum solvent models and hydrophobic interaction when analyzing the solvation of nonpolar molecules. The calculation of the three energy terms needs analytical expressions for the different energy contributions but also requires knowledge of solvent molecule distribution around the solute, which, in turn, depends on the balance between the potential and the kinetic energy of molecules. This distribution can be obtained from diffraction experiments or more frequently it is calculated by means of solvent modeling. We now comment on the expression for evaluating the energy contributions. The first two terms in equation [2.1.1] can be expressed by means of the following energy partition: ΔE i + ΔE ij = ΔE el + ΔE pol + ΔE d – r

[2.1.2]

Analytical expressions for the three terms (electrostatic, polarization and dispersion-repulsion energies) are obtained from the intermolecular interactions theory. 2.1.2.1 Electrostatic The electrostatic contribution arises from the interaction of the unpolarized charge distribution of molecules. This interaction can be analyzed using a multipolar expansion of the charge distribution of the interacting subsystems. If both the solute and the solvent are considered to be formed by neutral polar molecules (with a permanent dipolar moment different from zero), due to an asymmetric distribution of its charges, the electric interaction of the type dipole-dipole will normally be the most important term in the electrostatic

16

2.1 Solvent effects on chemical systems

interaction. The intensity of this interaction will depend on the relative orientation of the dipoles. If the molecular rotation is not restricted, we then consider the weighted average over different orientations 2 2

μ1 μ2 2  E d – d = – --- ---------------------------3 ( 4πε ) 2 kTr 6 where:

μ1, μ2 k ε T r

[2.1.3]

dipole moments Boltzmann constant relative permittivity absolute temperature intermolecular distance

The most stable orientation is the antiparallel, except the case that the molecules in play are very voluminous. Two dipoles in the rapid thermal movement will be orientated sometimes in such a way that they are attracted and at other times in a way that they are repelled. On average, the net energy turns out to promote attractive interFigure 2.1.1. The dipoles of two molecules can approach one another under an infinite variety of attrac- action. It also has to be borne in mind that tive orientations, among which these two extreme orien- the thermal energy of the molecules is a tations are very dependent on the temperature. serious obstacle for dipoles to be oriented in an optimum manner. The average potential energy of the dipole-dipole interaction, or of orientation, is dependent on temperature. In the event that one of the species involved was not neutral (for example an anionic or cationic solute), the predominant term in the series which gave the electrostatic interaction would be the ion-dipole which is given by the expression: 2 2

qi μj  E i – d = – ------------------------------2 4 6 ( 4πε ) kTr

[2.1.4]

Because biomolecules are embedded in a highly polar medium, electrostatics is a fundamental component of solvation effects on the molecular level.23 For this reason, an appropriate description of electrostatics is a prerequisite for understanding the macromolecular function, and the critical role of water in modulating the properties of proteins and nucleic acids.23 A comprehensive book chapter contains a detailed discussion of this subject.23 The electrostatic forces between electroneutral molecules or assemblies that are free to mutually orient occur even at zero temperature.24 A book chapter addresses the thermodynamic implications arising from the existence of interaction potentials and illustrates them with many examples.24 In Marcus electron transfer theory, the electron-transfer reaction barrier arises from reorganization energy.25 The barrier height depends on the reorganization energy (of the

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solvent and reactant) and the driving force, which is the difference in free energy between the products and the reactants.25 The reorganization energy is the energy required for making products in the nuclear configuration of the reactants.25 The solvent behavior is of key importance for the electron-transfer process.25 This subject is discussed in detail, elsewhere.25 2.1.2.2 Polarization If we dissolve a polar substance in a nonpolar solvent, the molecular dipoles of the solute are capable of distorting the electronic clouds of the solvent molecules inducing the orientation in these new dipoles. The dipoles of solute and those induced will line up, will be attracted, and the energy of this interaction (also called interaction of polarization or induction) is given by the equation: 2

αj μi  E d – id = – -------------------2 6 ( 4πε ) r where:

μi αj r

[2.1.5]

dipole moment polarizability intermolecular distance

In a similar way, the dissolution of an ionic substance in a nonpolar solvent will also occur with an induction of dipoles in the solvent molecules by the solute ions. The equation makes reference to the interactions between two molecules. Because the polarization energy (of solute or solvent) is not of pairwise additive magnitude, the consideration of a third molecule should be carried out simultaneously, since it impossible to decompose the interaction of the three bodies in a sum of the interactions of two bodies. The interactions between molecules in solution are different from those which take place between isolated molecules. For this reason, the dipolar moment of a molecule may differ considerably between the gas phase and the solution, and it will depend in a complicated fashion on the interactions which may take place between the molecule of solute and its specific surroundings by solvent molecules. 2.1.2.3 Dispersion Even when solvent and solute are constituted of nonpolar molecules, there is an interaction between them. It was F. London who was first to face up to this problem, for which reason these forces are known as London's forces, but also as dispersion forces, chargefluctuation forces, or electrodynamic forces. Their origin is as follows: when a substance is nonpolar it indicates that the distribution of charges of its molecules is symmetrical throughout a wide average time span. But, without doubt, in an interval of time sufficiently restricted, the molecular movements generate displacements of their charges which break that symmetry giving birth to instantaneous dipoles. Since the orientation of the dipolar moment vector is varying constantly due to the molecular movement, the average dipolar moment is zero, which does not prevent the existence of these interactions between momentary dipoles. Starting with two instantaneous dipoles, they will be oriented to reach a disposition which will favor them energetically. The energy of this dispersion interaction can be given, to the first approximation, by:

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2.1 Solvent effects on chemical systems

αi αj 3I i I j - --------E disp = – ------------------------------------2 6 2 ( 4πε ) ( I i + I j ) r

[2.1.6]

where Ii, Ij αi , α j r

ionization potentials polarizabilities intermolecular distance

From equation [2.1.6] it becomes evident that dispersion is an interaction, which is more noticeable the greater the volume of molecules involved. The dispersion forces are often more intense than the electrostatic forces and, in any case, are universal for all the atoms and molecules, given that they are not seen to be subjected to the requirement that permanent dipoles should exist beforehand. These forces are responsible for the aggregation of substances which possess neither free charges nor permanent dipoles and are also the protagonists of phenomena such as surface tension, adhesion, flocculation, physical adsorption, etc. Although the origin of the dispersion forces may be understood intuitively, it has a quantum mechanical nature. London induced dipole-induced dipole interaction is a long-range force that can be effective at a large distance (>10 nm) to interatomic spacing. The dispersion is non-additive and the dispersion of two molecules is affected by the presence of the third molecule. This attractive force occurs because the electrons of one atom oscillate in such a way as to make it a rapidly fluctuating (about 1015 to 1016 Hz) dipolar atom, which in turn polarizes an adjacent atom, making it, too, a rapidly fluctuating dipole atom such that the two atoms attract each other.26 The generated force varies inversely as the sixth power of the distance between the atoms.26 Quantum mechanics predicts that at distances greater than 100 Å (10 nm) one atom cannot polarize another.26 The attractive force is typically considered to be about 1 kcal per mole.26 2.1.2.4 Repulsion Between two molecules under influence of attractive forces, which could cause them to be superimposed, it is evident that repulsive forces exist as well, which determine the distance to which molecules (or atoms) approach one another. These repulsive forces are a consequence of overlapping of the electronic molecular clouds when these are nearing one another. These are also known as steric repulsion, hardcore repulsion, or exchange repulsion. They are forces of short-range which grow rapidly when molecules, which interact, approach one another and enter environs of quantum mechanics. Throughout the years, different empirical potentials have been obtained with which the effect of these forces can be reproduced. In the model of hard sphere potential, the molecules are supposed to be rigid spheres, such that the repulsive force becomes suddenly infinite, after a certain distance during the approach (Figure 2.1.2a). Mathematically this potential is given by the following equation: σ ∞ E rep =  ---  r

[2.1.7]

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where: r σ

intermolecular distance hard sphere diameter

Other repulsion potentials are the power-law potentials: σ E rep =  ---  r

n

[2.1.8]

where: r n σ

intermolecular distance integer, usually between 9 and 16 sphere diameter

and the exponential potentials: r E rep = C exp  – ----- σ0

[2.1.9]

where: r C σ0

intermolecular distance adjustable constant adjustable constant

These last two potentials allow a certain compressibility of molecules, more in consonance with reality, and for this reason, they are also known as soft repulsions (Figure 2.1.2b). If we represent the repulsion energy by a term proportional to r-12, and given that the energy of attraction between molecules decreases in proportion to r-6 at distances above the molecular diameter, we can obtain the total potential of interaction: E = – Ar

–6

+ Br

– 12

[2.1.10]

where: r A B

Figure 2.1.2. Hard-sphere repulsion (a) and soft repulsion (b) between two atoms.

intermolecular distance constant constant

which receives the name of potential “6-12” or potential of Lennard-Jones,27 widely used for its mathematical simplicity (Figure 2.1.3). Solvation forces depend not only on the properties of solvent but also on the chemical/physical properties of a solute.28 For example, solvent action differs in case of sol-

20

2.1 Solvent effects on chemical systems

utes which are hydrophilic or hydrophobic, smooth or rough, amorphous or crystalline (atomically structured), homogeneous or heterogeneous, or natural or patterned.28 It is often difficult to distinguish between a solvation force that results from the properties of the solvent molecules and a surface force that depends on the properties of solute molecules.28 Two smooth surfaces that can bind a layer of solvent molecules can serve as an example.28 These surfaces resist coming closer to each other than the Figure 2.1.3. Lennard-Jones potential between two distance of the size of two solvent moleatoms. cules. This “steric” repulsion is due to a strong solvent-surface interaction rather than any solvent-solvent interaction.28 On the other hand, if the solute surfaces do not cause solvent-surface binding, a “solvation” force would act at a small separation distance.28 2.1.2.5 Specific interactions Water, the most common liquid, the “universal solvent”, is just a little “extraordinary”, and this exceptional nature of the “liquid element” is essential for our universe. It is not normal that a substance in its solid state should be less dense than in the liquid, but if on one ill-fated day a piece of ice spontaneously stopped floating on liquid water, all would be lost, because huge mass of ice which is floating on the surface of cold seas would sink thus raising the level of water in the oceans. For a liquid with such a small molecular mass, water has melting and boiling temperatures and a latent heat of vaporization which are unexpectedly high. Also unusual are its low compressibility, its high dipolar moment, its high relative permittivity and the fact that its density is at a maximum at 4ºC. All this proves that water is an extraordinarily complex liquid in which the intermolecular forces exhibit specific interactions, the socalled hydrogen bonds, about which it is necessary to know more. Hydrogen bonds appear in substances where there is hydrogen united covalently to very electronegative elements (e.g., F, Cl, O, and N), which is the case of water. The hydrogen bond can be either intermolecular (e.g., H2O) or intramolecular (e.g., DNA). The protagonism of hydrogen is due to its small size and its tendency to become positively polarized, specifically because of the elevated density of the charge which accumulates on the mentioned compounds. In this way, hydrogen is capable (e.g., in the case of water) of being doubly bonded: on the one hand, it is united covalently to an atom of oxygen belonging to its molecule and, on the other, it electrostatically attracts another atom of oxygen belonging to another molecule, so strengthening the attractions between molecules. In this way, each atom of oxygen of a molecule of water can take part in four links with four more molecules of water, two of these links being through the hydrogen atoms covalently bound to it and the other two links through hydrogen bonds thanks to the two pairs of solitary electrons which it possesses. The presence of the hydrogen bonds together

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with their tetrahedral coordination, the molecule of water constitutes the key to explaining its unusual properties (Figure 2.1.4). The energy of this bond (10-40 KJ/ mol) is found to be between that corresponding to the van der Waals forces (~1 KJ/ mol) and that of the simple covalent bond (200-400 KJ/mol). An energetic analysis of the hydrogen bond interaction shows that the leading term is the electrostatic one which explains that strong hydrogen bonds are found between hydrogen Figure 2.1.4. Tetrahedric structure of water in a crystal atoms with a partial positive charge and a basic site. The second term in the energy of ice. The dotted lines indicate the hydrogen bridges. decomposition of the hydrogen bond interaction is the charge transfer.29 The hydrogen bonds are crucial in explaining the form of the large biological molecules, such as proteins and nucleic acids, as well as how to begin to understand more particular chemical phenomena.30 Figure 2.1.5. Variation of maximum eigen values and boiling point The solutes which are capawith different molar ratios of ethyl alcohol + propylene glycol. [Adapted, by permission, from S. S. Sastry, S. M. Ibrahim, M. Sail- ble of forming hydrogen bonds aja, T. Vishwam, H. S. Tiong, J. Molec. Liq., 212, 612-7, 2015.] have a well-known affinity to solvents with similar characteristics, which is the case of water. The formation of hydrogen bonds between solute molecules and solvent explains, for example, the good solubility in water of ammonia and short chain organic acids. Intermolecular interactions between proton donor (ethyl alcohol) and proton acceptor (propylene glycol) result in the formation of hydrogen bonds.31 When they are used as cosolvent binary mixtures, the strength of their bonds depends on their composition (proportions).31 As Figure 2.1.5 shows, the strongest hydrogen bonds were obtained for 0.2 ethyl alcohol and 0.8 propylene glycol composition.31 This observation is also supported by the increase in boiling point.31 The increase in boiling point occurs because the molecules are getting larger with more electrons, and so van der Waals dispersion forces become greater.31 The sudden decrease in boiling point at a molar ratio of 0.2/0.8 combination is due to decrease in van der Waals forces, acidic nature, and the effect of intramolecular bonding.31

22

2.1 Solvent effects on chemical systems

The hydrogen bonding environment of deep eutectic solvents can be varied via changing the cation or hydrogen bond donor and, therefore, the solvent quality in application to poly(ethylene oxide).32 The solvent quality of deep eutectic solvents for poly(ethylene oxide) was reduced when the alkyl chain length was increased from ethyl to butyl because the longer alkyl chain reduced the density of hydrogen bonding sites.32 The solvent quality was increased when glycerol was replaced with ethylene glycol, even though ethylene glycol contains a smaller number of hydrogen bond donor sites.32 This implies that the cohesive interactions in the deep eutectic solvents are stronger when the hydrogen bond donor is glycerol compared to ethylene glycol, meaning hydrogen bond donor protons are less available to poly(ethylene oxide).32 A strong hydrogen bond basicity (β) of ionic liquids results in a high partition coefficient of methacrylic acid, providing directions for molecular design of ionic liquids for the highly efficient extractive separation of methacrylic acid from dilute aqueous solution.33 The ionic liquid with strong hydrogen bond basicity, namely, methyltrioctylammonium chloride was used to extract methacrylic acid from dilute aqueous solution.33 Compared with hexane which is a conventional solvent used in methacrylic acid extractive separation, the methyltrioctylammonium chloride has 49 times higher of partition coefficient value and the extraction efficiency reaching 94.57% for a single-stage extraction.33 2.1.2.6 Hydrophobic interactions Nonpolar solutes which are not capable of forming hydrogen bonds with water (such is the case of the hydrocarbons) interact with water in a particular way. Let us imagine a molecule of solute incapable of forming hydrogen bonds in the midst of the water. The molecules of water which come close to such molecule of solute will lose some or all of the hydrogen bonds which they were sharing with the other molecules of water. This causes the molecules of water which surround molecules of solute to arrange themselves in space so that there is a loss of the number of hydrogen bonds with other molecules of water. Evidently, this rearrangement (solvation or hydration) of the water molecules around the nonpolar molecule of solute will be greatly conditioned by the form and the size of the nonpolar molecule. All this amounts to a low solubility of nonpolar substances in water, which is known as the hydrophobic effect. If we now imagine not one but two nonpolar molecules in the midst of the water, it emerges that the interaction between these two molecules is greater when they are interacting in a free space. This phenomenon, also related to the rearrangement of the molecules of water around those of the solute, receives the name of hydrophobic interaction. The hydrophobic interaction term is used to describe the tendency of nonpolar groups or molecules to aggregate in water solution.34 Hydrophobic interactions are believed to play a very important role in a variety of processes, especially in the behavior of proteins in aqueous media. The origin of this solvent-induced interactions is still unclear. In 1945 Frank and Evans35 proposed the so-called iceberg model, in which emphasis is made on the enhanced local structure of water around the nonpolar solute. However, computational studies and experimental advances have yielded increasing evidence against this traditional interpretation,36 and other alternative explanations, such as the reduced freedom of water molecules in the solvation shell,37 have been used.

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To understand the hydrophobic interaction at the microscopic level the molecular simulations of nonpolar compounds in water have been carried out.38 The potential of mean force between two nonpolar molecules shows a contact minimum with an energy barrier. Computer simulations also usually predict the existence of a second solvent-separated minimum. Although molecular simulations provide valuable microscopic information on hydrophobic interactions they are computationally very expensive, especially for large systems, and normally make use of oversimplified potentials. The hydrophobic interaction can also be alternatively studied by means of continuum models.39 Using this approach, a different but complementary view of the problem has been obtained. In the partition energy scheme used in the continuum models the cavitation free energy (due to the change in the solvent-solvent interactions) is the most important contribution to the potential of mean force between two nonpolar solutes in aqueous solution, being responsible for the energy barrier that separates the contact minimum. The electrostatic contribution to the potential of mean force for two nonpolar molecules in water is close to zero and the dispersion-repulsion term remains approximately constant. The cavitation free energy only depends on the surface of the cavity where the solute is embedded and on the solvent physical properties (such as the surface tension and density). 2.1.3 MODELING OF SOLVENT EFFECTS A useful pathway to understanding the interaction between the molecules of solvent and those of solute is by reproducing interactions using an adequate model. This task of simulation of the dissolution process usually goes beyond the use of simple and intuitive structural models, such as “stick” models, which prove to be very useful both in teaching and research and frequently require the performance of a very high number of complex mathematical operations. Even though in the first instance, we could think that a solution could be considered as a group of molecules united by relatively weak interactions, the reality is more complex, especially if we analyze the chemical reactivity in the presence of a solvent. The prediction of reaction mechanisms, the calculation of reaction rates, obtaining the structures of minimum energy and other aspects of the chemical processes in solution require the support of models with a very elaborated formalism and powerful computers. Traditionally, the models which permit the reproduction of the solute-solvent interactions are classified into three groups:40 i Models based on the simulation of liquids by means of computers. ii Models of the continuum. iii Models of the supermolecule type. In the models classifiable into the first group, the system analyzed is represented by a group of interacting particles and the statistical distribution of any property is calculated as an average of different configurations generated in the simulation. Especially notable among these models are either Molecular Dynamics or the Monte Carlo type. The continuum models center their attention on a microscopic description of the solute molecules, whereas solvent is represented by means of its macroscopic properties, such as its density, its refractive index, or its dielectric constant (relative permittivity).

24

2.1 Solvent effects on chemical systems

Finally, the supermolecule type models restrict the analysis to interactions among just a few molecules described at a quantum level which leads to a rigorous treatment of their interactions but does not allow us to have exact information about the global effect of solvent on the solute molecules, which usually is a very long range effect. The majority of these models have their origin in a physical analysis of the solutions but, with the passage of time, they have acquired a more chemical connotation. They have centered the analysis more on the molecular aspect. Recourse is more and more being made to combined strategies which use the best of each of the methods referred to in pursuit of a truer reproduction of the solute-disolvente (thinner) interactions. Especially useful has been shown to be a combination of the supermolecular method, used to reproduce the specific interactions between the solute and one or two molecules of the solvent, with those of continuum or of simulation, used to reproduce the global properties of the medium. 2.1.3.1 Computer simulations Obtaining the configuration or the conformation of minimum energy of a system provides us with a static view of the system, which may be sufficient to obtain many of its properties. However, direct comparison with experiments can strictly be done only if average thermodynamic properties are obtained. Simulation methods are designed to calculate average properties of a system over many different configurations which are generated by being representative of the system behavior. These methods are based on a calculation of average properties as a sum over discrete events: N

 F =  ( dR 1 … ) dR n P ( R )F ( R ) ≈

 Pi Fi

[2.1.11]

i=1

Two important difficulties arise in the computation of an average property as a sum. First, the number of molecules that can be handled in a computer is of the order of a few hundred. Secondly, the number of configurations needed to reach the convergence in the sum can be too great. The first problem can be solved by different computational strategies, such as the imposition of periodic boundary conditions.41 The solution of the second problem differs from the main used techniques in computer simulations. The two techniques most used in the dynamic study of the molecular systems are the Molecular Dynamics, whose origin dates back42 to 1957, and the Monte Carlo methods, which came into being following the first simulation of fluids by computer,43 which occurred in 1952. Molecular Dynamics In the Molecular Dynamic simulations, generation of new system configurations or sequence of events is made following the trajectory of the system which is dictated by the equations of motion. Thus, this method leads to the computation of time averages and permits the calculation of not only equilibrium but also transport properties. Given a configuration of the system, a new configuration is obtained moving the molecules according to the total force exerted on them:

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25

n

md R j ---------------- = –  ∇ j E ( R jk ) 2 dt k=1

[2.1.12]

If we are capable of integrating the equations of movement of all particles which constitute a system, we can find their pathways and velocities and we can evaluate the properties of the system in determined time intervals. Thus, we can find how the system under study evolves as time moves forward. In the first simulations by Molecular Dynamics of a condensed phase,42 use was made of potentials as simple as the hard sphere potential, under which the constituent particles move in a straight line until colliding elastically. The collisions happen when the separation between the centers of the spheres is equal to the diameter of the sphere. After each collision, the new velocities are obtained by making use of the principle of conservation of the linear moments. But a chemical system requires more elaborate potentials under which force, which at every instant act between two atoms or molecules, changes in relation to the variation of the distance between them. This permits us to integrate the equations of movement of a system in very small time intervals, in which it is assumed that the force which acts on each atom or molecule is constant, generally lying between 1 and 10 femtoseconds. For each of these intervals, the positions and velocities of each of the atoms are calculated, after which they are placed in their new positions and, once again, the forces are evaluated to obtain the parameters of a new interval, and so on, successively. This evolution in time, which usually requires the evaluation of hundreds of thousands of intervals of approximately 1 femtosecond each, allows us to know the properties of the system submitted to study during the elapsed of time. In fact, the task commences by fixing the atoms which make up the system under study in starting positions, and later move atoms continuously whilst the molecules being analyzed rotate, the bond angles bend, the bonds vibrate, etc., and during which the dispositions of the atoms which make up the system are tabulated at regular intervals of time, and the energies and other properties which depend on each of the conformations, through which the molecular system makes its way with the passage of time, are evaluated. Molecular Dynamics is chemistry scrutinized for each femtosecond. The Molecular Dynamics, MD, simulation is a powerful tool for analyzing properties of biomolecules that cannot be studied experimentally.44 The timescale of the MD simulation is not sufficient for examining the biologically significant events such as protein folding, domain movement, and so on, due to the computational limitation.44 The replica exchange molecular dynamics was adopted as a subsystem to reduce computational cost and improve timescale.44 An alternative method, the implicit solvent model, replaced real water environment consisting of discrete molecules by an infinite continuum medium with the dielectric and “hydrophobic” properties of water.45 The method has several advantages, such as lower computational cost, effective way to estimate free energy, and no need for lengthy equilibration of water (needed in explicit water simulation).45 Molecular dynamics simulation was performed for the systems consisting of a flexible regular tetrafunctional polymer network and a low molecular liquid crystal solvent.46 All interactions between non-bonded beads were described by the repulsive part of the

26

2.1 Solvent effects on chemical systems

Lennard-Jones potential.46 The study shows that the polymer component in the liquid crystal solution decreases the anisotropy of diffusion of mesogens.46 This decrease is connected with lower ordering of mesogens in the composite compared with pure liquid crystal.46 Lennard-Jones interactions between solute and anti-solvent and composition of antisolvent were essential variables to realized anti-solvent crystallization.47 The co-solvent and anti-solvent effects were represented by the Lennard-Jones interaction energy parameter, εij.47 Anti-solvent crystallization was introduced by changing some co-solvent molecules to anti-solvent molecules.47 The composition of the anti-solvent molecules in solution affected the configuration of the solute molecules.47 A Stochastic Event-Driven Molecular Dynamics algorithm was developed for the simulation of polymer chains suspended in a solvent.48 Stochastic Event-Driven Molecular Dynamics combines event-driven molecular dynamics with the Direct Simulation Monte Carlo method.48 The polymers are represented as chains of hard-spheres tethered by square wells and interact with the solvent particles with hard-core potentials.48 The algorithm uses event-driven molecular dynamics for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles.48 the use of Direct Simulation Monte Carlo instead of expensive Molecular Dynamics is suitable for problems where the detailed structure and chemical specificity of the solvent do not matter, and more general hydrodynamic forces and internal fluctuations dominate.48 Monte Carlo methods The first simulation by a computer of a molecular system was carried out using this method. It consists of generating configurations of a system introducing random changes in the position of its constituents. In order to obtain a good convergence in the sequence of configurations, Metropolis et al.43 suggested an interesting approach. This approach avoids the generation of very long random configurations as follows: instead of choosing random configurations and then weighing them according to the Boltzmann factor, one generates configurations with a probability equal to the Boltzmann factor and afterward weigh them evenly. For this purpose, once a new configuration is generated the difference in the potential energy with respect to the previous one is computed (ΔU) and a random number 0 < r < 1 is selected. If the Boltzmann factor exp(-ΔU/kT) > r then the new configuration is accepted, if exp(-ΔU/ kT) < r is rejected. In the Monte Carlo method, every new configuration of the system being analyzed can be generated starting from the random movement of one or more atoms or molecules, by rotation around a bond, etc. The energy of each new configuration is calculated starting from a potential energy function, and the configuration which corresponds to the least energy is selected. Once a configuration has been accepted, the properties are calculated. At the end of the simulation, the mean values of these properties are also calculated over the ensemble of accepted configurations. When it comes to modeling a dissolution process, certain doubts may arise about the convenience of using Molecular Dynamics or a Monte Carlo method. It must be accepted that a simulation with Molecular Dynamics is a succession of configurations which are

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linked together in time, in a similar way that a film is a collection of scenes which follow one after the other. When one of the configurations of the system analyzed by Molecular Dynamics has been obtained, it is not possible to relate it to configurations which precede it or configurations which follow, which is different than in the simulations of Monte Carlo type. In these, the configurations are generated in a random way, without fixed timing, and each configuration is only related to that which immediately preceded it. It would, therefore, seem advisable to make use of Molecular Dynamics to study a system through a period of time. On the other hand, the Monte Carlo method is usually the most appropriate in cases without the requirement of time. It is also useful to combine the two techniques in the different parts of the simulation, using a hybrid arrangement. In this way, the evolution of the process of the dissolution of a macromolecule can be followed by Molecular Dynamics and make use of the Monte Carlo method to resolve some of the steps of the overall process. On the other hand, a distinction is frequently made in the electronic description of solute and solvent. When the chemical attention is focused on the solute, a quantum treatment is used for it while the rest of the system is described at the molecular mechanics level.44 2.1.3.2 Continuum models In many dissolution processes the solvent merely acts to provide an envelope surrounding the solute molecules, the specific interactions with the solvent molecules are not important but the dielectric properties of solvent significantly affect the solute molecules. This situation can be confronted considering the solvent as a continuum, without including explicitly each of its molecules and concentrating on the behavior of a solute. A large number of models have been designed with this approach, either using quantum mechanics or resorting to empirical models. They are the continuum models.40 The continuum models are attractive due to their relative simplicity, and, therefore, a lesser degree of computational calculation, a favorable description of many chemical problems in dissolution from the point of view of the chemical equilibrium, kinetics, thermochemistry, spectroscopy, etc. Generally, the analysis of a chemical problem with a model of continuum begins by defining a cavity − in which a molecule of solute will be inserted − in the midst of the dielectric medium which represents the solvent. Unlike in the simulation methods, where the solvent distribution function is obtained during calculations, in the continuum models, this distribution is usually assumed to be constant outside the solute cavity and its value is taken to reproduce the macroscopic density of the solvent. Although the continuum models were initially created with the aim of the calculation of the electrostatic contribution to the solvation free energy,49 they have been extended to consideration of other energy contributions. The solvation free energy is usually expressed in these models as the sum of three different terms: ΔG sol = ΔG ele + ΔG dis – rep + ΔG cav

[2.1.13]

where the first term is the electrostatic contribution, the second one the sum of dispersion and repulsion energies and the third one the energy needed to create the solute cavity in the solvent. Specific interactions can be also added if necessary.

28

2.1 Solvent effects on chemical systems

For the calculation of the electrostatic term the system under study is characterized by two dielectric constants (relative permittivities), in the interior of the cavity, the constant will have a value of unity, and in the exterior the value of the relative permittivity of the solvent. From this point, the total electrostatic potential is evaluated. Beyond the mere classical outlining of the problem, Quantum Mechanics allows us to examine more deeply the analysis of the solute inserted in the field of reaction of solvent, making the relevant modifications in the quantum mechanical equations of the system under study with a view to introducing a term due to the solvent reaction field.50 This permits a widening of the benefits, in which the use of the continuum methods is granted to other facilities provided for a quantical treatment of the system, such as the optimization of the solute geometry,51 the analysis of its wave function,52 the obtaining of its harmonic frequencies,53 etc.; all of which are taken in the presence of the solvent. Continuum models essentially differ in: • How the solute is described, either classically or quantally • How the solute charge distribution and its interaction with the dielectric are obtained • How the solute cavity and its surface are described. Here we will consider in detail the last topic. 2.1.3.3 Cavity surfaces Earliest continuum models made use of oversimplified cavities for the insertion of the solute in the dielectric medium such as spheres or ellipsoids. In the last decades, the concept of the molecular surface has become more common. Thus, the surface has been used in microscopic models of the solution.50,54 Linear relationships were also found between molecular surfaces and solvation free energies.55 Moreover, given that molecular surfaces can help us in the calculation of interaction of a solute molecule with surroundings of solvent molecules, they are one of the main tools in understanding the solution processes and solvent effects on chemical systems. Another popular application is the generation of graphical displays.56 One may use different types of molecular cavities and surfaces definitions (e.g. equipotential surfaces, equidensity surfaces, van der Waals surfaces). Among them there is a subset that shares a common trait: they consider that a molecule may be repreFigure 2.1.6. Molecular Surface models. (a) sented as a set of rigid interlocking spheres. There van der Waals Surface; (b) Accessible Surface and (c) Solvent Excluding Surface. are three such surfaces: a) the van der Waals surface

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(WSURF), which is the external surface resulting from a set of spheres centered on the atoms or group of atoms forming the molecule (Figure 2.1.6a); b) the Accessible Surface (ASURF), defined by Richards and Lee57 as the surface generated by the center of the solvent probe sphere, when it rolls around the van der Waals surface (Figure 2.1.6b); and c) the Solvent Excluding Surface (ESURF) which was defined by Rich58 Figure 2.1.7. Variation of the area of the Solvent Acces- ards as the molecular surface composed sible Surface and Solvent Excluding Surface of methane of two parts: the contact surface and the dimer as a function of the intermolecular distance. reentrant surface. The contact surface is the part of the van der Waals surface of each atom which is accessible to a probe sphere of a given radius. The reentrant surface is defined as the inward-facing part of the probe sphere when this is simultaneously in contact with more than one atom (Figure 2.1.6c). We defined59 ESURF as the surface envelope of the volume excluded to the solvent, considered as a rigid sphere when it rolls around the van der Waals surface. This definition is equivalent to the definition given by Richards but more concise and simple. Each of these types of molecular surfaces is adequate for some applications. The van der Waals surface is widely used in graphic displays. However, for the representation of the solute cavity in a continuum model, the Accessible and the Excluding molecular surfaces are the adequate models as long as they take into account solvent. The main relative difference between both molecular surface models appears when one considers the separation of two cavities in a continuum model and more precisely the cavitation contribution to the potential of mean force associated with this process (Figure 2.1.7). In fact, we have shown39 that only using the Excluding surface the correct shape of the potential of mean force is obtained. The cavitation term cannot be correctly represented by interactions among only one center by a solvent molecule, such as the construction of the Accessible surface implies. The Excluding surface, which gives the area of the cavity not accessible to the solvent whole sphere and which should be close to the true envelope of the volume inaccessible to the solvent charge distribution, would be a more appropriate model (Figure 2.1.8).

Figure 2.1.8. The Solvent Excluding Surface of a particular solute is the envelope of the volume excluded to the solvent considered as a whole sphere that represents its charge density.

30

2.1 Solvent effects on chemical systems

2.1.3.4 Supermolecule models The study of the dissolution process can also be confronted in a direct manner analyzing the specific interactions between one or more molecules of solute with a large or larger group of solvent molecules. Quantum Mechanics is once again the ideal tool for dealing with this type of system. Paradoxically, the experimental study of a system becomes complicated when we try to make an abstraction of the solvent, and the theoretical study becomes extraordinarily complicated when we include it. In this way, Quantum Mechanics has been, since its origins, a useful and relatively simple to use tool in the study of isolated molecules, with the behavior of a perfect gas. For this reason, Quantum Mechanics becomes so useful in the study of systems which are found in especially rarefied gaseous surroundings, such as in the case of molecules present in the interstellar medium.60 When studying systems in solution, the precision of results grows with the number of solvent molecules included in calculations, but so also the computational effort increases. Because of this, the main limitation of the supermolecule model is that it requires computational possibilities which are not always accessible, especially if it is desired to carry out the quantum mechanical calculations with a high level of quality. This problem is sometimes resolved by severely limiting the number of solvent molecules which are taken into account. However, this alternative will limit our hopes to know what is the global effect of the solvent over the molecules of a solute, specifically the far-reaching interactions of solute-solvent. The supermolecule model is effective in the analysis of short distance interactions between the molecules of the solute and those of the solvent, provided a sufficient number of solvent molecules are included in the system being studied to reproduce the effect under study.61 In this manner, the supermolecule model has an advantage over other models used in the simulation of the solute-solvent interactions, such as the continuum models. Further advances are removing the boundaries between the different computational strategies that deal with solvent effects. A clear example is given by the Car-Parrinello approach where a quantum treatment of the solute and solvent molecules is used in a dynamic study of the system.62 2.1.3.5 Application example: glycine in solution A practical case to compare the advantages obtained with the utilization of different models can be found in the autoionization of aminoacids in aqueous solution. The chemistry of aminoacids in an aqueous medium has been at the forefront of numerous studies,62-69 due to its self-evident biological interest. Thanks to these studies, it is well known that, whilst in the gas phase the aminoacids exist as non-autoionized structures, in aqueous solution the zwitterionic form prevails (Figure 2.1.9). This transformation suggests that when an aminoacid molecule is introduced from vacuum into the middle of a polar medium, which is the case of the physiological cellular media, a severe change is produced in its properties, its geometry, its energy, the charges which its atoms support, the dipolar molecular moment, etc., set off and conditioned by the presence of the solvent. Utilizing Quantum Mechanics to analyze the geometry of the glycine in the absence of solvent, two energy minima are obtained (Figure 2.1.10), differentiated by the rotation of the acid group. One of them is the absolute energy minimum in the gas phase (I), and

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Figure 2.1.9. Neutral and zwitterionic form of glycine.

Figure 2.1.10. Quantum Mechanics predicts the existence of two conformers of glycine in the gas phase whose main difference is in the rotation of the acid group around the axis which joins the two carbons. The structure I, the furthest from the zwitterionic geometry, is revealed to be the most stable in the gas phase.

the other is the conformation directly related to the ionic structure (II): The structure which is furthest from the zwitterionic form, I, is by 0.7 kcal/mol more stable than II, which highlights the importance of the solvent for the autoionized form of the aminoacids to prevail. An analysis of the specific effects of solvent in the formation and the stability of the zwitterion can be addressed carrying out calculations of the reaction pathways with and without a molecule of water (Figure 2.1.11), this being within the philosophy of the supermolecule calculations. The discrete molecule of solvent has been found to actively participate in the migration of proton from oxygen to nitrogen.67 A molecule of water forms two hydrogen bonds with the neutral glycine in a zwitterionic form. When glycine is transformed from neutral configuration to a zwitterion the interchange of two atoms of hydrogen occurs between the aminoacid and the molecule of

32

2.1 Solvent effects on chemical systems

Figure 2.1.11. Intramolecular and intermolecular proton transfer in glycine, leading from the neutral form to the zwitterionic one.

solvent. Thus, we reproduce, from a theoretical point of view, the process of protonic transfer of an aminoacid with the participation of solvent (intermolecular mechanism). Table 2.1.2 shows the relative energies of the three solute-solvent structures analyzed, as well as the energy of the system formed by the aminoacid and the molecule of solvent. Table 2.1.2. Relative energies (in kcal/mol) for the complexes formed between a molecule of water with the neutral glycine (NE·H2O), the zwitterion (ZW·H2O), and the state of transition (TS·H2O), as well as for the neutral glycine system and independent molecule of water (NE+H2O), obtained with a base HF/6-31+G** NE·H2O

TS·H2O

ZW·H2O

NE+H2O

0

29.04

16.40

4.32

The table shows that the neutral glycine−molecule of water complex is the most stable. Moreover, the energy barrier which drives the state of transition is much greater than that which is obtained when Quantum Mechanics is reproducing the autoionization of the glycine in the presence of solvent by means of an intramolecular process.67 This data suggests that even in the case where a larger number of water molecules is included in the supermolecule calculation, the intramolecular mechanism will still continue to be preferred in the autoionization of the glycine. The model of supermolecule has been useful,

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33

along with other models,66,67 to shed light on the mechanism by which an aminoacid is autoionized in aqueous solution. If the calculations are repeated but in the presence of solvent by means of a continuum model (implemented by means of a dielectric constant (relative permittivity) = 78.4; for the water), the results become different.67,70-72 Now it is the conformation closest to the zwitterionic (II) which is the most stable, by some 2.7 kcal/mol. This could be explained on the basis of the greater dipolar moment of the structure (6.3 Debyes for the conformation II compared to 1.3 of the conformation I). The next step was to reproduce the formation of the zwitterion starting with the most stable initial structure in the midst of the solvent (II). Using the continuum model, we observe how the structure II evolves towards a state of transition which, and once overcome, it leads to zwitterion. This transition structure corresponds, then, to an intramolecular protonic transfer from the initial form to the zwitterionic form of the aminoacid. The calculations give an activation energy of 2.39 kcal/mol and a reaction energy of -1.15 kcal/ mol at the MP2/6-31+G** level. A more visual check of the process submitted to study is achieved by means of hybrid QM/MM Molecular Dynamics,70 which gives “snapshots”, which reproduce the geometry of the aminoacid surrounded by solvent. In Figure 2.1.12 four of these snapshots are shown, corresponding to times of 200, 270, 405 and 440 femtoseconds after initiation of the process. In the first of these, the glycine has still not been autoionized. Two molecules of water (identified as A and B) form hydrogen bonds with the nitrogen of the amine group, whilst only one (D) joins by a hydrogen bond with the O2. Two more molecules of water (C and E) appear to stabilize electrostatically hydrogen of acid (H1). The second snapshot has been chosen when the protonic transfer was happening. In this case, the proton (H1) appears jumping from the acid group to the amine group. However, the description of the first shell of hydratation around the nitrogen atoms, oxygen (O2) and proton in transit remain essentially unaltered as compared with the first snapshot. In the third snapshot, the aminoacid has now reached the zwitterionic form, although the solvent still has not relaxed to its surroundings. Now the molecules of water A and B have moved closer to the atom of nitrogen, and a third molecule of water appears between them. At the same time, two molecules of water (D and E) are connected by bridges of hydrogen with the atom of oxygen (O2). All these changes could be attributed to the charges which have been placed on the atoms of nitrogen and oxygen. The molecule of water (C) has followed a proton in its transit and has fitted in between this and the atom of oxygen (O2). In the fourth snapshot, the relaxing of the solvent, after the protonic transfer, is now observed, permitting the molecule of water (C) to appear better orientated between the proton transferred (H1) and the atom of oxygen (O2), and this now makes this molecule of solvent strongly attached to the zwitterion inducing into it appreciable geometrical distortions. From the theoretical analysis carried out, it can be inferred that the neutral conformer of the glycine II, has a brief life in aqueous solution, rapidly evolving to the zwitterionic species. The process appears to happen through an intramolecular mechanism and comes accompanied by a soft energetic barrier. For its part, the solvent plays a role which is cru-

34

2.1 Solvent effects on chemical systems

Figure 2.1.12. The microscopic environment, in which the formation of zwitterion takes place, is exhibited in these four “snapshots”. It is possible to see the re-ordering of the structure of the molecule of glycine, along with the re-ordering of the shell of molecules of water which surround it, at 200, 270, 405 and 440 femtoseconds from the beginning of the simulation process by Molecular Dynamics.

cial both to the stabilization of the zwitterion as well as to the protonic transfer. This latter is favored by fluctuations which take place in the surroundings. 2.1.4 THERMODYNAMIC AND KINETIC CHARACTERISTICS OF CHEMICAL REACTIONS IN SOLUTION It is very difficult for a chemical equilibrium not to be altered when passing from gas phase to solution. The free energy standard of reaction, ΔGº, is usually different in the gas phase compared to the solution because the solute-solvent interactions usually affect the reactants and the products with different results. This provokes a displacement of the equilibrium on passing from the gas phase to the midst of the solution.

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In the same way, and as it was projected in section 2.1.1, the process of dissolution may alter both the rate and the order of a chemical reaction. For this reason, it is possible to use a solvent as a tool both to speed up and to slow down the development of a chemical process. Unfortunately, little experimental information is available on how the chemical equilibria and the kinetics of reactions become altered on passing from the gas phase to the solution since as commented previously, the techniques which enable this kind of analysis are relatively recent. It is true that there is abundant experimental information on how the chemical equilibrium and the velocity of the reaction are altered when the same process occurs in the midst of different solvents. 2.1.4.1 Solvent effects on chemical equilibria The presence of solvent is known to have proven influences in a variety of chemical equilibria, such as acid-base, tautomerism, isomerization, association, dissociation, conformational, rotational, condensation reactions, phase-transfer processes, etc.,1 that its detailed analysis is outside the reach of a text such as this. We will limit ourselves to analyzing superficially the influence that the solvent has on the equilibrium of greatest relevance, the acid-base equilibrium. The solvent can alter an acid-base equilibrium not only through the acid or base character of solvent itself, but also by its dielectric effect and its capacity to solvate the different species which participate in the process. Whilst the acidic or basic force of a substance in the gas phase is an intrinsic characteristic of this substance, in solution this force is also a reflection of the acidic or basic character of the solvent and of the actual process of solvatation. For this reason, the scales of acidity or basicity in solution are clearly different from those corresponding to the gas phase. Thus, toluene is more acidic than water in the gas phase but less acidic in solution. These differences between the scales of intrinsic acidity-basicity have an evident repercussion on the order of acidity of some series of chemical substances. Thus, the order of acidity of the aliphatic alcohols becomes inverted on passing from the gas phase to solution: in gas phase: R

CH 2

OH < R

R'

R'

CH OH < R

C OH R''

in solution: R

CH 2

OH > R

R'

R'

CH OH > R

C OH R''

The protonation free energies of MeOH to t-ButOH have been calculated in gas phase and with a continuum model of a solvent.73 It has been shown that continuum models give solvation energies which are good enough to correctly predict the acidity ordering of alcohols in solution. Simple electrostatic arguments based on the charge delocalization concept, were used to rationalize the progressive acidity of the alcohols in the gas phase when hydrogen atoms are substituted by methyl groups, with the effect on the solution energies being just the opposite. Thus, both the methyl stabilizing effect and the electrostatic interaction with the solvent can explain the acid scale in solution. As both terms are

36

2.1 Solvent effects on chemical systems

related to the molecular size, this explanation could be generalized for acid and base equilibria of homologous series of organic compounds:

AH B+H

A+H BH

In vacuo, as the size becomes greater by adding methyl groups, displacement of the equilibria takes place towards the charged species. In solution, the electrostatic stabilization is lower when the size increases, favoring the displacement of the equilibria towards the neutral species. The balance between these two tendencies gives the final acidity or basicity ordering in solution. Irregular ordering in homologous series are thus not unexpected taking into account the delicate balance between these factors in some cases.74 Entropy plays a fundamental role in equilibrium and reactivity, and it may be strongly affected by solvation, especially in reactions involving ions or highly polar species.75 The ionic strength of the medium is considered to account for the change in activity coefficients of the different species involved in equilibria and the effect on rate constants, as follows75 I =

1

2

 --2- C i zi

[2.1.14]

i

where: I Ci zi

ionic strength concentrations of ions present their charge.

A description of the reaction equilibrium permits estimation of the attainable product yield and thermodynamic limits of the process.76 The addition of proper solvents may improve the equilibrium of alcohol yield under a supercritical condition.76 The selection of the supercritical solvent depends on the size of alcohol molecule, the reaction temperature and pressure, and the critical properties of the solvent.76 The n-hexane or n-heptane improve the methanol synthesis at temperature range from 200 to 210°C and pressure above 8 MPa.76 The n-dodecane is suitable for the higher alcohols synthesis at a higher temperature range (300-400°C).76 2.1.4.2 Solvent effects on the rate of chemical reactions When a chemical reaction takes place in the midst of a solution, it happens because, prior to this, the molecules of the reactants have diffused throughout the medium until they have met. This prior step of diffusion of the reactants can be considered as conditioning the performance of the reaction, especially in particularly dense and/or viscous surroundings. This is the consequence of the liquid phase having a certain microscopic order which, although much less than that of the solid state, is not depreciable. Thus, in a solution, each molecule of solute finds itself surrounded by a certain number of molecules of solvent which envelope solute molecules, forming the solvent cage. Before being able to escape from the solvent cage each molecule of solute collides many times with the molecules of solvent which surround it.

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In the case of a dilute solution of two reactants, A and B, their molecules remain for a certain time in solvent cages. If the time needed to escape the solvent cage by the molecules A and B is larger than the time needed to undergo a bimolecular reaction, we can say that this will not find itself limited by the requirement to overcome an energetic barrier, but that the reaction is controlled by the diffusion of the reactants. The corresponding reaction rate will, therefore, have a maximum value, known as diffusion-controlled rate. It can be demonstrated that the diffusion-limited bimolecular rate constants are of the order of 1010-1011 M-1s-1 when A and B are ions with opposite charges.77 For this reason, if a rate constant is of this order of magnitude, we must wait for the reaction to be controlled by the diffusion of the reactants. But, if the rate constant of a reaction is clearly less than the diffusion-limited value, the corresponding reaction rate is said to be chemically controlled. Focusing on the chemical aspects of reactivity, the rupture of bonds which goes along with a chemical reaction usually occurs in a homolytic manner in the gas phase. For this reason, the reactions which tend to prevail in this phase are those which do not involve a separation of electric charge, such as those which take place with the production of radicals. In solution, the rupture of bonds tends to take place in a heterolytic manner, and the solvent is one of the factors which determines the velocity with which the process takes place. This explains that the reactions which involve a separation or a dispersion of the electric charge can take place in the condensed phase. The effects of solvent on the reactions which involve a separation of charge will be related to the polar nature of the transition state of the reaction, whether this is a state of dipolar transition, isopolar or of the free-radical type. The influence of solvent, based on the electric nature of the substances which are reacting, will also be essential, and reactions may occur between neutral nonpolar molecules, between neutral dipolar molecules, between ions and neutral nonpolar molecules, between ions and neutral polar molecules, ions with ions, etc. Moreover, we should bear in mind that alongside with the non-specific solute-solvent interactions (electrostatic, polarization, dispersion, and repulsion), specific interactions may be present, such as the hydrogen bonding. Table 2.1.3. Relative rate constants of the Menschutkin reaction between triethylamine and iodoethane in different solvents at 50oC. In 1,1,1-trichloroethane the rate constant is 1.80x10-5 l mol-1 s-1. Data were taken from reference 52. Solvent 1,1,1-Trichloroethane

Relative rate constant 1

Solvent

Relative rate constant

Acetone

17.61

Chlorocyclohexane

1.72

Cyclohexanone

18.72

Chlorobenzene

5.17

Propionitrile

33.11

Chloroform

8.56

Benzonitrile

42.50

1,2-Dichlorobenzene

10.06

The influence of solvent on the rate at which a chemical reaction takes place was already made clear, in the final stages of the XIX century, with the Menschutkin reaction

38

2.1 Solvent effects on chemical systems

between tertiary amines and primary haloalkanes to obtain quaternary ammonium salts.78 The Menschutkin reaction between triethylamine and iodoethane carried out in different solvents shows this effect (Table 2.1.3). Effect of solvent on reaction rate constant of reaction between carbon dioxide and glycidyl methacrylate in the presence of Aliquat 336 as a catalyst was studied.79 The reaction rate constants were estimated by the mass transfer Figure 2.1.13. Representation of polypyrrole oxidation rate coeffi- mechanism accompanied by the cients (k) in different solvents: (1) methanol, (2) water, (3) acetone, pseudo-first-order fast reaction.79 (4) acetonitrile, (5) benzonitrile, (6) DMS, (7) DMF. [Adapted, by The solvent polarity was increased permission, from T. F. Otero, M. Alfaro, J. Electroanal. Chem., by the increase of solubility 777, 108-16, 2016.] parameter of the solvent and the was followed by the increase in the reaction rate.79 The empirical oxidation kinetics of polypyrrole was studied in different solvents.80 During the electrochemical reactions, the films of conducting polymers exchange counterions (charge balance) and solvent (osmotic balance) with the electrolyte.80 Seven solvents were studied including two protic (water and methanol) and four aprotic (acetonitrile, acetone, N,N-dimethylformamide dimethylsulfoxide and benzonitrile) solvents.80 The solvent had a strong influence on the reaction rate of electrochemical reactions involving dense reactive gels of conducting polymers.80 The reaction rate coefficient changed by one order of magnitude as a function of the dipolar moment and dielectric constant of the solvent. Figure 2.1.13 shows the effect of individual solvents.80 The presence of a solvent in the film modifies the various molecular interaction forces (polymer-polymer, polymerions, polymer-solvent) acting simultaneously as a plasticizer that favors conformational movements of chains.80 By changing the solvent or the solved salt all these interactions change, promoting changes in the reaction rate.80 2.1.4.3 Example of application: addition of azide anion to tetrafuranosides The capacity of the solvent to modify both the thermodynamic and the kinetic aspects of a chemical reaction is observed in a transparent manner by studying the stationary structures of the addition of azide anion to tetrafuranosides, particularly: methyl 2,3-dideoxy-2,3epimino-α-L-erythrofuranoside (I), methyl 2,3-anhydro-α-L-erythrofuranoside (II), and 2,3-anhydro-β-L-erythrofuranoside (III). An analysis using molecular orbital methods at the HF/3-21G level permits the potential energy surface in vacuo to be characterized, to locate the stationary points and the possible reaction pathways.81 The effect of the solvent can be implemented with the aid of a polarizable continuum model. Figure 2.1.14 shows

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Figure 2.1.14. Models of the reaction studied for the addition of azide anion to tetrafuranosides. The experimental product ratio is also given.

the three tetrafuranosides and the respective products obtained when azide anion attacks in C3 (P1) or in C4 (P2). The first aim of a theoretical study of a chemical reaction is to determine the reaction mechanism that corresponds to the minimum energy path that connects the minima of reactants and products and passes through the transition state (TS) structures on the potential energy surface. In this path, the height of a barrier that exists between the reactant and TS is correlated to the rate of each different pathway (kinetic control), while the relative energy of reactants and products is correlated to equilibrium parameters (thermodynamic control). The second aim is how the solute-solvent interactions affect the different barrier heights and relative energies of products, mainly when charged or highly polar structures appear along the reaction path. In fact, the differential stabilization of the different station-

40

2.1 Solvent effects on chemical systems

Figure 2.1.15. Representation of the stationary points (reactants, reactant complex, transition states, and products) for the molecular mechanism of compound I. For the TS´s the components of the transition vectors are depicted by arrows.

ary points in the reaction paths can treat one of them favorably, sometimes altering the relative energy order found in vacuo and, consequently, possibly changing the ratio of products of the reaction. An analysis of the potential energy surface for the molecular model I led to the location of the stationary points showed in Figure 2.1.15. The results obtained for the addition of azide anion to tetrafuranosides with different molecular models and in different solvents can be summarized as follows:81 • For compound I, in vacuo, P1 corresponds to the path with the minimum activation energy, while P2 is the more stable product (Figures 2.1.16 and 2.1.17). When the solvent effect is included, P1 corresponds to the path with the minimum activation energy and it is also the more stable product. For compound II, in vacuo, P2 is the more stable product and also presents the smallest activation energy. The inclusion of the solvent effect, in this case, changes the order of products and transition state stability. For compound III, P1 is the more stable product and presents the smallest activation energy both in vacuo and in solution. • A common solvent effect for the three reactions is obtained: as far as the relative permittivity of the solvent is augmented, the energy difference between P1 and P2 increases, favoring thermodynamically the path leading to P1. On the other hand, an opposite influence is evident in the case of the transition states, so an increase of the relative permittivity kinetically favors the path leading to P2.

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Figure 2.1.16. Schematic representation of the relative energies (in kcal/mol) for the products P1 and P2, in vacuo (ε = 1), DMF (ε = 36.7), or EtOH (ε = 24.3), and in water (ε = 78.4).

Figure 2.1.17. Schematic representation of the relative energies of activation (in kcal/mol) for the transition states TS1 and TS2, in vacuo (ε = 1), DMF (ε = 36.7), or EtOH (ε = 24.3), and in water (ε = 78.4).

All data show the crucial role which the solvent plays both in the thermodynamics and in the kinetics of the chemical reaction analyzed. 2.1.5 SOLVENT CATALYTIC EFFECTS Beyond the solvent as merely making possible an alternative scenery to the gas phase, beyond its capacity to alter the thermodynamics of a process, the solvent can also act as a catalyst of some reactions and can reach the point of altering the mechanism by which the reaction comes about. An example of a reaction in which the solvent is capable of altering the mechanism through which the reaction takes place is that of Meyer-Schuster, which is much Figure 2.1.18. Reaction of Meyer-Schuster. utilized in organic synthesis.82-87 It consists of the isomerization in an acid medium of secondary and tertiary α-acetylenic alcohols to carbonylic α,β-unsaturated compounds (Figure 2.1.18).

42

2.1 Solvent effects on chemical systems

Its mechanism consists of three steps (Figure 2.1.19). The first one is the protonation of the oxygen atom. The second, which determines the reaction rate, is that in which the 1.3 shift from the protonated hydroxyl group is produced through the triple bond to give way to the structure of alenol. The last stage corresponds to the deprotonation of the alenol, producing a keto-enolic tautomerism which displaces towards the ketonic form. For the step, which limits the reaction rate (rate limiting step), three mechanisms have been proposed, two of which are intramoFigure 2.1.19. Steps of the reaction of Meyer-Schuster. denominated lecular − intramolecular, as such, and solvolytic − and the other intermolecular (Figure 2.1.20). The first of these implies a covalent bond between water and the atoms of carbon during the transposition. In the solvolytic mechanism, there is an initial rupture from the O−C1 bond, followed by a nucleophilic attack of the H2O on the C3. Whilst the intermolecular mechanism corresponds to a nucleophilic attack of H2O on the terminal carbon C3 and the loss of the hydroxyl group protonated on the C1. The analysis of the first two mechanisms showed88 that the solvolytic mechanism was the most favorable localizing itself during the reaction pathway to an alquinylic car-

Figure 2.1.20. Three different mechanism for the rate-limiting step of the reaction of Meyer-Schuster.

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bocation interacting electrostatically with a molecule of water. This fact has been supported by the experimental detection of alquinylic carbocations in solvolytic conditions. Two alternatives remain for the slow stage of the Meyer-Schuster reaction, the solvolytic and the intermolecular mechanisms, and it seems that the solvent has a strong influence. Although both mechanisms involve two steps, these are notably different. In the intermolecular mechanism, the first transition state can be described as an almost pure electrostatic interaction of the entrant molecule of water with the C3, whereas the C1 remains bound covalently to the protonated hydroxyl group. This first transition state leads to an intermediate in which the two molecules of water are covalently bound to the C1 and C3 atoms. The step from the intermediate to the product takes place through a second transition state, in which the C3 is covalently bound to the molecule of entrant water and there is an electrostatic interaction of the other water molecule. In the mechanism which we call solvolytic, the first transition state corresponds to the conversion from covalent to electrostatic interaction of H2O connected to C1, that is to say, to a process of solvolysis, so, the water molecule remains interacting electrostatically with the carbons C1 and C3. The keto-enol isomerization of neutral and ionized acetaldehyde has been studied.89 The ionization favors the enolization of acetaldehyde both in thermodynamic and kinetic terms.89 Solvent molecules produce a catalytic effect, especially in the case of the methanol-solvated system, for which the transition state of the isomerization lies below the ground-state asymptote.89 Supercritical phase 2-butanol significantly increased the conversion of methanol synthesis from syngas by the conventional promotion effect of supercritical fluid and the catalytic effect of the 2-butanol solvent itself, breaking through the thermodynamic limitation of this reaction.90 Comparing the solvolytic and intermolecular processes a smaller potential barrier is observed for the latter, thus the solvent plays an active part in the Meyer-Schuster reaction, being capable of changing radically the mechanism through which it takes place. It seems pertinent that in the presence of aqueous solvents the nucleophilic attack on C3 precedes the loss of water (solvolysis): a lesser activation energy corresponds to the intermolecular process than to the solvolytic. Moreover, if we analyze the intermolecular mechanism we can verify that the solvent stabilizes both the reactants as well as the products by the formation of hydrogen bridges. REFERENCES 1 2 3 4 5 6 7 8 9 10

Ch. Reichardt, Solvents and Solvent Effects in Organic Chemistry, VCH, Weinheim, 1988, p. 1. H. Metzger, Newton, Stahl, Boerhaave et la doctrine chimique, Alcan, Paris, 1930, pp. 280-289. M. M. Pattison, A History of Chemical Theories and Laws, John Wiley & Sons, New York, 1907, p. 381. H. M. Leicester, Panorama histórico de la química, Alhambra, Madrid, 1967, pp. 148, 149. (Transcription from The Historical Background of Chemistry, John Wiley & Sons, New York.) J. L. Proust, J. Phys., 63, 369, 1806. M. Berthelot and L. Péan de Saint-Gilles, Ann. Chim. et Phys., Ser. 3, 65, 385 (1862); 66, 5 (1862); 68, 255 (1863). N. Menschutkin, Z. Phys. Chem., 6, 41 (1890). E. D. Hughes, C. K. Ingold, J. Chem. Soc., 244, 252 (1935). L. Claisen, Liebigs Ann. Chem., 291, 25 (1896). W. Wislicenus. Liebigs Ann. Chem., 291, 147 (1896).

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2.1 Solvent effects on chemical systems

11 12 13 14 15 16 17 18

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M. Born, Z. Physik, 1, 45 (1920); J. G. Kirkwood, J. Chem. Phys., 2, 351 (1934); J. G. Kirkwood, F. H. Westheimer, J. Chem. Phys., 6, 506 (1936); L. Onsager, J. Am. Chem. Soc., 58, 1486 (1936). E. Scrocco, J. Tomasi, Top. Curr. Chem., 42, 97 (1973). J. L. Pascual-Ahuir, E. Silla, J. Tomasi, R. Bonaccorsi, J. Comput. Chem., 8, 778 (1987). D. Rinaldi, J. L. Rivail, N. Rguini, J. Comput. Chem., B, 676 (1992). I. Tuñón, E. Silla, J. Bertrán, J. Chem. Soc. Faraday Trans., 90, 1757 (1994). X. Assfeld, D. Rinaldi, AIP Conference Proceedings ECCC1, F. Bernardi, J. L. Rivail, Eds., AIP, Woodbury, New York, 1995. F. M. Floris, J. Tomasi, J. L. Pascual Ahuir, J. Comput. Chem., 12, 784 (1991); C. J. Cramer and D. G. Trhular, Science, 256, 213 (1992); V. Dillet, D. Rinaldi, J. G. Angyan and J. L. Rivail, Chem. Phys. Lett., 202, 18 (1993). I. Tuñón, E. Silla, J. L. Pascual-Ahuir, Prot. Eng., 5, 715 (1992); I. Tuñón, E. Silla, J. L. Pascual-Ahuir, Chem. Phys. Lett., 203, 289 (1993); R. B. Hermann, J. Phys. Chem., 76, 2754 (1972); K. A. Sharp, A. Nicholls, R. F: Fine, B. Honig, Science, 252, 106 (1991). L. H. Pearl, A. Honegger, J. Mol. Graphics, 1, 9 (1983); R. Voorintholt, M. T. Kosters, G. Vegter, G. Vriend, W. G. H. Hol, J. Mol. Graphics, 7, 243 (1989); J. B. Moon, W. J. Howe, J. Mol. Graphics, 7, 109 (1989); E. Silla, F. Villar, O. Nilsson, J. L. Pascual-Ahuir, O. Tapia, J. Mol. Graphics, 8, 168 (1990). B. Lee, F. M. Richards, J. Mol. Biol., 55, 379 (1971). F. M. Richards, Ann. Rev. Biophys. Bioeng., 6, 151 (1977). J. L. Pascual-Ahuir, E. Silla, I. Tuñón, J. Comput. Chem., 15, 1127-1138 (1994). V. Moliner, J. Andrés, A. Arnau, E. Silla and I. Tuñón, Chem. Phys., 206, 57-61 (1996); R. Moreno, E. Silla, I. Tuñón and A. Arnau, Astrophysical J., 437, 532-539 (1994); A. Arnau, E. Silla and I. Tuñón, Astrophysical J. Suppl. Ser., 88, 595-608 (1993); A. Arnau, E. Silla and I. Tuñón, Astrophysical J., 415, L151-L154 (1993). M. D. Newton, S. J. Ehrenson, J. Am. Chem. Soc., 93, 4971 (1971). G. Alagona, R. Cimiraglia, U. Lamanna, Theor. Chim. Acta, 29, 93 (1973). J. E: del Bene, M. J. Frisch, J. A. Pople, J. Phys. Chem., 89, 3669 (1985). I. Tuñón, E. Silla, J. Bertrán, J. Phys. Chem., 97, 5547-5552 (1993). R. Car, M. Parrinello, Phys. Rev. Lett., 55, 2471 (1985). P. G. Jonsson and A. Kvick, Acta Crystallogr. B, 28, 1827 (1972). A. G. Csázár, Theochem., 346, 141-152 (1995). Y. Ding and K. Krogh-Jespersen, Chem. Phys. Lett., 199, 261-266 (1992). J. H. Jensen and M.S.J. Gordon, J. Am. Chem. Soc., 117, 8159-8170 (1995). F. R. Tortonda., J.L. Pascual-Ahuir, E. Silla, and I. Tuñón, Chem. Phys. Lett., 260, 21-26 (1996). T. N. Truong and E.V. Stefanovich, J. Chem. Phys., 103, 3710-3717 (1995). N. Okuyama-Yoshida et al., J. Phys. Chem. A, 102, 285-292 (1998). I. Tuñón, E. Silla, C. Millot, M. Martins-Costa and M. F. Ruiz-López, J. Phys. Chem. A, 102, 8673-8678 (1998). F. R. Tortonda, J. L. Pascual-Ahuir, E. Silla, I. Tuñón, and F. J. Ramírez, J. Chem. Phys., 109, 592-602 (1998). F. J. Ramírez, I. Tuñón, and E. Silla, J. Phys. Chem. B, 102, 6290-6298 (1998). I. Tuñón, E. Silla and J. L. Pascual-Ahuir, J. Am. Chem. Soc., 115, 2226 (1993). I. Tuñón, E. Silla and J. Tomasi, J. Phys. Chem., 96, 9043 (1992). M. Canle, M. I. Fernández Pérez, J. A. Santaballa, Physicochemical Basis of IL Effects on Separation and Transformation Processes: From Equilibrium to Reactivity in Ionic Liquids in Separation Technology, Elsevier 2014, pp. 95-106. Z. Qin, J. Liu, J. Wang, Fuel Process. Technol., 85, 8-10, 1175-92, 2004. K.A. Connors, Chemical Kinetics, VCH, New York, 1990, pp. 134-135. N. Menschutkin, Z. Phys. Chem., 6, 41 (1890); ibid., 34, 157 (1900). S.-W. Park, J.-W. Lee, Studies Surf. Sci. Catalysis, 159, 345-8, 2006. T. F. Otero, M. Alfaro, J. Electroanal. Chem., 777, 108-16, 2016 and J. Electroanal. Chem., 793, 25-33, 2017. J. Andrés, S. Bohm, V. Moliner, E. Silla, and I. Tuñón, J. Phys. Chem., 98, 6955-6960 (1994). S. Swaminathan and K. V. Narayan, Chem. Rev., 71, 429 (1971). N. K. Chaudhuri and M. Gut, J. Am. Chem. Soc., 87, 3737 (1965). M. Apparu and R. Glenat, Bull. Soc. Chim. Fr., 1113-1116 (1968). S. A. Vartanyan and S.O. Babayan, Russ. Chem. Rev., 36, 670 (1967). L. I. Olsson, A. Claeson and C. Bogentoft, Acta Chem. Scand., 27, 1629 (1973). M. Edens, D. Boerner, C. R. Chase, D. Nass, and M. D. Schiavelli, J. Org. Chem., 42, 3403 (1977).

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2.1 Solvent effects on chemical systems J. Andrés, A. Arnau, E. Silla, J. Bertrán, and O. Tapia, J. Mol. Struct. Theochem., 105, 49 (1983); J. Andrés, E. Silla, and O. Tapia, J. Mol. Struct. Theochem., 105, 307 (1983); J. Andrés, E. Silla, and O. Tapia, Chem. Phys. Lett., 94, 193 (1983); J. Andrés, R. Cárdenas, E. Silla, O. Tapia, J. Am. Chem. Soc., 110, 666 (1988). L. Rodriguez-Santiago, O. Vendrell, I. Tejero, M. Sodupe, J. Bertran, Chem. Phys. Lett., 334, 1-3, 112-8, 2001. P. Reubroycharoen, Y. Yoneyama, T. Vitidsant, N. Tsubaki, Fuel, 82, 18, 2255-7, 2003.

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2.2 MOLECULAR DESIGN OF SOLVENTS Koichiro Nakanishi Kurashiki University of Science & the Arts, Okayama, Japan

2.2.1 MOLECULAR DESIGN AND MOLECULAR ENSEMBLE DESIGN Many chemists seem to guess that the success in developing so-called high-functional materials is the key to the recovery of social responsibility. These materials are often composed of complex molecules, contain many functional groups, and their structure is of a complex nature. Before establishing the final target compound, we are forced to consider many factors, and we are expected to minimize the process of screening these factors effectively. A screening is called “design”. If the object of screening is a molecule, then it is called “molecular design”. In similar contexts “material design”, “solvent design”, “chemical reaction design”, etc are also used. We hope that the term “molecular ensemble design” may have citizenship in chemistry. The reason for this is as below. Definition of “molecular design” may be expressed as to find out the molecule which has appropriate properties for a specific purpose and to predict accurately via theoretical approach the properties of the molecule. If the molecular system in question consists of an isolated free molecule, then it is “molecular design”. If the properties are of complex macroscopic nature, then it is “material design”. The problem remains in the intermediate between the above two. Because the fundamental properties shown by the ensemble of molecules are not always covered properly by the above two types of design. This is because the molecular design is almost always based on the quantum chemistry of free molecule and the material design relies too much on empirical factor at the present stage. When we proceed to the molecular ensemble (mainly liquid phase), as a matter of fact, we must use statistical mechanics as the basis of theoretical approach. Unfortunately, statistical mechanics is not familiar even for the vast majority of chemists and chemical engineers. Moreover, fundamental equations in statistical mechanics cannot often be solved rigorously for complex systems, and the introduction of approximation becomes necessary to obtain useful results for real systems. In any theoretical approach to the molecular ensemble, we must confront the so-called many-body problems and two-body approximations. Even in the frameworks of this approximation, our knowledge on the intermolecular interaction, which is necessary for statistical mechanical treatment, is still poor. Under such a circumstance, the numerical method is often useful. In the case of statistical mechanics of fluids, we use Monte Carlo (MC) simulation based on the Metropolis scheme. All the static properties can be numerically calculated in principle by the MC method. The numerical integration of the equations of motion is another numerical method used to supplement the MC method. This kind of calculation used for simple molecular systems is called molecular dynamics (MD) method in which Newton or Newton-Euler

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equation of motion is solved numerically, and some dynamic properties of the molecule involved can be obtained. These two methods were invented, respectively, by the Metropolis group (MC, Metropolis et al., 1953)1 and Alder's group (MD, Alder, et al., 1957)2 and they were the molecular versions of computer experiments; therefore called now molecular simulation.3 Molecular simulation plays a central role in “molecular ensemble design”. It can reproduce thermodynamic properties, structure, and dynamics of a group of molecules by using a computer. For simple molecules, an empirical model potential such as based on Lennard-Jones potential and even hard-sphere potential can be used. But, for complex molecules, potential function and related parameter value must be determined by some theoretical calculations. For example, the contribution of hydrogen bond interaction is significant to the total interaction for such molecules as H2O, alcohols, etc., one can produce semi-empirical potential based on quantum-chemical molecular orbital calculation. Molecular ensemble design is now a complex unified method, which contains both quantum chemical and statistical mechanical calculations. 2.2.2 FROM PREDICTION TO DESIGN It is not new that the concept of “design” is brought into the field of chemistry. Essentially the same process as the above has been widely used earlier in chemical engineering. It is known as the prediction and correlation method of physical properties, that is, the method to calculate empirically or semi-empirically the physical properties − the method used in chemical engineering process design. The objects in this calculation include thermodynamic functions, critical constant, phase equilibria (vapor pressure, etc.) for one-component systems as well as the transport properties and the equation of state. Also included are physical properties of two-components (solute + pure solvent) and even of three-components (solute + mixed solvent) systems. A standard reference, “The properties of Gases and Liquids; Their Estimation and Prediction”,4 has been written by Sherwood and Reid. It was revised once about ten years interval by Reid and others. The latest 5th edition was published in 2001. This series of books contain an excellent and useful compilation of “prediction” method. However, to establish the method for molecular ensemble design, we need to follow three more stages. 1. Calculate the physical properties of any given substance. This is just the establishment and improvement of presently available “prediction” method. 2. Calculate physical properties of a model substance. This is to calculate physical properties not for each real molecule but for “model”. This can be done by computer simulation. At this stage, a compilation of a model substance database is essential. 3. Predict real substance (or corresponding “model”) to obtain the required physical properties. This is just the reverse of the stage (1) or (2). But, an answer in this stage is not limited to one particular substance. The scheme to execute these three stages for a large variety of physical properties and substances has been established only to a limited range. Especially noteworthy is the establishment of the third stage, and after that, “molecular ensemble design” will be worth to discuss.

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2.2.3 IMPROVEMENT IN THE PREDICTION METHOD Some attempts to improve prediction at the level of the stage (1) are discussed here. It is an example of repeated improvements of prediction method from empirical to the molecular level. The diffusion coefficient D1 of solute 1 in solvent 2 at infinitely dilute solution is a fundamental property. This is different from the self-diffusion coefficient D0 in pure liquid. Both D1 and D0 are important properties. The classical approach to D1 can be accomplished based on Stokes and Einstein relation, giving the following equation. D 1 η 2 = kT ⁄ 6πr 1

[2.2.1]

where D1 at constant temperature T can be determined by the radius r1 of the solute molecule and solvent viscosity η2 (k is the Boltzmann constant). However, this equation is valid only when the size of the solvent molecule is infinitely small, namely, for the diffusion in a continuous medium. It is then clear that this equation is inappropriate for molecular mixtures. The well known Wilke-Chang equation,5 which corrects comprehensively this point, can be used for practical purposes. However, the average error of about 10% is inevitable in comparison with experimental data. One attempt6 to improve the agreement with experimental data is to use HammondStokes relation in which the product D1η2 is plotted against the molar volume ratio of solvent to solute, Vr. The slope is influenced by the following few factors, namely, (1) self-association of solvent, (2) asymmetricity of solvent shape, and (3) strong solute-solvent interactions. If these factors are properly taken into account, the following equation is obtained 1⁄3

D1 η2 ⁄ T = K1 ⁄ V0

+ ( K 2 Vr ) ⁄ T

[2.2.2]

Here, constants K1 and K2 contain the parameters coming from the above factors and V0 is the molar volume of solute. This type of equation [2.2.2] cannot always give the best prediction, but the physical image is more apparent than with other purely empirical correlations. This is an example of the stage (1) of the procedure. To develop the stage (2) method, we need MD simulation data for the appropriate model. 2.2.4 ROLE OF MOLECULAR SIMULATION We have already pointed out that the statistical mechanical method is indispensable in “molecular ensemble design”. A full account of molecular simulation is given in some books,3 and it will not be reproduced here. Two types of approaches can be classified in applying this method. The first one makes every effort to establish and use as real as exact intermolecular interaction in MC and MD simulation. It may be limited to a specific type of compounds. The second is to use a simple model, which is an example of so-called Occam's razor. We may obtain a wide bird-view from there.

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2.2 Molecular design of solvents

In the first type of the method, intermolecular interaction potential is obtained based on quantum-chemical calculation. The method takes the following steps. 1. Geometry (interatomic distances and angles) of molecules involved is determined. For fundamental molecules, it is often available from electron diffraction studies. Otherwise, the energy gradient method in the molecular orbital calculation can be utilized. 2. The electronic energy for monomer E1 and those for dimers of various mutual configurations E2 are calculated by the so-called ab initio molecular orbital method, and the intermolecular energy E2-2E1 is obtained. 3. By assuming an appropriate molecular model and semi-empirical equation, parameters are optimized to reproduce intermolecular potential energy function. A representative example of the preparation of such potential energy function, known as ab initio potential would be MCY potential for water-dimer by Clementi et al.7 Later, similar potentials have been proposed for hetero-dimer such as water-methanol.8 In the case of hydrogen-bonded dimers, the intermolecular energy E2-2E1 can be fairly large value and determination of fitted parameters is successful. In the case of weak interaction, ab initio calculation optimization of parameter becomes more complicated. Some attempts were made for potential preparation, e.g., for benzene and carbon dioxide with limited success. To avoid repeated use of lMO calculation, Jorgensen et al.9 has proposed MO-based transferable potential parameters called TIPS potential. This is a potential version of additivity rule, which has now an empirical character. It is, however, useful for practical purposes. 2.2.5 MODEL SYSTEM AND PARADIGM FOR DESIGN The approximation that any molecule can behave as if obeying Lennard-Jones potential seems to be satisfactory. This (one-center) LJ model is valid only for rare gases and simple spherical molecules. But this model may also be valid for other simple molecules as a zeroth approximation. We may also use the two-center LJ model where interatomic interactions are concentrated on the major two atoms in the molecule. One-center and two-center LJ models play a role of Occam's razor. We propose a paradigm for physical properties prediction as shown in Figure 2.2.1. This corresponds to the stage (2) and may be used to prepare the process of stage (3), namely, the molecular ensemble design for solvents. Main procedures in this paradigm are as follows; we first adopt target molecule or mixture and determine their LJ parameters. For any mixture, in addition to LJ parameters for each component, combining rule (or mixing rule) for unlike interaction should be prepared. Even for the simple liquid mixture, the conventional Lorentz-Berthelot rule is not a good answer. Once potential parameters have been determined, we can start calculation downward following arrow in the figure. The first key quantity is radial distribution function g(r) which can be calculated by the use of theoretical relation such as Percus-Yevick (PY) or hypernetted chain (HNC) integral equation. However, these equations are approximations. Exact values can be obtained by molecular simulation. If g(r) is obtained accurately as functions of temperature and pressure, then all the equilibrium properties of fluids and

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Figure 2.2.1. A scheme for the design of molecular ensembles.

fluid mixtures can be calculated. Moreover, information on the fluid structure is contained in g(r) itself. On the other hand, we have, for the non-equilibrium dynamic property, the time correlation function TCF, which is the dynamic counterpart of g(r). One can define various TCF's for each purpose. However, at the present stage, no extensive theoretical relation has been derived between TCF and φ(r). Therefore, direct determination of self-diffusion

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2.2 Molecular design of solvents

coefficient, viscosity coefficient by the molecular simulation gives a significant contribution to dynamics studies. Concluding Remarks Of presently available methods for the prediction of solvent physical properties, the solubility parameter theory by Hildebrand10 may still supply one of the most accurate and comprehensive results. However, the solubility parameter used has no purely molecular character. Many other methods are more or less of empirical nature. REFERENCES 1 2 3 4 5 6 7 8 9 10

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys., 21, 1087 (1953). B. J. Alder and T. E. Wainwright, J. Chem. Phys., 27, 1208 (1957). (a) M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987. (b) R. J. Sadus, Molecular Simulation of Fluids, Elsevier, Amsterdam, 1999. J. M. Prausnitz and J. E. Poling, J. P. O’Connell, The Properties of Gases and Liquids; Their Estimation and Prediction, 5th Ed., McGraw-Hill, New York, 2001. C. R. Wilke and P. Chang, AIChE J., 1, 264 (1955). K. Nakanishi, Ind. Eng. Chem. Fundam., 17, 253 (1978). O. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys., 60, 1351 (1976). S. Okazaki, K. Nakanishi and H. Touhara, J. Chem. Phys., 78, 454 (1983). W. L. Jorgensen, J. Am. Chem. Soc., 103, 345 (1981). J. H. Hildebrand and R. L. Scott, Solubility of Non-Electrolytes, 3rd Ed., Reinhold, New York, 1950.

APPENDIX PREDICTIVE EQUATION FOR THE DIFFUSION COEFFICIENT IN DILUTE SOLUTION Experimental evidence is given in Figure 2.2.2 for the prediction based on equation [2.2.1]. The diffusion coefficient D0 of solute A in solvent B at an infinite dilution can be calculated using the following equation: –8

 9.97 × 10 – 8 240 × 10 A B S B V B T - + ------------------------------------------------ -----D 0 =  -------------------------1⁄3 IA SA VA  [ IA VA ]  ηB

[2.2.3]

where D0 is in cm2 s-1. VA and VB are the liquid molar volumes in cm3 mol-1 of A and B at the temperature T in K, and the factors I, S, and A are given in original publications,4,6 and η is the solvent viscosity, in cP. Should the pure solute not be a liquid at 298 K, it is recommended that the liquid volume at the boiling point be obtained either from data or from correlations.4 Values of D0 were estimated for many (149) solute-solvent systems and average error was 9.1%.

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Figure 2.2.2. Hammond-Stokes plot for diffusion of iodine and carbon tetrachloride in various solvents using data for the same solvent from different sources. [Adapted, by permission, from K. Nakanishi, Bull. Chem. Soc. Japan, 51, 713 (1978).]

2.3 BASIC PHYSICAL AND CHEMICAL PROPERTIES OF SOLVENTS George Wypych ChemTec Laboratories, Toronto, Canada This section contains information on the basic relationships characterizing the physical and chemical properties of solvents and some suggestions regarding their use in solvent evaluation and selection. The methods of testing which allow us to determine some of the physical and chemical properties are found in Chapter 12. The differences between solvents of various chemical origin are discussed in Chapter 3, Section 3.3. The fundamental relationships in this chapter and the discussion of different groups of solvents are based on a large CD-ROM database of solvents which can be obtained from ChemTec Publishing. The database has 110 fields which contain various data on solvent properties which are discussed below. The database can be searched by the chemical name, empirical formula, molecular weight, CAS number, or any property. In the first case, full information on a particular solvent is returned. In the second case, a list of solvents and their values for the selected property are given in tabular form in ascending order of the property in question. 2.3.1 MOLECULAR WEIGHT AND MOLAR VOLUME The molecular weight of a solvent is a standard but underutilized component of the information on properties of solvents. Many solvent properties depend directly on their molecular weights. The hypothesis of Hildebrand-Scratchard states that solvent-solute interaction occurs when solvent and polymer segment have similar molecular weights. This is related to the hole theory according to which a solvent occupying a certain volume leaves the same volume free when it is displaced. This free volume should be sufficient to fit the polymer segment which takes over the position formerly occupied by the solvent molecule. Based on this same principle, the diffusion coefficient of a solvent depends on its molecular mass. If there were no interactions between solvent and solute, the evaporation rate of the solvent would depend on the molecular weight of the solvent. Because of various interactions, this relationship is more complex but solvent molecular weight does play an essential role in solvent diffusion. This is illustrated best by membranes which have pore sizes which limit the size of molecules which may pass through. The resistance of a material to solvents is partially controlled by the molecular weight of the solvent since solvent molecules have to migrate to the location of the interactive material in order to interact with it. The chemical potential of a solvent also depends on its molecular weight. If all other influences and properties are equal, the solvent having the lower molecular weight is more efficiently dissolving materials, readily forms gels, and swells materials. All this is controlled by the molecular interactions between solvent and solute. In other words, at least one molecule of solvent involved must be available to interact with a particular segment of solute, gel, or network. If solvent molecular weight is low more molecules per unit weight are available to influence such changes. Molecular surface area and molecular volume are

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2.3 Basic physical and chemical properties of solvents

part of various theoretical estimations of solvent properties and they are in part dependent on the molecular mass of the solvent. Many physical properties of solvents depend on their molecular weight, such as boiling and freezing points, density, the heat of evaporation, flash point, and viscosity. The relationship between these properties and molecular weight for a large number of solvents of the different chemical composition is affected by numerous other influences but within the same chemical group (or similar structure) molecular weight of solvent correlates well with its physical properties. Figure 2.3.1. Hildebrand solubility parameter vs. heat of vaporization of selected solvents. Figure 2.3.1 gives an example of the interrelation of seemingly unrelated parameters: Hildebrand solubility parameter and heat of vaporization (see more on the subject in the Section 2.3.19). As the heat of vaporization increases, the solubility parameter also increases. Molar volume is a rather speculative, theoretical term. It can be calculated from Avogadro's number but it is temperature dependent. In addition, free volume is not taken into consideration. Molar volume can be expressed as molecular diameter but solvent molecules are rather non-spherical therefore diameter is often a misrepresentation of the real dimensional structure. It can be measured from the studies on interaction but results differ widely depending on the model used for interpretation. 2.3.2 BOILING AND FREEZING POINTS Boiling and freezing points are two basic properties of solvents often included in specifications. Based on their boiling points, solvents can be divided to low (below 100oC), medium (100-150oC) and high boiling solvents (above 150oC). The boiling point of a liquid is frequently used to estimate the purity of a liquid. A similar approach is taken for solvents. Impurities cause the boiling point of solvents to increase but this increase is very small (in the order of 0.01oC per 0.01% impurity). Considering that the error of boiling point can be large, contaminated solvents may be undetected by boiling point measurement. If purity is important it should be evaluated by some other, more sensitive methods. The difference between a boiling point and vapor condensation temperature is usually more sensitive to admixtures. If this difference is more than 0.1oC, the presence of admixtures can be suspected. The boiling point can also be used to evaluate interactions due to the association among molecules of solvents. For solvents with the low association, Trouton's rule, given by the following equation, is fulfilled:

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ΔH bp o - = 88 J mol – 1 K – 1 ΔS bp = -----------T bp where:

o

ΔS bp o ΔH bp Tbp

[2.3.1]

molar change of enthalpy molar change of entropy boiling point

If the enthalpy change is high it suggests that the solvent has a strong tendency to form associations. Boiling point depends on molecular weight but also on the solvent structure. It is generally lower for branched and cyclic solvents. Boiling and freezing points are important considerations for solvent storage. Solvents are frequently stored under a nitrogen blanket and they contribute to substantial emissions during storage. The freezing point of some solvents is above temperatures encountered in temperate climatic conditions. Although solvents are usually very stable in their undercooled state, they rapidly crystallize when subjected to any mechanical or sonar impact. Figures 2.3.2 to 2.3.6 illustrate how the boiling points of individual solvents in a group are related to other properties. Figure 2.3.2 shows that chemical structure of a solvent affects the relationship between its viscosity and the boiling point. Alcohols, in particular, show a much larger change in viscosity relative to boiling point than do aromatic hydrocarbons, esters, and ketones. This is caused by strong associations between molecules of alcohols, which contain hydroxyl groups. Figure 2.3.3 shows that alcohols are also less volatile than other three groups of solvents and for the same reason. Viscosity and evaporation rate of aromatic hydrocarbons, esters, and ketones follow single relationship for all three groups of solvents, meaning that the boiling point has a strong influence on these two properties. There are individual points on this set of graphs which do not fall close to the fitted curves. These discrepancies illustrate that chemical interactions influ-

Figure 2.3.2. Effect of boiling point on solvent viscosity.

Figure 2.3.3. Effect of boiling point on solvent evaporation rate (relative to butyl acetate = 1).

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2.3 Basic physical and chemical properties of solvents

Figure 2.3.4. Specific heat of solvents vs. their boiling point.

Figure 2.3.5. Flash point of solvents vs. their boiling point.

Figure 2.3.6. Odor threshold of solvent vs. its boiling point.

Figure 2.3.7. Relationship between boiling and freezing points of solvents.

ence viscosity and evaporation rate. However, for most members of the four groups of solvents, properties correlate most strongly with boiling point. All linear relationships in Figure 2.3.4 indicate that specific heat is strongly related to the boiling point which is in agreement with the fact that the boiling point is influenced by molecular weight. However, there are substantial differences in the relationships between different groups of solvents and many experimental points are scattered. Figure 2.3.5 verifies the origin of the flash point which has a strong correlation with its boiling point. Here, all four chemical groups of solvents have the same relationship.

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Odor threshold is an approximate but quite unreliable method of detection of solvent vapors. As the boiling point increases, the odor threshold (concentration in the air when odor becomes detectable) decreases (Figure 2.3.6). This may suggest that slower evaporating solvents have longer residence time close to the source of contamination. Figure 2.3.7 shows the relationship between boiling and freezing points. A general rule is that the difference between boiling and freezing points for analyzed solvents is 190±30oC. The relatively small fraction of solvents does not follow this rule. Natural solvent mixtures such as aromatic or aliphatic hydrocarbons deviate from the rule (note that hydrocarbons in Figure 2.3.7 depart from the general relationship). If more groups of solvents are investigated, it will be seen that CFCs, amines, and acids tend to have a lower temperature difference between boiling and freezing points whereas some aliphatic hydrocarbons and glycol ethers have a tendency towards a larger difference. 2.3.3 SPECIFIC GRAVITY The specific gravity of most solvents is lower than that of water. When the solvent is selected for extraction it is easy to find one which will float on the surface of water. Two groups of solvents: halogenated solvents and polyhydric alcohols have a specific gravity greater than that of the water. The specific gravity of alcohols and ketones increases with increasing molecular weight whereas the specific gravity of esters and glycol ethers decreases as their molecular weight decreases. The specific gravity of solvents affects their industrial use in several ways. Solvents with a lower density are more economical to use because solvents are purchased by weight but many final products are sold by volume. The specific gravity of solvent should be considered in the designs for storage systems and packaging. When switching the solvent types in storage tanks, one must determine the weight of a new solvent which can be accommodated in the tank. A container of CFC with a specific gravity twice that of most solvents may be too heavy to handle. When metering by volume, temperature correction should always be used because solvent specific gravity changes substantially with temperature. The specific gravity of solvent is important in the formulation because it influences the torque and horsepower of a mixer. 2.3.4 REFRACTIVE INDEX Refractive index is the ratio of the velocity of light of a specified wavelength in the air to its velocity in the examined substance. When this principle of measurement is used it may be defined as the sine of the angle of incidence divided by the sine of the angle of refraction. The absolute angle of refraction (relative to vacuum) is obtained by dividing the refractive index relative to air by a factor of 1.00027 which is the absolute refractive index of air. The ratio of the sines of the incident and refractive angles of light in the tested liquid is equal to the ratio of light velocity to the velocity of light in a vacuum (that is why both definitions are correct). This equality is also referred to as Snell's law. Figures 2.3.8 and 2.3.9 show the relationship between the molecular weight of a solvent and its refractive index. Figure 2.3.8 shows that there is a general tendency for the refractive index to increase as the molecular weight of the solvent increases. The data also indicates that there must be an additional factor governing refractive index. The chemical

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2.3 Basic physical and chemical properties of solvents

Figure 2.3.8. Refractive index for four groups of solvents as the function of their molecular weight.

Figure 2.3.9. Refractive index of normal and branched alcohols as the function of number of carbon atoms in alcohol.

structure of the molecule also influences refractive index (Figure 2.3.9). Normal alcohols have a slightly higher refractive index than do branched alcohols. Cyclic alcohols have higher refractive indices than the linear and branched alcohols. For example, 1-hexanol has a refractive index of 1.416, 4-methyl-2-pentanol 1.41, and cyclohexanol 1.465. Aromatic hydrocarbons are not dependent on molecular weight but rather on the position of the substituent in the benzene ring (e.g., m-xylene has a refractive index of 1.495, oxylene 1.503, and p-xylene 1.493). The data also show that the differences in the refractive indices are rather small. This imposes restrictions on the precision of their determination. Major errors stem from poor instrument preparation and calibration and inadequate temperature control. The refractive index may change on average by 0.0005/oC. Refractive index is a useful tool for determination of solvent purity but the precision of this estimation depends on the relative difference between the solvent and the impurity. If this difference is small, the impurities, present in small quantities, will have little influence on the reading. The choice of mobile-phase solvent and its difference with a refractive index of a solution of the measured compound have a profound effect on the sensitivity of HPLC detection. The accuracy of the light-scattering measurement also depends on prior determinations of the solvent refractive index and of the specific refractive index increment of the sample in the solvent. 2.3.5 VAPOR DENSITY AND PRESSURE The relative vapor density of solvents is given by the following equation: M d vp = ---------sM air where: Ms the molecular mass of solvents Mair the molecular mass of air (28.95 Daltons)

[2.3.2]

George Wypych

Figure 2.3.10. Vapor density relative to air of alcohols and ketones vs. their molecular weight.

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Figure 2.3.11. Vapor pressure at 25oC of normal and branched alcohols vs. number of carbon atoms in their molecule.

Figure 2.3.10 shows that the vapor density has a linear correlation with molecular mass and that for both alcohols and ketones (as well as the other solvents) the relationships are similar. The data also show that solvent vapor densities are higher than the air density. This makes ventilation a key factor in the removal of these vapors in the case of spill or emissions from equipment. Otherwise, the heavier than air vapors will flow above floors and depressions filling pits and subfloor rooms and leading to toxic exposure and/or risk of ignition and subsequent explosions. The Clausius-Clapeyron equation gives the relationship between the molecular weight of solvent and its vapor pressure: d ln p MΛ ----------- = ---------2 dT RT

[2.3.3]

where: p T M Λ R

vapor pressure temperature molecular mass of solvent heat of vaporization gas constant

Figure 2.3.11 shows that the vapor pressure of alcohols increases as the number of carbon atoms in the molecules and the molecular mass increase. A small increase in vapor pressure is produced when branched alcohols replace normal alcohols. Vapor pressure at any given temperature can be estimated by the use of Antoine (eq. [2.3.4]) or Cox (eq. [2.3.5]) equation (or chart). Both equations are derived from ClausiusClapeyron equation:

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2.3 Basic physical and chemical properties of solvents

B log p = A – -------------C+T

[2.3.4]

B log p = A – ------------------T + 230

[2.3.5]

where: A, B, C

constants. The constants A and B are different in each equation. The equations coincide when C = 230 in the Antoine equation.

From the above equations, it is obvious that vapor pressure increases with temperature. 2.3.6 SOLVENT VOLATILITY The evaporation rate of solvents is important in many applications. This has resulted in attempts to model and predict solvent volatility. The evaporation rate of a solvent depends on its vapor pressure at the processing temperature, the boiling point, specific heat, enthalpy and heat of vaporization of the solvent, the rate of heat supply, the degree of association between solvent and solute molecules, the surface tension of the liquid, the rate of air movement above the liquid surface, and humidity of air surrounding the liquid surface. The vapor pressure of solvent was found in the previous section to depend on its molecular weight and temperature. Figure 2.3.3 shows that the evaporation rate of a solvent may be predicted based on knowledge of its boiling point and Figure 2.3.4 shows that the specific heat of solvent also relates to its boiling point. The boiling point of solvent also depends on its molecular weight as does enthalpy and heat of vaporization. But there is no a high degree of correlation among these quantities because molecular associations exist which cannot be expressed by a simple, universal relationship. For this reason, experimental values are used to compare properties of different solvents. The two most frequently used reference solvents are diethyl ether (Europe) and butyl acetate (USA). The evaporation rate of other solvents is determined under identical conditions and the solvents are ranked accordingly. If diethyl ether is used as a reference point, solvents are grouped into four groups: high volatility < 10, moderate volatility 10-35, low volatility 3550, and very low volatility > 50. If butyl acetate is used as the reference solvent, the solvents are grouped into three classes: rapid evaporation solvents > 3, moderate 0.8-3, and slow evaporating solvents < 0.8. In some applications such as coatings, casting, etc., the evaporation rate is not the only important parameter. The composition must be adjusted to control rheological properties, prevent shrinkage, precipitation, the formation of haze, and to provide the required morphology. Solvents with different evaporation rates can address all existing requirements. Both the surface tension of mixture and solvent diffusion affect the evaporation rate. This becomes a complex function dependent not only on the solvents present but also on the influence of solutes on both surface tension and diffusion. These relationships affect the real evaporation rates of solvents from the complicated mixtures in the final products. In addition, solvent evaporation also depends on relative humidity and air movement.

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2.3.7 FLASH POINT Flash point is the lowest temperature, corrected to normal atmospheric pressure (101.3 kPa), at which the application of an ignition source causes the vapors of a specimen to ignite under the specific conditions of the test. Flash point determination methods are designed to be applied to a pure liquid but, in practice, mixtures are also evaluated. It is important to understand limitations of such data. The flash point of a solvent mixture can be changed by adding various quantities of other solvents. For example, the addition of water or halogenated hydrocarbons will generally increase Figure 2.3.12. Flash point vs. vapor pressure of flash point temperature of the mixture. the solvent. The flash point can also be changed by forming an azeotropic mixture of solvents or by increasing the interaction between solvents. At the same time, the flash point of a single component within the mixture is not changed. If conditions during production, application, or in a spill allow the separation or removal of a material added to increase the flash point, then the flash point will revert to that of the lowest boiling flammable component. An approximate flash point can be estimated from the boiling point of solvent using the following equation: Flash point = 0.74Tb

[2.3.6]

Figure 2.3.5 shows that there is often a good correlation between the two but there are instances where the relationship does not hold. The correlation for different groups of solvents varies between 0.89 to 0.96. Flash point can also be estimated from vapor pressure using the following equation: Flash point = a logp + b

[2.3.7]

The constants a and b are specific to each group of solvents. Figure 2.3.12 shows that estimation of flash point from the vapor pressure of the solvent is less accurate than its estimation from the boiling point. 2.3.8 FLAMMABILITY LIMITS Two limits of solvent flammability exist. The lower flammability limit is the minimum concentration of solvent vapor in oxidizing gas (air) that is capable of propagating a flame through a homogeneous mixture of the oxidizer and the solvent vapor. Below the lower flammability limit, the mixture is too lean to burn or explode. The upper flammability limit is the maximum concentration of solvent vapor in an oxidizing gas (air) above which propagation of flame does not occur. Mixtures with solvent vapor concentrations above

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2.3 Basic physical and chemical properties of solvents

the upper flammability limit are too rich in a solvent or too lean in oxidizer to burn or explode. The flammable limits depend on oxygen concentration, the concentration of gases other than oxygen, the inert gas type and concentration, the size of the equipment, the direction of flame propagation, and the pressure, temperature, turbulence and composition of the mixture. The addition of inert gases to the atmosphere containing solvent is frequently used to reduce the probability of an explosion. It is generally assumed that if the concentration of oxygen is below 3%, no ignition will occur. Figure 2.3.13. Lower flammability limit of solvents vs. The type of inert gas is also important. Cartheir flash points. bon dioxide is more efficient inert gas than nitrogen. The size of equipment matters because of the uniformity of vapor concentration. A larger headspace tends to increase the risk of inhomogeneity. The cooling effect of the equipment walls influences the evaporation rate and the vapor temperature and should be used in risk assessment. The flash point is not the temperature at which the vapor pressure in air equals the lower flammable limit. Although both parameters have some correspondence, there are large differences between groups of solvents (Figure 2.3.13). There is a general tendency for solvents with a lower flammability limit to have a lower flash point. The flash point determination uses a downward and horizontal propagation of flame. Flame propagation in these directions generally requires a higher vapor concentration than it is required for the upward flame propagation used to determine flammability limits. The flame in flash point determination is at some distance from the surface where the vapor concentration is at its highest (because vapors have higher density than air) than exists on the liquid surface thus flush analysis underestimates concentration of vapor. An increased vapor pressure typically increases the upper limit of flammability and reduces the lower limit of flammability. Pressures below atmospheric have little influence on flammability limits. An increase in temperature increases the evaporation rate and thus decreases the lower limit of flammability. There are a few general rules which help in the estimation of flammability limits. In the case of hydrocarbons, the lower limit can be estimated from simple formula: 6/number of carbon atoms in molecule; for benzene and its derivatives, the formula changes to 8/ number of carbon atoms. To calculate the upper limits, the number of hydrogen and carbon atoms is used in calculation.

George Wypych

Figure 2.3.14. Minimum ignition energy vs. stoichiometric ratio of air to methyl ethyl ketone. [Data from H F Calcote, C A Gregory, C M Barnett, R B Gilmer, Ind. Eng. Chem., 44, 2656 (1952)].

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Figure 2.3.15. Minimum ignition energy vs. temperature for selected solvents. [Data from V S Kravchenko, V A Bondar, Explosion Safety of electrical Discharges and Frictional Sparks, Khimia, Moscow, 1976].

The lower flammability limit of a mixture can be estimated from Le Chatelier's law: 100 LFL mix = ------------------------------------------------------------------φ2 φn φ1 ------------- + ------------- + … + -----------LFL 1 LFL 2 LFL n where:

[2.3.8]

φ fraction of components 1, 2, ..., n LFLi lower flammability limit of component 1, 2, ..., n

2.3.9 SOURCES OF IGNITION AND AUTOIGNITION TEMPERATURE Sources of ignition can be divided into mechanical sources (impact, abrasive friction, bearings, misaligned machine parts, choking or jamming of material, drilling and other maintenance operations, etc), electrical (broken light, cable break, electric motor, switch gear, liquid velocity, surface or personal charge, rubbing of different materials, liquid spraying or jetting, lightning, stray currents, radio frequency), thermal (hot surface, smoking, hot transfer lines, electric lamps, metal welding, oxidation and chemical reactions, pilot light, arson, change of pressure, etc.), and chemical (peroxides, polymerization, catalysts, lack of inhibitor, heat of crystallization, thermite reaction, unstable substances, decomposition reactions). This long list shows that when making efforts to eliminate ignition sources, it is also essential to operate at safe concentrations of volatile, flammable materials because of numerous and highly varied sources of ignition. The energy required for ignition is determined by the chemical structure of the solvent, the composition of the flammable mixture, and temperature. The energy of ignition of hydrocarbons decreases in the following order: alkanes > alkenes > alkynes (the presence of double or triple bond decreases the energy required for ignition). The energy

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Figure 2.3.16. Autoignition temperature of selected solvents vs. their molecular weight.

2.3 Basic physical and chemical properties of solvents

Figure 2.3.17. Heat of combustion vs. number of carbon atoms in molecule.

requirement increases with an increase in molecular mass and an increased branching. The conjugated structure generally requires less ignition energy. Substituents increase the required ignition energy in the following order: mercaptan < hydroxyl < chloride < amine. Ethers and ketones require higher ignition energy but an aromatic group has little influence. Peroxides require extremely little energy to ignite. Figure 2.3.14 shows the effect of changing the ratio of air to methyl ethyl ketone on the minimum spark ignition energy. The ignition energy decreases within the studied range as the amount of air increases (less flammable content). Figure 2.3.15 shows the effect of temperature on the minimum ignition energy of selected solvents. There are differences between solvents resulting from differences in chemical structure as discussed above but the trend is consistent − a decrease of required energy as temperature increases. The autoignition temperature is the minimum temperature required to initiate combustion in the absence of a spark or flame. The autoignition temperature depends on the chemical structure of solvent, the composition of the vapor/air mixture, the oxygen concentration, the shape and size of the combustion chamber, the rate and duration of heating, and on catalytic effects. Figure 2.3.16 shows the effect of chemical structure on autoignition temperature. The general trend for all groups of solvents is that the autoignition temperature decreases as molecular weight increases. Esters and ketones behave almost identically in this respect and aromatic hydrocarbons are very similar. The presence of a hydroxyl group substantially reduced autoignition temperature. The effect of the air to solvent ratio on autoignition temperature is similar to that on ignition energy (see Figure 2.3.14). As the oxygen concentration increases within the range of the flammability limits, the autoignition temperature increases. The autoignition temperature increases when the size of combustion chamber decreases. Rapid heating reduces the autoignition temperature and catalytic substance may drastically reduce it.

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2.3.10 HEAT OF COMBUSTION The heat of combustion, also known as calorific value, is the quantity of energy per mole released during combustion. It coincides with the heat of reaction. Solvents have higher heats of combustion than typical fuels such as natural gas, propane or butane. They can be very good source of energy in plants which process solutions. In addition to supplying energy, the combustion of solvents can be developed to be one of the cleanest methods of processing from solutions. Two approaches are commonly used: solvent vapors are directed to a combustion chamber or spent solvents are burned in furnaces. The heat of combustion of a liquid solvent is less than 1% lower than the heat of combustion of a vapor. Figure 2.3.17 shows the relationship between the heat of combustion and the number of carbon atoms in the molecule. The heat of combustion increases as molecular weight increases and decreases when functional groups are present. 2.3.11 HEAT OF FUSION The heat of fusion is the amount of heat required to melt the frozen solvent. It can be used to determine the freezing point depression of solute. The magnitude of heat of fusion and heat of vaporization is related to the nature and strength of forces which hold the molecules of the solvent together in the solid or the liquid state. The larger the value of heat of fusion or heat of vaporization, the stronger the intermolecular binding forces in the solid or liquid. The heat of fusion is used for estimation of the freezing point depression when a solvent dissolves a solute. 2.3.12 ELECTRIC CONDUCTIVITY Electric conductivity is the reciprocal of specific resistance. The units typically used are either ohm-1 m-1 or, because the conductivities of solvents are very small, picosiemens per meter which is equivalent to 10-12 ohm-1 m-1. The electric conductivity of solvents is very low (typically between 10-3 − 10-9 ohm-1 m-1). The presence of acids, bases, salts, and dissolved carbon dioxide might contribute to increased conductivity. Free ions are solely responsible for the electric conductivity of solution. This can be conveniently determined by measuring the conductivity of the solvent or the conductivity of the water extract of solvent impurities. The electronics industry and aviation industry have major interest in these determinations. The electric conductivity is important when industrial coatings are electrostatically applied. With too low a conductivity, overspray losses increase but when the conductivity is too high, surface properties are affected because charged particles have an increased tendency to stick together. 2.3.13 RELATIVE PERMITTIVITY (DIELECTRIC CONSTANT) The dielectric constant (or relative permittivity) of a solvent reflects its molecular symmetry. The value of the relative permittivity is established from a measurement relative to vacuum. The effect is produced by the orientation of dipoles along an externally applied electric field and from the separation of charges in apolar molecules. This orientation causes polarization of the molecules and a drop in electric field strength. Relative permittivity data may be used in many ways. In particular, it is the factor which permits the eval-

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2.3 Basic physical and chemical properties of solvents

Figure 2.3.18. Dielectric constant (relative permititivity) vs. molecular weight of selected solvents.

Figure 2.3.19. Dielectric constant (relative permittivity) of selected solvents vs. their refractive index.

uation of electrostatic hazards. The rate of charge decay is a product of relative permittivity and resistivity. In the solvent studies, relative permittivity has a special place as a parameter characteristic of solvent polarity. The relative permittivity, ε, is used to calculate dipole moment, μ: ε–1 μ = ----------- V M ε–2

[2.3.9]

where: VM molar volume

The product of dipole moment and relative permittivity is called the electrostatic factor and it is a means of classifying solvents according to their polarity. Figure 2.3.18 shows that the relative permittivity correlates with molecular weight. It is only with aliphatic hydrocarbons that the relative permittivity increases slightly as the molecular weight increases. The relative permittivity of alcohols, esters, and ketones decreases as their molecular weight increases, but only alcohols and ketones have the same relationship. The relative permittivities of esters are well below those of alcohols and ketones. The relative permittivity also correlates with refractive index (Fig. 2.3.19). In the case of aliphatic hydrocarbons, the relative permittivity increases slightly as refractive index increases. Both aromatic and aliphatic hydrocarbons have relative permittivities 2 which follow the relationship: ε ≈ n D . The relative permittivities of alcohols, esters, and ketones decrease as the refractive constants increase but only alcohols and ketones form a similar relationship. The relative permittivities of ketones poorly correlate with their refractive indices.

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Solvents such as N,N-dimethylformamide may be added to a solution to increase its dielectric property to improve a fiber morphology because a solution with a greater dielectric constant reduces the beads formation and the diameter of the resultant electrospun fiber. The dielectric constant is also a factor in a solvent's electrostatic hazard. A solvent's relaxation time (a measure of the rate at which an electrostatic charge will decay) is a product of dielectric constant. 2.3.14 OCCUPATIONAL EXPOSURE INDICATORS The measurement of solvent concentration in the workplace is required by national regulations. These regulations specify, for individual solvents, at least three different concentrations points: the maximum allowable concentration for an 8 hour day exposure, the maximum concentration for short exposure (either 15 or 30 min), and concentration which must not be exceeded at any time. These are listed in the regulations for solvents. The listing is frequently reviewed and updated by the authorities based on the most currently available information. In the USA, the threshold limit value, time-weighted average concentration, TLVTWA, is specified by several bodies, including the American Conference of Governmental Industrial Hygienists, ACGIH, the National Institute of Safety and Health, NIOSH, and the Occupational Safety and Health Administration, OSHA. The values for individual solvents included on these three lists are very similar. Usually, the NIOSH TLV-TWA values are lower than the values on the other two lists. Similar specifications are available in other countries (for example, OES in the UK, or MAK in Germany). The values for individual solvents are selected based on the presumption that the maximum allowable concentration should not cause injury to a person working under these conditions for 8 hours a day. For solvent mixtures, the following equation is used in Germany to calculate allowable limit: i=n

I MAK =

ci

 --------------MAK i

[2.3.10]

i=1

where: IMAK c MAK

evaluation index concentrations of components 1, 2, ..., n maximum permissible concentrations for components 1, 2, ..., n

The maximum concentrations for short exposure are the most frequently specified limit of an exposure of 15 min. with a maximum of 4 such occurrences per day each occurring at least 60 min. apart from each other. These values are 0-4 times larger than TLVs. They are selected based on the risks associated with an individual solvent. Solvent concentrations which should not be exceeded at any time are seldom specified in regulations but, if they are, the values stated as limits are similar to those on the three lists.

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2.3 Basic physical and chemical properties of solvents

In addition, to maintaining concentration below limiting values, adequate protection should be used to prevent the inhalation of vapors and contact with the skin (see Chapter 22). 2.3.15 ODOR THRESHOLD The principles for odor threshold measurements were developed to relate the human sense of smell to the concentration of the offending substances. If the substance is toxic, its detection may provide early warning of the danger. However, if the odor threshold is larger than the concentration at which harm may be caused it is not an effective warning system. On the other hand, if the odor threshold is lower than the exposure limit(s), a person will notice the presence of the solvent before a concentration of it is sufficiently high to cause a concern. Toxic substances may have very little or no odor (e.g., carbon monoxide) and an individual's sense of smell may vary widely in its detection capabilities. A knowledge of odor threshold is most useful in determining the relative nuisance factor for an air pollutant when designing a control system to avoid complaints from neighboring people surrounding a facility. Regulations often state (as they do for example in Ontario, Canada) that, even when the established concentration limits for air pollutants are met, if neighbors complain, penalties will be applied. Figure 2.3.6 shows that odor threshold is related to the boiling point (although odor threshold decreases with boiling point increasing). It is known from comparisons of TLV and odor detection that odor detection is not a reliable factor. 2.3.16 TOXICITY INDICATORS Lethal dose, LD50, and lethal concentration, LC50, are commonly used indicators of substance toxicity. LD50 is reported in milligrams of substance per kilogram of body weight to cause death in 50% of tested animals (exception is LC50 which is given in ppm over usually the period of 4 hours to produce the same effect). It is customary to use three values: LD50-oral, LD50-dermal, and LC50-inhalation which determine the effect of a chemical substance on ingestion, contact with skin, and inhalation. The preferred test animal for LD50-oral and LC50-inhalation is the rat. The rabbit is commonly used for LD50-dermal determination but other test animals are also used. There is no official guideline on how to use this data but the Hodge-Sterner table is frequently referred to in order to assign a particular substance to a group which falls within certain limits of toxicity. According to this table, dangerously toxic substances are those which have LD50 < 1 mg/kg, seriously toxic − 1-50, highly toxic − 50-500, moderately toxic − 500-5,000, slightly toxic − 5,000-15,000, and extremely low toxic − >15,000 mg/kg. Using this classification one may assess the degree of toxicity of solvents based on a lethal dose scale. No solvent is classified as a dangerously toxic material. Ethylenediaminetetraacetic acid and furfural are seriously toxic materials. Butoxyethanol, ethylene oxide, formaldehyde, metasulfonic acid, 3-methyl-2-butanone, N-nitrosodimethylamine, and triethylamine are classified as highly toxic material. The remaining solvents fall into the moderately, slightly, and extremely low toxic material classes.

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The LD50-oral is usually assigned a lower value than LD50-dermal but there are many cases where the opposite applies. Toxicity information is usually further expanded by adding more details regarding test animals and target organs. In addition to estimates of toxicity for individual solvents, there are lists which designate individual solvents as carcinogenic, mutagenic, and reproductively toxic. These lists contain the name of solvent with yes or no remark (or similar). If a solvent is not present on the list that does not endorse its benign nature because only materials that have been tested are included in the lists. To further elaborate, materials are usually divided into three categories: substance known to cause effect on humans, substance which has caused responses in animal testing and given reasons to believe that similar reactions can be expected with human exposures, and substance which is suspected to cause responses based on experimental evidence. In the USA, four agencies generate lists of carcinogens. These are the Environmental Protection Agency, EPA, the International Agency for Research on Cancer, IRAC, the National Toxicology Program, NTP, and the Occupational Safety and Health Administration, OSHA. Although there is a good agreement between all four lists, each assessment differs in response. The following solvents made at least one of the lists (no distinction is given here to the category assignment but any known or suspected carcinogen found on any list is given (for more details see Chapter 3): acetone, acrolein, benzene, carbon tetrachloride, dichloromethane, 1,4-dioxane, ethylene oxide, formaldehyde, furfural, dlimonene, N-nitrosodimethyl amine, propylene oxide, tetrachloroethylene, 2,4-toluenediisocyanate, 1,1,2-trichloroethylene, and trichloromethane. Mutagenic substances have the ability to induce genetic changes in DNA. The mutagenicity list maintained in the USA includes the following solvents: all solvents listed above for carcinogenic properties with exception of dichloromethane, d-limonene, and tetrachloroethylene. In addition, the following long list solvents: 1-butanol, 2-butanol, γbutyrolactone, 2-(2-n-butoxyethoxy)ethanol, chlororodifluoromethane, chloromethane, diacetone alcohol, dichloromethane, diethyl ether, dimethyl amine, dimethylene glycol dimethyl ether, dimethyl sulfoxide, ethanol, 2-ethoxyethanol, 2-ethoxyethanol acetate, ethyl acetate, ethyl propionate, ethylbenzene, ethylene glycol diethyl ether, ethylene glycol methyl ether acetate, ethylene glycol monophenyl ether, ethylenediaminetetraacetic acid, formic acid, furfuryl alcohol, heptane, hexane, methyl acetate, 3-methyl-2-butanol, methyl ester of butyric acid, methyl propionate, N-methylpyrrolidone, monomethylamine, 1-octanol, 1-pentanol, 1-propanol, propyl acetate, sulfolane, 1,1,1-trichloroethane, triethylene glycol, triethylene glycol dimethyl ether, trifluoromethane, trimethylene glycol, and xylene (mixture only). It is apparent that this much longer list includes commonly used solvents from the groups of alcohols, halogenated solvents, hydrocarbons, glycols, and esters. The following solvents are reported to impair fertility: chloroform, ethylene glycol and its acetate, 2-methoxypropanol, 2-methoxypropyl acetate, dichloromethane, methylene glycol and its acetate, and N,N-dimethylformamide.

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2.3.17 OZONE − DEPLETION AND CREATION POTENTIAL Ozone depletion potential is measured relative to CFC-11 and it represents the amount of ozone destroyed by emission of a vapor over its entire atmospheric lifetime relative to that caused by the emission of the same mass of CFC-11. Urban ozone formation potential is expressed relative to ethene. It represents the potential of an organic solvents vapor to form ozone relative to that of ethene ((g O3/g solvent)/(g O3/g ethene)). Several groups of solvents, including alcohols, aldehydes, amines, aliphatic and aromatic hydrocarbons, esters, ethers, and ketones are active in ozone formation. Aldehydes, xylenes, some unsaturated compounds, and some terpenes are the most active among those. It should be noted that solvents with high smog formation potential, such as methylene chloride, trichloroethylene, tetrachloroethyelene, have low ozone depletion potential and low global warming potential because they are quickly oxidized by hydroxyl radicals in the lower atmosphere. 2.3.18 OXYGEN DEMAND There are several indicators of solvent biodegradation. Most solvents have a biodegradation half-life of days to weeks and some biodegrade even faster. The amount of oxygen required for its biodegradation is a measure of a solvent's impact on natural resources. Several factors are used to estimate this, such as biological oxygen demand, BOD, after 5-day and 20-day aerobic tests, chemical oxygen demand, COD, and theoretical oxygen demand, TOD. All results are given in grams of oxygen per gram of solvent. COD is the amount of oxygen removed during oxidation in the presence of permanganate or dichromate. TOD is the theoretically calculated amount of oxygen required to oxidize solvent to CO2 and H2O. Most alcohols and aromatic hydrocarbons have the highest BOD5. They consume twice their own weight in oxygen. 2.3.19 SOLUBILITY The prediction of solubility of various solutes in various solvents is a major focus of research. An early theory has been that “like dissolves like”. Regardless of the apparent merits of this theory, it is not sufficiently rigorous and it is overly simple. A universal approach was developed by Hildebrand who assumed that the mutual solubility of components depends on the cohesive pressure, c. The square root of cohesive pressure is the Hildebrand's solubility parameter, δ: δ = where:

ΔHv R T Vm M d

c =

ΔH v – RT -----------------------Vm

heat of vaporization gas constant temperature molar volume of solvent = M/d molecular mass of solvent density of solvent

[2.3.11]

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Frequently, the term RT is neglected because it accounts for only 5-10% of the heat of vaporization. This equation explains the reasons for the correlation between the Hildebrand solubility parameter and heat of vaporization as given in Figure 2.3.1. The Hildebrand model takes into account only the dimensions of molecules or the molecular segments participating in the process of solvation and dispersion interactions. The model is useful, therefore, in predicting the solubility of nonpolar substrates. The solubility parameters of solFigure 2.3.20. Kauri butanol number vs. Hildebrand sol- vents and solutes are compared and if they ubility parameter. are similar there is a high probability (exceptions exist) that the solvents are miscible and that a solute is soluble in a solvent. Two solvents having the same solubility parameters should have the same dissolving capabilities. If one solvent has solubility parameter slightly below the solubility parameter of solute and the second solvent has solubility parameter above the solute, the mixture of both solvents should give better results than either solvent alone. This model is an experimental and mathematical development of the simple rule of “like dissolves like”. Solvents and solutes also interact by donor-acceptor, electron pair, and hydrogen bonding interactions. It can be predicted that the above concept is not fully universal, especially in the case of solutes and solvents which may apply these interactions in their solubilizing action. Hansen developed a three-dimensional scale with parameters to expand theory in order to include these interactions. Hansen defined solubility parameter by the following equation: 2

2

2

2

δ = δd + δp + δh where:

δd δp δh

[2.3.12]

dispersion contribution to solubility parameter polar contribution to solubility parameter hydrogen bonding contribution to solubility parameter

Hansen defined solvent as a point in three-dimensional space and solutes as volumes (or spheres of solubility). If a solvent point is within the boundaries of a solute volume space then the solute can be dissolved in the solvent. If the point characterizing the solvent is outside the volume space of a solute (or resin) such a solvent does not dissolve the solute. The solubility model based on this concept is broadly applied today by modern computer techniques using data obtained for solvents (the three components of solubility parameters) and solutes (characteristic volumes). A triangular graph can be used to outline the limits of solubility and place different solvents within the matrix to determine their potential dissolving capability for a particular resin.

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2.3 Basic physical and chemical properties of solvents

Figure 2.3.21. Kauri butanol number vs. aniline point.

Figure 2.3.22. Hildebrand solubility parameter vs. surface tension for four groups of solvents.

Simpler methods are also used. In the paint industry, Kauri-butanol values are determined by establishing the tolerance of a standard solution of Kauri resin in n-butanol to the addition of diluents. This method is applicable to hydrocarbons (both aromatic and aliphatic) and CFCs. Figure 2.3.20 shows that there is a good correlation between the Kauributanol number and the Hildebrand solubility parameter. The Kauri-butanol number can be as high as 1000 (amyl ester of lactic acid) or 500 (Freon solvent M-162). The aniline point determination is another method of establishing the solubilizing power of a solvent by simple means. Here, the temperature is measured at which a solution just becomes cloudy. Figure 2.3.21 shows that there is a good correlation between the Kauri-number and the aniline point. Also, dilution ratio of cellulose solution is measured by standardized methods (see Chapter 12). 2.3.20 OTHER TYPICAL SOLVENT PROPERTIES AND INDICATORS There are many other solvent properties and indices which assist in solvent identification and selection and help us to understand the performance characteristics of solvents. The data characterizing the most important properties were discussed in the sections above. The solvent properties and classification indicators, which are discussed below, are included in the Solvent Database available on CD-ROM from ChemTec Publishing. Name. A solvent may have several names such as common name, Chemical Abstracts name, and name according to IUPAC systematic nomenclature. Common names have been used throughout this book and in the CD-ROM database because they are well understood by potential users. Also, CAS numbers are given in the database to allow user of the database to use the information with Chemical Abstract searches. In the case of commercial solvents which are proprietary mixtures, the commercial name is used. The molecular formula for each solvent is given in the database, followed by the molecular formula in Hills notation, and the molecular mass (if solvent is not a mixture).

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The CAS number identifies the chemical compound or composition without ambiguity. RTECS number is the symbol given by Registry of Toxic Effects of Chemical Substances (e.g., AH4025000) to identify toxic substances. Composition is given for solvents which are manufactured under trade name and have a proprietary composition (if such information is available). Solvent purity (impurities) is given as a percent and known impurities and their concentrations are provided. Hygroscopicity and water solubility of solvents is an important characteristic in many applications. The data are given in the database either in mg of water per kilogram of solvent or in a generic statement (e.g., miscible, slight). Many solvents are hygroscopic, especially those which contain hydroxyl groups. These solvents will absorb water from their surroundings until equilibrium is reached. The equilibrium concentration depends on the relative humidity of air and the temperature. If solvents must maintain a low concentration of water, vents of storage tanks should be fitted with silica gel or molecular sieves cartridges or tanks should be sealed and equipped with pressure and vacuum relief vents which open only to relieve pressure or to admit a dry inert gas to replace the volume pumped out. Preferably prevention of water from contacting solvents or the selection of solvents with a low water content is more economical than the expensive operation of drying a wet solvent. Surface tension and solubility parameter have been related using the following equation: γ δ = 21K ---------1⁄3 V

a

[2.3.13]

where: d K, a g V

Hildebrand solubility parameter constants surface tension molar volume of the solvent

However, Figure 2.3.22 shows that the parameters correlate only for aromatic hydrocarbons. For three other groups, the points are scattered. The equation has a very limited predictive value. Viscosity. Figure 2.3.2 shows that viscosity of solvents correlates with their boiling point. There are substantial differences in the viscosity − boiling point relationship among alcohols and other groups of solvents. These are due to the influence of hydrogen bonding on the viscosity of alcohols. Thermal conductivity of solvents is an important property which determines the heat transfer in a solvent or solution and influences the evaporation rate of solvents as a solution is being dried. Activity coefficients may be applied to different processes. In one application, the activity coefficient is a measure of the escaping tendency from liquid to another liquid or a gaseous phase (in the liquid to gas phase they can be quantified using Henry's law coefficient). These activity coefficients are derived from distillation data at temperatures near

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the boiling point or from liquid-liquid extraction calculations. In another application as defined by Hildebrand and Scratchard solvent activity to dissolve a non-electrolyte solute is given by equation: 2

V m ( δ solute – δ solvent ) ln f = ---------------------------------------------------RT

[2.3.14]

where: f Vm δsolute δsolvent

activity coefficient molar volume of solute solubility parameter of solute solubility parameter of solvent RT gas constant x temperature

This coefficient is used to express rate constants of bimolecular reactions. Azeotropes. One solvent may form azeotropes with another solvent due to molecular association. This physical principle can be exploited in several ways. The most important in solvent applications is the possibility of reducing the boiling temperature (some azeotropes have lower boiling point) therefore an applied product such as a coating may lose its solvents and dry faster. The formation of such azeotrope also lowers flash point by which it increases hazards in product use. The formation of an azeotrope is frequently used to remove water from a material or a solvent. It affects the results of a distillation since azeotrope formation makes it difficult to obtain pure components from a mixture by distillation. Azeotrope formation can be suppressed by lowering the boiling point (distillation under vacuum). One benefit of azeotropic distillation is the reduction in the heat required to evaporate solvents. Henry's constant is a measure of the escaping tendency of a solvent from a very dilute solution. It is given by a simple equation: Henry's constant = p x φ, where p is the pressure of pure solvent at the solution temperature and φ is the solvent concentration in the liquid phase. A high value of Henry's constant indicates that solvent can be easily stripped from dilute water solution. It can also be used to calculate TLV levels by knowing concentration of a solvent in a solution according to the equation: TLV (in ppm) = [18 H (concentration of solvent in water)]/ molecular weight of solvent. pH and corrosivity. The pH of solvents is of limited value but it is sometimes useful if the solvent has strong basic or acidic properties which could cause corrosion problems. The acid dissociation constant is the equilibrium constant for ionization of an acid and it is expressed in negative log units. The color of a solvent may influence the effect of solvent on the final product and allow the evaluation of solvent quality. The colorless solvents are most common but there are many examples of intrinsically colored solvents and solvents which are colored because of an admixture or inadequate storage conditions or too long storage. Odor. Odor threshold (discussed above) is not a precise tool for estimation concentration of vapors. The description of odor has little relevance to the identification of solvent but description of odors in the database may be helpful in the selection of solvent to minimize odor or make it less intrusive.

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UV absorption maxima for different solvents given in the database are useful to predict the potential effect of solvent on UV absorption from sunlight. The collection of data is also useful for analytical purposes. Solvent partition − activated carbon and between octanol and water. Solvents can be economically removed from dilute solutions by activated carbon or ion exchange resins. Activated carbon partition coefficient which helps to determine the amount of activated carbon needed to remove a contaminant can be obtained using the following equation: w m = -----Pc

[2.3.15]

where: w P c

total weight of solvent in solution partition coefficient residual concentration of solvent remaining after treatment.

The octanol/water partition coefficient is the log of solubility of the solvent in water relative to that in octanol. This coefficient is used to estimate biological effects of solvents. It can also be used to estimate the potential usefulness of a solvent extraction from water by any third solvent. Soil adsorption constant is a log of the amount of a solvent absorbed per unit weight of organic carbon in soil or sediment. Atmospheric half-life of solvents due to reaction in the atmosphere with hydroxyl radicals and ozone is a measure of the persistence of particular solvent and its effect on atmospheric pollution. Hydroxyl rate constant is the reaction rate constant of the solvent with hydroxyl radicals in the atmosphere. Global warming potential of a well-mixed gas is defined as the time-integrated commitment to radiative forcing from the instantaneous release of 1 kg of trace gas expressed relative to that from the release of 1 kg of CO2. Biodegradation half-life determines persistence of the solvent in soil. Commercial proprietary solvents mixtures are classified as biodegradable and solvents having known chemical compositions are classified according to the time required for biodegradation to cut their initial mass to half. Target organs most likely affected organs by exposure to solvents. The database contains a list of organs targeted by individual solvents. Hazchem Code was developed in the UK for use by emergency services to determine appropriate actions when dealing with transportation emergencies. It is also a useful to apply as a label on storage tanks. It consists a number and one or two letters. The number informs about the firefighting medium to be used. The first letter gives information on explosion risk, personal protection and action. A second letter (E) may be added if evacuation is required.

3

Production Methods, Properties, and Main Applications 3.1 DEFINITIONS AND SOLVENT CLASSIFICATION Christian Reichardt and George Wypych Fachbereich Chemie, Philipps-Universität, Marburg, Germany ChemTec Laboratories, Toronto, Canada Chemists have a choice among hundreds of solvents and solvent/mixtures for their use as a medium for the chemical reaction under study or other applications. The selection is usually affected by solvent characteristics that are related to their chemical constitution, physical properties, Brønsted and Lewis acid/base behavior, nonspecific (e.g., van der Waals) and specific (e.g., hydrogen bonding) solute/solvent interactions, solvent polarity, commercial availability with adequate purity, toxicity, reasonable price, and others. Several definitions needed to classify solvents are given in Table 3.1.1. Table 3.1.1 Definitions for solvents and their characteristics Term Solvents

Definition Substances that dissolve other material(s) to form a homogeneous solution. Commonly, the component which is in excess is called the solvent, and the minor component(s) is the solute. Common solvents are liquid at room temperature but can also be solid (e.g., ionic solvents) or gaseous (e.g., carbon dioxide). Solvents are either molecular, ionic, or atomic (e.g., Hg, Ga) solvents, with covalent, ionic, or metallic bonds, respectively. Solvents are usually differentiated from plasticizers by limiting their boiling point to a maximum of 250°C. Solvents are considered to be chemically non-reactive, interacting with the solute only by nonspecific and specific intermolecular forces without chemical alteration.

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3.1 Definitions and solvent classification

Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Solvent polarity

When applied to solvents, this rather ill-defined term covers their overall solvation capability (solvation power) for solutes (i.e., in chemical equilibria: reactants and products; in reaction rates: reactants and activated complex; in light absorptions: ions or molecules in the ground and excited state), which in turn depends on the action of all possible, nonspecific and specific, intermolecular interactions between solute ions or molecules and solvent molecules or ions, excluding such interactions leading to definite chemical alterations of the ions or molecules of the solute. Occasionally, the term solvent polarity is restricted to nonspecific solute/solvent interactions only (i.e., to van der Waals forces).1 Concerning this definition of polarity, when discussing dipolar molecules, the dipolarity (rather than polarity) of solvents should be considered. Molecules with a permanent dipole moment are dipolar (not polar). Molecules, which are lacking permanent dipole moment should be called apolar (or nonpolar). In literature, the terms polar and apolar are used indiscriminately to characterize a solvent by its relative permittivity as well as its permanent dipole moment, even though dipole moments and relative permittivities are not directly related to each other.

Electronic polarizability, α

The ease of distortion of the electron cloud of an atomar or molecular entity by an external electric field (such as that due to the proximity of a charged species). It is experimentally measured as the ratio of induced dipole moment, μind, to the field strength, E, which induces it (α = μind/E). The SI unit of the electronic polarizability is Cm2V-1, but it is usually expressed in cgs units as polarizability volume. In the ordinary usage, α refers to the “mean polarizability,” i.e., the average over three rectilinear axes of the atom or molecule.1,2

Dipolar aprotic solvents

Solvents with a comparatively high relative permittivity (εr > 15) and a sizable permanent dipole moment (μ > 2 Debye) that cannot donate suitably labile H-atoms to form intermolecular hydrogen bonds to the solute (e.g., dimethyl sulfoxide, acetonitrile, acetone, etc.). The term “aprotic” is a misnomer because in reactions with suitable bases a proton can be easily removed from some of these solvents. “Aprotic solvent” should be replaced by “non-HBD solvent” (HBD = hydrogen-bond donating). In describing a solvent, it is better to be explicit about its intrinsic properties, therefore, better “dipolar non-HBD solvent”.1-4

Normal solvents

Normal solvents do not undergo strong intermolecular solvent/solvent interactions leading to highly-structured fluids (e.g., water), in contrast to lessstructured solvents with only weak mutual solvent/solvent interactions (e.g., hydrocarbons).

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Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Aprotic/protic solvents

Aprotic solvents (also called inert, indifferent, non-dissociating, or non-ionizing solvents) are solvents which are not capable of acting as hydrogenbond donors and should be better called non-HBD solvents. The term “aprotic” is a misnomer because in reactions with suitable bases a proton can be easily removed from some of these solvents (e.g., dimethyl sulfoxide, acetonitrile, acetone, etc.). Protic solvents (also called protogenic solvents) are solvents capable of acting as hydrogen-bond donors because of the presence of suitable functional groups (e.g., OH, NH, etc.). It is better to classify solvents according to their capability to donate or not donate, as well as to accept or not accept, hydrogen bonds to or from the solute, according to:1-4 Hydrogen-bond donating solvents = HBD solvents = formerly protic or protogenic solvents; Non-hydrogen-bond donating solvents = non-HBD solvents = formerly aprotic solvents; Hydrogen-bond accepting solvents = HBA solvents = formerly protophilic solvents; Non-hydrogen-bond accepting solvents = non-HBA solvents. This solvent classification is in agreement with the intentions of Parker, who introduced the terms “aprotic/protic solvent” in 1962, with “aprotic” meaning indeed non-hydrogen-bond donating.3

Amphiprotic solvents

Self-ionizing solvents possessing characteristics of both Brønsted acids and bases (e.g., 2 H2O → H3O+ + HO−), in contrast to non-HBD solvents, which do not self-ionize to a measurable extent (e.g., DMF, DMSO, THF, hydrocarbons).1

Protogenic solvents

Solvents capable of acting as hydrogen-bond donor = HBD solvents. This term is preferred to “protic”, “protogenic”, or “acidic” solvents.1

Protophilic solvents

Solvents capable of acting as hydrogen-bond acceptor = HBA solvents.1 This term is preferred to “protophilic” solvents.1

Acidic/basic solvents

The Brønsted-Lowry acidity/basicity of a chemical species determines its ability to donate (to a base) or accept (from an acid) a proton. The extent of the proton-transfer reaction in solution is determined by the corresponding acid or base dissociation constant. As most solvents possess acid or base properties, the strengths of acids and bases depend on the medium in which they are dissolved. − The Lewis acidity/basicity of a chemical species determines its ability to accept (from a donor) or donate (to an acceptor) a pair of electrons to form a dative covalent bond between the EPA (electron-pair acceptor) and EPD (electron-pair donor) molecules or ions. Quantitative measures of the solvent's Lewis acidity resp. basicity are the Acceptor (AN) and Donor Numbers (DN), based on 31P-NMR chemical shifts and on calorimetric measurements with a reference Lewis base (Et3P=O) and a reference Lewis acid (SbCl5), introduced by Gutmann et al.1,5 The DN scale can be replaced by the more precise and comprehensive BF3 Lewis basicity scale of Gal et al.5b,6

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3.1 Definitions and solvent classification

Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Hydrogen-bonding

Attractive (mostly electrostatic) interaction between an electronegative atom (e.g., N, O, F) and a hydrogen atom covalently bound to a second electronegative atom (e.g., NH, OH, FH); also described as an interaction between a hydrogen-bond donor (HBD) and a hydrogen-bond acceptor (HBA) group. Hydrogen bonds may be intra- or intermolecular.1

Hydrophilic solvents

“Water loving” solvents which undergo stabilizing interactions with polar solvents such as water, to an extent greater than with nonpolar solvents.1

Solvation

Stabilizing interaction between solvent and solute or between solvent and functional groups of insoluble materials (e.g., ionic groups of ion-exchange resins). Such interactions generally involve non-specific van der Waals and the electrostatic forces, as well as chemically more specific interactions such as hydrogen-bonding.1,4a For aqueous solutions the term used is hydration.

Solvent (polarity) parameter

Quantitative measures of the capability of solvents for interaction with solutes, based on experimentally (empirically) determined physicochemical quantities such as relative permittivity, refractive index, rate and equilibrium constants of solvent-dependent chemical reference reactions, as well as solvent-dependent UV/Vis-, IR-, and NMR spectra of suitable probe molecules. Depending on the molecular structure of the reference compound, solvent parameters can measure either the solvent's overall solvation capability (= solvent polarity) or only particular aspects of the solute/solvent interactions such as nonspecific dispersion and specific hydrogen-bond interactions. Such solvent parameters are used in the correlation analysis of solvent-dependent processes, either in single- or multiparameter correlation equations.1,4a,7

Hydrophobic interaction

The tendency of hydrocarbons (or of lipophilic hydrocarbon-like groups in solutes) to form inter- (or intra-) molecular aggregates in an aqueous medium, and analogous intramolecular interactions. The name arises from the attribution of the phenomenon to the apparent repulsion between water and hydrocarbons. However, the phenomenon ought to be attributed to the effect of the hydrocarbon-like groups on the water/water interaction.1 Analogous interactions found in the self-associated, highly-structured solvents others than water (e.g., glycerol) are called “solvophobic interactions.”4a

Solvolysis

Generally, the chemical reaction of a solute with the solvent, involving the rupture of one or more bonds in the reacting solute. More specifically the term is used for substitution, elimination and fragmentation reactions in which a solvent species serves as the nucleophile or base. Solvolysis can also be classified as hydrolysis, alcoholysis, or ammonolysis, etc., if the reacting solvent is water, alcohol, or ammonia, etc.1

Solvatochromism

Solvent-induced shift of the electronic UV/Vis/NIR absorption (or emission) band (and sometimes change in intensity) of the light-absorbing (or emitting) solute. A hypsochromic (blue) band shift with increasing solvent polarity is called negative solvatochromism, a corresponding bathochromic (red) band shift is called positive solvatochromism.1,4

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Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Relative permittivity A measure of the reduction of the magnitude of the potential energy of interaction between the charges ongoing from vacuum to a condensed medium (dielectric constant) (such as gas or liquid). The dimensionless relative permittivity, εr, of a substance is measured by comparing the capacitance of a capacitor with (C) and without (vacuum: C0) of the sample present (εr = C/C0).3 The term “dielectric constant” is obsolete because it is not a constant: each solvent has its own specific, temperature- and frequency-dependent εr value.

εr

Electric dipole moment μ

Mathematical product of the distance, l, between the centers of charge of the equal and opposie charges in a dipolar molecule and the magnitude of these charges, q(μ = l.q)

Miscible solvents

Solvents are usually miscible and the binary mixture obtained is nearly ideal when their Hildebrand solubility parameters, δ, do not differ by more than about seven SI units (= MPa1/2). This simple rule applies when mainly dispersion interactions exist between solvent molecules, i.e., it does not apply to polar solvents.

Good solvent

Substances readily dissolve if the Hildebrand solubility parameters, δ, of a solute and a solvent are relatively close to each other (less than about seven SI units, MPa1/2). This rule is not valid for polar solvents and has some exceptions (e.g., PVC is not soluble in toluene even though the difference of their solubility parameters is only 2.5). The ability of a solvent to dissolve a compound is also called its “solvency”.

Theta solvent

The chain conformation of dissolved polymers is affected by intramolecular polymer/polymer and by intermolecular polymer/solvent interactions. In good solvents, interactions between the polymer segments and solvent cause polymer coils to expand, whereas in poor solvents the polymer/polymer interactions are preferred, and the polymer coils shrink. The solution temperature at which chain expansion is exactly balanced by chain contraction is called theta (or Tθ) temperature. A solvent at this temperature is called an ideal or theta (or θ) solvent.

Reactivity in solvents

Solvents are usually considered as macroscopic continuum characterized by their macroscopic physical properties (i.e., boiling point, vapor pressure, density, index of refraction, relative permittivity, thermal conductivity, surface tension, viscosity, etc.) and, by definition, do not directly participate in chemical reactions carried out in solution. From the molecular-microscopic point of view, solvents represent a discontinuum, consisting of individual, mutually interacting solvent molecules, characterized by their molecular properties (i.e., dipole moment, electronic polarizability, hydrogen-bond donor (HBD) and -acceptor (HBA) capability, etc.), interacting with the solute by means of nonspecific and specific solute/solvent forces (e.g., van der Waals forces, hydrogen-bonding, etc.). This leads to differential solvation and stabilization of reactants and products as well as of reactants and activated complexes (transition structures), thus influencing the equilibrium and rate constants of chemical reactions carried out in solution. If solvent is consumed by the chemical reaction, then it is no more a solvent only but also a reaction partner.

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3.1 Definitions and solvent classification

Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Hygroscopy of solvents

Hygroscopy is the phenomenon of attracting and holding water molecules from the surrounding environment, usually humid air at room temperature, achieved through either absorption or adsorption. Hygroscopic solvents (e.g., alcohols, glycols, glycerol, etc.) are unsuitable for applications which require a moisture-free environment or a predetermined freezing point. The process by which a substance absorbs moisture from the atmosphere until it dissolves and forms a solution is called deliquescence (e.g., CaCl2, NaOH, etc.). Such compounds can be used to remove the water produced by chemical reactions in solution. Non-hygroscopic solvents may still contain traces of dissolved water and have to be likewise dried before their use as waterfree media.

Solvent strength

In adsorption chromatography the solvent's eluting power can be quantitatively measured by means of so-called solvent strength parameters such as ε0, a dimensionless number related to the free energy of adsorption of the solvent per unit area of adsorbent with unit activity (e.g., SiO2, Al2O3), introduced by Snyder.8 A series of solvents ordered by their increasing eluting power, as for example measured by the ε0 values, is called an eluotropic solvent series. − The term solvent strength is also used to establish a required solvent concentration to form a clear solution and to estimate the diluting capabilities of a pre-designed system. Quantities used for this purpose are the standardized dimensionless Kauri-butanol (Kb) values and the aniline points (in °C). A high Kb value corresponds to high solvent strength.

Solvent partitioning

Solvent partitioning (also known as liquid-liquid or solvent extraction) means partitioning of a solute A between two immiscible solvents, based on the relative solubilities of A in the two different solvents (usually water and an organic solvent), and quantitatively described by the partition constant P as ratio of the molar concentrations of A [P = cA(org)/cA(aq)]. The solventenriched in solute A is called the extract. Solvent partitioning constants are essential for designing new solvent systems for solvent extraction of a great variety of substrates. Of particular importance is the Hansch-Leo 1-octanol/ water partition constant PO/W [= cA(1-octanol)/cA(water)], which is a measure of the hydrophobicity of solute A: the larger the PO/W of A, the larger its hydrophobicity.9 The Gibbs energy-based form lg PO/W has served as the basis of so-called Quantitative Structure/Activity Relationships (QSARs), applied above all in biochemistry as well as pharmaceutical and medicinal chemistry.9,10

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Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Volatility of solvents

Volatility is a measure of the tendency of a liquid to evaporate at normal temperature and pressure and depends on its vapor pressure. The Knudsen, Henry, Cox, Antoine, and Clausius-Clapeyron equations are used to estimate the vapor pressure of a liquid, its evaporation rate, and the composition of the atmosphere over the liquid. The liquid's boiling point indicates the evaporation rate but is insufficient for its accurate estimation because of the influence of the molar enthalpy of evaporation. Solvents have also been classified by their evaporation number, using diethyl ether as a reference (evaporation number = 1 at 20°C and 65 vol% relative air humidity). Most solvents belong to the group of so-called volatile organic compounds (VOCs) that can easy disperse in the environment and can show both acute and chronic toxicities.

Residue

The residue is a substance that remains after a process such as combustion or evaporation. This may refer to either the non-volatile residue or the potential for residual solvent left after processing. The former can be estimated from the solvent specification, the later is determined by system and technology design.

Carcinogenic solvents

A carcinogen is any substance that promotes carcinogenesis, i.e., the formation of cancer in organisms. This may be due to the ability to damage the genome or to the disruption of cellular metabolic processes. Several groups of solvents have representatives in this category (see listings in Section 3.3).11

Mutagenic solvent

A mutagen is any substance that promotes mutagenesis, i.e., changes of the cell's genetic material (usually affecting transcription and replication of DNA) of an organism and thus increasing the frequency of mutations above the natural background level (see listings in Section 3.3). Frequently, mutagens are also carcinogens.12

Reprotoxic solvents

A reprotoxic chemical is any substance that promotes reprotoxicity, i.e., impairing reproduction or fertility of people (man and woman), effects on the unborn child, and damage to the baby via breastfeeding. Several solvents in the group of amides and glycol ethers are considered to impair fertility. For cancerogenic, mutagenic, and reprotoxic substances the abbreviation “CMRs” is now commonly used.13

Toxicity of solvents

The short-term acute toxicity of a chemical is measured by its LD50 (lethal dose) and LC50 (lethal concentration) values, i.e., the amount of substance given all at once (oral, dermal, or inhalational) required to kill 50% of the test population, usually given in mg chemical per kg body weight of the test animal (LD50), or in mg chemical per liter of breathing air for a 4-hour exposure (LC50) of the test animal.14 − The long-term chronic toxicity of a compound is usually described by its adopted Threshold Limit Value (TLV®), i.e., by the time-weighted average (TWA)-TLV in parts of vapor or gas per million parts of contaminated air by volume (mL/m3; ppm) at 25°C and 1013 hPa at the workplace.15 − Odor threshold values have limited use in evaluating the potential danger of solvent exposure.

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Table 3.1.1 Definitions for solvents and their characteristics Term

Definition

Flammable solvents

Flammability is the ability of volatile liquids to ignite and burn, to cause fire or combustion, and can be assessed by their flash point and autoignition temperature. The flash point of a liquid is the lowest temperature at which its vapor will ignite in a normal atmosphere when given an external ignition source. The autoignition temperature is the lowest temperature at which the vapor self-ignites spontaneously without an ignition source. − Liquids with a flash point of less than 37.8°C (100°F) are called flammable, and those with a flash point at or above 37.8°C (100°F) are called combustible. − The maximum and minimum vapor concentrations of a flammable or combustible volatile liquid (expressed as percent by volume in air), at which an ignition-induced explosion will occur in a confined area, are called flammable or explosive limits, defining the safe ranges of solvent vapor concentrations.

Combustible solvents

Combustible liquids have a flash point at or above 37.8°C (100°F) and will ignite and burn at temperatures that are usually above working temperatures. Flammable liquids have a flash point below 37.8°C (100°F) and ignite and burn easily already at normal temperatures (see also an entry for Flammable solvents). − The net heat of combustion and the calorific value help to estimate the potential energy which can be recovered from burning used solvents. Also, the composition of the combustion products has to be considered to evaluate their corrosiveness and their impact on the environment.

Ozone-depleting solvents

Ozone-depleting substances (ODSs) are volatile chemicals that destroy the ozone layer located in the earth's stratosphere (at the height of about 20-45 km), which limits the sun's harmful UV-B rays (285 to 315 nm) from reaching the earth's surface. The ozone depleting potential (ODP) of ODSs (e.g., chlorofluorocarbons, CFCs, and hydrochlorofluorocarbons, HCFCs) is given relative to that of CFC-11 (trichlorofluoromethane), the ODP value of which was assigned to 1.0. − The photochemical ozone creating potential (POCP) of volatile organic compounds (VOCs) is a relative value compared to that of ethene to form ozone in the troposphere (POCP = 100 for ethene). − Numerous solvents belong to both groups.

UV cut-off

The wavelength at which the solvent absorbance in a 1 cm path-length cell equals to 1 AU (absorbance unit) using water in the reference cell. Acetonitrile, pentane, and water have very low UV cut-off at 190 nm.

Biodegradability

Biodegradable chemical substances are capable of being decomposed over time by the action of biological agents, especially microorganisms such as bacteria. The rate of biodegradation can be measured in a number of ways such as biodegradation half-life, biological oxygen demand, as well as chemical and theoretical oxygen demand. For example, poly(lactic acid) is a plastic that biodegrades quickly, in contrast to polyethylene.

Cost of solvents

The cost of a solvent and its recovery after the process under study is a critical factor in solvent selection.

The above list of terms and parameters connected to solvents is not exhaustive. These and related subjects are discussed at length in other parts of this book. Table 3.1.1 is presented to assist the reader in an understanding of different solvent classifications using

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various characteristics. Numerical values of all the solvent characteristics mentioned in this Table can be found elsewhere.16 A review of the selected definitions given in Table 3.1.1 suggests that there are many essential determinants which have to be considered in the choice of a suitable solvent for the specific process under study. Some of the solvent parameters are conflicting, some are not well quantified, and each solvent application requires a set of solvent performance criteria. It can be thus anticipated, prior to any analysis, that the solvent’s chemical structure can be used as the best means of solvent classification for any application. Such a classification is used in this book because of its broad application. Traditional instead of systematic chemical names are preferably used as names because all solvent users generally understand them. An important classification criterion is the solvent’s overall solvation capability, also called solvent polarity, which has been determined empirically using carefully selected, convenient to measure, strongly solvent-sensitive chemical or physical reference processes, i.e., equilibria or rates of chemical reactions or spectral absorptions of suitable solvatochromic chromophores. Well-known empirical parameters of solvent polarity are the so-called ET(30) resp. ETN values, introduced by Dimroth and Reichardt in 19634a-d,17a and improved later on by Reichardt in 1983.4a-d,17b The ET(30) values are the molar electronic transition energies of a strongly solvatochromic pyridinium-N-phenolate betaine dye (# 30 in ref.17a), given by the following equation: ET(30)/(kcal∙mol‒1) = h·c·νmax∙NA = 28591/λmax

[3.1.1]

where h is Planck’s constant, c speed of light, NA Avogadro’s number, and νmax and λmax the wavenumber (cm‒1) resp. wavelength (nm) of the long-wavelength Vis absorption band of the reference betaine dye # 30. The ET(30) scale ranges from 63.1 (water) to 30.7 kcal∙mol‒1 (tetramethylsilane, TMS), and has been later normalized to give the dimensionless ETN scale, using water (ETN = 1) and TMS (ETN = 0) as most and least polar reference solvents, according to the following equation [ET = ET(30)]:17b ETN = [ET(solvent) – ET(TMS)]/[ET(water) – ET(TMS)] = = [ET(solvent) – 30.7]/32.4

[3.1.2]

ET(30) resp. ETN values are known for several hundred molecular and ionic solvents as well as for numerous solvent mixtures.4a-d,16 Because the solvatochromic absorption band of the reference betaine dye # 30 lies within the visible region, a rough estimate of the solvent polarity can even be made with the naked eye. The first UV/Vis spectroscopically derived empirical solvent polarity parameter was introduced by Kosower already in 1958 and called Z-values.18 They were based on the solvent-dependent intermolecular charge-transfer transition of 1-ethyl-4-(methoxycarbonyl)pyridinium iodide, but, for solubility reasons, they are directly available only for a limited set of solvents. Both sets of polarity data can be easily converted using the following correlation equation:

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ET(30)/(kcal∙mol‒1) = 0.787∙Z/(kcal∙mol‒1) ‒ 10.2

[3.1.3]

The dimensionless Acceptor Numbers, AN, introduced by Gutmann et al.5 as an empirical measure of the solvent’s Lewis acidity (for definition see entry Acidic/Basic solvents in Table 3.1.1), also correlate linearly with the ET(30) values according to the following equation:19 ET(30)/(kcal∙mol‒1) = 0.541∙AN + 32.4

[3.1.4]

In this way, Z and AN values can be used to calculate ET(30) values which are not otherwise available. The ET(30) resp. ETN values exhibit in general good to satisfactory linear correlations with other solvent-dependent processes, i.e., equilibrium constants, reaction rates, and light absorptions.4 However, they do not measure the solvent’s Lewis basicity. The Lewis basicity of solvents can be quantified by Gutmann’s Donor Numbers, DN (for definition see entry Acidic/Basic solvents in Table 3.3.1).5 The DN scale can be replaced by the more precise and comprehensive BF3 Lewis base (LB) affinity scale, introduced by Gal et al., and defined as the negative enthalpy, ∆H°, of the reaction LB(CH2Cl2 solution) + BF3(g) → LB‒BF3 (CH2Cl2 solution), which is known for approx. 350 Lewis bases.5b,6 For a correlation analysis of many solvent effects, a combination of normalized ET(30) and DN values in a two-parameter equation was often more successful than the one-parameter treatment.20 An excellent correlation analysis of all kinds of solvent effects can be often achieved by applying one of the multiparameter correlation equations introduced by Koppel and Palm,7a Kamlet and Taft,7b Catalán,7c and Laurence et al.,7d which generally include four, mostly empirically derived, orthogonal (= unrelated to each other) sub-parameters describing the solvent’s polarizability, dipolarity, as well as Lewis acidity and basicity, responsible for the solute/solvent interactions.4a,7 Using these empirical parameters of solvent polarity and other solvent properties, numerous solvent classification schemes have been developed. Based on the large data set of ET(30) resp. ETN values, molecular solvents can be roughly classified into three groups: hydrogen-bond donor (HBD) or protic solvents (ETN from 0.5 to 1.0), dipolar non-hydrogen-bond donor (non-HBD) or dipolar aprotic solvents (ETN from 0.3 to 0.5), and apolar non-HBD solvents (ETN from 0.0 to 0.3), confirming the earlier qualitative solvent classification of Parker.3 Using chemometric or multivariate statistical methods, i.e., multiple linear regression analysis (MRA) and principal component analysis (PCA) of large solvent data sets, many useful, more detailed classification schemes for solvents have been proposed. For example, nine groups of solvents were defined by Chastrette et al., based on the cluster analysis of eight independent solvent descriptors of 83 solvents.21 Clustering of 774 solvents into eleven solvent groups was found by Katritzky et al., applying their CODESSAPROTM program to 774 solvents.22 In addition to these efforts, many other solvent classifications are known, based on more practical-orientated descriptors related to specific applications. For example, in adsorption chromatography solvents were arranged according to their eluting power under

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standardized conditions, as measured by Snyder’s ε0 values,8 or by the gas-liquid partition coefficients of selected solutes, experimentally determined by Rohrschneider.23 Using the available comprehensive data sets,16 further classifications can be made by the solvent’s volatility (evaporation numbers), flammability (flashpoints), explosive limits, acute and chronic toxicity (LD50 and TL-TWA values), environmental fate, etc. REFERENCES 1 2 3 4

5

6

7

8 9 10 11 12

13 14 15 16

C. L. Perrin et al., Glossary of Terms used in Physical Organic Chemistry – IUPAC Recommendations 2019. 3rd ed., in preparation; 2nd ed. 1994: P. Müller, Pure Appl. Chem., 66, 1077-1184 (1994). E. R. Cohen et al., Quantities, Units and Symbols in Physical Chemistry – IUPAC Recommendations 2007. 3rd ed., RSC Publishing, Cambridge, UK, 2007. A. J. Parker, Quart. Rev. Chem. Soc., 16, 163-187 (1962); (b) A. J. Parker, Chem. Rev., 69, 1-32 (1969). (a) C. Reichardt, T. Welton, Solvents and Solvent Effects in Organic Chemistry. 4th ed., Wiley-VCH, Weinheim, Germany, 2011; (b) C. Reichardt, Chem. Rev., 94, 2319-2358 (1994); (c) V. G. Machado, R. I. Stock, C. Reichardt, Chem. Rev., 114, 10429-10475 (2014); (d) J. P. Cerón-Carrasco, D. Jacquemin, C. Laurence, A. Planchat, C. Reichardt, K. Sraïdi, J. Phys. Org. Chem., 27, 512-518 (2014); (e) E. Buncel, R. A. Stairs, Solvent Effects in Chemistry. 2nd ed., Wiley, Hoboken/NJ, USA, 2016. (a) V. Gutmann, The Donor-Acceptor Approach to Molecular Interactions. Plenum Press, New York/ NJ, USA, 1978; (b) C. Laurence, J.-F. Gal, Lewis Basicity and Affinity Scales – Data and Measurement. Wiley, Chichester, UK, 2010; (c) R. van Eldik et al., Gutmann Donor and Acceptor Numbers for Ionic Liquids. Chem. Eur. J., 18, 10969-10982 (2012). (a) P.-C. Maria, J.-F. Gal, A Lewis Basicity Scale for Nonprotogenic Solvents: Enthalpies of Complex Formation with Boron Trifluoride in Dichloromethane. J. Phys. Chem., 89, 1296-1304 (1985); (b) C. Laurence, J. Graton, J.-F. Gal, An Overview of Lewis Basicity and Affinity Scales. J. Chem. Educ., 88, 1651-1657 (2011). (a) I. A. Koppel, V. A. Palm, The Influence of the Solvent on Organic Reactivity. In N. B. Chapman, J. Shorter (Eds.), Advances in Linear Free Energy Relationships. Plenum Press, London, New York, 1972; Chapter 5, p. 203-280; (b) M. J. Kamlet, J.-L. M. Abboud, M. H. Abraham, R. W. Taft, J. Org. Chem., 48, 2877-2887 (1983); (c) J. Catalán, J. Phys. Chem. B, 113, 5951-5960 (2009); (d) C. Laurence et al., J. Phys. Chem. B, 119, 3174-3184 (2015). L. R. Snyder, J. J. Kirkland, J. W. Dolan, Introduction to Modern Liquid Chromatography. 3rd ed., Wiley, Hoboken/NJ, USA, 2010; Appendix I: Properties of HPLC Solvents, p. 879ff. A. Leo, C. Hansch, D. Elkins, Partition coefficients and their use. Chem. Rev., 71, 525-616 (1971). H. Kubinyi, QSAR: Hansch Analysis and Related Approaches. VCH, Weinheim, Germany, 1993. E. Lynge, A. Anttila, K. Hemminki, Organic Solvents and Cancer. Cancer Causes & Control, 8 (3), 406-419 (1997). (a) B. N. Ames, Identifying environmental chemicals causing mutations and cancer. Science, 204 (No. 4393), 587-593 (1979); (b) H. Vainio, M. D. Waters, H. Norppa, Mutagenicity of selected organic solvents. Scandinavian Journal of Work, Environment & Health, 11 (Suppl. 1), 75-82 (1985). D. Darcey, R. Langley, Solvents. In L. M. Frazier, M. L. Hage (Eds.), Reproductive Hazards of the Workplace. Van Nostrand Reinhold, New York/NY, USA, 1998. P. Patnaik, A Comprehensive Guide to the Hazardous Properties of Chemical Substances. 3rd ed., Wiley, Hoboken/NJ, USA, 2007; Chapter 27, p. 537ff.: Industrial Solvents. 2018 Threshold Limited Values (TLVs®) for Chemical Substances and Physical Agents, adopted by the American Conference of Governmental Industrial Hygienists (ACGIH®), available from ACGIH, 1330 Kemper Meadow Drive, Cincinnati/OH 45240-4148, USA. (a) A. and G. Wypych, Solvents Database v.4.0 (on CD-ROM). 4th ed., ChemTec Publishing, Toronto/ON, Canada, 2014 (with over 1800 solvents the largest existing database on solvents); (b) A. and G. Wypych, Databook of Green Solvents. ChemTec Publishing, 2nd ed. Toronto/ON, Canada, 2019 (with more than 300 of the most used solvents);

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17 18

19 20 21 22 23

3.1 Definitions and solvent classification (c) Y. Marcus, The Properties of Solvents. Wiley, Chichester, UK, 1998; (d) Y. Marcus, Solvent Mixtures – Properties and Selective Solvation. Dekker, New York, Basel, 2002. (a) K. Dimroth, C. Reichardt, T. Siepmann, F. Bohlmann, Justus Liebigs Ann. Chem. 661, 1-37 (1963); (b) C. Reichardt, E. Harbusch-Görnert, Liebigs Ann. Chem. 721-743 (1983); (c) See also refs. 4a-c (a) E. M. Kosower, J. Am. Chem. Soc., 80, 3253-3260 (1958); (b) E. M. Kosower, An Introduction to Physical Organic Chemistry. Wiley, New York/NY, USA, 1968, p. 293ff.; (c) T. R. Griffiths, D. C. Pugh, Coord. Chem. Rev., 29, 129-211 (1979). Y. Marcus, Chem. Soc. Rev., 22, 409-416 (1993); see also p. 160 in ref. 16c (a) T. M. Krygowski, W. R. Fawcett, J. Am. Chem. Soc., 97, 2143-2148 (1975); (b) T. M. Krygowski, W. R. Fawcett, Can. J. Chem., 54, 3283-3292 (1976). M. Chastrette, M. Rajzmann, M. Chanon, K. F. Purcell, J. Am. Chem. Soc., 107, 1-11 (1985). A. R. Katritzky, D. C. Fara, M. Kuanar, E. Hur, M. Karelson, J. Phys. Chem. A, 109, 10323-10341 (2005). (a) L. Rohrschneider, Anal. Chem., 45, 1241-1247 (1973); (b) C. F. Poole, S. K. Poole, Chem. Rev., 89, 377-395 (1989).

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3.2 OVERVIEW OF METHODS OF SOLVENT MANUFACTURE George Wypych ChemTec Laboratories, Toronto, Canada Crude oil is the primary raw material source for solvents. Physical processes used in the petrochemical industry produce aliphatic and aromatic hydrocarbons. Other solvents are synthetic, but their starting raw materials are usually products of the petrochemical industry. Figure 3.2.1 shows the main groups of materials produced by the petrochemical industry from crude oil. Two observations are pertinent: the primary goal of the petrochemical industry is to convert crude oil into fuels. Solvents are only a small fraction of materials produced. Figure 3.2.2 shows that petrochemical products are not only used directly as solvents but are also the building blocks in the manufacture of a large number of materials produced by organic chemistry plants. Desalting of crude oil is the first step in crude oil processing. It is designed to remove corrosive salts which may cause catalyst deactivation. After desalting, crude oil is subjected to atmospheric distillation. Figure 3.2.3 shows a schematic diagram of the crude oil distillation process. The raw material is heated to 400oC and separated into fractions on 30-50 fraction trays in a distillation column. The diagram in Figure 3.2.3 shows the main fractions obtained from this distillation. The heavier fraction cannot be distilled under atmospheric pressure therefore in the next step vacuum is applied to increase volatilization and separation. Specific fractions from the distillation of crude oil are further refined in thermal cracking (visbreaking), coking, catalytic cracking, catalytic hydrocracking, alkylation, isomerization, polymerization, catalytic reforming, solvent extraction, and other operations. Thermal cracking (visbreaking) uses heat and pressure to break large hydrocarbon molecules into lower molecular weight products. Most refineries do not use this process but use instead of its replacement − catalytic cracking which gives a better yield of gasoline. Feedstock includes light and heavy oils from the crude oil distillation process. The cracking process occurs at a temperature of 550oC and under increased pressure. The cracking reaction is discontinued by mixing with cooler recycle stream. The mixture is stripped of lighter fractions which are then subjected to fractional distillation. Figure 3.2.4 is a schematic flow diagram of catalytic cracking. Hydrocracking is a somewhat different process which occurs under higher pressure and in the presence of hydrogen. It is used to convert fractions which are difficult to crack, such as middle distillates, cycle oils, residual fuel oils, and reduced crudes. Alkylation is used to produce compounds from olefins and isoparaffins in a catalyzed process. Isomerization converts paraffins to isoparaffins. Polymerization converts propene and butene to high octane gasoline. The application of these three processes has increased the output and performance of gasoline.

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Figure 3.2.1. Schematic diagram of petroleum industry products and yields. [Reproduced from reference 1]

Catalytic reforming processes gasoline and naphthas from the distillation unit into aromatics. Four major reactions occur including dehydrogenation of naphthenes to aromatics, dehydrocyclization of paraffins to aromatics, isomerization, and hydrocracking.

George Wypych

Figure 3.2.2. Organic chemicals and building block flow diagram. [Reproduced from reference 2]

Figure 3.3.3. Crude oil distillation. [Reproduced from reference 1]

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3.2 Overview of methods of solvent manufacture

Figure 3.3.4. Simplified catalytic cracking flow diagram. [Reproduced from reference 1]

In some cases, mixtures of solvents are needed to meet a particular requirement. For example, linear paraffins have a very low viscosity. Branched paraffins have high viscosity but excellent low-temperature properties and low odor. A combination of the two carried out in the conversion process (not by mixing) results in a solvent which has the desirable properties of both solvents: low viscosity and good low temperature properties.3 The recovery of pure aromatics from hydrocarbon mixtures is not possible using the distillation process because the boiling points of many non-aromatics are very close to benzene, toluene, etc. Also, azeotropes are formed between aromatics and aliphatics. Three principal methods are used for separation: azeotropic distillation, liquid-liquid extraction, and extractive distillation. Three major commercial processes have been developed for separation: Udex, Sulpholane, and Arosolvan. Over 90% of plants now use one of these processes. Each uses the addition of a solvent such as a mixture of glycols, tetramethylene sulfone, or N-methyl-2-pyrrolidone to aid in the extraction of aromatics. This occurs with high precision and efficiency. These processes produce pure benzene, toluene, and xylene. These three solvents are used for the synthesis of several other essential solvents. Benzene is used in the production of ethylbenzene (alkylation), cyclohexanone, cyclohexanol, cyclohexane, aniline (hydrogenation), acetone, nitrobenzene, and chlorobenzene.

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Toluene is used in the production of cresol and benzene. Xylene is the raw material for the production of ethylbenzene and the fractionation of the xylene mixture to isomers. Lower boiling fractions from the primary distillation are also used in the production of solvents. Ethylene is used to produce ethylene dichloride, ethylene glycol, ethanol, and ethylbenzene. Propylene is used to produce isopropyl alcohol. Halogenation, hydrohalogenation, alkylation, and hydrolysis reactions are used in these conversions. With different feedstock and methods of processing, it is inevitable that there will be some differences between products coming from different feedstock sources and manufacturers. Over the years processes have been refined. Long practice, globalization of technology has occurred, and restrictions have been imposed. Today, these differences are small, but in some technological processes, even these very small differences in solvent quality may require compensating actions. There are many other unitary operations which are used by organic chemistry plants to manufacture synthetic solvents. These include: alkoxylation (ethylene glycol), halogenation (1,1,1-trichloroethane), catalytic cracking (hexane), pyrolysis (acetone and xylene), hydrodealkylation (xylene), nitration (nitrobenzene), hydrogenation (n-butanol, 1,6-hexanediol), oxidation (1,6-hexanediol), esterification (1,6-hexanediol), and many more. In the manufacture of oxygenated solvents, the typical chemical reactions are hydration, dehydration, hydrogenation, dehydrogenation, dimerization, and esterification. For example, methyl ethyl ketone is manufactured from 1-butene in a two-step reaction. First, 1-butene is hydrated to 2-butanol then a dehydrogenation step converts it to methyl ethyl ketone. The production of methyl isobutyl ketone requires several steps. First acetone is dimerized producing diacetone alcohol which, after dehydration, gives mesityl oxide subjected in the next step to hydrogenation to result in the final product. Ethylene glycol is a product of the addition (ethylene oxide and ethanol) followed by esterification with acetic acid. The 18% of all phenol production is converted to cyclohexanone.4 Some solvents are obtained by fermentation processes (e.g., ethanol, methanol). Synthetic routes are usually quite complex. For example, the manufacture of Nmethyl-2-pyrrolidone involves the reaction of acetylene with formaldehyde. The resulting but-2-ine-1,4-diol is hydrated to butane-1,4-diol and then dehydrated to γ-butyrolactone then reacted with monomethyl amine to give the final product. Strict process control is essential to obtain very high purity. Processes have been developed to produce solvents which are based on non-conventional materials (e.g., lactide and drying oil). The resultant solvent is non-volatile and useful in the production of coatings, paints, and inks.5 The need to reduce VOCs drive these technological processes. The fermentation of carbohydrates to acetone, butanol, and ethanol by solventogenic Clostridia is known for decades.6 Clostridia produce butanol by conversion of a suitable carbon source into acetyl-CoA. Substrate acetyl-CoA then enters into the solventogenesis pathway to produce butanol using six concerted enzyme reactions.6 The solvent production process according to the invention comprises of culturing a fast-growing microorganism and separating the solvent from the culture medium. The solvent produced is an aliphatic hydrocarbon comprising 1-butanol, 2-butanol, isobutanol, 2,3-butanediol or 2butanone.6 Methods and systems are provided for the separation of butanol and other sim-

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ilar solvents from a fermentative solventogenesis reaction medium that utilizes Clostridium beijerinckii.7 Acetone, butanol, ethanol are produced using the anaerobic fermentation by butanolacetone- and ethanol-producing bacteria.8 The process includes saccharifying the pretreated plant material with enzymes which degrade or convert the material into soluble sugars, removing organic solvents and fermentation gases, and recovering end-product.8 Separation and purification processes of the crude product are employed to allow recovery of the ethyl acetate solvent, optionally recovery of ethanol, obtained from the hydrogenation of acetic acid, is also conducted.9 Lower dialkyl sulfides are often employed as valuable solvents.10 Most organic sulfides with low molecular mass have intense, unpleasant odors.10 Commercial dimethyl sulfide contains highly malodorous impurities such as carbon disulfide, carbonyl sulfide, methyl thiol, dimethyldisulfide, hydrogen sulfide and other sulfurous compounds at low levels.10 Dialkyl sulfide borane complexes of high purity are used to produce low odor dialkyl sulfides by enantioselective reduction.10 A method of raising the flash point of a green solvent by adding alpha terpene alcohol (alpha-terpineol) to the green solvent. Green solvents are derived from organic matter, such as plants.11 The addition of alpha terpene alcohol improves both the freeze resistance and the shelf life of the final green solvent solution.11 Because of food shortages due to an increase in world population, the development of biofuels from inedible lignocellulosic feedstock may be more sustainable direction.12 The combination of heat-integrated technique and intensified technique, extractive dividing wall column, was used for the purification section.12 A biosolvent, glycerol (product of biodiesel production) was used as the extracting solvent to obtain a high degree of integration.12 The heat-integrated and intensified process can save up to 47.6% and 56.9% of the total annual costs and total carbon dioxide emissions in the purification section, respectively, compared to the conventional purification process.12 The Aspergillus niger mycelium-surface displayed lipase showed great synthetic activity and high operational stability in the synthesis of green biosolvent isopropyl esters in a solvent-free system.13 The Aspergillus niger whole-cell biocatalyst showed operational stability at 65°C.13 The above-selected patent literature indicates that biosynthesis of solvents, their separation and purification, decreasing solvent odor, increasing flash point and use of green solvents are major directions of recent research. Many solvents could be made from biomass, but their production from fossil fuels is still less expensive and less damaging for the environment. The major cost in the production of solvents from biomass is their isolation which is frequently energy extensive. It appears that new more economical methods of solvent biosynthesis and their separatism from products of fermentation are required to make biosolvents more competitive. REFERENCES 1 2

EPA Office of Compliance Sector Notebook Project. Profile of the Petroleum Refining Industry. US Environmental Protection Agency, 1995. EPA Office of Compliance Sector Notebook Project. Profile of the Organic Chemical Industry. US Environmental Protection Agency, 1995.

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R J Wittenbrink, S E Silverberg, D F Ryan, US Patent 5,906,727, Exxon Research and Engineering Co., 1999. A M Thayer, Chem. Eng. News, 76, 16, 32-34 (1998). D Westerhoff, US Patent 5,506,294, 1996. T W Smoor, World Patent WO/2009/109580, DSM, 2009. J Kouba, A Oroskar, World Patent WO/2009/36076, Tetravitae Bioscience Inc., 2009. E R Davidov, World Patent WO/2010/87737, 2010. W J Johnston, L Sarager, R J Warner, R Cunningham, T Horton, R Jevtic, World Patent WO/2011/97197, Celanese, 2011. E Burkhardt, K Neigh, US Patent Application 20110124920, BASF, 2011. H W Howard, European Patent Application EP2391702, Greensolve Llc, 2011. Nhien, LC; Long, NVD; Lee, M, Energy Conversion Manag., 141, 367-77, 2017. Pan, Z; Jin, S; Zhang, X; Zheng, S; Han, S; Pan, L; Lin, Y, J. Molecul. Catal. B: Enzymatic, 131, 10-7, 2016.

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3.3 SOLVENT PROPERTIES George Wypych ChemTec Laboratories, Toronto, Canada The purpose of this section is to provide analysis of properties of major groups of solvents. The data on individual solvents are included in a separate publication on CD-ROM as a searchable database containing over 1800 of the most common solvents.1 The 4th Edition of Solvent Database, published by ChemTec Publishing, is the world largest database of solvent properties. It is used by thousands of corporations and universities as the reference material. The information on the properties of solvents is included in 140 fields containing chemical identification of solvent, physical-chemical properties, health and safety data, its environmental fate, and uses. Here, the analysis of this data is provided in a form of tables to show the range of properties for different groups of solvents and their strengths and weaknesses. For each group of solvents, a separate table is given below. No additional discussion is provided since data are self-explanatory. The data are analyzed in the final table to highlight the best performance of various groups of solvents in different properties. By their nature, these data have a general meaning and for the exact information on the particular solvent, full data on CD-ROM should be consulted. For example, in the list of target organs, there are included all organs involved in exposure to solvents included in the group which does not necessarily apply to a particular solvent. The data are given to highlight overall performance of entire group which may contain very diverse chemical materials. One very obvious method of use of this information is to review the list of carcinogens and mutagens and relate them to actually used in particular application. These solvents should be restricted from use and possibly eliminated or equipment engineered to prevent exposure of workers and release to the environment. The comparative tables also provide suggestions as to where to look for suitable substitutes based on physical-chemical characteristics and potential health and environmental problems. Another application of this data is in the selection of solvents for new products. The bulk of the data allows to analyze potential requirements critical for application and select a group or groups which contain solvents having these properties. Further, based on their health and environmental characteristics suitable candidates can be selected. The bulk data are also very useful in constructing a set of requirements for specification. Many specifications for industrial solvents are very simplistic, which is partially caused by the lack of data provided by manufacturers of these solvents. This may cause potential fear of future problems with such solvents as a solvent replacement in the formulated product is not always a trivial substitution. It is also possible that solvents for which inadequate data exist at the present moment will be more studied in future for their environmental and health impacts and will then require replacement. Also, incomplete specification means that solvents may contain undesirable admixtures and contaminations and were used on premises that manufacturer considered its application for a particular purpose which was, in fact, never intended by the solvent manufacturer for this particular

100

3.3 Solvent properties

application. These details should be obtained from manufacturers and relevant parameters included in the specification. It is known from the experience of creation of the database of solvents that there are still large gaps in information which should be eliminated by future efforts. The practice of buying solvents based on their boiling point and specific gravity does not serve the purpose of selecting a reliable range of raw materials. These and other aspects of created reference tables should be continuously updated in future to provide a reliable base of data which will be broadly used by industry. Application of full information allows decreasing the quantities of solvents required for the task and eliminate questionable materials and wastes due to solvent evaporation too rapid to make an impact on product properties at the time of its application. Also, many sources of the problems with formulated products are due to various manifestations of incompatibility which can be eliminated (or predicted) based on solvent's characteristics.

George Wypych

101

3.3.1 ACIDS

Value

Property

minimum

maximum

boiling temperature, C

20

250

freezing temperature, oC

−118.0

128

flash point, C

40

133

autoignition temperature, oC

330

482

1.285

1.470

0.9

1.563

o

o

refractive index specific gravity, g/cm3 vapor density (air=1)

0.70

5

vapor pressure, kPa

0.0002

413

viscosity, mPa.s

0.256

8.08

surface tension, mN/m

19.80

28.10

donor number, DN, kcal/mol

10.5

20.0

acceptor number, AN

18.5

105.0

polarity parameter, ET(30), kcal/mol

43.9

55.4

coefficient of cubic expansion, 10-4/oC

8.43

15.30

heat of combustion, MJ/kg

15.50

35.77

2.6

84.2

relative permittivity (dielectric constant) Hildebrand solubility parameter, MPa

1/2

20.46

45.06

Henry’s Law constant, atm m3 mol-1

1.13e-07

9.8e-05

evaporation rate (butyl acetate = 1)

0.02

1.34

2

20

threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm LD50 oral rat, mg/kg

6

37

250

7,000

route of entry

Skin, Eye, Inh, Ing

target organs

RspSys,Skin,Eye,Teeth,Bones

carcinogenicity

N

mutagenic properties

N to possible

theoretical oxygen demand, g/g

0.39

biodegradation probability

2.20 days-weeks

octanol/water partition coefficient

−2.38

3.94

urban ozone formation potential

0.00

0.09

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3.3 Solvent properties

3.3.2 ALCOHOLS Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC autoignition temperature, oC

minimum

maximum

64.55

259

−129

71

11

156

231

470

refractive index

1.277

1.539

specific gravity, g/cm3

0.79

1.51

vapor density (air=1)

1.10

5.50

vapor pressure, kPa

0.00

21.20

viscosity, mPa.s

0.59

41.1

surface tension, mN/m

21.99

40.0

5

44

donor number, DN, kcal/mol acceptor number, AN polarity parameter, ET(30), kcal/mol coefficient of cubic expansion, 10-4/oC

22.2

66.7

41

65.3

9

12.2

specific heat, J/K mol

180.04

241.33

heat of combustion, MJ/kg

22.66

38.83

relative permittivity (dielectric constant)

8.17

32.66

Hildebrand solubility parameter, MPa1/2

18.94

26.43

Henry’s Law constant, atm m3 mol-1

4.1e-09

3.44e+01

evaporation rate (butyl acetate = 1)

0.005

2.9

1

1,000

threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm LD50 oral rat, mg/kg

4

500

275

50,000

route of entry

Skin, Eye, Inh, Ing

target organs

RspSys,Skin,Eye,Teeth,Bones, Kdny,Lvr,CNS

carcinogenicity

N

mutagenic properties

1-butanol, 2-butanol, ethanol, 1-octanol, 1-pentanol, 1-propanol

theoretical oxygen demand, g/g

1.5

biodegradation probability

2.9 days-weeks

octanol/water partition coefficient

−1.57

2.97

urban ozone formation

0.04

0.45

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3.3.3 ALDEHYDES

Property

Value minimum

maximum

−21

253

freezing temperature, C

−123

12.4

flash point, oC

−39

102

o

boiling temperature, C o

o

autoignition temperature, C

180

424

refractive index

1.33

1.62

specific gravity, g/cm3

0.70

1.25

vapor density (air=1)

1

4.5

vapor pressure, kPa

0.00

438

viscosity, mPa.s

0.32

5.4

surface tension, mN/m

23.14

41.1

coefficient of cubic expansion, 10-4/oC

8.20

26.87

heat of combustion, MJ/kg

25.18

39.26

relative permittivity (dielectric constant)

5.00

38.00

Hildebrand solubility parameter, MPa1/2

18.06

23.93

Henry’s Law constant, atm m3 mol-1

3.36e-07

1.18e-04

evaporation rate (butyl acetate = 1)

5.53

10.33

threshold limiting value − 8h average, ppm

0.1

100

maximum concentration (15 min exp), ppm

0.3

150

LD50 oral rat, mg/kg

46

3,078

route of entry

Skin, Eye, Inh, Ing

target organs

RspSys,Skin,Eye,Lvr,Hrt

carcinogenicity

acetaldehyde, formaldehyde, furfural

mutagenic properties

acrolein, formaldehyde, furfural

theoretical oxygen demand, g/g

1.07

biodegradation probability

2.00 days-weeks

octanol/water partition coefficient

0.35

1.48

urban ozone formation

0.94

1.55

104

3.3 Solvent properties

3.3.4 ALIPHATIC HYDROCARBONS Value

Property

minimum

maximum

−11.7

285

o

boiling temperature, C o

freezing temperature, C

−189

18

flash point, oC

−104

129

autoignition temperature, oC

202

640

refractive index

1.29

1.46

specific gravity, g/cm3

0.51

0.84

vapor density (air=1)

1

5.9

vapor pressure, kPa

0.00

1976

viscosity, mPa.s

0.21

1.58

surface tension, mN/m

15

40

coefficient of cubic expansion, 10-4/oC

8.0

15.0

specific heat, J/K mol

184.22

910.0

heat of combustion, MJ/kg

4.35

49.58

relative permittivity (dielectric constant)

1.8

2.15

Kauri-butanol number

22

56

o

aniline point, C

21

165

14.11

15.34

Henry’s Law constant, atm m3 mol-1

2.59e-4

1.36e00

evaporation rate (butyl acetate = 1)

0.006

17.5

threshold limiting value − 8h average, ppm

0.1

1,000

maximum concentration (15 min exp), ppm

375

1,000

218

29,820

Hildebrand solubility parameter, MPa1/2

LD50 oral rat, mg/kg route of entry

Skin, Eye, Inh, Ing

target organs

RspSys,Skin,Eye,Teeth,Bones, Kdny,Lvr,CNS,Blood,GI,Lung

carcinogenicity

N

mutagenic properties

n-hexane

theoretical oxygen demand, g/g

3.46

biodegradation probability

3.56 days-weeks

octanol/water partition coefficient

2.3

5.98

urban ozone formation

0.11

0.13

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105

3.3.5 AMIDES Value

Property o

boiling temperature, C o

minimum

maximum

153

290

freezing temperature, C

−61

81

flash point, oC

58

155

autoignition temperature, oC

400

500

refractive index

1.425

1.576

specific gravity, g/cm3

0.905

1.160

vapor density (air=1)

1.6

6.7

vapor pressure, kPa

0.000747

133

viscosity, mPa.s

0.802

3.65

surface tension, mN/m

32.43

37.96

donor number, DN, kcal/mol

24.0

32.2

acceptor number, AN

13.6

39.8

polarity parameter, ET(30), kcal/mol

41.4

55.8

-4 o

coefficient of cubic expansion, 10 / C relative permittivity (dielectric constant) Hildebrand solubility parameter, MPa1/2

7.5

9.8

37.78

84.00

17.96

38.86

Henry’s Law constant, atm m3 mol-1

2.1e-08

5.39e-08

evaporation rate (butyl acetate = 1)

0.14

1.0

10

20

1,500

7,000

threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg route of entry

Abs, Con, Skin, Eye, Ing, Inh

target organs

Skin,Eye,Lvr

carcinogenicity

2A (acetamide), 2B (dimethylformamide, N,N-)

mutagenic properties

Y (dimethylformamide, N,N-)

theoretical oxygen demand, g/g

1.80

1.86

octanol/water partition coefficient

−1.51

2.02

106

3.3 Solvent properties

3.3.6 AMINES

Property

Value minimum

maximum

−33

372

freezing temperature, C

−115

142

flash point, oC

−37

198

o

boiling temperature, C o

o

autoignition temperature, C

210

685

refractive index

1.32

1.62

specific gravity, g/cm3

0.70

1.66

vapor density (air=1)

0.54

10.09

vapor pressure, kPa

0.00

1.013

viscosity, mPa.s

0.13

4,000

surface tension, mN/m

19.11

48.89

24

61

acceptor number, AN

1.4

39.8

polarity parameter, ET(30), kcal/mol

32.1

55.8

donor number, DN, kcal/mol

relative permittivity (dielectric constant)

2.42

37.78

Henry’s Law constant, atm m3 mol-1

1.7e-23

3.38e+01

evaporation rate (butyl acetate = 1)

0.001

3.59

0.1

100

threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm LD50 oral rat, mg/kg

6

35

100

12,760

route of entry

Abs, Con, Ing, Inh

target organs

RspSys,Skin,Eye,LS,Kdny,Lvr, Lung

carcinogenicity

p-chloroaniline, hydrazine, N-nitrosodimethylamine, o-toluidine

mutagenic properties

dimethylamine, ethylene diamine tetracetic acid, methylamine, N-methylpyrrolidone, N-nitrosomethyl amine, tetraethylene pentamine

theoretical oxygen demand, g/g

0.65

biodegradation probability

2.85 days-weeks

octanol/water partition coefficient

−1.66

1.92

urban ozone formation

0.00

0.51

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107

3.3.7 AROMATIC HYDROCARBONS Property boiling temperature, oC freezing temperature, oC flash point, oC autoignition temperature, oC refractive index specific gravity, g/cm3 vapor density (air=1) vapor pressure, kPa viscosity, mPa.s surface tension, mN/m donor number, DN, kcal/mol acceptor number, AN polarity parameter, ET(30), kcal/mol coefficient of cubic expansion, 10-4/oC specific heat, J/K mol heat of combustion, MJ/kg relative permittivity (dielectric constant) Kauri-butanol number aniline point, oC Hildebrand solubility parameter, MPa1/2 Henry’s Law constant, atm m3 mol-1 evaporation rate (butyl acetate = 1) threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm LD50 oral rat, mg/kg route of entry target organs carcinogenicity mutagenic properties theoretical oxygen demand, g/g biodegradation probability octanol/water partition coefficient urban ozone formation

Value minimum

maximum

74 288 −96 5.5 −11 144 204 550 1.43 1.61 0.71 1.02 2.8 4.8 0.00 21.3 0.58 6.3 24.3 36.8 0.1 10 6.8 8.2 32.44 63.48 8 10.7 133.0 266.0 41.03 43.5 2.04 2.6 33 112 7 85 17.77 21.68 5.19e-03 3.6e-01 0.006 5.1 0.3 100 6 150 636 6,989 Abs, Con, Ing, Inh RspSys,Skin,Eye,Bones,Kdny,Lvr,CNS,Blood,GI, Lung benzene, styrene benzene, ethylbenzene, xylene 0.92 2.53 days-weeks 2.13 4.83 0.03 1.13

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3.3 Solvent properties

3.3.8 BIODEGRADABLE SOLVENTS

Property o

boiling temperature, C o

Value minimum

maximum

174.0

290.0

freezing temperature, C

-75.0

18.1

flash point, oC

62.0

177.0

autoignition temperature, oC refractive index

395

400

1.4225

1.4527

specific gravity, g/cm3

0.835

1.261

vapor pressure, kPa

0.003

0.9997

vapor density (air=1)

1.59

3.17

viscosity, mPa.s

2.9

1,000

surface tension, mN/m

29.9

44.5

evaporation rate (butyl acetate = 1)

0.007

7.0

2,000

6,000

LD50 oral rat, mg/kg route of entry

Inh, Ing, Skin, Eye

carcinogenicity

no data available

mutagenic properties

no evidence/no data available

biodegradation probability

97% (18 days)

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109

3.3.9 BIORENEWABLE SOLVENTS Value

Property

minimum

maximum

21.7

358.9

o

boiling temperature, C o

freezing temperature, C

-140.0

98.9

flash point, oC

-11.0

158.0

autoignition temperature, oC

180

405

refractive index

1.405

1.474

specific gravity, g/cm3

0.79

1.08

vapor density (air=1)

1.6

4.5

vapor pressure, kPa

0.07198

10.13

viscosity, mPa.s

0.473

954

surface tension, mN/m

23.3

31.1

pH

7

7.9

pKa

14.4

15.9

relative permittivity (dielectric constant)

4.76

17.0

Kauri-butanol number

300

600

evaporation rate (butyl acetate = 1)

0.005

4.2

heat of combustion, MJ/kg

18.045

29.7

LD50 oral rat, mg/kg

1,750

15,670

route of entry

Inh, Skin, Eye

target organs

Lvr, Skin

carcinogenicity

N

mutagenic properties

no data

biodegradation probability octanol/water partition coefficient, log kow

63.8% (28 days) to 100% biodegradable -1.76

1.59

110

3.3 Solvent properties

3.3.10 CHLOROFLUOROCARBONS Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC

minimum

maximum

−81.4

92.8

−189.0

26.0

49

70

refractive index

1.261

1.412

specific gravity, g/cm3

1.020

1.800

vapor density (air=1)

3.03

14.00

vapor pressure, kPa

6.73

2799

viscosity, mPa.s

0.016

1.21

surface tension, mN/m

5.0

22.73

specific heat, J/K mol

117.15

184.1

2.13

2.60

relative permittivity (dielectric constant) Kauri-butanol number

32.0

500.0

Hildebrand solubility parameter, MPa1/2

11.25

17.26

Henry’s Law constant, atm m3 mol-1

3.62e-04

8.53e00

evaporation rate (butyl acetate = 1)

1.00

10.20

threshold limiting value − 8h average, ppm

100

1,000

maximum concentration (15 min exp), ppm

200

500

1,000

43,000

LD50 oral rat, mg/kg route of entry

Inh,Ing,Con

target organs

CVS,CNS,PNS,GI,RspSys,Skin,Eye,Heart,Kdny, Lvr,Lung

carcinogenicity

N

mutagenic properties

N,Y

theoretical oxygen demand, g/g

0.08

biodegradation probability

0.19 weeks

octanol/water partition coefficient

1.65

3.41

urban ozone formation

0.00

0.08

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111

3.3.11 DEEP EUTECTIC SOLVENTS Value

Property o

freezing temperature, C o

glass transition temperature, C refractive index 3

minimum

maximum

-69.3

190

-101.6

109.55

1.43

1.53

specific gravity, g/cm

1.04

2.4

viscosity, mPa.s

9.2

85,000

surface tension, mN/m

37.0

77.3

polarity parameter, ET(30), kcal/mol

57.2

58.5

ionic conductivity, mS/cm

0.017

12

octanol/water partition coefficient

0.061

0.141

112

3.3 Solvent properties

3.3.12 ESTERS Property boiling temperature, oC freezing temperature, oC flash point, oC autoignition temperature, oC refractive index specific gravity, g/cm3 vapor density (air=1) vapor pressure, kPa viscosity, mPa.s surface tension, mN/m donor number, DN, kcal/mol acceptor number, AN polarity parameter, ET(30), kcal/mol coefficient of cubic expansion, 10-4/oC specific heat, J/K mol heat of combustion, MJ/kg relative permittivity (dielectric constant) Kauri-butanol number Hildebrand solubility parameter, MPa1/2 Henry’s Law constant, atm m3 mol-1 evaporation rate (butyl acetate = 1) threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm LD50 oral rat, mg/kg route of entry target organs carcinogenicity mutagenic properties

theoretical oxygen demand, g/g biodegradation probability octanol/water partition coefficient urban ozone formation

Value minimum

maximum

32 343 −148.0 27.5 −19.0 240 252 505 1.34 1.56 0.81 1.38 2.5 9.6 0.00 64.0 0.42 32.7 23.75 41.39 11 23.7 6.7 18.3 36.7 48.6 8.76 10.3 131.8 497.4 18.5 36.35 4.75 64.9 62 1,000 16.77 22.19 9.9e-08 1.9e-02 0.001 11.8 0.2 400 2 310 500 42,000 Abs,Inh,Ing,Con CNS,GI,RspSys,Skin,Eye,Lung,Blood,Brain, Spleen 2B (ethyl acrylate), 2B (vinyl acrylate) methyl ester of butyric acid, γ-butyrolactone, dibutyl phthalate, 2-ethoxyethyl acetate, ethyl acetate, ethyl propionate, methyl propionate, n-propyl acetate 1.09 2.44 days-weeks −0.56 3.97 0.02 0.42

George Wypych

113

3.3.13 ETHERS

Property o

boiling temperature, C o

Value minimum

maximum

34.4

289

freezing temperature, C

−137

64

flash point, oC

−46

135

autoignition temperature, oC

189

618

refractive index

1.35

1.57

specific gravity, g/cm3

0.71

1.21

vapor density (air=1)

1.5

6.4

vapor pressure, kPa

0.00

174.7

viscosity, mPa.s

0.24

1.1

surface tension, mN/m

17.4

38.8

6

24

acceptor number, AN

3.3

10.8

polarity parameter, ET(30), kcal/mol

16.0

43.1

specific heat, J/K mol

120.26

251.72

heat of combustion, MJ/kg

34.69

38.07

donor number, DN, kcal/mol

relative permittivity (dielectric constant)

2.2

13.0

Hildebrand solubility parameter, MPa1/2

14.32

20.56

Henry’s Law constant, atm m3 mol-1

5.4e-10

8.32e00

evaporation rate (butyl acetate = 1)

0.004

1.88

threshold limiting value − 8h average, ppm

1

1,000

maximum concentration (15 min exp), ppm

2

500

72

30,900

LD50 oral rat, mg/kg route of entry

Abs,Inh,Ing,Con

target organs

CNS,RspSys,Skin,Eye,Lung,Blood,Kdny,Lvr

carcinogenicity

1 (bis(chloromethyl) ether, 1 (chloromethyl methyl ether), 1 (ethylene oxide), 2A (epichlorohydrin), 2B (1,4-dioxane), 2B (propylene oxide)

mutagenic properties

diethyl ether, 1,4-dioxane, ethylene oxide, propylene oxide

theoretical oxygen demand, g/g

1.07

biodegradation probability

2.95 days-weeks

octanol/water partition coefficient

−0.56

5.10

urban ozone formation

0.02

0.49

114

3.3 Solvent properties

3.3.14 FATTY ACID METHYL ESTERS Value

Property

minimum

maximum

100.0

404.0

o

boiling temperature, C o

freezing temperature, C

-49.0

41.0

flash point, oC

65.6

260.0

autoignition temperature, oC

262

363

refractive index

1.42

1.458

specific gravity, g/cm3

0.84

0.946

vapor pressure, kPa

0.005

2.666

viscosity, mPa.s

2.0

23.0

surface tension, mN/m

27.7

31.5

Kauri-butanol number

38

318

aniline point, oC

-10

-17

3e-03

9e-03

0.002

0.2

3

Henry’s Law constant, atm m mol

-1

evaporation rate (butyl acetate = 1) threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg

10

200

2,000

23,000

route of entry

Eye, Skin, Inh, Ing

target organs

Skin, Eye

carcinogenicity

N

mutagenic properties

N

biodegradation probability octanol/water partition coefficient

95% (28 days) to 100% biodegradable 2.81

8.35

George Wypych

115

3.3.15 GENERALLY RECOGNIZED AS SAFE, GRAS, SOLVENTS AND THEIR PRECURSORS Value

Property

minimum

maximum

boiling temperature, C

54.3

350.0

freezing temperature, oC

-80.0

65.0

flash point, C

-20

196.1

autoignition temperature, oC

395

513

o

o

refractive index

1.36

1.473

specific gravity, g/cm3

0.847

1.260

vapor density (air=1)

1.00

9.80

vapor pressure, kPa

0.0001

25.6

viscosity, mPa.s

0.412

945

surface tension, mN/m

24.0

37.58

donor number, DN, kcal/mol

19.0

acceptor number, AN

38.7

83.6

polarity parameter, ET(30), kcal/mol

40.9

57.7

coefficient of cubic expansion, 10-4/oC

4.64

14.1

specific heat, J/K mol

99.04

192.76

heat of combustion, MJ/kg

6.02

24.38

relative permittivity (dielectric constant)

3.10

58.0

Hildebrand solubility parameter, MPa1/2

20.52

33.10

Henry’s Law constant, atm m3 mol-1

1.67e-07

2.20e-04

evaporation rate (butyl acetate = 1)

0.01

6.93

5

100

threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm

10

LD50 oral rat, mg/kg

730

22,000

route of entry

Eye, Ing, Inh, Con, Skin, Subcutaneous

target organs

CNS,GI,Bld,RspSys,Skin,Kdny,Lvr,Eye

carcinogenicity

N

mutagenic properties

N,Y

theoretical oxygen demand, g/g

0.35

biodegradation probability

8.23 days-weeks

octanol/water partition coefficient

-1.76

3.05

urban ozone formation

0.00

0.18

116

3.3 Solvent properties

3.3.16 GLYCOL ETHERS Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC

minimum

maximum

117

265

−148

14

27

143

autoignition temperature, oC

174

406

refractive index

1.39

1.53

specific gravity, g/cm3

0.83

1.11

vapor density (air=1)

3.0

8.01

vapor pressure, kPa

0.00

1.33

viscosity, mPa.s

0.7

20.34

surface tension, mN/m

25.6

42.0

acceptor number, AN

9.0

36.1

polarity parameter, ET(30), kcal/mol

38.6

52.0

coefficient of cubic expansion, 10-4/oC

9.7

11.5

specific heat, J/K mol

103.9

451.4

heat of combustion, MJ/kg

24.3

30.54

relative permittivity (dielectric constant)

5.1

29.6

Hildebrand solubility parameter, MPa1/2

16.77

19.23

Henry’s Law constant, atm m3 mol-1

6.5e-10

7.3e-5

evaporation rate (butyl acetate = 1)

0.001

1.05

threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg

5

100

470

16,500

route of entry

Abs, Ing, Inh, Con

target organs

CNS,GI,LS,Lung,Bld,RspSys,Skin,Kdny,Lvr,Eye, Brain

carcinogenicity

N

mutagenic properties

diethylene glycol monobutyl ether, diethylene glycol dimethyl ether, 2-ethoxyethanol, ethylene glycol diethyl ether, ethylene glycol monophenyl ether, triethylene glycol dimethyl ether

theoretical oxygen demand, g/g

1.07

biodegradation probability

3.03 days-weeks

octanol/water partition coefficient

−1.57

3.12

urban ozone formation

0.27

0.58

George Wypych

117

3.3.17 HALOGENATED Property o

boiling temperature, C freezing temperature, oC flash point, oC autoignition temperature, oC refractive index specific gravity, g/cm3 vapor density (air=1) vapor pressure, kPa viscosity, mPa.s surface tension, mN/m donor number, DN, kcal/mol acceptor number, AN polarity parameter, ET(30), kcal/mol coefficient of cubic expansion, 10-4/oC specific heat, J/K mol heat of combustion, MJ/kg relative permittivity (dielectric constant) Kauri-butanol number Hildebrand solubility parameter, MPa1/2 Henry’s Law constant, atm m3 mol-1 evaporation rate (butyl acetate = 1) threshold limiting value − 8h average, ppm maximum concentration (15 min exp), ppm LD50 oral rat, mg/kg route of entry target organs carcinogenicity

mutagenic properties theoretical oxygen demand, g/g biodegradation probability octanol/water partition coefficient

Value minimum

maximum

4.0 232.0 −142.0 87.0 −50 127 260 685 1.388 1.633 0.882 2.90 1.8 8.7 0.000101 573.33 0.27 22.76 15.19 41.5 1.0 31.0 8.6 45.9 32.4 60.8 6.93 22.73 80.33 131.34 6.57 29.14 2.20 22.1 104.0 136.0 14.47 22.30 3.31e-07 7.8e-02 1.0 27.5 0.5 1,000 2 250 71 13,000 Abs, Con, Inh, Skin, Eye, Ing Eye,RspSys,Skin,Lvr,Hrt,Kdny,Blood,Heart,CNS 1 (bis(chloromethyl)ether), 2A (1,2-dichloromethane), 2A (perchloroethylene), 2B (benzotrichloride), 2B (benzyl chloride), 2B (carbon tetrachloride), 2B (p-chloroaniline), 2B (chloroform), 2B (m- & o-chlorophenol), 2B (1,4-dichlorobenzene), 3B (benzal chloride) benzal chloride, bromomethane, carbon tetrachloride, chloroform, chloromethane, dichloromethane 0.21 2.06 days-years −0.47 3.79

118

3.3 Solvent properties

3.3.18 HETEROCYCLIC Value

Property

minimum

maximum

10.4

290.0

freezing temperature, C

−130

44.10

flash point, oC

−36.0

174.0

o

boiling temperature, C o

o

180

537

refractive index

autoignition temperature, C

1.3597

1.583

specific gravity, g/cm3

0.816

1.18

vapor density (air=1)

1.52

4.50

vapor pressure, kPa

0.000027

174.666

viscosity, mPa.s

0.3

81.5

surface tension, mN/m

23.5

40.7

donor number, DN, kcal/mol

6.0

51.0

acceptor number, AN

3.3

17.5

polarity parameter, ET(30), kcal/mol

35.5

51.0

-4 o

coefficient of cubic expansion, 10 / C

6.71

21.8

specific heat, J/K mol

123.89

166.1

heat of combustion, MJ/kg

13.45

39.02

relative permittivity (dielectric constant)

2.21

39.0

Hildebrand solubility parameter, MPa

1/2

17.47

29.56

Henry’s Law constant, atm m3 mol-1

1.56e-08

5.38e-03

evaporation rate (butyl acetate = 1)

2.42

5.7

threshold limiting value − 8h average, ppm

0.1

200

maximum concentration (15 min exp), ppm

5

250

LD50 oral rat, mg/kg

72

14,430

route of entry

Skin, Eye, Inh, Ing, Subcutaneous, Intravenous

target organs

CNS,Skin,RspSys,Eye,Lvr,Kdny,Blood

carcinogenicity

2A (epichlorohydrin), 2B (1,4-dioxane), 2B (furan)

mutagenic properties

γ-butyrolactone, 1,4-dioxane, ethylene oxide, Nmethylpyrrolidone

theoretical oxygen demand, g/g

1.05

biodegradation probability

2.75 days-weeks

octanol/water partition coefficient

−1.03

2.16

urban ozone formation

0.00

0.49

George Wypych

119

3.3.19 HYDROFLUOROCARBONS Value

Property

minimum

maximum

−26.0

178.0

freezing temperature, C

−103.0

−12.4

flash point, oC

−18.0

none

o

boiling temperature, C o

o

412

770

refractive index

autoignition temperature, C

1.294

1.482

specific gravity, g/cm3

0.93

1.69

vapor density (air=1)

3.5

10.0

vapor pressure, kPa

0.1227

666

viscosity, mPa.s

0.202

0.60

surface tension, mN/m

14.6

19.3

relative permittivity (dielectric constant)

3.3

8.07

Kauri-butanol number

56

79

threshold limiting value − 8h average, ppm

100

200

240

25,000

maximum concentration (15 min exp), ppm

250

LD50 oral rat, mg/kg route of entry

Inh, Ing, Con, Eye, Skin

target organs

RspSys,CNS,CVS,GI,Eye,Skin,Lvr,Kdny,Blood

carcinogenicity

N

mutagenic properties

N

octanol/water partition coefficient

0.63

2.30

urban ozone formation

0.00

0.03

120

3.3 Solvent properties

3.3.20 HYDROFLUOROETHERS Value

Property o

boiling temperature, C o

minimum

maximum

41.0

98.0

freezing temperature, C

-138

-29

flash point, oC

none

none

autoignition temperature, oC

375

450

specific gravity, g/cm3

1.27

1.6

vapor density (air=1)

4.7

9.1

vapor pressure, kPa

5.58

55.01

viscosity, mPa.s

0.4

5.0

surface tension, mN/m

13.6

18.0

Kauri-butanol number

33

58

evaporation rate (butyl acetate = 1)

33

70

threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg

100

750

1,235

7,900

route of entry

Skin, Eye, Inh

target organs

CNS

biodegradation probability octanol/water partition coefficient

none to 22 wt% (28 days) 3.9

4.2

George Wypych

121

3.3.21 IONIC LIQUIDS Value

Property o

freezing temperature, C o

glass transition temperature, C

minimum

maximum

-140

113

-87

flash point, oC

-37 200

refractive index

1.41

1.49

specific gravity, g/cm3

0.882

1.524

viscosity, mPa.s

1.7

1,500

surface tension, mN/m

29.8

44.9

polarity, ET(30), kcal/mol

51

61.6

17.9

31.6

decomposition temperature, C

240

480

conductivity, mS/cm

1.7

233

-0.18

3.55

Hildebrand solubility parameter, MPa0.5 o

acute toxicity to Vibrio fischeri, logEC50, μM route of entry

Ing, Skin, Eye

carcinogenicity

N

122

3.3 Solvent properties

3.3.22 KETONES Value

Property o

boiling temperature, C o

minimum

maximum

56.1

306

freezing temperature, C

−92

28

flash point, oC

−18

143

autoignition temperature, oC

393

620

refractive index

1.35

1.55

specific gravity, g/cm3

0.74

1.19

vapor density (air=1)

2

4.9

vapor pressure, kPa

0.00

30.8

viscosity, mPa.s

0.30

2.63

surface tension, mN/m

22.68

35.05

11

18

polarity parameter, ET(30), kcal/mol

36.3

42.2

coefficient of cubic expansion, 10-4/oC

9.7

13.0

specific heat, J/K mol

124.8

243.4

heat of combustion, MJ/kg

26.82

40.11

relative permittivity (dielectric constant)

11.98

20.56

Hildebrand solubility parameter, MPa1/2

13.42

22.58

4.4e-08

2.7e-07

0.02

6.6

donor number, DN, kcal/mol

3

Henry’s Law constant, atm m mol

-1

evaporation rate (butyl acetate = 1) threshold limiting value − 8h average, ppm

5

750

maximum concentration (15 min exp), ppm

75

1,000

148

5,800

LD50 oral rat, mg/kg route of entry

Abs, Con, Ing, Inh

target organs

CNS,Eye,Kdny,Lvr,Lung,PNS,ResSys,Skin

carcinogenicity

N

mutagenic properties

diacetone alcohol, methyl isopropyl ketone

theoretical oxygen demand, g/g

1.67

biodegradation probability

2.93 days-weeks

octanol/water partition coefficient

−1.34

2.65

urban ozone formation

0.01

0.65

George Wypych

123

3.3.23 MISCELLANEOUS Value

Property o

boiling temperature, C o

minimum

maximum

31.6

259.0

freezing temperature, C

−122.0

5.0

flash point, oC

−28.0

149.0

autoignition temperature, oC

234

570

refractive index

1.333

1.658

specific gravity, g/cm3

0.770

1.688

vapor density (air=1)

2.1

6.20

vapor pressure, kPa

0.0007

66.5

viscosity, mPa.s

0.33

13.0

surface tension, mN/m

25.0

36.4

donor number, DN, kcal/mol

11.7

38.8

acceptor number, AN

9.8

54.8

polarity parameter, ET(30), kcal/mol

39.5

63.1

coefficient of cubic expansion, 10-4/oC

9.87

12.5

relative permittivity (dielectric constant)

3.0

81.0

Hildebrand solubility parameter, MPa

1/2

18.76

47.05

8.08e-10

2.3e-02

evaporation rate (butyl acetate = 1)

0.01

0.9

threshold limiting value − 8h average, ppm

0.005

1

Henry’s Law constant, atm m3 mol-1

maximum concentration (15 min exp), ppm

0.5

20

LD50 oral rat, mg/kg

380

386,000

route of entry

Inh, Ing, Con, Skin, Eye

target organs

RspSys,Bld,Lung,Spleen,Eye,Skin,CNS,Stmch, Lvr,Kdny,GI

carcinogenicity

N

mutagenic properties

hexamethyl thiophosphoramide

theoretical oxygen demand, g/g

1.05

biodegradation probability

1.71 days-weeks

octanol/water partition coefficient

−1.38

3.70

urban ozone formation

0.02

0.08

124

3.3 Solvent properties

3.3.24 NITRILES Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC autoignition temperature, oC

minimum

maximum

77.0

234.0

−112.0

49.6

−1.0

195.0

414

590

refractive index

1.344

1.55

specific gravity, g/cm3

0.782

1.246

vapor density (air=1)

1.4

4.2

vapor pressure, kPa

0.0123

11.0

viscosity, mPa.s

0.34

1.96

surface tension, mN/m

24.4

43.9

donor number, DN, kcal/mol

2.7

16.6

acceptor number, AN

14.8

20.5

polarity parameter, ET(30), kcal/mol

41.2

46.7

coefficient of cubic expansion, 10-4/oC

8.14

14.2

relative permittivity (dielectric constant)

23.24

37.5

Hildebrand solubility parameter, MPa

1/2

19.43

25.24

Henry’s Law constant, atm m3 mol-1

9.8e-06

1.2e-04

evaporation rate (butyl acetate = 1)

0.71

2.3

threshold limiting value − 8h average, ppm

1

100

maximum concentration (15 min exp), ppm

10

60

LD50 oral rat, mg/kg

21

5,000

route of entry

Inh, Ing, Skin, Eye, Con

target organs

CNS,CVS,Blood,Lvr,NS,RspSys,Skin,Eye, Tyroid,Heart

carcinogenicity

2B (acrylonitrile), 2B (nitrobenzene), 2B (2-nitropropane)

mutagenic properties

acrylonitrile

theoretical oxygen demand, g/g

1.95

3.17

octanol/water partition coefficient

-0.94

2.09

George Wypych

125

3.3.25 PERFLUOROCARBONS Value

Property o

boiling temperature, C o

minimum

maximum

29.0

253.0

−127

freezing temperature, C flash point, oC

−50 not applicable

autoignition temperature, oC

not applicable

refractive index 3

1.151

1.303

specific gravity, g/cm

1.22

2.00

vapor density (air=1)

3.03

33.4

vapor pressure, kPa

0.00266

81.1

0.17

5.1

surface tension, mN/m

9.0

18.0

coefficient of cubic expansion, 10-4/oC

10.0

15.6

112.97

857.72

1.0

7.0

viscosity, mPa.s

specific heat, J/K mol relative permittivity (dielectric constant) Hildebrand solubility parameter, MPa

1/2

Henry’s Law constant, atm m3 mol-1 LD50 oral rat, mg/kg

11.88

13.83

5.15e00

1.84e+04

5,000

7,900

route of entry

Con, Inh, Ing, Eye

target organs

Eye,Skin,RspSys,CVS,CNS,Lvr,Kdny

carcinogenicity

N

mutagenic properties

N

biodegradation probability

days-weeks

octanol/water partition coefficient

1.18

urban ozone formation

0.00

7.80

126

3.3 Solvent properties

3.3.26 POLYHYDRIC ALCOHOLS Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC

minimum

maximum

171

327.3

−114

60

85

274

autoignition temperature, oC

224

490

refractive index

1.43

1.48

specific gravity, g/cm3

0.92

1.22

vapor density (air=1)

2.14

6.7

vapor pressure, kPa

0.00

0.32

21

114.6

33.1

48.49

19

20

viscosity, mPa.s surface tension, mN/m donor number, DN, kcal/mol acceptor number, AN

34.5

46.6

polarity parameter, ET(30), kcal/mol

51.8

56.3

specific heat, J/K mol

150.9

294.0

heat of combustion, MJ/kg

19.16

29.86

relative permittivity (dielectric constant)

7.7

35.0

Hildebrand solubility parameter, MPa1/2

21.89

32.4

Henry’s Law constant, atm m3 mol-1

4.91e-13

2.3e-07

evaporation rate (butyl acetate = 1)

0.001

0.01

threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg

1

25

105

50,000

route of entry

Abs, Con, Ing, Inh

target organs

Blood,Eye,GI,Kdny,LS,Lvr,Lung,ResSys,Skin, Spleen

carcinogenicity

N

mutagenic properties

tetraethylene glycol, triethylene glycol, trimethylene glycol

theoretical oxygen demand, g/g

1.07

biodegradation probability

1.68 days-weeks

octanol/water partition coefficient

−2.02

−0.92

urban ozone formation

0.16

0.47

George Wypych

127

3.3.27 SILOXANES Value

Property o

boiling temperature, C o

minimum

maximum

26.0

210.0

freezing temperature, C

-99.0

-40.0

flash point, oC

60.6

392.0

autoignition temperature, oC

392

450

refractive index

1.358

1.408

specific gravity, g/cm3

0.646

0.98

vapor pressure, kPa

0.01

75.0

viscosity, mPa.s

0.236

4,000

surface tension, mN/m

20.0

21.0

polarity parameter, ET(30), kcal/mol

30.7

coefficient of cubic expansion, 10-4/oC

18.4

relative permittivity (dielectric constant)

1.92

Hildebrand solubility parameter, MPa1/2

12.37

Henry’s Law constant, atm m3 mol-1

3.06e-01

4.25

evaporation rate (butyl acetate = 1)

0.04

1.0

threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg

10

10

2,000

5,000

route of entry

Skin, Eye, Ing, Inh

target organs

Lvr

carcinogenicity

N

octanol/water partition coefficient

3.24

5.2

128

3.3 Solvent properties

3.3.28 SULFOXIDES Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC

minimum

maximum

158

285

−10.0

32.0

53

166

refractive index

1.415

1.483

specific gravity, g/cm3

0.832

1.426

vapor density (air=1)

2.69

5.6

vapor pressure, kPa

0.0008266

0.43

viscosity, mPa.s

1.991

50.9

surface tension, mN/m

35.5

42.98

donor number, DN, kcal/mol

14.8

31.0

acceptor number, AN

19.2

19.3

polarity parameter, ET(30), kcal/mol

38.4

45.1

153.18

179.91

relative permittivity (dielectric constant)

15.9

46.45

Hildebrand solubility parameter, MPa1/2

18.65

25.73

4.96e-08

4.85e-06

0.01

0.03

1,941

14,500

specific heat, J/K mol

3

Henry’s Law constant, atm m mol

-1

evaporation rate (butyl acetate = 1) LD50 oral rat, mg/kg route of entry

Eye, Skin, Ing, Inh, Con

target organs

Lvr,Skin,CNS,GI,Lung

carcinogenicity

N

mutagenic properties

dimethyl sulfoxide, sulfolane

theoretical oxygen demand, g/g

1.73

biodegradation probability

1.84 days-weeks

octanol/water partition coefficient

−1.35

1.84

urban ozone formation

0.07

0.23

George Wypych

129

3.3.29 SUPERCRITICAL FLUID (CARBON DIOXIDE) Property

Value

o

freezing temperature, C

-78.5

specific gravity, g/cm3

1.56

vapor density (air=1)

1.53

vapor pressure, kPa

5825 (21oC)

surface tension, mN/m

16.2

relative permittivity (dielectric constant) 3

Henry’s Law constant, atm m mol

1.60

-1

2.18e-02

threshold limiting value − 8h average, ppm

5,000-10,000

maximum concentration (15 min exp), ppm

30,000

route of entry

Skin, Eye, Inh

carcinogenicity

N

mutagenic properties

N

theoretical oxygen demand, g/g

0.00

octanol/water partition coefficient

0.83

urban ozone formation

0.00

130

3.3 Solvent properties

3.3.30 TERPENES Value

Property o

boiling temperature, C o

freezing temperature, C flash point, oC o

autoignition temperature, C

minimum

maximum

101.0

230.0

-96.7

-55.0

29

149

150

500

refractive index

1.4642

1.482

specific gravity, g/cm3

0.838

0.984

vapor density (air=1)

1.0

4.8

vapor pressure, kPa

0.0226

0.69

viscosity, mPa.s

0.8

1.52

surface tension, mN/m

26.0

26.87

coefficient of cubic expansion, 10-4/oC

7.02

9.00

heat of combustion, MJ/kg

40.96

46.61

relative permittivity (dielectric constant)

2.3

2.7

Kauri-butanol number

67.0

15.0

evaporation rate (butyl acetate = 1)

0.2

1.0

threshold limiting value − 8h average, ppm LD50 oral rat, mg/kg

20

100

2,760

5,000

route of entry

Inh, Con, Ing, Skin

target organs

RspSys,Skin,Eye,GI,CNS,CVS,Kdny

carcinogenicity

N

mutagenic properties

N

theoretical oxygen demand, g/g

2.35

biodegradation probability

3.29 days-weeks

octanol/water partition coefficient

2.97

4.83

urban ozone formation

0.51

0.95

George Wypych

131

3.3.31 COMPARATIVE ANALYSIS OF ALL SOLVENTS

Property o

boiling temperature, C o

Value minimum

maximum

chlorofluorocarbon

fatty acid methyl ester

freezing temperature, C

aliphatic hydrocarbon

deep eutectic fluid

flash point, oC

aliphatic hydrocarbon

hydrofluorocarbon, perfluorocarbon

terpene

perfluorocarbon

perfluorocarbon

miscellaneous

autoignition temperature, oC refractive index 3

specific gravity, g/cm

aliphatic hydrocarbon

halogenated

vapor density (air=1)

amine

perfluorocarbon

vapor pressure, kPa viscosity, mPa.s surface tension, mN/m donor number, DN, kcal/mol

heterocyclic

carbon dioxide

chlorofluorocarbon

amine, siloxane

chlorofluorocarbon

amine

aromatic hydrocarbon

amine

acceptor number, AN

amine

acid

polarity parameter, ET(30), kcal/mol

ether

alcohol

coefficient of cubic expansion, 10-4/oC specific heat, J/K mol heat of combustion, MJ/kg relative permittivity (dielectric constant)

GRAS

aldehyde

halogenated

aliphatic hydrocarbon

aliphatic hydrocarbon

aliphatic hydrocarbon

perfluorocarbon

acid

Kauri-butanol number

aliphatic hydrocarbon

ester

aniline point, oC

fatty acid methyl ester

aliphatic hydrocarbon

Hildebrand solubility parameter, MPa1/2

chlorofluorocarbon

miscellaneous

Henry’s Law constant, atm m3 mol-1

amine

perfluorocarbon

evaporation rate (butyl acetate = 1)

amine, ester, glycol ester, polyhydric alcohol

hydrofluoroether

threshold limiting value − 8h average, ppm

miscellaneous

carbon dioxide

maximum concentration (15 min exp), ppm

aldehyde

carbon dioxide

nitrile

miscellaneous

LD50 oral rat, mg/kg route of entry

Abs, Con, Skin, Eye, Ing, Inh, Subcutaneous, Intravenous

target organs

Blood,Eye,GI,Kdny,LS,Lvr,Hrt,Lung,ResSys,Skin, Theeth,Bones,Spleen,CNS,CVS,PNS,Brain,Stmch, Tyroid

carcinogenicity

most (none)

halogenated > ethers > aldehydes

132

3.3 Solvent properties

Property mutagenic properties

theoretical oxygen demand, g/g biodegradation probability octanol/water partition coefficient urban ozone formation

Value minimum

maximum

esters > alcohols, amines, halogenated > glycol ethers, heterocyclic > aldehydes, aromatic hydrocarbons, polyhydric alcohols carbon dioxide

aliphatic hydrocarbon

hydrofluoroethers

biodegradable

acid

fatty acid methyl ester

0.00 (most)

aldehydes

The comparative chart allocates for each group the highest and the lowest position in relation to their respective values of particular parameters. The chart shows that the fact of having many good solvent properties does not warrant that solvent is suitable for use. For example, CFCs have many characteristics of good solvents but they are still eliminated from use because they cause ozone depletion and are considered to be a reason for global warming. On the other hand, esters do not appear on this chart frequently but they are very common solvents. The chart also shows that solvents offer a very broad choice of properties, which can be selected to satisfy any practical application. It is quite evident that “green solvents” are not well studied and require a substantial amount of work to confirm their properties and suitability for replacement.

4

General Principles Governing Dissolution of Materials in Solvents 4.1 SIMPLE SOLVENT CHARACTERISTICS Valery Yu. Senichev, Vasiliy V. Tereshatov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Polymer dissolution is a necessary step in many polymer processing methods, such as blending, separation, coating, casting, etc. The developments in the physical chemistry of non-electrolyte solutions relate the capabilities of solvents to dissolve materials to their physical properties. The relationships were developed within the framework of the concept of solubility parameters. 4.1.1 SOLVENT POWER A selection of a proper solvent(s) for a given polymer or task is a typical problem in polymer engineering. Selection procedure calls for solvent and polymer to form a thermodynamically stable mixture within a certain range of concentrations and temperatures. Such choice is facilitated by the use of numerical criterion known as a solvent power. Solvent power might be taken from the thermodynamic treatment (for example, a change of Gibbs' free energy or chemical potentials of mixing the polymer with solvent) but these criteria depend not only on solvent properties but also on polymer structure and its concentration. Various approaches were proposed to estimate the solvent power. Kauri-butanol value, KB, is used for evaluation of dissolving ability of hydrocarbon solvents. It is obtained by titration of a standard Kauri resin solution (20 wt% in 1-butanol) with solvent until a cloud point is reached (for example, when it becomes impossible to read a text through the solution). The amount of solvent used for titration is taken as KB value. The relationship between KB and solubility parameter, δ, fits the following empirical dependence:1 δ = 12.9 + 0.06KB

[4.1.1]

134

4.1 Simple solvent characteristics

The KB value is the primary measure of aromaticity of solvents. Using KB value, it is possible to arrange solvents in sequence: aliphatic hydrocarbons < naphthenic hydrocarbons < aromatic hydrocarbons. Dilution ratio, DR, is used to express the tolerance of solvents to diluents, most frequently, toluene. DR is the volume of a solvent added to a given solution that causes precipitation of the dissolved resin. This ratio can characterize the compatibility of a diluent with a resin solution in a solvent of the first kind. When compatibility is high, more diluent can be added. Only a multi-parameter approach provides a satisfactory correlation with solubility parameters.2-3 DR depends on polymer concentration. With polymer concentration increasing, DR increases as well. Temperature influences DR in a similar manner. Determination of DR must be performed under standard conditions. DR can be related to the solubility parameters but such correlation depends on concentration. Aniline point, AP, is a temperature of a phase separation of aniline in a given solvent (the volume ratio of aniline to solvent = 1:1) in the temperature decreasing mode. AP is a critical temperature of the aniline-solvent system. AP can be related to KB using the following equations: At KB < 50 5 KB = 99.6 – 0.806ρ – 0.177AP +  358 – --- T b  9 

[4.1.2]

At KB>50 5 KB = 177.7 – 10.6ρ – 0.249AP + 0.10  358 – --- T b  9 

[4.1.3]

where: Tb

a solvent boiling point.

AP depends on the number of carbon atoms in the hydrocarbon molecule. AP is useful for describing complex aromatic solvents. The solvent power can also be presented as a sum of factors that promote solubility or decrease it:4 S=H+B−A−C−D

[4.1.4]

where: H B A C D

a factor characterizing the presence of active sites of opposite nature in solvent and polymer that can lead to a formation of hydrogen bond between polymer and solvent a factor related to the difference in sizes of solute and solvent molecules a factor characterizing solute “melting” a factor of the self-association between solvent molecules a factor characterizing the change of nonspecific cohesion forces in the course of transfer of the polymer molecule into solution.

The equations for calculation of the above-listed factors are as follows: Vm B = ( a + b ) ------- ( 1 – ϕ p ) Vs

[4.1.5]

Valery Yu. Senichev, Vasiliy V. Tereshatov

135

Vm - ( δ' – δ' s ) 2 ( 1 – ϕ p ) 2 D = ------RT p

[4.1.6]

K ( 1 – ϕp ) H = ln 1 + ----------------------Vs

[4.1.7]

1 + ( K pp ⁄ V m ) C = ln ---------------------------------------1 + ( K pp ϕ p ⁄ V m )

[4.1.8]

where: a b Vm Vs ϕp δp, δs K Kpp

constant depending on the choice of the equation for the entropy of mixing. Usually it equals 0.5 constant depending on the structure of solvent. b = 1 for unstructured solvents, b = −1 for solvents with single H-bond (e.g., alcohols) and b = −2 for solvents with double H-bonds, such as water. the molar volume of a repeating segment the molar volume of solvent the volume fraction of polymer modified solubility parameters without regard to H-bonds. the stability constant of the corresponding solvent-polymer hydrogen bond the constant of the self-association of polymer segments

Some polymers such as polyethylmethacrylate, polyisobutylmethacrylate, and polymethylmethacrylate were studied according to Huyskens-Haulait-Pirson approach. The main advantage of this approach is that it accounts for entropy factors and other essential parameters affecting solubility. The disadvantages are more numerous, such as lack of physical meaning of some parameters, a great number of variables, and insufficient coordination between factors influencing solubility that have reduced this approach to an approximate empirical scheme. 4.1.2 ONE-DIMENSIONAL SOLUBILITY PARAMETER APPROACH The thermodynamic affinity of solution components is important for quantitative estimation of mutual solubility. The concept of solubility parameters is based on enthalpy of the interaction between solvent and polymer. The solubility parameter is the square root of the cohesive energy density, CED: δ = ( CED ) where:

ΔEi Vi

1⁄2

ΔE =  ---------i  Vi 

1⁄2

[4.1.9]

cohesive energy molar volume

The solubility parameters are measured in (MJ/m3)1/2 = (MPa)1/2 or (cal/cm3)1/2; 1 (MJ/m3)1/2 = 2.054 (cal/cm3)1/2. The cohesive energy equals in magnitude and it is opposite in sign to the potential energy of a volume unit of liquid. The molar cohesive energy is the energy associated with all molecular interactions in one mole of the material, i.e., it is the energy of a liquid relative to its ideal vapor at the same temperature (see Chapter 5).

136

4.1 Simple solvent characteristics

The δ is a parameter of the intermolecular interaction of an individual liquid. The aim of many studies was to find a relationship between the energy of mixing of liquids and their δ. The first attempt was made by Hildebrand and Scatchard5,6 who proposed the following equation: ΔU

m

ΔE 1 = ( x 1 V 1 + x 2 V 2 )  ----------  V1 

1⁄2

ΔE 2 1 ⁄ 2 2 –  ---------- ϕ1 ϕ2 =  V2 

= ( x 1 V 1 + x 2 V 2 ) ( δ 1 – δ 2 )ϕ 1 ϕ 2 where:

ΔUm x1,x2 V1, V2 ϕ 1, ϕ 2

[4.1.10]

internal energy of mixing, that is a residual between energies of a solution and components, molar fractions of components molar volumes of components volume fractions of components

The Hildebrand-Scatchard equation became the basis of the Hildebrand theory of regular solutions.5 They interpreted a regular solution as a solution formed due to the ideal entropy of mixing and the change of an internal energy. They assumed that lack of volume change makes an enthalpy or heat of mixing equated with the right members of the equation. The equation permits calculation of heat of mixing of two liquids. It is evident from the equation that these heats can only be positive. Because of the equality of components, ΔHm = 0. The free energy of mixing of solution can be calculated from the following equation: ΔG

m

ΔE 1 ⁄ 2  ΔE 2 1 ⁄ 2 2 = ( x 1 V 1 + x 2 V 2 )  ---------1- –  ---------- ϕ 1 ϕ 2 – TΔS id = V1 V2 2

= V ( δ 1 – δ 2 ) ϕ 1 ϕ 2 – TΔS

[4.1.11]

The change of entropy, ΔSid, is calculated from the Gibbs equation of mixing of ideal gases. The calculated values are always positive. ΔS id = – R ( x 1 ln x 1 + x 2 ln x 2 )

[4.1.12]

where: R

gas constant

Considering the signs of the parameters ΔSid and ΔHm, the ideal entropy of mixing promotes a negative value of ΔGm, i.e., the dissolution and the value of ΔHm reduces the ΔGm value. It is pertinent that the most negative ΔGm value is when ΔHm = 0, i.e., when δ of components are equal. With these general principles in mind, the components having solubility parameters close to each other have the best mutual solubility. The theory of regular solutions has essential assumptions and restrictions.7 The Eq. [4.1.10] is deduced under the assumption of the central role of dispersion forces of interaction between components of the solution that is correct only for the dispersion forces. Only in this case, it is possible to accept that the energy of contacts between heterogeneous molecules is a geometric mean value of energy of contacts between homogeneous molecules:

Valery Yu. Senichev, Vasiliy V. Tereshatov

*

ε 12 = where:

*

137

*

ε 11 ε 22

*

ε ii

[4.1.13]

the potential energy of a pair of molecules

This assumption is not justified in the presence of the dipole-dipole interaction and other more specific interactions. Therefore, the theory of regular solutions poorly suits description of the behavior of solutions of polar substances. Inherent in this analysis is the assumption of molecular separation related to molecular diameters which neglects polar or specific interactions. The theory also neglects volume changes on dissolution. This leads to a disparity (sometimes very large) between internal energy of mixing used in the theory and the constant pressure enthalpy measured experimentally. The correlation between these values is given by the equation: m

m

m

( ΔH ) p = ( ΔU ) v + T ( ∂p ⁄ ∂T ) v ( ΔV ) p where:

( ∂p ⁄ ∂T ) v

[4.1.14]

the thermal factor of pressure which has a value of the order 10-14 atm/degree for solutions and liquids.

Therefore, even at small changes of volume, the second term remains very large and brings a substantial contribution to the value of (ΔHm)p. For example, for a system benzene (0.5 mol) − cyclohexane (0.5 mol): ΔV

m

3

m

m

= 0.65 cm , ( ΔH ) p = 182 cal, (ΔU ) v = 131 cal

The theory also assumes that the ideal entropy is possible for systems when m ΔH ≠ 0 . But the change of energy of interactions occurs in the course of dissolution that determines the inevitable change of entropy of molecules. It is assumed that the interactive forces are additive and that the interactions between a pair of molecules are not influenced by the presence of other molecules. Certainly, such an assumption is simplistic, but at the same time, it has allowed us to estimate solubility parameters using group contributions or molar attractive constants (see Subchapter 5.3). The solubility parameter δ is relative to the cohesion energy and it is an effective characteristic of intermolecular interactions. It varies from a magnitude of 12 (MJ/m3)1/2 for nonpolar substances up to 23 (MJ/m3)1/2 for water. Knowing δ of solvent and solute, we can eliminate solvents in which particular polymer cannot be dissolved. For example, polyisobutylene for which δ is in the range from 14 to 16 (MJ/m3)1/2 will not be dissolved in solvents with δ = 20-24 (MJ/m3)1/2. The polar polymer with δ = 18 (MJ/m3)1/2 will not be dissolved in solvents with δ = 14 or δ = 26 (MJ/m3)1/2. These are important data because they help to narrow down a group of solvents potentially suitable for a given polymer. However, the opposite evaluation is not always valid because polymers and solvents with the identical solubility parameters are not always compatible. This limitation comes from the integral character of the solubility parameter. The solubility depends on the presence of functional groups in molecules of solution components which are capable to interact with each other and this model does not address such interactions. The latter

138

4.1 Simple solvent characteristics

statement has become a premise for the development of the multi-dimensional approaches to solubility that will be the subject of the following subchapter. The values of solubility parameters are included in Table 4.1.1. Table 4.1.1 Solubility parameters and their components (according Hansen’s approach) for different solvents Solvent

V1, kmol/m3

δ, (MJ/m3)1/2

δd, (MJ/m3)1/2

δp, (MJ/m3)1/2

δh, (MJ/m3)1/2

14.1

0

0

Alkanes n-Butane

101.4

14.1

n-Pentane

116.2

14.3

14.3

0

0

n-Hexane

131.6

14.8

14.8

0

0

n-Hexane

147.4

15.1

15.1

0

0

n-Octane

163.5

14.0

14.0

0

0

n-Nonane

178.3

15.4

15.4

0

0

n-Decane

195.9

15.8

15.8

0

0

n-Dodecane

228.5

16.0

16.0

0

0

Cyclohexane

108.7

16.7

16.7

0

0

Methylcyclohexane

128.3

16.0

16.0

0

0.5

Aromatic hydrocarbons Benzene

89.4

18.7

18.4

1.0

2.9

Toluene

106.8

18.2

18.0

1.4

2.0

Naphthalene

111.5

20.3

19.2

2.0

5.9

Styrene

115.6

19.0

17.8

1.0

3.1

o-Xylene

121.2

18.4

17.8

1.0

3.1

Ethylbenzene

123.1

18.0

17.8

0.6

1.4

Mesitylene

139.8

18.0

18.0

0

0.6

Halo hydrocarbons Chloromethane

55.4

19.8

15.3

6.1

3.9

Dichloromethane

63.9

20.3

18.2

6.3

7.8

Trichloromethane

80.7

18.8

17.6

3.0

4.2

n-Propyl chloride

88.1

17.4

16.0

7.8

2.0

1,1-Dichloroethene

79.0

18.6

17.0

6.8

4.5

1-Chlorobutane

104.5

17.2

16.2

5.5

2.0

1,2-Dichloroethane

79.4

20.0

19.0

7.4

4.1

Carbon tetrachloride

97.1

17.6

17.6

0

0

Perchloroethylene

101.1

19.0

19.0 18.8

6.5 0

2.9 1.4

Valery Yu. Senichev, Vasiliy V. Tereshatov

139

Table 4.1.1 Solubility parameters and their components (according Hansen’s approach) for different solvents Solvent

V1, kmol/m3

δ, (MJ/m3)1/2

δd, (MJ/m3)1/2

δp, (MJ/m3)1/2

δh, (MJ/m3)1/2

1,1,2,2-Tetrachloroethane

105.2

19.8

18.8

5.1

9.4 5.3

Chloro-difluoromethane (Freon 21)

72.9

17.0

12.3

6.3

5.7

1,1,2-Trichloro-trifluoroethane (Freon 113)

119.2

14.8

14.5

1.6

0

Dichloro-difluoromethane (Freon 12)

92.3

12.2

12.2

2.0

0

Chlorobenzene

102.1

19.5

18.9

4.3

2.0

o-Dichlorobenzene

112.8

20.4

19.1

6.3

3.3

Bromoethane

76.9

19.6

15.8

3.1

5.7

Bromobenzene

105.3

20.3

20.5 18.9

5.5 4.5

4.1 5.1

Ethers Epichlorohydrin

72.5

18.5

17.8

1.8

5.3

Tetrahydrofuran

79.9

22.5

19.0

10.2

3.7

1,4-Dioxane

81.7

18.5

16.8

5.7

8.0

Diethyl ether

85.7

20.5

19.0

1.8

7.4

Diisopropyl ether

104.8

15.6

14.4

2.9

5.1

Ketones Acetone

74.0

19.9

15.5

10.4

6.9

Methyl ethyl ketone

90.1

18.9

15.9

9.0 8.4

5.1

Cyclohexanone

104.0

18.8

16.3

7.1

6.1

Diethyl ketone

106.4

18.1

15.8

7.6

4.7

Mesityl oxide

115.6

16.7

15.9 17.6

3.7

4.1

Acetophenone

117.4

19.8

16.5

8.2

7.3

Methyl isobutyl ketone

125.8

17.5

15.3

6.1

4.1

Methyl isoamyl ketone

142.8

17.4

15.9

5.7

4.1

Isophorone

150.5

18.6

16.6

8.2

7.4

Diisobutyl ketone

177.1

16.0

16.0

3.7

4.1

Acetaldehyde

57.1

21.1

14.7

8.0

11.3

Furfural

83.2

22.9

18.6

14.9

5.1

Aldehydes

140

4.1 Simple solvent characteristics

Table 4.1.1 Solubility parameters and their components (according Hansen’s approach) for different solvents V1, kmol/m3

δ, (MJ/m3)1/2

δd, (MJ/m3)1/2

δp, (MJ/m3)1/2

δh, (MJ/m3)1/2

n-Butyraldehyde

88.5

18.4

14.7 18.7

5.3 8.6

7.0

Benzaldehyde

101.5

19.2

19.4

7.4

5.3

Ethylene carbonate

66.0

29.6

19.4

21.7

Solvent

Esters 30.1

Methyl acetate

79.7

19.6

15.5

7.2

7.6

Ethyl formate

80.2

19.6

15.5

8.4

8.4

Propylene-1,2-carbonate

85.0

27.2

20.0

18.0

4.1

n-Propyl formate

97.2

19.5

15.0

5.3

11.2

Propyl acetate

115.1

17.8

15.5

4.5

7.6

Ethyl acetate

98.5

18.6

15.8

5.3

7.2

n-Butyl acetate

132.5

17.4

15.8

3.7

6.3

n-Amyl acetate

149.4

17.3

15.6

3.3

6.7

Isobutyl acetate

133.5

17.0

15.1

3.7

6.3

Isopropyl acetate

117.1

17.3

14.4

6.1

7.4

Diethyl malonate

151.8

19.5

15.5

4.7

10.8

Diethyl oxalate

135.4

22.5

15.5

5.1

15.5

Isoamyl acetate

148.8

16.0

15.3

3.1

7.0

163

21.9

18.6

10.8

4.9

Dimethyl phthalate Diethyl phthalate

198

20.5

17.6

9.6

4.5

Dibutyl phthalate

266

19.0

17.8

8.6

4.1

Dioctyl phthalate

377

16.8

16.6

7.0

3.1

Phosphorous compounds Trimethyl phosphate

116.7

25.2

16.7

15.9

10.2

Triethyl phosphate

169.7

22.2

16.7

11.4

9.2

Tricresyl phosphate

316

23.1

19.0

12.3

4.5

Nitrogen compounds Acetonitrile

52.6

24.3

15.3

17.9

6.1

n-Butyronitrile

86.7

20.4

15.3

12.5

5.1

Propionitrile

70.9

22.1

15.3

14.3

5.5

Benzonitrile

102.6

19.9

17.4

9.0

3.3

Nitromethane

54.3

25.1

15.7

18.8

5.1

Nitroethane

71.5

22.6

15.9

15.9

4.5

Valery Yu. Senichev, Vasiliy V. Tereshatov

141

Table 4.1.1 Solubility parameters and their components (according Hansen’s approach) for different solvents V1, kmol/m3

δ, (MJ/m3)1/2

δd, (MJ/m3)1/2

δp, (MJ/m3)1/2

δh, (MJ/m3)1/2

2-Nitropropane

86.9

20.4

16.1

12.0

4.1

Solvent

Nitrobenzene

102.7

20.5

20.0

8.6

4.1

Ethylenediamine

67.3

25.2

16.6

8.8

17.0

2-Pyrrolidinone

76.4

30.1

19.4

17.4

11.3

Pyridine

80.9

21.9

19.0

8.8

5.9

Morpholine

87.1

22.1

18.8

4.9

9.2

Aniline

91.5

21.1

19.4

5.1

10.2

n-Butylamine

99.0

17.8

16.2

4.5

8.0

2-Aminoethanol

59.7

31.3

17.1

15.5

21.2

Di-n-propyl amine

136.8

15.9

15.3

1.4

4.1

Diethylamine

103.2

16.4

14.9

2.3

6.1

Quinoline

118.0

22.1

19.4

7.0

7.6

Formamide

39.8

39.3

17.2

26.2

19.0

N,N-Dimethylformamide

77.0

24.8

17.4

13.7

11.2

Sulfur compounds Carbon disulfide

60.0

20.3

20.3

0

0

Dimethyl sulfoxide

71.3

26.4

18.4

16.3

10.2

Diethyl sulfide

107.6

17.2

16.8

3.1

2.0

75

29.7

19.0

19.4

12.3

12.2

22.2

Dimethyl sulfone

Monohydric alcohols and phenols Methanol

40.7

29.1

15.1

Ethanol

66.8

26.4

15.8

8.8

19.4

Allyl alcohol

68.4

24.1

16.2

10.8

16.8

1-Propanol

75.2

24.4

15.8

6.7

17.3

2-Propanol

76.8

23.5

15.8

6.1

16.4

Furfuryl alcohol

86.5

25.6

17.4

7.6

15.1

1-Butanol

91.5

23.1

15.9

5.7

15.7

2-Butanol

92.0

22.1

15.8

5.7

14.5

1-Pentanol

108.3

21.6

15.9

4.5

13.9

Benzyl alcohol

103.6

24.8

18.4

6.3

13.7

Cyclohexanol

106.0

23.3

17.3

4.1

13.5

Ethylene glycol monomethyl ether

79.1

23.3

16.2

9.2

16.4

142

4.1 Simple solvent characteristics

Table 4.1.1 Solubility parameters and their components (according Hansen’s approach) for different solvents V1, kmol/m3

δ, (MJ/m3)1/2

δd, (MJ/m3)1/2

δp, (MJ/m3)1/2

δh, (MJ/m3)1/2

Ethylene glycol monoethyl ether

97.8

21.5

16.2

9.2

14.3

Ethylene glycol monobutyl ether

142.1

20.8

15.9

4.5

12.7

1-Octanol

157.7

21.1

17.0

3.3

11.9

m-Cresol

104.7

22.7

18.0

5.1

12.9

Solvent

Carboxylic acids Formic acid

37.8

24.8

14.3

11.9

16.6

Acetic acid

57.1

20.7

14.5

8.0

13.5

n-Butyric acid

110

21.5

14.9

4.1

10.6

Polyhydric alcohols Ethylene glycol

55.8

33.2

16.8

11.0

25.9

Glycerol

73.3

43.8

17.3

12.0

29.2

Diethylene glycol

95.3

29.8

16.0

14.7

20.4

Triethylene glycol

114.0

21.9

16.0

12.5

18.6

Water

18.0

47.9

15.5

16.0

42.3

4.1.3 MULTI-DIMENSIONAL APPROACHES These approaches can be divided into three types: 1. H-bonds are not considered. This approach can be applied only to nonpolar and weak polar liquids. 2. H-bonds taken into account by one parameter. 3. H-bonds taken into account by two parameters. Blanks and Prausnitz8,9 proposed two-component solubility parameters. They decomposed the cohesion energy into two contributions of polar and non-polar components: E nonpolar E polar E - – ------------- = λ 2 + τ 2 – ------ = – -------------------V1 V1 V1 where:

λ τ

[4.1.15]

non-polar contribution to the solubility parameter polar contribution to the solubility parameter

This approach has become a component of the Hansen approach and has not received a separate treatment. Polar interactions can be divided into two types: • Polar interactions in which molecules having permanent dipole moments interact in solution with the dipole orientation in a symmetrical manner. It follows that

Valery Yu. Senichev, Vasiliy V. Tereshatov

143

the geometric mean rule is obeyed for orientation interactions and the contribution of dipole orientations to the cohesive energy and dispersion interactions. • Polar interactions accompanied by the dipole induction. These interactions are asymmetrical. Thus for a pure polar liquid without hydrogen bonds:10 2

2

2

δ = δ d + δ or + 2δ d δ in where:

δd δor δin

[4.1.16]

dispersion contribution to the solubility parameter orientation contribution to the solubility parameter induction contribution to the solubility parameter.

A more traditional approach of the contribution of the induction interaction was published elsewhere;11 however, it was used only for the estimation of the common value of the δ parameter rather than for evaluation of solubility: 2

2

2

2

δ = δd + δp + δi

[4.1.17]

The first method taking into account the hydrogen bonding was proposed by Beerbower et al.,12 who expressed hydrogen bonding energy through the hydrogen bonding number Δv. The data for various solvents were plotted into a diagram with the solubility parameter along the horizontal axis and the hydrogen bonding number Δv along the vertical axis. Data were obtained for a given polymer for suitable solvents. All solvents in which a given polymer was soluble got certain regions. Lieberman also plotted twodimensional graphs of solubility parameters versus hydrogen-bonding capabilities.13 On the base of work by Gordy and Stanford, the spectroscopic criterion, related to the extent of the shift to lower frequencies of the OD infrared absorption of deuterated methanol, was selected. It provides a measure of the hydrogen-bonding acceptor power of a solvent.14,15 The spectrum of a deuterated methanol solution in the test solution was compared with that of a solution in benzene, and the hydrogen-bonding parameter was defined as γ = Δν ⁄ 10 where:

Δν

[4.1.18]

OD absorption shift (in wavenumber).

Crowley et al.16 used an extension of this method by including the dipole moment of solvents. One of the axes represented solubility parameter, the other the dipole moment, and the third hydrogen bonding expressed by spectroscopic parameter γ. Because this method involved an empirical comparison of a number of solvents it was impractical. Nelson et al.17 utilized this approach to hydrogen bond solubility parameters. Hansen (see the next section) developed this method. Chen introduced a quantity χH:18

144

4.1 Simple solvent characteristics

V 2 2 χ H = -------S- [ ( δ d, S – δ d, P ) + ( δ p, S – δ p, P ) ] RT where:

δd,S, δd,P, δp,S, δp,P

[4.1.19]

are Hansen's parameters of solvent and polymer (see the next section).

Chen implied that χH was the enthalpy contribution to the Flory-Huggins parameter χ1 and plotted the solubility data in δh − χH diagram where δh was the H-bond parameter in the Hansen approach. In these diagrams, sphere-like volumes of Hansen's solubility have degenerated to circles. The disadvantage of this method lies in the beforehand estimation of characteristics of the polymer. Among other two-dimensional methods used for the representation of solubility data was the δp-δh diagram proposed by Henry19 and the δ-δh diagram proposed by Hoernschemeyer,20 but their representations of the solubility region were less correct. All these approaches involving hydrogen bond parameter ignored the fact that the hydrogen bond interaction was the product of hydrogen bonding donating and accepting capability.21-23 On the basis of a chemical approach to hydrogen bonding, Rider proposed a model of solubility for liquids in which the enthalpy limited the miscibility of polymers with solvents.24,25 For substances capable to form hydrogen bonds, Rider proposed a new factor relating miscibility with an enthalpy of mixing which depended on an enthalpy of the hydrogen bond formation. He has introduced the quantity of a hydrogen bond potential (HBP). If the quantity of HBP is positive it promotes miscibility and if it is negative it decreases miscibility. HBP = ( b 1 – b 2 ) ( C 1 – C 2 )

[4.1.20]

where: b1, b2 C1, C2

donor parameters of solvent and solute, respectively acceptor parameters of solvent and solute, respectively

For certain polymers, Rider has drawn solubility maps. The area of solubility was represented by a pair of symmetric quarters of a plane lying in coordinates b,C.24 Values of parameters were defined from data for enthalpies of hydrogen bonds available from the earlier works. The model is a logical development of the Hansen method. A shortcoming of this model is in neglecting all other factors influencing solubility, namely dispersion and polar interactions, change of entropy, and molecular mass of polymer and its phase condition. The model was developed as a three-dimensional dualistic model (see Section 4.1.5), and as a similar later approach of Stefanis and Panayiotou.26 4.1.4 HANSEN'S SOLUBILITY The Hansen approach27-31 assumed that the cohesive energy can be divided into contributions of dispersion interactions, polar interactions, and hydrogen bonding.

Valery Yu. Senichev, Vasiliy V. Tereshatov

E = Ed + E p + E h

145

[4.1.21]

where: E total cohesive energy Ed, Ep, Eh contributions of dispersion cohesion energy, polar cohesion energy, and hydrogen bonding cohesion energy.

Dividing this equation by the molar volume of solvent, V1, gives: E E E E ------ = -----d- + -----p- + -----hV1 V1 V1 V1

[4.1.22]

or 2

2

2

2

δ = δd + δp + δh where:

[4.1.23]

δ total solubility parameter δd, δp, δh components of the solubility parameter determined by the corresponding contributions to the cohesive energy.

Hansen gave a visual interpretation of his method by means of three-dimensional spheres of solubility, where the center of the sphere has coordinates corresponding to the values of components of the solubility parameter of the polymer. The sphere can be coupled with a radius to characterize a polymer. All good solvents for a particular polymer (each solvent has been represented as a point in a three-dimensional space with coordinates) should be inside the sphere, whereas all non-solvents should be outside the solubility sphere. An example is given in Section 4.1.7. In the original work, these parameters were evaluated by experimental observations of solubility. It was assumed that if each component of the solubility parameter of one liquid is close to the corresponding values of another liquid, then the process of their mixing should readily occur with a more negative free energy. The solubility volume has dimensions δd, δp, 2δh. The factor 2 was proposed to account for the spherical form of solubility volumes and had no physical sense. However, it is necessary to notice that, for example, Lee and Lee32 have evaluated spherical solubility volume of polyimide with good results without using the factor 2. Because of its simplicity, the method has become very popular. Using the Hansen approach, the solubility of any polymer in solvents (with known Hansen's parameters of polymer and solvents) can be predicted. The determination of polymer parameters requires an evaluation of solubility in a great number of solvents with known values of Hansen parameters. Arbitrary criteria of determination are used because Hansen made no attempts to offer precise calculations of thermodynamic parameters. The separation of the cohesion energy into contributions of various forces implies that it is possible to substitute energy for parameter and sum contributions proportional to the second power of a difference of corresponding components. Hansen's treatment permits evaluation of the dispersion and polar contribution to cohesive energy. The fitting parameter of the approach (the solubility sphere radius) reflects on the supermolecular structure of the polymer-solvent system. Its values should be higher for amorphous polymers and lower for glass or crystalline polymers.

146

4.1 Simple solvent characteristics

The weak point of the approach is the incorrect assignment of the hydrogen bond contribution in the energy exchange that does not permit its use for polymers forming strong hydrogen bonds. A large number of data were accumulated for different solvents and polymers (see Tables 4.1.1, 4.1.2). Table 4.1.2. Solubility parameters and their components for polymers (after refs 38,41,43-45, 48-50) δ, (MJ/m3)1/2

Polymer

δd, (MJ/m3)1/2

δp, (MJ/m3)1/2

δh, (MJ/m3)1/2

Polyamide-66

22.77

18.5

5.1

12.2

Polyacrylonitrile

25.10

18.19

15.93

6.74

Polyvinylchloride

21.41

18.68

10.01

3.06

Polymethylmethacrylate

20.18

17.72

5.72

7.76

Polystyrene

19.81

19.68

0.86

2.04

Polytetrafluoroethylene

13.97

13.97

0.00

0.00

Polyethyleneterephthalate

21.60

19.50

3.47

8.58

Poly(ε-caprolactone) 70oC

17.39

15.53

2.42

7.44

Epoxy resin

18.77

16.55

5.98

6.53

Alkyd resin

20.11

19.11

3.96

4.86

Poly(ethylene glycol)

21.97

17.0

10.7

8.9

Poly(tetramethylene glycol)

14.67

13.09

1.81

6.38

Hydrogenated nitrile rubber with acrylonitrile content of 25% (Therban 2568)

19.9

18.4

6.0

4.5

Ethylene propylene diene rubber (Nordel IP 4520)

17.5

17.2

2.0

2.6

A variation of the Hansen method is the Teas’ approach.34 He has shown for some polymer-solvent systems that it was possible to use fractional cohesive energy densities plotted on a triangular chart to represent solubility limits: 2

2

2

δd δp δ E d = ----2-, E p = ----2-, E h = ----h2δ0 δ0 δ0 where:

2

2

2

2

δ0 = δd + δp + δh

Teas used fractional parameters defined as

[4.1.24]

Valery Yu. Senichev, Vasiliy V. Tereshatov

147

100δ d 100δ p 100δ h -, f = ---------------------------, f = --------------------------f d = --------------------------δd + δp + δh p δd + δp + δh h δd + δp + δh

[4.1.25]

This representation was completely empirical without any theoretical justification. Some correlations between components of solubility parameters and physical parameters of liquids (surface tension, dipole moment, refraction index) were generalized elsewhere.11 2

2

–1 ⁄ 3

2

δ d + 0.632δ p + 0.632δ h = 13.9V 1 2

2

–1 ⁄ 3

2

δ d + δ p + 0.06δ h = 13.9V 1 2

2

where:

γl

γl

–1 ⁄ 3

2

δ d + 2δ p + 0.48δ h = 13.9V 1

γl

γl

non-alcohols

[4.1.26]

alcohols

[4.1.27]

acids, phenols

[4.1.28]

surface tension.

Koenhan and Smolder proposed the following equation applicable to the majority of solvents, with exception of cyclic compounds, acetonitrile, carboxylic acids, and multifunctional alcohols.35 2

–1 ⁄ 3

2

δ d + 2δ p = 13.8V 1

γl

[4.1.29]

They also proposed a correlation between the polar contribution to the solubility parameter and refractive index: δ d = 9.55n D – 5.55

[4.1.30]

where: refractive index

nD

Alternatively, Keller et al.36 estimated that for nonpolar and slightly polar liquids δ d = 62.8x 2

δ d = – 4.58 + 108x – 119x + 45x where:

3

for x ≤ 0.28

[4.1.31]

for x > 0.28

[4.1.32]

2

nD – 1 x = --------------2 nD + 2

Peiffer suggested the following expression:36 2

2

δ d = K ( 4πIα ⁄ 3d ) ( N ⁄ V 1 )

3

where: K I α N

packing parameter ionization potential molecular polarizability number of molecules in the volume unit

[4.1.33]

148

4.1 Simple solvent characteristics = Nr*3/K the equilibrium distance between molecules.

V1 r*

For the estimation of a nonpolar component of δ, Brown et al.37 proposed the homomorph concept. The homomorph of a polar molecule is the nonpolar molecule most closely resembling it in the size and the structure (e.g., n-butane is the homomorph of nbutyl alcohol). The nonpolar component of the cohesion energy of a polar solvent is taken as the experimentally determined total vaporization energy of the corresponding homomorph at the same reduced temperature (the actual temperature divided by the critical temperature in Kelvin's scale). For this comparison, the molar volumes must also be equal. Blanks and Prausnitz proposed plots of dependencies of dispersion energy density on a molar volume of straight-chain, alicyclic and aromatic hydrocarbons. If the vaporization energies of appropriate hydrocarbons are not known they can be calculated by one of the methods of group contributions (See Chapter 5). Hansen and Scaarup29 calculated the polar component of solubility parameter using Bottcher's relation to estimating the contribution of the permanent dipoles to the cohesion energy: 12108- ε – 1 2 -----------------2- ( n 2D + 2 )μ 2 δ p = -------------2 V 1 2ε – n D where:

ε µ

[4.1.34]

relative permittivity, dipole moment

μ δ p = 50.1 ---------3⁄4 V1

[4.1.35]

Peiffer11 proposed the expressions which separate the contributions of polar forces and induction interactions to the solubility parameters: 2

4

δ p = K ( 2πμ ⁄ 3kTp ) ( N ⁄ V 1 ) 2

δ i = K ( 2παμ ⁄ i ) ( N ⁄ V 1 ) where:

ε* N

3

3

[4.1.36] [4.1.37]

interaction energy between two molecules at the distance r* number of hydroxyl groups in molecule 4

p = 2μ ⁄ 3kTε* 2

i = 2αμ ⁄ ε*

[4.1.38] [4.1.39]

It should be noted that in Hansen's approach these contributions are cumulative: 2

2

2

δ = δp + δi

[4.1.40]

Valery Yu. Senichev, Vasiliy V. Tereshatov

149

Stefanis and Panayiotou51 proposed to consider the nature of the acid and base of 2 2 2 substances by using the following equation: δ h = δ a + δ b , where δa is the acidic element and δb is the basic element of the hydrogen-bonding component of the solubility parameter, correspondingly. The authors confirmed that their proposal is only effective when one of the acidic or basic components is too small. Their scheme was used to correct for calculation of radii of Hansen's spheres of solubility, therefore it did not come out from the framework of Hansen's approach. For the calculation of hydrogen-bonding component, δh, Hansen and Scaarup29 proposed an empirical expression based on OH−O bond energy (5000 cal/mol) applicable to alcohols only: δ h = ( 20.9N ⁄ V 1 )

1⁄2

[4.1.41]

In Subchapter 5.3, the values of all the components of a solubility parameter are calculated using group contributions. 4.1.5 THREE-DIMENSIONAL DUALISTIC MODEL The heat of mixing of two liquids is expressed by the classical theory of regular polymer solutions using Eq. [4.1.10]. This expression is not adequate for systems with specific interactions. Such interactions are expressed as a product of the donor parameter and the acceptor parameter. The contribution of H-bonding to the enthalpy of mixing can be written in terms of volume units as follows:21 ΔH' mix ( A 1 – A 2 ) ( D 1 – D 2 )ϕ 1 ϕ 2

[4.1.42]

where: A1 , A 2 D1, D2 ϕ 1, ϕ 2

effective acceptor parameters donor parameters, volume fractions

Hence enthalpy of mixing of two liquids per volume unit can be expressed by:33 2

ΔH mix = [ ( δ' 1 – δ' 2 ) + ( A 1 – A 2 ) ( D 1 – D 2 ) ]ϕ 1 ϕ 2 = Bϕ 1 ϕ 2

[4.1.43]

This equation is used for the calculation of the enthalpy contribution to the Huggins parameter (see Subchapter 4.2) for a polymer-solvent system: 2

χ H = V 1 [ ( δ' 1 – δ' 2 ) + ( A 1 – A 2 ) ( D 1 – D 2 ) ] ⁄ RT where:

δ' 1, δ' 2

[4.1.44]

dispersion-polar components of solubility parameters (values of solubility parameters excluding H-bonds contributions).

Results of calculations using Eq. [4.1.44] of three-dimensional dualistic model coincide with the experimental values of χH and the χH values calculated by other methods.38 Values A, D, and δ' can be obtained from IR-spectroscopy and Hansen's parameters.24,25 Values of the TDM parameters are presented in Tables 4.1.3, 4.1.4. It should be noted that

150

4.1 Simple solvent characteristics

Hansen parameters are used for estimation of values of TDM parameters from the equa2 2 2 tion δ di + δ pi = δ, δ hi = A i D i . Table 4.1.3. TDM parameters of some solvents. [Adapted, by permission, from V.Yu. Senichev, V.V. Tereshatov, Vysokomol. Soed., B31, 216 (1989).] #

Solvent

D

δ’

δ

V1x106 m3/mol

13.3

20.0

23.6

76.8

A 3 1/2

(MJ/m )

1

Isopropanol

11.8

2

Pentanol

9.9

11.2

19.7

22.3

108.2

3

Acetone

3.8

13.1

18.5

19.8

74.0

4

Ethyl acetate

4.9

10.4

17.0

18.3

98.5

5

Butyl acetate

4.8

9.0

16.4

17.6

132.5

6

Isobutyl acetate

4.8

8.4

15.7

16.9

133.3

7

Amyl acetate

4.7

7.8

16.2

17.3

148.9

8

Isobutyl isobutyrate

4.7

7.4

14.6

15.7

165.0

9

Tetrahydrofuran

5.2

12.2

17.7

19.4

81.7

10 o-Xylene

0.5

7.4

18.3

18.4

121.0

11 Chlorobenzene

0.6

7.3

19.3

19.4

102.1

12 Acetonitrile

2.7

14.0

24.4

24.5

52.6

13 n-Hexane

0

0

14.9

14.9

132.0

14 Benzene

0.6

8.5

18.6

18.8

89.4

15 N,N-Dimethylformamide

8.2

15.4

22.0

27.7

77.0

16 Toluene

0.6

7.8

18.1

18.2

106.8

17 Methanol

18.2

17.0

23.5

29.3

41.7

18 Ethanol

14.4

14.7

21.7

26.1

58.5

19 1-Propanol

11.9

13.4

21.0

24.5

75.2

20 Methyl ethyl ketone

2.3

11.6

18.3

19.0

90.1

21 Cyclohexanone

2.7

11.1

19.5

20.3

104.0

22 Diethyl ether

7.6

12.4

12.0

15.4

104.8

23 Ethylbenzene

0.3

7.3

17.9

18.0

123.1

24 Pyridine

1.9

19.6

21.0

21.8

80.9

25 Propyl acetate

4.8

9.6

16.4

17.8

115.2

26 1,4-Dioxane

8.3

12.9

17.7

20.5

85.7

27 Aniline

6.2

16.8

20.0

22.5

91.5

Valery Yu. Senichev, Vasiliy V. Tereshatov

151

Table 4.1.4. TDM parameters of some polymers, (MJ/m3)1/2. [Adapted, by permission, from V.Yu. Senichev, V.V. Tereshatov, Vysokomol. Soed., B31, 216 (1989).] A

δ’

δ

2.5

6.5

18.6

19.8

4.9

10.4

17.8

19.2

Polymer

D

Polymethylmethacrylate Polyvinylacetate Polystyrene

0.3

7.3

17.9

18.0

Polyvinylchloride

11.6

10.6

16.1

19.5

The δh can be separated into donor and acceptor components using values of enthalpies of the hydrogen bond formation between proton-donors and proton-acceptors. In the absence of such data, it is possible to evaluate TDM parameters by means of analysis of parameters of compounds having similar chemical structure. For example, propyl acetate parameters can be calculated by the interpolation of corresponding parameters of butyl acetate and ethyl acetate.24 The benzene parameters can be calculated by decomposition of δh into acceptor and donor components in the way used for toluene.25 The solubility prediction can be made using the relationship between solubility and the χ1 parameter (see Subchapter 4.2). The total value of the χ1 parameter can be evaluated by adding the entropy contribution: χ1 = χS + χH where:

χS

[4.1.45]

an empirical value. Usually, it is 0.2-0.4 for good solvents.

The value of this parameter is inversely proportional to the coordination number that is a number of molecules of a solvent interacting with a segment of the polymer. The value of the entropy contribution to the parameter should be included in solubility calculations. The value χS = 0.34 is then used in approximate calculations. 4.1.6 SOLUBILITY CRITERION The polymer superstructure influences its solubility. Askadskii and Matveev proposed a new criterion of solubility for linear polymers based on the interaction of forces of a surface tension on wetting.39 The solubility parameter of polymer should be lower or equal to the work of rupture by the solvent of a bond relative to a volume unit of the bond element. The condition of solubility can be expressed as follows: γ 1⁄2 μ ≤ 2pΦ  ---p-  γ s where:

2

[4.1.46] 2

µ

= δp ⁄ δs

δp, δs

solubility parameters for polymer and solvent, respectively.

152

4.1 Simple solvent characteristics p

ε max r s ρ = -------------s ε max r p

[4.1.47] 1⁄2

4 ( Vp Vs ) Φ = ----------------------------------1⁄2 1⁄2 2 ( Vp + Vs ) where:

p

s

ε max, ε max rs,rp

[4.1.48]

maximum deformations of polymer and solvent at rupture characteristic sizes of Frenkel's swarms for solvent and small radius of the globule of bond for the polymer, respectively molar volumes of polymer and solvent (per unit)

Vp,Vs Φ≈1 ρ ≈ const

The above expression was obtained by neglecting the preliminary swelling. Consideration of swelling requires correction for the surface tension of swelled surface layers: 2

μ < 2ρΦ [ Φ – ( Φ – 1 + a )

1⁄2

]

[4.1.49]

where:

a = γ ps ⁄ γ p

[4.1.50]

γ ps = γ p + γ s – 2Φ ( γ p γ s )

1⁄2

[4.1.51]

For practical purposes, the magnitude of ρ estimated graphically is 0.687. Thus μ < 1.374β

2

for β = Φ [ Φ – ( Φ – 1 + a )

1⁄2

]

[4.1.52]

For both polymers and solvents, the values of solubility parameters can be obtained experimentally (see Subchapters 5.1, 5.3). The surface tension of polymer can be calculated using parahor: P 4 γ =  ----  V

[4.1.53]

where: V

molar volume of a repeated polymer unit

Then the value of Vp is calculated: N A  ΔV i i V p = ----------------------k av

where: kav

= 0.681

[4.1.54]

Valery Yu. Senichev, Vasiliy V. Tereshatov

153

Figure 4.1.2. Representation of the two-component solubility parameter system in the Rider’s approach. b2 and C2 are the values of Rider’s parameters for polymer.

Figure 4.1.1. Representation of the one-component solubility parameter system. The curve represents Eq. [4.1.56] for polymer with δ =18 (MJ/m3)1/2.

If the density of polymer dp is known, then Vp = M/dp, where M is the molecular mass of a repeating unit. The values of parahors are given in Table 4.1.5. Table 4.1.5. Values of parahors Atom

C

H

O

O2

N

S

F

Cl

Br

I

P

4.8

17.1

20.0

60.0

12.5

48.2

27.5

54.3

68.0

91.0

Increment

Double bond

Triple bond

3-member ring

4-member ring

5-member ring

6-member ring

P

23.2

46.4

16.7

11.6

8.5

6.1

The value of Φ is calculated from Eq. [4.1.48]. Vp and Vs are defined by ratios Vp=M/dp and Vs=M/ds, where dp, ds are the densities of polymer and solvent, respectively. Then µ is calculated from Eq. [4.1.49]. The obtained value of µ from Eq. [4.1.49] is com2 2 pared with the value of μ = δ p ⁄ δ s if the last value is lower or equal to the value of µ calculated from Eq. [4.1.49], the polymer should dissolve in a given solvent with a probability of 85%. 4.1.7 SOLVENT SYSTEM DESIGN One-component system. Solvents can be arranged in accordance with their solubility parameter as shown in Figure 4.1.1. It is apparent that a set of compatible solvents can be selected for the polymer, determining their range based on the properties of the polymer.

154

4.1 Simple solvent characteristics

Figure 4.1.3. The solubility volume for cellulose acetate butyrate in terms of one-component solubility parameter, δ, dipole moment, μ, and (on vertical axis) the spectroscopic parameter, γ, from the approach developed by Crowley et al.2 [Adapted, by permission, from J.D. Crowley, G.S. Teague and J.W. Lowe, J. Paint Technol., 38, 269 (1966).]

Figure 4.1.4. Hansen’s solubility volume of polyimide synthesized from 3,3’,4,4’-benzophenone tetracarboxylic dianhydride and 2,3,5,6-tetramethyl-p-phenylene diamine (after Lee31). [Adapted, by permission, from H.-R. Lee, Y.-D. Lee, J. Appl. Polym. Sci., 40, 2087 (1990).]

The simplest case is expressed by the Gee's equation for equilibrium swelling:42 2

Q = q max exp [ – V s ( δ s – δ p ) ] where:

δs, δp

[4.1.55]

solubility parameters for solvent and polymer.

The value of solubility parameter of solvent mixture with components having similar molar volumes is relative to their volume fractions and solubility parameters: δ =

 δi ϕi

[4.1.56]

i

The solute is frequently soluble in a mixture of two non-solvents, for example, the mixture of diisopropyl ether (δ = 15.6 (MJ/m3)1/2 and ethanol (δ = 26.4 (MJ/m3)1/2 is a solvent for nitrocellulose (δ = 23 (MJ/m3)1/2. Two-component systems. Two parametrical models of solubility use two-dimensional graphs of solubility area. Two-dimensional solubility areas may be closed or open. In accordance with the approach of Blanks and Prausnitz, the solubility area is displayed as a plane with two coordinates, λ,τ.8,9 The parameters are related to Hansen's parameters by 2

2 1⁄2

λ = δ d, τ = ( δ p + δ h )

Valery Yu. Senichev, Vasiliy V. Tereshatov

155

Solubility areas in this approach are closed because they are degenerated from Hansen's spheres (see below). Another example of the application of degenerate Hansen’s spheres was given by Chen.18 Instead of parameters δp, δd, the value χH was used which was calculated from the difference of the polar and dispersing contributions, δp, δd. The zone of solubility is a circle. Lieberman13 used planes with coordinates δ, γ where γ is a spectroscopic paramFigure 4.1.5. Volume of the increased swelling of crosseter (see Section 4.1.3). These planes were linked polybutadiene urethane elastomer, χ H ≤ 0.85 . Labels of points: 1 − outside volume, points with coor- open and had the areas of solubility, nondinates corresponding to solvents; 2 − inside volume, solubility, and intermediate. points with coordinates corresponding to solvents; 3 − In Rider's approach, the solubility the points with coordinates corresponding to polymer. This is the center of the volume. 4 − points placed on a area was a system of two quarters on a plane with coordinate d = 18 (MJ/m3)1/2. Number of sol- plane; two other quarters were the areas of vent (not underlined number) corresponds to their posinon-solubility (Figure 4.1.2). Coordinates tion in the Table 4.1.3. The underlined number of this plane were accepting and donating corresponds to swelling ratio at equilibrium. abilities. Rider's approach found application for solvents with high H-bond interactions. Three-component systems. Crowley et al.2 proposed the three-dimensional solubility volumes (Figure 4.1.3). Better known are Hansen's three-dimensional solubility volumes (Figure 4.1.4). In Hansen's approach, the components of solubility parameters for mixed solvents δj are calculated from Eq. [4.1.56]: δj =

 ϕi δ ji

[4.1.57]

i

The choice of a solvent for the polymer is based on coordinates of polymer in space of coordinates δd, δp, δh and the radius of a solubility volume. For mixed solvents, their coordinates can be derived by connecting coordinates of individual solvents. This can be used to determine synergism in solvents for a particular polymer but it cannot demonstrate antisynergism of solvent mixtures (a mixture is less compatible with polymer than the individual solvents). Some attempts were made to improve the concept of the solubility volume. Jacquel et al. found a relationship between the radius of the value for three approaches (Hildebrand model, Hansen model, and Beerbower model) and some conditions (temperature, crystallinity, and molecular weight).46 Hughes et al. tried to find the theoretical base for the Hansen's solubility volume essentially in the case of dipolar interactions.47 The attempt included taking into account more reasonable partial parameters. But it was not able to overcome limitations of the initial approach. The reason can be referred to contradictory basic postulates.

156

4.1 Simple solvent characteristics

In the TDM approach, the solubility volume has also three coordinates, but the Hbond properties are taken into account. For this reason, solubility volume can be represented by hyperbolic paraboloid (Figure 4.1.5). The use of this model permits to evaluate the potential of synergism and antisynergism of solvent mixtures. It can be demonstrated by the position of a point of a solvent mixture moving from a zone of good compatibility into the similar zone through the zone of inferior compatibility or, on the contrary, from a zone of an incompatibility into a similar zone through the zone of the improved compatibility. In the case of polymers that have no hydrogen bond forming abilities, this approach is equivalent to the Hansen or Blanks-Prausnitz approaches. The above review of the methods of solvent evaluation shows that there is a broad choice of various techniques. Depending on the complexity of solvent-polymer interactions, the suitable method can be selected. For example, if solvents and/or polymer do not have functional groups to interact with, the one-dimensional model is adequate. If weak hydrogen bonding is present, Hansen's approach gives good results (see further applications in Subchapter 5.3). In even more complex interactions, TDM model is always the best choice. A similar approach of Stefanis and Panayiotou26 is more complex but the corresponding parameters of the model can be used in the framework of TDM approach as well. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

W.W. Reynolds and E.C. Larson, Off. Dig. Fed. Soc. Paint Technol., 34, 677 (1972). J.D. Crowley, G.S.Teague and J.W. Lowe, J. Paint Technol., 38, 269 (1966). H. Burrel, Off. Dig. Fed. Paint. Varn. Prod. Clubs, 27, 726 (1955). P.L. Huyskens, M.C.Haulait-Pirson, Org. Coat. Sci. Technol., 8, 155 (1986). I.H. Hildebrand, J. Amer. Chem. Soc., 38, 1452, (1916). G. Scatchard, J. Amer. Chem. Soc., 56, 995 (1934). A.A. Tager, L.K. Kolmakova, Vysokomol. Soed., A22, 483 (1980). R.F. Blanks, J.M. Prausnitz, Ind. Eng. Chem., Fundam., 3, 1, (1964). R.F. Weimer and J.M. Prausnitz, Hydrocarbon Process., 44, 237 (1965). R.A Keller, B.L.Karger and L.R. Snyder, Gas Chromatogr., Proc. Int Symp. (Eur), 8, 125 (1971). D.G. Peiffer, J. Appl. Polym. Sci., 25, 369 (1980). A. Beerbower, L.A. Kaye and D.E. Pattison, Chem. Eng., 118 (1967). E.P. Lieberman, Off. Dig. Fed. Soc. Paint Technol., 34, 30 (1962). W. Gordy and S.C. Stanford, J. Chem. Phys., 8, 170 (1940). W. Gordy and S.C. Stanford, J. Chem. Phys., 9, 204 (1941). J.D. Crowley, G.S. Teague and J.W. Lowe, J. Paint Technol., 39, 19 (1967). R.C. Nelson, R.W. Hemwall and G.D Edwards, J. Paint Technol., 42, 636 (1970). S.-A. Chen, J. Appl. Polym. Sci., 15, 1247 (1971). L.F. Henry, Polym. Eng. Sci., 14, 167 (1974) D. Hoernschemeyer, J. Appl. Polym. Sci., 18, 61 (1974). P.A. Small, J. Appl. Chem., 3, 71 (1953). H. Burrel, Adv. Chem. Ser., No. 124, 1 (1973). H. Renon, C.A Reckert and J.M. Prausnitz, Ind. Eng. Chem., 3, 1(1964). P.M. Rider, J. Appl. Polym. Sci., 25, 2975 (1980). P.M. Rider, Polym. Eng. Sci., 23, 180 (1983). E. Stefanis, C. Panayiotou, Int. J. Pharm., 426, 29 (2012). C.M. Hansen, J. Paint. Technol., 39, 104 (1967). C.M. Hansen, J. Paint. Technol., 39, 505 (1967). C.M. Hansen and K. Scaarup, J. Paint. Technol., 39, 511 (1967). C.M. Hansen, Three Dimensional Solubility Parameters and Solvent Diffusion Coefficient, Danish Technical Press, Copenhagen, 1967. C.M. Hansen and A. Beerbower in Kirk-Othmer Encyclopedia of Chemical Technology, Suppl. Vol.,

Valery Yu. Senichev, Vasiliy V. Tereshatov

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48. 49. 50. 51.

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2nd ed., A.Standen Ed., John Wiley, 889, 1971. H.-R. Lee, Y.-D. Lee, J. Appl. Polym.Sci., 40, 2087 (1990). V.Yu. Senichev, V.V. Tereshatov, Vysokomol. Soed., B31, 216 (1989). J.P. Teas, J. Paint Technol., 40, 19 (1968). D.M. Koenhen, C.A. Smolder, J. Appl. Polym. Sci., 19, 1163 (1975). R.A. Keller, B.L. Karger and L.R. Snyder, Gas Chromatogr., Proc. Int Symp. (Eur), 8, 125 (1971). H.C. Brown, G.K. Barbaras, H.L. Berneis, W.H. Bonner, R.B. Johannesen, M. Grayson and K.L. Nelson, J. Amer. Chem. Soc., 75, 1 (1953). A.E. Nesterov, Handbook on physical chemistry of polymers. V. 1. Properties of solutions, Naukova Dumka, Kiev, 1984. A.A. Askadskii, Yu.I. Matveev, M.S. Matevosyan, Vysokomol. Soed., 32, 2157 (1990). Yu.I. Matveev, A.A. Askadskii, Vysokomol. Soed., 36, 436 (1994). S.A. Drinberg, E.F. Itsko, Solvents for paint technology, Khimiya, Leningrad, 1986. A.F. Barton, Chem Rev., 75, 735 (1975). J.-C. Huang, K.-T. Lin, R.D. Deanin, J. Appl. Polym. Sci., 100, 2002 (2006). K.H. Han, G.S. Jeon, I.K. Hong, S.B. Lee, J. Ind. Eng. Chem., 19, 1130 (2013). C. Özdemir, A. Güner, Eur. Polym. J., 43, 3068 (2007). N. Jacquel, C.-W. Lo, Y.-H. Wei, S.S. Wang, AIChE J., 53, 2704 (2007). J.M. Hughes, D. Aherne, J.N. Coleman, J. Appl. Polym. Sci., 127, 4483 (2013). T.B. Nielsen, C.M. Hansen, Polym. Testing, 24, 1054 (2005). J.-C. Huang, R.D. Deanin, Fluid Phase Equilibria, 227, 125 (2005). G. Liu, M. Hoch, C. Wrana, K. Kulbaba, G. Qiu, Polym. Testing, 32, 1128 (2013). E. Stefanis, C. Panayiotou, Int. J. Pharm., 426, 29 (2012).

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4.2 EFFECT OF SYSTEM VARIABLES ON SOLUBILITY Valery Yu. Senichev, Vasiliy V. Tereshatov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Solubility in solvents depends on various internal and external factors. Chemical structure, the molecular mass of solute, and crosslinking of polymer fall into the first group of factors, in addition to the temperature and pressure in the second group of factors involved. 4.2.1 GENERAL CONSIDERATIONS The process of dissolution is determined by a combination of enthalpy and entropy factors. The dissolution description can be based on the Flory-Huggins equation. Flory1-3 and Huggins4 calculated the entropy of mixing of long-chain molecules under the assumption that polymer segments occupy sites of a “lattice” and solvent molecules occupy single sites. The theory implies that the entropy of mixing is combinatorial, i.e., it is stipulated by permutations of molecules into solution in which the molecules of mixed components differ significantly in size. The next assumption is that ΔVmix = 0 and that the enthalpy of mixing does not influence the value of ΔSmix. The last assumptions are the same as in the Hildebrand theory of regular solutions.5 The expression for the Gibbs energy of mixing is V ΔG -------- = x 1 ln ϕ 1 + x 2 ln ϕ 2 + χ 1 ϕ 1 ϕ 2  x 1 + x 2 -----2-  V 1 RT

[4.2.1]

where: x1, x2 χ1

molar fractions of solvent and polymer, respectively Huggins interaction parameter

The first two terms result from the configurational entropy of mixing and are always negative. For ΔG to be negative, the χ1 value must be as small as possible. The theory assumes (without experimental confirmation) that the χ1 parameter does not depend on concentration. The χ1 is a dimensionless quantity characterizing the difference between the interaction energy of solvent molecule immersed in the pure polymer compared with interaction energy in the pure solvent. It is a semi-empirical constant. This parameter was introduced by Flory and Huggins in the equation for solvent activity to extend their theory of athermic processes to the non-athermic processes of mixing: Δμ 2 ln a 1 = ---------1 = ln ( 1 – ϕ 2 ) + ϕ 2 + χ 1 ϕ 2 RT where: a1

*

solvent activity, *

ε 11, ε 22

the energy of 1-1 and 2-2 contacts formation in pure components,

ε 12 µ1

the energy of 1-2 contacts formation in the mixture, chemical potential of solvent.

*

[4.2.2]

Valery Yu. Senichev, Vasiliy V. Tereshatov *

χ 1 = zΔε 12 ⁄ kT *

*

159

[4.2.3] *

*

Δε 12 = 0.5 ( ε 11 + ε 22 ) – ε 12 The critical value of χ1 sufficient for solubility of a polymer having large molecular mass is 0.5. Good solvents have a low χ1 value. The χ1 is a popular practical solubility criterion, and comprehensive compilations of these values have been published.6-9 Temperature is another factor. It defines the difference between polymer and solvent. The solvent is more affected than polymer. This difference in free volumes is stipulated by different sizes of molecules of polymer and solvent. The solution of the polymer in the chemically identical solvent should have unequal free volumes of components. It has critical thermodynamic consequences. The most principal among them is the deterioration of compatibility between polymer and solvent at high temperatures leading to phase separation. The theory of regular solutions operates with solutions of spherical molecules. For the long-chain polymer molecules composed of segments, the number of modes of arrangement in a solution lattice differs from a solution of spherical molecules, and hence it follows the reduction in deviations from the ideal entropy of mixing. It is clear that the polymer-solvent interactions differ qualitatively because of the presence of segments. Some statistical theories of solutions of polymers use the χ1 parameter, too. They predict the dependence of the χ1 parameter on temperature and pressure. According to the Prigogine theory of deformable quasi-lattice, a mixture of a polymer with solvents of different chain length is described by the equation:10 Rχ 1 = A ( r A ⁄ T ) + ( BT ⁄ r A )

[4.2.4]

where: A, B rA

constants number of chain segments in homological series of solvents.

These constants can be calculated from heats of mixing, values of parameter χ1, and from swelling ratios. The Prigogine theory was further developed by Patterson, who proposed the following expression:11 U C p1 2 2 - τ χ 1 =  -------1- ν +  ------ RT  2R  where: U1 Cp1 ν, τ

[4.2.5]

configuration energy (-U1 − enthalpy energy) solvent thermal capacity molecular parameters

The first term of the equation characterizes distinctions in the fields of force of both sizes of segments of polymer and solvent. At high temperatures, in mixtures of chemically similar components, its value is close to zero. The second term describes the structural contribution to χ1 stipulated by the difference in free volumes of polymer and solvent. Both terms of the equation are larger than zero, and as temperature increases the first term

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4.2 Effect of system variables on solubility

decreases and the second term increases. The expression can be given in a reduced form (with some additional substitutions):12 * ˜ 1 ⁄ 3 X  ˜ 1⁄3 P1 χ V V 1 12 1 -  ---------------------------------------- τ2 -* -----------------------1*- = --------+  * 1⁄3 1⁄3 ˜ ˜ V1 RT 1 V 1 – 1  P 1  2 ( 4 ⁄ 3 – V 1 )

where:

˜ , P *, T * V 1 1 1 X12

[4.2.6]

the reduced molar volume of solvent, pressure, and temperature consequently contact interaction parameter.

These parameters can be calculated if factors of the volumetric expansion, isothermal compressibility, thermal capacity of a solvent and enthalpy of mixing of solution components are known. With temperature decreasing, the first term on the right side of the expression [4.2.6] increases and the second term decreases. Such behavior implies the presence of the upper and lower critical temperatures of mixing. Later Flory developed another expression for χ1 that includes the parameter of contact interactions, X12:13,14 *

*

*

2

P 1 V 1  s 2 2 X 12 α 1 T   P 2 s X 12  - ---- -------- + ----------   ----- τ – ---2- ------χ 1 = -------------* *   ˜ s 1 P *  2 P  V 1 RT s 1 P 1 1 1

[4.2.7]

where: s1, s2

ratios of surfaces of molecules to their volumes obtained from structural data.

A large amount of experimental data is then an essential advantage of Flory's theory.9 Simple expressions exist for parameter X12 in terms of Xij characteristic parameters for chemically different segments of molecules of components 1 and 2. Each segment or chemical group has an assigned value of characteristic length (αi, αj) or surface area as a fraction of the total surface of molecule:15 X 12 =

 ( α i, 1 – α i, 2 ) ( αj, 1 – αj, 2 )X ij

[4.2.8]

i, j

Bondi's approach may be used to obtain surface areas of different segments or chemical groups.16 To some extent, Huggins' theory17-21 is similar to Flory's theory. 4.2.2 CHEMICAL STRUCTURE Chemical structure and polarity determine dissolution of polymers. If the bonds in polymer and solvent are similar, then the energy of interaction between homogeneous and heterogeneous molecules is nearly identical which facilitates solubility of the polymer. If the chemical structures of polymer and solvent molecule differ significantly in polarity, then swelling and dissolution do not happen. It is reflected in an empirical rule that “like dissolves alike”. Nonpolar polymers (polyisoprene, polybutadiene) mix infinitely with alkanes (hexane, octane, etc.) but do not mix with such polar liquids like water and alcohols. Polar polymers (cellulose, polyvinylalcohol, etc.) do not mix with alkanes and readily swell in

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water. Polymers of the average polarity dissolve only in liquids of average polarity. For example, polystyrene is not dissolved or swollen in water and alkanes, but it is dissolved in aromatic hydrocarbons (toluene, benzene, xylene), methyl ethyl ketone and some ethers. Polymethylmethacrylate is not dissolved nor swollen in water nor alkanes, but it is dissolved in dichloroethane. Polychloroprene does not dissolve in water, restrictedly swells in gasoline and dissolves in 1,2-dichloroethane and benzene. The solubility of polyvinylchloride was considered in terms of the relationship between the size of a solvent molecule and the distance between polar groups in the polymer.22 The above examples are related to the concept of the one-dimensional solubility parameter. However, the effects of specific interactions between some functional groups can change the compatibility of the system. Chloroalkanes compared with esters are known to be better solvents for polymethylmethacrylate. Aromatic hydrocarbons although having solubility parameters much higher than those of alkanes, dissolve some rubbers at least as well as alkanes. Probably it is related to increasing entropy of mixing that has a positive effect on solubility. The molecular mass of the polymer significantly influences its solubility. With a molecular mass of polymer increased, the energy of interaction between chains also increases. The separation of long chains requires more energy than short chains. 4.2.3 FLEXIBILITY OF A POLYMER CHAIN The dissolution of the polymer is determined by chain flexibility. The mechanism of dissolution consists of separating chains from each other and their transfer into the solution. If a chain is flexible, its segments can be separated without a significant expenditure of energy. Thus functional groups in the polymer chain may interact with solvent molecules. Thermal movement facilitates the swelling of polymers with flexible chains. The flexible chain separated from an adjacent chain penetrates easily into the solvent, and the diffusion occurs at the expense of sequential transition of links. The spontaneous dissolution is accompanied by the decrease in free energy (ΔG < 0) and that is possible at some defined values of ΔH and ΔS. At the dissolution of high-elasticity polymers ΔH ≥ 0 , ΔS > 0 then ΔG < 0. Therefore, highly elastic polymers are completely dissolved in solvents. The rigid chains cannot move gradually because of the separation of two rigid chains requires large energy. At usual temperatures, the value of interaction energy of links between polymer chains and molecules of a solvent is insufficient for full separation of polymer chains. Amorphous linear polymers with rigid chains having polar groups swell in polar liquids but do not dissolve at normal temperatures. For dissolution of such polymers, the interaction between polymer and solvent (polyacrylonitrile in N,N-dimethylformamide) must be stronger. Glassy polymers with a dense molecular structure swell in solvents with the heat absorption ΔH > 0. The value of ΔS is very small. Therefore, ΔG > 0 and spontaneous dissolution is not observed, and the limited swelling occurs. To a greater degree, this concerns crystalline polymers which are dissolved if ΔH < 0 and |ΔH| > |TΔS|. When the molecular mass of elastic polymers is increased, ΔH does not change, but ΔS decreases. The ΔG becomes less negative. In glassy polymers, the increase in molecu-

162

4.2 Effect of system variables on solubility

lar mass is accompanied by a decrease in ΔH and ΔS. The ΔS value changes faster than the ΔH value, therefore, the ΔG value becomes more negative, which means that the dissolution of polymeric homologs of the higher molecular weight becomes less favorable. Crystalline polymers dissolve usually less readily than amorphous polymers. Dissolution of crystalline polymers requires large expenditures of energy for chain separation. Polyethylene swells in hexane at the room temperature and dissolves at elevated temperature. Isotactic polystyrene does not dissolve at the room temperature in solvents capable to dissolve atactic polystyrene. To be dissolved, isotactic polystyrene must be brought to elevated temperature. 4.2.4 CROSSLINKING The presence of even a small amount of crosslinks hinders chain separation and polymer diffusion into solution. The solvent can penetrate the polymer and cause swelling. The swelling degree depends on crosslink density and compatibility of polymer and solvent. The correlation between thermodynamic parameters and the value of an equilibrium swelling is given by Flory-Rehner equation23 used now in a modified form:24 ν 2 1 ⁄ 3 2ϕ ln ( 1 – ϕ 2 ) + ϕ 2 + χ 1 ϕ 2 = – ----2- V s  ϕ 2 – --------2- V  f  where:

ϕ2 ν2/V f

[4.2.9]

polymer volume fraction in a swollen sample volume concentration of elastically active chains the functionality of the polymer network

The value of ν2/V is determined by the concentration of network knots. These knots usually have a functionality of 3 or 4. The functionality depends on the type of curing agent. Crosslinked polyurethanes cured by polyols with three OH groups are examples of the three-functional network. Rubbers cured through double bond addition are examples of four-functional networks. Eq. [4.2.9] has different forms depending on the form of elasticity potential but for practical purposes (evaluation of crosslink density of polymer networks) it is more convenient to use the above form. The equation can be used in a modified form if the concentration dependence of the parameter χ1 is known. The value of equilibrium swelling can be a practical criterion of solubility. Good solubility of linear polymers is expected if the value of equilibrium swelling is of the order of 300-400%. The high resistance of polymers to solvents indicates that the equilibrium swelling does not exceed several percents. In engineering data on swelling obtained at non-equilibrium conditions (for example, for any given time), swelling is frequently linked to the diffusion parameters of a system (see more on this subject in Subchapter 6.1).25 An interesting effect of swelling decrease occurs when the swollen polymer is placed in a solution of the linear polymer of the same structure as the crosslinked polymer. The decrease of solvent activity causes this effect. The quantitative description of these processes can be made by the scaling approach.26

Valery Yu. Senichev, Vasiliy V. Tereshatov

Figure 4.2.1 Two contributions to the χ1 parameter. 1 − χH, 2 − χS, 3 − the total value of χ1.

163

Figure 4.2.2 The χ1 parameter as a function of pressure at T = 300K, r1 = 3.5. The curves are for the fol* * lowing values of ε 11 ⁄ ε 22 = 0.85; 1.0 and 1.3 (After refs. 9,28).

4.2.5 TEMPERATURE AND PRESSURE The temperature effect on solubility may have different characters depending on the molecular structure of solute. For systems of liquid-amorphous or liquid-liquid polymers, the temperature rise can cause improvement of compatibility. Such systems are considered to have the upper critical solution temperature (UCST). If the system of two liquids becomes compatible at any ratio at the temperature below the defined critical point, the system is considered to have the lower critical solution temperature (LCST). Examples of a system with UCST are mixtures of methyl ethyl ketone-water (150oC) and phenol-water (65.8oC). An example of a system with LCST is the mixture of water-triethylamine (18oC). There are systems with both critical points, for example, nicotine-water and glycerol-benzyl-ethylamine. Presence of UCST in some cases means a rupture of hydrogen bonds on heating; however, in many cases, UCST is not determined by specific interactions, especially at high temperatures, and it is close to a critical temperature for the liquid-vapor system. There are suppositions that the UCST is the more common case, but one of the critical points for the polymer-solvent system is observed only at high temperatures. For example, polystyrene (M = 1.1×105) with methylcyclopentane has LCST 475K and UCST 370K. More complete experimental data on the phase diagrams of polymer-solvent systems are published elsewhere.27 The solubility of crystalline substances increases with temperature increasing. The higher the melting temperature of the polymer, the worse it’s solubility. Substances having higher melting heat are less soluble, with other characteristics being equal. Many crystalline polymers such as polyethylene or polyvinylchloride are insoluble at the room tem-

164

4.2 Effect of system variables on solubility

perature (only some swelling occurs); however, at the elevated temperature, they dissolve in some solvents. The experimental data on the temperature dependence of χ1 of polymer-solvent systems are described by the dependence χ1 = α + β/T. Often in temperatures below 100oC, β < 0.9 In a wide temperature range, this dependence decreases non-linearly. The negative contribution to ΔS and positive contribution to the χ1 parameter are related to the difference in free volume. On heating, the difference in free volumes of polymer and solvent increases as does the contribution into χS (Figure 4.2.1). For example, polyvinylchloride with dibutyl phthalate, tributylphosphate, and some other liquids have values β > 0. Figure 4.2.3. A phase diagram with the lower critical The dependence of solubility on pressolution temperature (LCST). 1 − binodal, 2 − spinodal; I − zone of non-stable conditions, II − zone of metasta- sure can be described only by modern theoble conditions, III − zone of the one phase conditions. ries taking into account the free volume of components.28 The corresponding state’s 12 theory predicts a pressure dependence of the χ1 parameter through the effect on the free volume of the solution components. This dependence is predicted by the so-called solubility parameters theory as well,28 where the interaction between solvent and solute is described by the solubility parameters with their dependencies on temperature and pres* * sure (Fig. 4.2.2). When ε 11 ⁄ ε 22 ≤ 1 then δ1 < δ2 and hence ∂χ 1 ⁄ ∂P < 0 in the solubility * * parameters theory and the corresponding states theory. When ε 11 ⁄ ε 22 is greater than unity, δ1 > δ2 and the solvent becomes less compressible with the polymer. Pressure can increase the δ1 − δ2 value, giving ∂χ 1 ⁄ ∂P > 0 . 4.2.6 METHODS OF CALCULATION OF SOLUBILITY BASED ON THE THERMODYNAMIC PRINCIPLES Within the framework of the general principles of thermodynamics of solutions, the evaluation of solubility implies the assessment of the value of the Gibbs energy of mixing in the whole range of concentrations of solution. However, such assessment is difficult and, for practical purposes, frequently unnecessary. The phase diagrams indicate areas of stable solutions. But affinity of solvent to polymer in each zone of phase diagram differs. It is more convenient to know the value of the interaction parameter, possibly with its concentration dependence. Practical experience from solvent selection for rubbers gives a foundation for the use of equilibrium swelling of a crosslinked elastomer in a given solvent as a criterion of solubility. The equilibrium swelling is related to the χ1 parameter by Eq. [4.2.9]. As previously discussed in Subchapter 4.1, the value of the χ1 parameter can be

Valery Yu. Senichev, Vasiliy V. Tereshatov

165

determined as a sum of entropy and enthalpy contributions. In the one-dimensional solubility parameter approach, one may use the following equation: 2

( δ1 – δ2 ) V1 χ 1 = χ S + ----------------------------RT where:

χS

[4.2.10]

the entropy contribution

In TDM approach, Eq. [4.1.45] can be used. Similar equations can be derived for the Hansen approach. All existing systems of solubility imply some constancy of the entropy contribution or even constancy of some limits of a change of the cohesion characteristics of polymers. Frequently χ1 = 0.34 is used in calculations. Phase diagrams are characterized by critical temperatures, spinodals, and binodals. A binodal is a curve connecting equilibrium structures of a stratified system. A spinodal is a curve defining the boundary of metastable condition (Fig. 4.2.3). Binodals are evaluated experimentally by light scattering at cloud point,29 by volume changes of coexisting phases,30 or by the electron probe R-spectral analysis.31 It is possible to calculate phase behavior, considering that binodals correspond to a condition: ( Δμ i )′ = ( Δμ i )″

[4.2.11]

where: i ( Δμ i )′, ( Δμ i )″

a component of a solution changes of chemical potential in phases of a stratified system

The equation for the spinodal corresponds to the condition 2 ∂ ( Δμ i ) ∂-----------------( ΔG ) - = 0 = ---------------2 ∂ϕ i ∂ϕ i

where:

ΔG Δϕ i

[4.2.12]

the Gibbs free mixing energy the volume fraction of a component of a solvent.

At a critical point, binodal and spinodal coincide. 3

2 ∂ ( Δμ i ) ∂-----------------( ΔG ) = -----------------2 3 ∂ϕ i ∂ϕ i

[4.2.13]

In the elementary case of a two-component system, the Flory-Huggins theory gives the following solution:3

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4.2 Effect of system variables on solubility

r 2 Δμ i = RT ln ϕ i +  1 – ---i ( 1 – ϕ i ) + r i χ 1 ϕ i  r j

[4.2.14]

where: ri, rj

numbers of segments of the corresponding component.

The last equation can be solved if one takes into account the equality of chemical potentials of a component in two co-existing phases of a stratified system. x x 2 2 ln ϕ i ′ +  1 – ----i ϕ j ′ + x i χ ij ( ϕ i ′ ) = ln ϕ i ″ +  1 – ----i ϕ j ″ + x i χ ij ( ϕ i ″ )   x j x j

[4.2.15]

The quantitative solubility of small amounts of solvents and plasticizers in glassy polymers can be described using the free-volume hole-filling model.32 This model takes pre-existing sites of the material that can be filled by absorption of molecules. However, corresponding calculations lead to significant errors often emphasizing the complexity of real interactions between solvents and glassy polymers. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

P.J. Flory, J. Chem. Phys., 9, 660, (1941). P.J. Flory, J. Chem. Phys., 10, 51 (1942). P.J. Flory, Principles of polymer chemistry, Cornell University Press, Ithaca, 1953. M.L. Huggins, J. Chem. Phys., 9, 440 (1941). J.H. Hildebrand and R.L. Scott, Solubility of none-electrolytes. 3rd ed., Reinhold, New-York, 1950. R.M.Masegosa, M.G. Prolonga, A. Horta, Macromolecules, 19, 1478 (1986) G.M. Bristow, J. Polym. Sci., 36, 526 (1959). J. Rehner, J. Polym. Sci., 46, 550 (1960). A.E. Nesterov, Handbook on physical chemistry of polymers. V. 1. Properties of solutions, Naukova Dumka, Kiev, 1984. I. Prigogine, The molecular theory of solutions, New York, Interscience, 1959. D. Patterson, G. Delmas, T. Somsynsky, J. Polym. Sci., 57, 79 (1962). D. Patterson, Macromolecules, 2, 672 (1969). P.J. Flory, R.A. Orwoll, A Vrij, J. Amer. Chem. Sci., 86, 3507 (1968). P.J. Flory, J. Amer. Chem. Sci., 87, 1833 (1965). A. Abe, P.J Flory, J. Amer. Chem. Sci., 87, 1838 (1965). V. Crescenzi, G. Manzini, J. Polym. Sci., C, 54, 315 (1976). A. Bondi, Physical properties of molecular crystals, liquids and glasses. New York, Wiley, 1968 M.L. Huggins, J. Phys. Chem., 74, 371 (1970). M.L. Huggins, Polymer, 12, 389 (1971). M.L. Huggins, J. Phys. Chem., 75, 1255 (1971). M.L. Huggins, Macromolecules, 4, 274 (1971). K. Thinius, Chem. Techn., 6, 330 (1954). P.J. Flory, J. Rehner, J. Chem. Phys., 11, 512 (1943). A.E. Oberth, R.S. Bruenner, J. Polym. Sci., 8, 605 (1970). U.S. Aithal, T.M. Aminabhavi, Polymer, 31, 1757 (1990). J. Bastide, S. Candau, L. Leibner, Macromolecules, 14, 319 (1981). A.E.Nesterov, Y.S. Lipatov, Phase condition of polymer solutions and mixtures, Naukova dumka, Kiev, 1987. J. Biros, L. Zeman, D.Patterson, Macromolecules, 4, 30 (1971). J.W. Kennedy, M. Gordon, G.A. Alvarez, J. Polym. Sci., 20, 463 (1975). R. Konningsveld, Brit. Polym. J., 7, 435 (1975). N.N. Avdeev, A.E. Chalych, Y.N. Moysa, R.C. Barstein, Vysokomol. soed., A22, 945 (1980). J.C. Arnold. Eur. Polym. J., 46, 1131 (2010).

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4.3 SOLVATION DYNAMICS: THEORY AND EXPERIMENTS Yogita Silori and Arijit K. De Department of Chemical Sciences, Indian Institute of Science Education and Research Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab 140 306, India. 4.3.1 INTRODUCTION Majority of chemical and biological processes take place in solution phase where the solvent dynamically controls the rates of many fundamental reactions (for example, electron and proton transfer) at ultrafast time scale.1-4 Solvent-induced dynamics or solvation dynamics have been extensively studied for polar solvents (as well as for non-polar solvents but to a much lesser extent). Usually, solvation dynamics refers to how solvent molecules respond to a sudden charge of re-distribution of a probe solute to stabilize the overall free energy of the solute-solvent system; however, same motions of the solvent molecules, that lead to such stabilization, can also be studied directly without using a probe molecule. There has been a great development of the theory of solvation using dielectric continuum models to understand the essential physics of polar solvation and extending it to much more sophisticated atomistic simulation to capture the underlying molecular motions. On the other hand, direct and indirect experimental measurement of motion of solvent molecules in response to a fast perturbation has shed insights into the nature of the local environment in a variety of chemical and biological systems. In this chapter, we wish to provide a concise yet comprehensive review of this vast field of research covering both developments of theoretical as well as experimental aspects of polar solvation dynamics with more emphasis on the latter. Starting with an overview of theoretical models, we aim to focus on providing a thorough discussion on a variety of experimental techniques followed by the wide-ranging applications of polar solvation dynamics. We would like to mention here that a chapter on the same topic in the earlier edition of this book5 focused only on the analytic theory and numerical simulation of polar solvation and it is highly recommended to an astute reader willing to have a deeper insight into the theoretical aspects. We organize this chapter in the following sections: In section 4.3.2, we first outline different theoretical models for bulk water, namely the “continuum model” (in section 4.3.2.1.1) and the “molecular model” (in section 4.3.2.1.2). We then discuss the model for “confined water” (in section 4.3.2.1.2). In the following section, we discuss different experimental techniques, those which use a probe solute (in section 4.3.3.1) and those which do not (in section 4.3.3.2). For either, we discuss some techniques including the most recent ones. In section 4.3.4, we provide an overview of the vast applications of solvation dynamics in systems with interfaces, namely supramolecular assemblies and biological macromolecules. The subsequent section summarizes solvation dynamics in solvents other than commonly used polar medium, for example, ionic liquids. Finally, we conclude with a note on future directions.

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4.3 Solvation dynamics: theory and experiments

4.3.2 THEORETICAL MODELS FOR SOLVATION DYNAMICS Some theoretical models on solvation dynamics were developed among which here we present a few. 4.3.2.1 Models for bulk solvation 4.3.2.1.1 Continuum model In this model,2,6-8 the polar solute is assumed as a spherical cavity with radius (a) containing a dipole at the center and the surrounding solvent is taken as a dielectric continuum with εc relative permittivity or dielectric constant. The potential energy from solute-solvent interaction can be shown as: 1 ΔE ( t ) = – --- ( ε c + 2 )μ ( t )R ( t ) 3

[4.3.1]

where, εc is the relative permittivity (dielectric constant) of a spherical cavity, R(t) is the time-dependent reaction field, μ(t) is solute's dipole moment at time t and |μ(t)| is the magnitude in the gas phase. At shorter times, ΔE(t) will be positive when the change in the direction of dipole moments is large (more than π/2) and hence the fluorescence spectrum shifts to blue due to increase in the energy gap. After reorientation of solute and solvent, it shifts to red. Frequency dependent dielectric constant ε(ω) of polar solvents can be assumed in two forms: (a) single exponential decay of orientational polarization corresponding to Debye form, (b) bi-exponential form (Budo form) but these can break down at high frequencies. If the solute's polarizability is neglected, then the time-dependent Stokes shift will not be dependent on the change in dipole moment. These polarizability effects are present in the reaction field R(t), which can be given by quasi-static boundary value calculation as follows: R ( ω ) = r ( ω )μ ( ω )

[4.3.2]

2  [ ε ( ω ) – εc ]  1 - × --- ( ε + 2 ) where r ( ω ) =  ----3  ---------------------------------- a  ε c [ 2ε ( ω ) + ε c ]  3 c  

[4.3.3]

After inverse Fourier transformation the equation can be written as: t

R(t) =

 dt'r ( t – t' )μ ( t' )

[4.3.4]

–∞

Here, r(t) is a stationary function of time which means polarizability of solute should not change. Frequency dependent dielectric constant can be calculated as: ε0 – ε∞ ε ( ω ) = ε ∞ + -------------------1 – iωτ D

[4.3.5]

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where, ε ∞ is the frequency dielectric constant of solvent at infinite time and τD is the Debye relaxation time. Here, it is assumed that r(t) is single exponential and r(t) can be written as: εc + 2 ( ε c – ε ∞ ) ( ε c + 2ε 0 ) t 2 - ------------------- ε – ε + --------------------------------------------- × exp  – ----- [4.3.6] r ( t ) =  ----------------- 3a 3 ε τ  2ε ∞ + ε c 0 c  τ L ε c + 2ε ∞ c D

ε c + 2ε ∞ where τ L = -------------------- τ D ε c + 2ε 0

[4.3.7]

Hence the correct relaxation time is τL which can be smaller than τD for highly polar solvents. For ion, this model shows faster solvation as follows: ε ∞ τ τ L =  ---- ε0  D

[4.3.8]

For multi exponential orientational correlation function of solvent molecules, frequency dependent dielectric constant can be shown as: N

ε ( ω ) = ε∞ + ( ε0 – ε∞ )

gk

 1------------------– iωτ k

k=1

[4.3.9] N

where, gk are the relative contributions with  g k = 1 . k=1

If dielectric relaxation is bi-exponential (Budo form) for most of the liquid monoal1 cohols with time constants τ1 and τ2, then C(t) is bi-exponential with rate constants τF and 2 τ as follows: F 1

–1

[4.3.10]

2

–1

[4.3.11]

τ F = ( S + + 2D ) τ F = ( S - + 2D )

1⁄2 1 2 where S + = --- [ A − + ( A – 4B ) ] 2

[4.3.12]

[ ( 2ε ∞ + ε c ) ( τ 1 + τ 2 ) + 2 ( ε 0 – ε ∞ ) ( g 1 τ 2 + g 2 τ 1 ) ] A = ------------------------------------------------------------------------------------------------------------------τ 1 τ 2 ( 2ε ∞ + ε c )

[4.3.13]

2ε 0 + ε c B = ----------------------------------τ 1 τ 2 ( 2ε ∞ + ε c )

[4.3.14]

where, D is the rotational diffusion constant of solute. The correlation function can be written as:

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4.3 Solvation dynamics: theory and experiments

 Δν f ( t ) –  Δν f ( ∞ ) C ( t ) = -------------------------------------------------- Δν f ( 0 ) –  Δν f ( ∞ )

[4.3.15]

ε∞ – 1  2 ε0 – 1 - – ----------------- ( μe – μg )2 where  Δν = -------3-  ---------------  + 1 + 1 2ε 2ε 0 ∞ ha

[4.3.16]

The above relation is also known as Ooshika-Lippert-Mataga equation. The dielectric relaxation times for propanol at 20oC are τ1 = 430 ps and τ2 = 21.9 ps, g1 = 0.91, g2 = 0.09, ε0 = 21.1, ε ∞ = 2.08 and D = 5×108 s-1 for a sphere of 5Å. Thus, 2 1 τ F =13 ps and τ F = 92 ps. Hence solvation correlation function C(t) shows a 1/e time 6 of ≈ 33 ps. If there is any charge transfer (CT) formation due to the intramolecular motion of solute, this theory cannot be compared with experimental values. Also, this theory breaks down when the change in the dipole is very large after photoexcitation. 4.3.2.1.2 Molecular model Linear response theory of solvation can be applied in molecular models.9 The Hamiltonian can be written as a sum over the unperturbed system (H0), i.e., a potential surface on which nucleus is moving and a perturbation (H') as follows: 0

H = H + H' where H' =

[4.3.17]

 Xj Fj ( t )

[4.3.18]

j

The perturbation can be shown as a sum of products of system variables Xj which are electric field components of solvent acting on solute and surrounding perturbations depending on time Fj(t) which are variable charge distribution. The first order change in the system can be written as:10 t 1

 X i ( t ) =

  Fj ( t' )Φ ij ( t – t' ) dt'

[4.3.19]

j –∞

The pulse response function Φij(t) is the linear response of average over ensemble which can be shown as: 1 0 Φ ij ( t ) = -------  X i X j ( t ) kT

[4.3.20]

This expression is related to the time-correlated function (TCF) of the system when the perturbation is absent. The small step change in solute's properties can be considered as: Fj ( t ) =

0, t < 0 Fj , t ≥ 0

[4.3.21]

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The general fluctuation-dissipation response can be written as: 1 1 1 0 0 0  X i ( t ) –  X i ( ∞ ) = -------  F j [  X i X j ( t ) –  X i  X j ] kT

[4.3.22]

j

When the system is equilibrated to perturbation, the value of Xi can be written as  X i ( ∞ ) . The electrostatic free energy of solvation corresponding to multipoles of solute is represented as:  1 ⁄ 2q ( t )  V ( t ) ch arg e  E solv ( t ) =  – 1 ⁄ 2μ z ( t )  E z ( t ) dipole   – 1 ⁄ 2Q zz ( t )  V zz ( t ) quadrupole

[4.3.23]

where q is the charge, μz is the dipole and Qzz is the quadruple moments' magnitudes of the spherical solute. V, Ez and Vzz are the electric potential, field and field gradient 2 2 ( – ∂ V ⁄ ∂z ) components induced by multipoles of solute while interacting with the solvent. The time-dependent perturbation corresponding to change in solute's quadrupole is H' = V zz ΔQ zz

[4.3.24]

This change can give rise to change in first order solvation free energy as: 1

1

ΔE solv ( t ) – ΔE solv ( ∞ )

1 1 1 = – --- Q zz [  V zz ( t ) –  V zz ( ∞ ) ] 2

[4.3.25]

1 0 0 0 = – ---------- Q zz ΔQ zz [  V zz V zz ( t ) –  V zz  V zz ( t ) ] 2kT 1 = – ---------- Q zz ΔQ zz  δV zz δV zz ( t ) 2kT where, superscripts 0 and 1 show field gradient in absence and presence of perturbation respectively. Hence the response function S(t) can be defined as: ΔE solv ( t ) – ΔE solv ( ∞ ) S ( t ) = -----------------------------------------------------ΔE solv ( 0 ) – ΔE solv ( ∞ )

[4.3.26]

The non-equilibrium response S(t) can be related to equilibrium time correlated function C(t) as follows:

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4.3 Solvation dynamics: theory and experiments

    Δq    C ( t ) ↔ S ( t )  Δμ z    ΔQ zz   ∂V zz ∂V zz ( t )  -----------------------------------2   ∂V zz   ∂V∂V ( t ) --------------------------2  ∂V   ∂E z ∂E z ( t ) -----------------------------2  ∂E z 

[4.3.27]

The temporal decay of fluctuations in V, Ez and Vzz shown above is collected from equilibrium MD simulations. For this model, solute should be of spherical symmetry as all the observables have radial dependency only and hence average over all directions will be easier. 4.3.2.2 Model for confined water The water molecules which are present in the vicinity of proteins or some other biomolecules known as “biological water” and show different behaviors (“bound” due to H-bonding as well as “free” due to dielectric relaxation) as compared with bulk water because of its vicinity to the interface. Nandi and Bagchi11 gave a theoretical model for dielectric relaxation of interfacial water. They showed that there is equilibrium for the dynamical exchange of free and bound water within the biomolecule as shown in Figure 4.3.1. [ H 2 O ] free ↔ [ H 2 O ] bound

[4.3.28]

The equilibrium constant can be shown as: 0 k – ΔG ⁄ RT K = ----2- = e k1

[4.3.29]

where ΔG0 is the difference in free energy per mole of H-bond between bound and free water. The orientation of free ( Ω f ) and bound ( Ω b ) water with fluctuation densities ρ f ( Ω f, t ) and ρ b ( Ω b, t ) , respectively in the hydration shell, are also included in this theoretical model. The orientation of bound water depends on the orientation of biomolecules due to H-bond coupling. The potential energy surface of bound water is lower in energy than free water due to H-bonding and the activation energy for the bound water to become free ΔG* is as shown in Figure 4.3.2. The diffusion equations for confined water can be written as: ∂ρ f ( Ω f, t ) 2 ----------------------- = Dw R ∇ Ω f ρ f ( Ω f , t ) – ρ f ( Ω f , t )  k 1 ( Ω f → Ω b ) dΩ b + ∂t +  k 2 ( Ω b → Ω f )ρ b ( Ω b, t ) dΩ b ∂ρ b ( Ω b, t ) ------------------------- = D BR ∇ 2Ω ρ b ( Ω b, t ) – ρ b ( Ω b, t )  k 2 ( Ω b → Ω f ) dΩ f + b ∂t

[4.3.30]

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Figure 4.3.1. Schematic diagram of free vs. bound water at a biomolecular surface in which k1 and k2 represent rate constants of dynamic exchange between free and bound water molecules in the hydration shell. [Adapted, by permission, from N. Nandi and B. Bagchi, J. Chem. Phys., 5647, 10954-61 (1997).]

+

Figure 4.3.2. Schematic representation of PES vs. reaction coordinate of free and bound water in which the free energy difference between both is shown by ΔG0 due to H-bonding and the activation energy is shown by ΔG* [Adapted, by permission, from N. Nandi and B. Bagchi, J. Chem. Phys., 5647, 10954-61 (1997).]

 k 1 ( Ω f → Ωb )ρf ( Ω f, t ) dΩf w

[4.3.31]

B

where D R and D R are rotational diffusion constant for free and bound water govern by biomolecule respectively. It is assumed that the orientation of water molecule does not change during the exchange and hence the rate constants are approximated as δ functions k1 ( Ωf → Ωb ) = δ ( Ωf → Ωb )

[4.3.32]

k2 ( Ωb → Ωf ) = δ ( Ωb → Ωf ) If the biomolecule is spherical, ten as:

[4.3.33] B DR

is isotropic, hence above equations can be writ-

∂ρ f ( Ω f, t ) 2 ----------------------- = Dw R ∇ Ω f ρ f ( Ω f, t ) – k 1 ρ f ( Ω f, t ) + k 2 ρ b ( Ω f, t ) ∂t

[4.3.34]

∂ρ b ( Ω b, t ) ------------------------- = D BR ∇ 2Ω ρ b ( Ω b, t ) – k 2 ρ b ( Ω b, t ) + k 1 ρ b ( Ω b, t ) b ∂t

[4.3.35]

Using above equations the differential equations for free and bound water can be written as:

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4.3 Solvation dynamics: theory and experiments 2

∂ ρ f ( Ω f, t ) B ∂ρ f ( Ω f, t ) ------------------------- + [ l ( l + 1 )D w R + k 1 + k 2 + l ( l + 1 )D R ] ------------------------ + 2 ∂t ∂t 2

w

2

B

w

B

+ [ l ( l + 1 )k 2 D R + l ( l + 1 ) D R D R + k 1 l ( l + 1 )D R ]ρ f ( Ω f, t ) = 0

[4.3.36]

2

∂ρ b ( Ω b, t ) ∂ ρ b ( Ω b, t ) --------------------------- + [ k 1 + k 2 + l ( l + 1 )D BR ] ------------------------ + 2 ∂t ∂t B

+ l ( l + 1 )k 1 D R ρ b ( Ω b, t ) = 0

[4.3.37]

The time dependent density ρ f ( Ω f, t ) can be represented as a spherical harmonics of rank l and projection m: ρ f ( Ω f, t ) =

f

 alm ( t )Ylm ( Ωf )

[4.3.38]

lm f

where a lm ( t ) represents the expansion coefficients corresponding to harmonics of different ranks and projections. The solution of the above equations for free water can be written as: f

a lm ( t ) = C 1 e

l

–n1 t

l

+ C2 e

–n2 t

[4.3.39] l

l

where, C1 and C2 are coefficients of two relaxation modes n 1 and n 2 have the forms given below: 2

2

– X – X – 4Y l – X + X – 4Y l n 1 = – ---------------------------------------, n 2 = – --------------------------------------2 2

[4.3.40]

where, w

B

X = [ l ( l + 1 )D R + k 1 + k 2 + l ( l + 1 )D R ] w

2

2

w

[4.3.41]

B

B

Y = [ l ( l + 1 )D R k 2 + l ( l + 1 ) D R D R + l ( l + 1 )k 1 D R ]

[4.3.42]

Similarly for bound water, solution can be written as: b

a lm ( t ) = C 3 e

l

–n3 t

l

+ C4 e

–n4 t

[4.3.43]

where, 2

2

– M – M – 4N l – M + M – 4N l n 3 = – -----------------------------------------, n 4 = – ----------------------------------------2 2

[4.3.44]

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where, B

M = [ k 1 + k 2 + l ( l + 1 )D R ]

[4.3.45]

B

N = [ l ( l + 1 )k 1 D R ] If

B DR

is very small,

b

b a lm ( t )

[4.3.46] can be written as:

l

a lm ( t ) = C 3 e

–n3 t

+ C4

[4.3.47]

At t=0, C1 + C2 = 1 = C3 + C4

[4.3.48]

b a lm ( t ) .

At t = ∞ , we get Hence C3 = 1 and C4 = 0 The conserved densities during exchange of free and bound water, give the following expression:  ρ f [ C 1 n 1 + C 2 n 2 ] +  ρ b  [ C 3 n 3 ] = 0

[4.3.49]

where  ρ f and  ρ b are the average densities of free and bound water respectively. They also proposed the moment-moment correlation function for a system having free as well as bound water molecules as given below: 2 N 2 2 N C MM ( t ) = N  -----f  μ f ( t ) μ f ( 0 ) +  -----b-  μ b ( t ) μ b ( 0 )  N  N

[4.3.50]

where μ f and μ b are the dipole moments and Nf and Nb are the number of free and bound water molecules per mole respectively. Also, Nf + Nb = N. Hence the above equation can be written as: C MM ( t ) = N μ n f  C 1 e  2 2

l

2

l

–n1 t

l

l

+ C2 e

l

B

 + n 2  e –n 3 t  e – t ⁄ τR b   

–n2 t

l

B

–n1 t –n2 t –n3 t –t ⁄ τR 2 2  + w2 e  + w3  e   e = N μ  w1 e     

[4.3.51]

where nf and nb are the fractions of free and bound water respectively and w1, w2, w3 are the weightage of relaxation modes. Here, it is assumed that the biomolecule and surrounding solvation shell (biological water) are spherical and beyond this shell, the water molecules are termed as bulk water. The relaxation process for hydration shell and bulk water (Debye type) is explained by frequency dependent dielectric function εB(ω) and εw(ω) respectively. For isotropic geometries, the net dipole moment per unit volume of hydration shell is generated by an external field as follows:

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4.3 Solvation dynamics: theory and experiments B

B

ε (ω) – ε (∞)  m z ( t ) E ( ∞ ) = ------------------------------------ V shell E z ( t ) 4π

[4.3.52]

where, Vshell is the volume and Ez(t) is the electric field inside the hydration shell. This field can be obtained by electrostatic boundary value calculations12 as follows: w

3ε ( ω ) E( ∞)( t) E z ( t ) = --------------------------------------w B 2ε ( ω ) + ε ( ω )

[4.3.53]

Hence the normalized moment-moment correlation function φ(t) can be written as: B

B

w

w

w

B

d [ ε ( ω ) – ε ( ∞ ) ] [ 2ε ( ω ) + ε ( ω ) ] [ 2ε ( 0 ) – ε ( 0 ) ] - [4.3.54] ∠ – ----- φ ( t ) = -------------------------------------------------------------------------------------------------------------------------------w B B B w w dt [ 2ε ( ω ) + ε ( ω ) ] [ ε ( 0 ) – ε ( ∞ ) ] [ 2ε ( 0 ) + ε ( ∞ ) ] where, ∠ represents Laplace transform using variable z = iω. This equation is used to calculate frequency dependent dielectric relaxation of confined water. 4.3.3 EXPERIMENTAL TECHNIQUES As outlined in the introduction, the dynamics of solvent molecules can be estimated experimentally either by using a probe molecule or directly probing the solvent molecules. In the former method, a probe is used to measure the dynamics of surrounding polar solvent molecules by observing changes in the excited state of probe caused by intermolecular relaxation as shown in Figure 4.3.3. However, in non-polar solFigure 4.3.3. Schematic diagram for potential energy surface of sol- vents only vibrational energy ute involved in solvation process. [Adapted, by permission, from relaxation of probe happens simiS. K. Pal, J. Peon, B. Bagchi and A. H. Zewail, J. Phys. Chem. B, lar to the gas phase. Another 106, 12376-12395(2002).] method explores dynamics directly from a neat solvent by measuring vibrational lifetime, molecular reorientation and spectral diffusion of solvent molecules as well as modes and shape fluctuations without relying on the properties of the probe molecule. 4.3.3.1 Solvation dynamics studies using a probe For indirect solvation dynamics studies, a suitable probe is chosen which has a very low dipole moment in the ground electronic state and solvents molecules around it are randomly pre-oriented. After photoexcitation charge redistribution happens and it becomes highly polar in the excited state. Due to instantaneous photoexcitation, initially (at t = 0) the solvent molecules remain randomly oriented but, with time, the solvent dipoles reori-

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ent gradually to stabilize the probe molecule and the energy gap of probe decreases. This leads to a spectral shift of emission of the probe as a function of time known as TimeResolved Fluorescence Stokes Shift (TRFSS) which directly relates to solvent correlation function by the following relation: ν( t) – ν( ∞) C ( t ) = ----------------------------ν(0) – ν(∞)

[4.3.55]

where, ν(0), ν(t) and ν( ∞ ) are the (central) frequencies at the time 0, t and ∞ , respectively. 4.3.3.1.1 Time-resolved fluorescence spectroscopy A variety of techniques like TCSPC, fluorescence up conversion, etc. have been extensively used in the past few decades to study solvation dynamics depending upon fluorescence properties of probe molecule. Time-correlated single photon counting (TCSPC) is one of the initial techniques with ~10-100 ps time resolution that has been used to study solvation dynamics by constructing TRES (time-resolved emission spectra) of the excited state. TRES can be recorded directly in TCSPC, but it has a serious limitation as it contains no deconvolution using IRF (instrument response function). Hence the recorded TRES show distorted spectra. Another way of recording TRES is an indirect way in which a series of time-resolved decays can be recorded at a number of selected wavelengths corresponding to steady state emission, F0(λ).13 The decays are rapid at shorter wavelength due to contribution from both emission and relaxation to a longer wavelength. However, at longer wavelengths, a growth component followed by decay is observed due to relaxation prior to emission. All the intensity decays I(λ,t) are usually fitted in a multi-exponential model as follows: n

I ( λ, t ) =

 αi ( λ ) exp i=1

t – -----------τi ( λ )

[4.3.56] n

where, αi(λ) are the amplitudes corresponding to decay times τi(λ) and  α i = 1 . Using i=1 this approach, the normalized TRES can be calculated as F0 ( λ ) F ( λ, t ) = I ( λ, t ) ------------------------∞ I ( λ , t ) d t 0

[4.3.57]

where, F0(λ) indicates steady state fluorescence spectrum of the chromophore in solution phase and I(λ,t) is the decay series (containing all lifetimes 'τ's and corresponding amplitudes 'α's) at some wavelengths of fluorescence spectrum. TRES can be used to define the nature and timescales of the relaxation process using equation [4.3.55]. However, using the above technique only the picosecond-nanosecond components of solvation can be captured but the early time component cannot be explored due instrument response (~300 ps). This can be improved to ~10 ps by using fast detectors, like a multichannel plate photomultiplier (MCP-PMT)13 along with numerical deconvolution. However, sub-10 ps component cannot be explored by this technique.

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4.3 Solvation dynamics: theory and experiments

Further time resolution can be obtained by fluorescence upconversion method using femtosecond lasers.14-17 The laser beam is split into two, in which one is delayed by an optical delay line (known as gate pulse) and the other excites the sample. The emitted fluorescence from the sample and the gate pulse finally overlaps in the nonlinear crystal in such a way that the phase matching condition between both the pulses is satisfied. The intensity of the upconverted signal is shown as the product of intensities of two incoming fields as follows: I upconv ( t ) ∼ I gate ( t ) × I fluorecence ( t )

[4.3.58]

Since the intensity of gate pulse is kept constant, the intensity of the unconverted signal is directly proportional to fluorescence intensity. With delaying the gate pulse, the fluorescence intensity can be calculated as a function of time. As the frequencies of the gate pulse and recorded signal (measured experimentally) are known, the frequency of fluorescence can be calculated by the following relation: 1 1 1 -------------------- = ---------------------------- + ----------λ recorded λ fluorescence λ gate

[4.3.59]

Hence, spectro-temporal data can also be collected using broadband upconversion method by scanning both wavelengths as well as delay.17 Fluorescence upconversion is an optical method, so the resolution completely depends on the pulse width of laser which is on the order of femtoseconds. The upconversion data is fitted by global fitting in the form of S(t) as 1 22 S ( t ) = α g exp  – --- ω t  + α 1 exp ( – t ⁄ τ 1 ) + α 2 exp ( – t ⁄ τ 2 )  2 

[4.3.60]

where, αg, α1 and α2 are the amplitudes of initial Gaussian and the exponential decays with corresponding relaxation times τ1 and τ2, respectively. Fleming and coworkers18 have shown the dynamics of water using coumarin 343 as water shows an extremely fast response. By using above fitting procedure, they found that the initial decay is faster than 55 fs (Gaussian component) and contributes 50% of the total decay whereas the other two components are 126 fs and 880 fs with 20% and 35% contributions. Numerical Figure 4.3.4. Steady state spectra of C153 in hexane (top simulations19 have shown that the ultrafast panel) and in methanol (solid curve) at bottom panel in which the dotted and connected points (triangles corre- component is mainly due to libration sponding to 0.1 ps, squares to 1 ps and circles to 50 ps) motion of water molecules whereas the line show time zero spectra after extrapolation to t=0. slow relaxation is due to translation. [Adapted, by permission, from R.S. Fee and M. Maroncelli, Chem. Phys, 183, 235-247 (1994)].

Yogita Silori and Arijit K. De

179

Figure 4.3.5. Plots of logarithmic correlation function for n-propanol (253K) using extrapolation method by taking ν(t) as: (1) average of half height points, (2) high frequencies half height point, (3) peak frequency of fitted data and (4) average frequency of fitted data at 280, 330, 230 and 320 ps time scales. [Adapted, by permission, from M. Maroncelli and G. R. Fleming, J. Chem. Phys., 86, 6221(1987).]

However, the time zero of solvation is the major problem in TRFSS using both the techniques TCSPC and upconversion, etc. Fee and Maroncelli20 have proposed a method to get time zero frequency (for the solvents other than H-bonded ones, which show fast solvation components, such as water and methanol) by taking the absorption and emission spectra of Figure 4.3.6. Schematic diagram of intermolecular vs. intramolecuthe probe in a non-polar solvent, lar relaxation using two different probes (top panel) and construction of correlation function using IRF (bottom left panel) and such as hexane as shown in Figure excitation frequency as time zero frequency of solvation (bottom 4.3.4. Another way is extrapola- right panel) shown by purple color. The blue, green and red curves tion method discussed by Maron- are corresponding to 50 ps, 350 ps and 10 ns respectively in w=3 reverse micelles. [Adapted, by permission, from Y. Silori, S. Dey celli and Fleming21 in which ν(t) and A.K. De, Chem. Phys. Lett., 693, 222-226 (2018).] data is extrapolated to t → 0 and ν ( ∞ ) is chosen by the limiting behavior of C(t) as the best guess at t = ∞ , when the change in ν ( ∞ ) is negligible (no effect on the fitting of C(t)) as shown in Figure 4.3.5. Recently, an ionic probe (e.g., fluoresceins, rhodamines) with very small Stokes shift, which is largely contributed by vibrational relaxation, has been used to probe water dynamics in bulk and confined medium.22 Unlike coumarins, these dyes are not at all suitable for probing solvation dynamics since both vibrational and inertial solvation relaxation are concurrent in solvents like water as shown in Figure 4.3.6. For such a non-ideal probe, a different method was proposed in which the excitation spectrum (zero time spec-

180

4.3 Solvation dynamics: theory and experiments

trum) itself was taken as time zero spectrum of solvation; this method was argued to hold for any narrow-band laser excitation (for example, laser diode excitation in TCSPC).22 4.3.3.1.2 Photon echo spectroscopy In three pulse photon-echo spectroscopy,23,24 three pulses interact with chromophore in which the first pulse (k1) creates coherence between two states; second pulse (k2) comes at a delay of 'τ' with respect to the first and converts the coherence into the population in the excited state; finally, the third pulse k3 comes at a delay of T with respect to second and creates coherence again and finally the echo signal ks is observed in phase matching direction − k1 + k2 + k3. In the population period, T spectral diffusion takes place. The 1-2-3 pulse sequence (τ>0) leads to integrated rephasing function (whereas 2-1-3 sequence (τ 0

[4.4.57] I

II

If this condition is not fulfilled between some concentrations ϕ 2 and ϕ 2 , demixing is obtained and the minimum of the Gibbs free energy of mixing between both concentrations is given by the double tangent at the corresponding curve of ΔmixG vs. ϕ 2 , Equation [4.4.8]. The resulting curve in the T vs. ϕ 2 diagram, see Figure 4.4.19a, is the binodal curve. Applying Equations [4.4.3 to 4.4.5 and 4.4.13a], one gets two relations which have to be solved simultaneously to fit an empirical χ(T)-function to experimental binodal (coexistence) data. For the most simple case of χ being only a function of T (or P) and not of ϕ 2 (the so-called one-parameter approach) these relations read: I

( 1 – ϕ2 )  1 I II I2 II2 ln -------------------+ 1 – --- ( ϕ 2 – ϕ 2 ) + χ ( ϕ 2 – ϕ 2 ) = 0 II   r ( 1 – ϕ2 )

[4.4.58.a]

and I

ϕ2  1 1 I II I2 II2 --- ln -----– 1 – --- ( ϕ 2 – ϕ 2 ) + χ ( ϕ 2 – ϕ 2 ) = 0 r ϕ II  r

[4.4.58b]

2

where:

I

ϕ2 II ϕ2 r χ

the volume fraction of the polymer in coexisting phase I the volume fraction of the polymer in coexisting phase II ratio of molar volumes V2/V1 what is the number of segments with Vseg = V1 Flory-Huggins interaction function of the solvent

and solvent activities result from Equation [4.4.13a]. However, this simple approach is of limited quality. More sophisticated models have to be applied to improve calculation results. A special curve is obtained with the borderline to the instability region, i.e., the spinodal curve, for which the second derivative in Equation [4.4.57] is equal to zero. If one applies again the one-parameter approach with an empirical χ(T)−function, the following simple result can be derived: 2χ ( T where:

spinodal

1 1 - – ----------------------------- = 0 ) – --------------------spinodal spinodal 1 – ϕ2 rϕ 2

[4.4.59]

spinodal temperature Tspinodal spinodal ϕ2 the volume fraction of the polymer at the spinodal curve

which has to fit an empirical χ(T)−function. An example for the spinodal relation of a polydisperse polymer was given above by Equations [4.4.44 and 4.4.45].

Christian Wohlfarth

241

The common point of the spinodal and binodal curve is the critical point. The critical point conditions are: 2

2

3

3

( ∂ Δ mix G ⁄ ∂ ϕ 2 ) P, T = 0 ; ( ∂ Δ mix G ⁄ ∂ ϕ 2 ) P, T = 0 and

[4.4.60] 2

4

( ∂ Δ mix G ⁄ ∂ ϕ 2 ) P, T > 0 If one applies again the one-parameter approach with an empirical χ(T)−function, two simple results can be derived: crit

ϕ2 where:

crit

ϕ2 Tcrit

0.5

= 1 ⁄ ( 1 + r ) and χ

crit

(T

crit

0.5 2

) = 0.5 ( 1 + 1 ⁄ r )

[4.4.61]

the volume fraction of the polymer at the critical point critical temperature

This means that the critical concentration is shifted to lower values with increasing segment number (molar mass) of the polymer and becomes zero for infinite molar mass. Equation [4.4.61] explains also why the χ(T)-function becomes 0.5 for infinite molar mass. The critical temperature of these conditions is then called theta-temperature. Solvent activities can be calculated from critical χ(T)-function data via Equation [4.4.13]. However, results are in most cases of approximate quality only. 4.4.3.2.8 Swelling equilibrium Polymers, crosslinked sufficiently to form a three-dimensional network, can absorb solvent up to a large extent. The maximum possible solvent concentration and the degree of swelling are the functions of solvent activity. If a solvent is present in excess, this swelling equilibrium is reached when the chemical potential of the pure solvent outside the network is equal to the chemical potential inside the swollen sample. This means, there must be an additional contribution to the Gibbs free energy of mixing (as is the case with the osmotic equilibrium) besides the common terms caused by mixing the (virtually) infinite-molarmass polymer and the solvent. This additional part follows from the elastic deformation of the network. The different aspects of chemical and physical networks will not be discussed here, for some details please see Refs.201-205 The following text is restricted to the aspect of solvent activities only. One method to obtain solvent activities in swollen polymer networks in equilibrium is to apply vapor pressure measurements. This is discussed in detail above in the Section 4.3.1.1 and most methods can be used also for network systems, especially all sorption methods, and need no further explanation. The VPO-technique can be applied for this purpose, e.g., Arndt.206,207 IGC-measurements are possible, too, if one realizes a definitely crosslinked polymer in the column, e.g., Refs.208-210 Besides vapor sorption/pressure measurements, definite swelling and/or deswelling experiments lead to information on solvent activities. Swelling experiments work with pure solvents, deswelling experiments use dilute solutions of macromolecules (which must not diffuse into or adsorb at the surface of the network) and allow measurements in

242

4.4 Methods for the measurement of solvent activity of polymer

dependence on concentration. Deswelling experiments can be made in dialysis cells to prevent diffusion into the network. The determination of the equilibrium swelling/ deswelling concentration can be made by weighing, but, in most cases, by measuring the swelling degree. Some methods for measuring the swelling degree are: measuring the buoyancy difference of the sample in two different liquids of known density, e.g., Rijke and Prins,211 measuring the volume change by cathetometer, e.g., Schwarz et al.,212 measuring the volume change by electrical (inductive) measurements, e.g., Teitelbaum and Garwin.213 The swelling degree can be defined as the ratio of the masses (mass-based degree) or of the volumes (volume-based degree) of the swollen to the dry polymer network sample: Q m = 1 + m 1 ⁄ m N or Q v = 1 + ν 1 ⁄ ν n = 1 + ( Q m – 1 ) ( ρ n ⁄ ρ 1 )

[4.4.62]

where: Qm Qv m1 mN ν1 νn ρ1 ρn

mass based degree of swelling volume based degree of swelling absorbed mass of the solvent mass of the dry polymer network absorbed volume of the solvent volume of the dry polymer network density of the solvent density of dry polymer network

Since Qv = 1/ ϕ 2 , usually volume changes were measured. If the sample swells isotropically, the volume change can be measured by the length change in one dimension. Calculation of solvent activities from measurements of the swelling degree needs a statistical thermodynamic model. According to Flory,46 a closed thermodynamic cycle can be constructed to calculate the Gibbs free energy of swelling from the differences between the swelling process, the solution process of the linear macromolecules, the elastic deformation and the crosslinking. The resulting equation can be understood in analogy to the Flory-Huggins relation, Equation [4.4.13a] with r → ∞ , and reads: 2

1⁄3

Δμ 1 ⁄ RT = ln ( 1 – ϕ 2 ) + ϕ 2 + χϕ 2 + ν c V 1 ( Aηϕ 2 where:

νc V1 η A B Mc ϕ2 χ

– Bϕ 2 )

[4.4.63]

network density νc = ρN/Mc molar volume of the pure liquid solvent 1 at temperature T memory term microstructure factor volume factor molar mass of a network chain between two network knots equilibrium swelling concentration = 1/Qv Flory-Huggins χ-function

A numerical calculation needs knowledge of the solvent activity of the corresponding homopolymer solution at the same equilibrium concentration j (here characterized by the value of the Flory-Huggins χ-function) and the assumption of a deformation model that provides values of the factors A and B. There is an extensive literature for statistical thermodynamic models which provide, for example, Flory:46 A = 1 and B = 0.5; Her-

Christian Wohlfarth

243

mans:214 A=1 and B=1; James and Guth215 or Edwards and Freed:216 A = 0.5 and B = 0. A detailed explanation was given recently by Heinrich et al.203 The swelling equilibrium depends on temperature and pressure. Both are related to the corresponding dependencies of solvent activity via its corresponding derivative of the chemical potential: ∂T- 1 ∂μ 1 T ∂μ 1  -------= ---------  --------- = ----------  ---------  ∂ϕ 1 P ΔS 1  ∂ϕ 1 P, T ΔH 1  ∂ϕ 1 P, T where:

ϕ1 ΔS1 ΔH1

[4.4.64]

equilibrium swelling concentration of the solvent differential entropy of dilution at equilibrium swelling differential enthalpy of dilution at equilibrium swelling where ΔH1 = TΔS1

The first derivative in Equation [4.4.64] describes the slope of the swelling curve. Since the derivative of the chemical potential is always positive for stable gels, the positive or negative slope is determined by the differential enthalpy or entropy of dilution, Rehage.217 ∂μ ∂P- 1  -------= ------------------------  --------1-  ∂ϕ 1 T ( V 1 – V 1 )  ∂ϕ 1 P, T

[4.4.65]

where: V1 V1

the partial molar volume of the solvent in the polymer solution at temperature T molar volume of the pure solvent at temperature T

In analogy to membrane osmometry, swelling pressure measurements can be made to obtain solvent activities. Pure solvents, as well as dilute polymer solutions, can be applied. In the case of solutions, the used macromolecules must not diffuse into or adsorb at the surface of the network. Two types of swelling pressure apparatuses have been developed. The anisochoric swelling pressure device measures swelling degrees in dependence on pressure and swelling volume, e.g., Borchard.218 The isochoric swelling pressure device applies a compensation technique where the volume is kept constant by an external pressure which is measured, e.g., Borchard.219 Swelling pressures can also be measured by sedimentation equilibrium using an ultracentrifuge for details, please see Borchard.220,221 The swelling pressure πswell is directly related to the solvent activity by: Δμ 1 = RT ln a 1 = – Vπ swell

[4.4.66]

and may be in the range of some MPa. In comparison with all methods of determination of solvent activities from swelling equilibrium of network polymers, the gravimetric vapor sorption/pressure measurement is the easiest applicable procedure. It gives the most reliable data and should be preferred. 4.4.4 THERMODYNAMIC MODELS FOR THE CALCULATION OF SOLVENT ACTIVITIES OF POLYMER SOLUTIONS Since measurements of solvent activities of polymer solutions are very time-consuming and can hardly be made to cover the whole temperature and pressure ranges, good thermo-

244

4.4 Methods for the measurement of solvent activity of polymer

dynamic theories, and models are necessary, which are able to calculate them with sufficient accuracy and which can interpolate between and even extrapolate from some measured basic data over the complete phase and state ranges of interest for a special application. Many attempts have been made to find theoretical explanations for the non-ideal behavior of polymer solutions. There exist books and reviews on this topic, e.g., Refs.2,41,42,46-49 Therefore, only a short summary of some of the most important thermodynamic approaches and models will be given here. The following explanations are restricted to the concentrated polymer solutions only because one has to describe mainly concentrated polymer solutions when solvent activities have to be calculated. For dilute polymer solutions, with the second virial coefficient region, Yamakawa's book222 provides a good survey. There are two different approaches for the calculation of solvent activities of polymer solutions: (i) the approach which uses activity coefficients, starting from Equation [4.4.11] (ii) the approach which uses fugacity coefficients, starting from Equations [4.4.5 and 4.4.6]. From the historical point of view and also from the number of applications in the literature, the common method is to use activity coefficients for the liquid phase, i.e., the polymer solution, and a separate equation-of-state for the solvent vapor phase, in many cases the truncated virial equation of state as for the data reduction of experimental measurements explained above. To this group of theories and models also free-volume models and lattice-fluid models will be added because they are usually applied within this approach. The approach where fugacity coefficients are calculated from one equation of state for both phases was applied to polymer solutions more recently, but it is the more promising method if one has to extrapolate over larger temperature and pressure ranges. Theories and models are presented below without going into details and without claiming completeness since this text is not dedicated to theoretical problems but will only provide some help to calculate solvent activities. 4.4.4.1 Models for residual chemical potential and activity coefficient in the liquid phase Since polymer solutions in principle do not fulfill the rules of the ideal mixture but show strong negative deviations from Raoult's law due to the difference in molecular size, the athermal Flory-Huggins mixture is usually applied as the reference mixture within polymer solution thermodynamics. Starting from Equation [4.4.11] or from ∂nΔ mix G 0 RT ln a 1 = RT ln x 1 γ 1 = Δμ 1 = μ 1 – μ 1 =  -------------------- ∂n 1  T, P, n j ≠ 1 where: a1 x1 λ1 μ1 0 μ1

activity of the solvent mole fraction of the solvent activity coefficient of the solvent in the liquid phase with activity a1 = x1γ1 chemical potential of the solvent chemical potential of the solvent at standard state conditions

[4.4.67]

Christian Wohlfarth R T n1 n ΔmixG

245 gas constant absolute temperature amount of substance (moles) of the solvent total amount of substance (moles) in the polymer solution molar Gibbs free energy of mixing,

the classical Flory-Huggins theory46,47 leads, for a truly athermal binary polymer solution, to: athermal

1 ⁄ RT = ln ( 1 – ϕ 2 ) +  1 – --- ϕ 2  r

athermal

= Δμ 1

athermal

1 1 = ln 1 –  1 – --- ϕ 2 +  1 – --- ϕ 2   r r

ln a 1

[4.4.68a]

or ln γ 1 where:

ϕ2

[4.4.68b]

the volume fraction of the polymer

which is also called the combinatorial contribution to solvent activity or chemical potential, arising from the different configurations assumed by polymer and solvent molecules in solution, ignoring energetic interactions between molecules and excess volume effects. The Flory-Huggins derivation of the athermal combinatorial contribution contains the implicit assumption that the r-mer chains placed on a lattice are perfectly flexible and that the flexibility of the chain is independent of the concentration and of the nature of the solvent. Generalized combinatorial arguments for molecules containing different kinds of energetic contact points and shapes were developed by Barker223 and Tompa,224 respectively. Lichtenthaler et al.225 have used the generalized combinatorial arguments of Tompa to analyze VLE of polymer solutions. Other modifications have been presented by Guggenheim226,227 or Staverman228 (see below). The various combinatorial models are compared in a review by Sayegh and Vera.229 Freed and coworkers230-232 developed a latticefield theory, that, in principle, provides an exact mathematical solution of the combinatorial Flory-Huggins problem. Although the simple Flory-Huggins expression does not always give the (presumably) correct, quantitative combinatorial entropy of mixing, it qualitatively describes many features of athermal polymer solutions. Therefore, for simplicity, it is used mostly in the further presentation of models for polymer solutions as the reference state. The total solvent activity/activity coefficient/chemical potential is simply the sum of the athermal part (as given above) and a residual contribution: athermal

ln a 1 = ln a 1

residual

+ ln a 1

[4.4.69a]

or 0

athermal

μ1 = μ1 + μ1

residual

+ μ1

[4.4.69b]

246

4.4 Methods for the measurement of solvent activity of polymer

The residual part has to be explained by an additional model and a number of suitable models is now listed in the following text. The Flory-Huggins interaction function of the solvent is the residual function used residual 2 ⁄ RT = χϕ 2 . It was first and it is given by Equations [4.4.12 and 4.4.13] with μ 1 originally based on van Laar's concept of solutions where excess entropy and excess volume of mixing could be neglected and χ is represented only in terms of an interchange energy Δε/kT. In this case, the interchange energy refers not to the exchange of solvent and solute molecules but rather to the exchange of solvent molecules and polymer segments. For athermal solutions, χ is zero, and for mixtures of components that are chemically similar, χ is small compared to unity. However, χ is not only a function of temperature (and pressure) as was evident from this foundation, but it is also a function of composition and polymer molecular mass, see e.g., Refs.5,7,8 If we neglect these dependencies, then the Scatchard-Hildebrand theory,233,234 i.e., their solubility parameter concept, could be applied: residual

μ1

2

2

⁄ RT = ( V 1 ⁄ RT ) ( δ 1 – δ 2 ) ϕ 2

[4.4.70]

with 0

δ 1 ( Δ vap U 1 ⁄ V 1 )

1⁄2

[4.4.71]

where: V1 0 Δ vap U 1 δ1 δ2

molar volume of the pure liquid solvent 1 at temperature T molar energy of vaporization of the pure liquid solvent 1 at temperature T solubility parameter of the pure liquid solvent solubility parameter of the polymer

Solubility parameters of polymers cannot be calculated from the energy of vaporization since polymers do not evaporate. Usually, they have been measured according to Equation [4.4.70], but details need not be explained here. Equation [4.4.70] is not useful for an accurate quantitative description of polymer solutions but it provides a good guide for a qualitative consideration of polymer solubility. For good solubility, the difference between both solubility parameters should be small (the complete residual chemical potential term cannot be negative, which is one of the disadvantages of the solubility parameter approach). Several approximate generalizations have been suggested by different authors − a summary of all these models and many data can be found in the books by Barton.11,12 Calculations applying additive group contributions to obtain solubility parameters, especially of polymers, are also explained in the book by Van Krevelen.235 Better-founded lattice models have been developed in the literature. The ideas of Koningsveld and Kleintjens, e.g., Ref.,51 lead to useful and easy to handle expressions, as is given above with Equations [4.4.15, 4.4.17 and 4.4.46] that have been widely used, but mainly for liquid-liquid demixing and not so much for vapor-liquid equilibrium and solvent activity data. Comprehensive examples can be found in the books by Fujita41 or Kamide.42 The simple Flory-Huggins approach and the solubility parameter concept are inadequate when tested against experimental data for polymer solutions. Even for mixtures of

Christian Wohlfarth

247

n-alkanes, the excess thermodynamic properties cannot be described satisfactorily − Flory et al.236-239 In particular, changes of volume upon mixing are excluded and observed excess entropies of mixing often deviate from simple combinatorial contributions. To account for these effects, the PVT-behavior has to be included in theoretical considerations by an equation of state. Pure fluids have different free volumes, i.e., different degrees of thermal expansion depending on temperature and pressure. When liquids with different free volumes are mixed, that difference contributes to the excess functions. Differences in free volumes must be taken into account, especially for mixtures of liquids whose molecules differ greatly in size, i.e., the free volume dissimilarity is significant for polymer solutions and has important effects on their properties, such as solvent activities, excess volume, excess enthalpy, and excess entropy. Additionally, the free volume effect is the main reason for liquid-liquid demixing with LCST behavior at high temperatures.240,241 There are two principal ways to develop an equation of state for polymer solutions: first, to start with an expression for the canonical partition function utilizing concepts similar to those used by van der Waals (e.g., Prigogine,242 Flory et al.,236-239 Patterson,243,244 Simha and Somcynsky,245 Sanchez and Lacombe,246-248 Dee and Walsh,249 Donohue and Prausnitz,250 Chien et al.251), and second, which is more sophisticated, to use statistical thermodynamics perturbation theory for freely-jointed tangent-sphere chain-like fluids (e.g., Hall and coworkers,252-255 Chapman et al.,256-258 Song et al.259,260). A comprehensive review of equations of state for molten polymers and polymer solutions was given by Lambert et al.261 Here, only some resulting equations will be summarized under the aspect of calculating solvent activities in polymer solutions. The theories that are usually applied within activity coefficient models are given now, the other theories are summarized in Section 4.4.4.2. The first successful theoretical approach of an equation of state model for polymer solutions was the Prigogine-Flory-Patterson theory.236-242 It became popular in the version by Flory, Orwoll and Vrij,236 and is a van-der-Waals-like theory based on the corresponding-states principle. Details of its derivation can be found in numerous papers and books and need not be repeated here. The equation of state is usually expressed in a reduced form and reads: ˜ ˜ 1⁄3 1 P˜ V V - – -------------- = ------------------1⁄3 ˜ T˜ ˜ V T˜ V –1

[4.4.72]

where the reduced PVT-variables are defined by P˜ = P ⁄ P*,˜T = T ⁄ T*,˜V = V ⁄ T*, P*V*=rcRT

[4.4.73]

and where a parameter c is used (per segment) such that 3rc is the number of effective external degrees of freedom per (macro)molecule. This effective number follows from Prigogine's approximation that external rotational and vibrational degrees of freedom can be considered as equivalent translational degrees of freedom. The equation of state is valid for liquid-like densities and qualitatively incorrect at low densities because it does not ful-

248

4.4 Methods for the measurement of solvent activity of polymer

fill the ideal gas limit. To use the equation of state, one must know the reducing or characteristic parameters P*, V*, T*. These have to be fitted to experimental PVT-data. Parameter tables can be found in the literature − here we refer to the book by Prausnitz et al.,49 a review by Rodgers,262 and the contribution by Cho and Sanchez263 to the edition of the Polymer Handbook. To extend the Flory-Orwoll-Vrij model to mixtures, one has to use two assumptions: (i) the hard-core volumes υ* of the segments of all components are additive and (ii) the intermolecular energy depends in a simple way on the surface areas of contact between solvent molecules and/or polymer segments. Without any derivation, the final result for the residual solvent activity in a binary polymer solution reads: * * ˜ 1⁄3 – 1 P1 V1 ˜ 1 1 V ----------- 3T 1 ln ------------------- +  ------ – ---- + = 1⁄3 ˜ V ˜ RT ˜ 1 V V –1

residual ln a 1

*

*

V X 12 2 PV 1 ˜ ˜ - θ + ---------- ( V – V 1 ) + -------1-  ------˜  2 RT RT  V

[4.4.74]

where interaction parameter surface fraction of the polymer

X12 θ2

The last term in Equation [4.4.74] is negligible at normal pressures. The reduced volume of the solvent 1 and the reduced volume of the mixture are to be calculated from the same equation of state, Equation [4.4.72], but for the mixture, the following mixing rules have to be used (if random mixing is assumed): *

*

*

P = P 1 ψ 1 + P 2 ψ 2 – ψ 1 θ 2 X 12 *

*

*

*

[4.4.75a] *

T = ( P* ) ⁄ [ ( P 1 ψ 1 ⁄ T 1 ) + ( P 2 ψ 2 ⁄ T 2 ) ]

[4.4.75b]

where the segment fractions ψ i and the surface fractions θi have to be calculated according to: *

*

*

ψ i = n i V i ⁄  n k V k = m i V spez, i ⁄  m k V θi = ψi si ⁄  ψk sk

*

spez, k

= xi ri ⁄  xk rk

[4.4.76a] [4.4.76b]

where: mi xi ri si

mass of component i mole fraction of component i * * number of segments of component i, here with ri/rk = V i ⁄ V k and r1 = 1 number of contact sites per segment (proportional to the surface area per segment)

Now it becomes clear from Equation [4.4.74] that the classical Flory-Huggins χ2 residual function ( χψ 2 = ln a 1 ) varies with composition, as found experimentally. However, to calculate solvent activities by applying this model, a number of parameters have to be

Christian Wohlfarth

249

considered. The characteristic parameters of the pure substances have to be obtained by fitting to experimental PVT-data as explained above. The number of contact sites per segment can be calculated from Bondi's surface-to-volume parameter tables264 but can also be used as a fitting parameter. The X12-interaction parameter has to be fitted to experimental data of the mixture. Fitting to solvent activities, e.g., Refs.,265,266 does not always give satisfactorily results. Fitting to data for the enthalpies of mixing gives comparable results.266 Fitting to excess volumes alone does not give acceptable results.142 Therefore, a modification of Equation [4.4.74] was made by Eichinger and Flory142 by appending the term * 2 – ( V 1 ⁄ R )Q 12 θ 2 where the parameter Q12 represents the entropy of interaction between unlike segments and is an entropic contribution to the residual chemical potential of the solvent. By adjusting the parameter Q12, a better representation of solvent activities can be obtained. There are many papers in the literature that applied the Prigogine-Flory-Patterson theory to polymer solutions as well as to low-molecular mixtures. Various modifications and improvements were suggested by many authors. Sugamiya267 introduced polar terms by adding dipole-dipole interactions. Brandani268 discussed effects of non-random mixing on the calculation of solvent activities. Kammer et al.269 added a parameter reflecting differences in a segment size. Shiomi et al.270,271 assumed non-additivity of the number of external degrees of freedom with respect to segment fraction for mixtures and assumed the sizes of hard-core segments in pure liquids and in solution to be different. Also, Panayiotou272 accounted for differences in segment size by an additional parameter. Cheng and Bonner273 modified the concept to obtain an equation of state which provides the correct zero pressure limit of the ideal gas. An attractive feature of the theory is its straightforward extension to multi-component mixtures,274 requiring only parameters of pure components and binary ones as explained above. A general limitation is its relatively poor description of the compressibility behavior of polymer melts, as well as its deficiencies regarding the description of the pressure dependence of thermodynamic data of mixtures. Dee and Walsh249 developed a modified version of Prigogine's cell model that provides an excellent description of the PVT-behavior of polymer melts: ˜ ˜ 1⁄3 2 1.2045 1.011 P˜ V V - – ---  --------------- – ------------------- = -----------------------------------1⁄3 ˜ ˜2 ˜ ˜4  T T˜ V – 0.8909q V V

[4.4.77]

where the reduced variables and characteristic parameters have the same definitions as in the Flory model above. Equation [4.4.77] is formally identical with Prigogine's result, except for the additional constant parameter q, which can also be viewed as a correction to the hard-core cell volume. The value of q = 1.07 corresponds approximately to a 25% increase in the hard-core volume in comparison with the original Prigogine model. Characteristic parameters for this model are given in Refs.249,262 The final result for the residual solvent activity in a binary polymer solution reads: residual

ln a 1

* * ˜ 1 ⁄ 3 – 0.8909q P1 V1 ˜ V 1.2045 1.2045 0.5055 0.5055 1 - 3T 1 ln ------------------------------------ +  ---------------- – ---------------- –  ---------------- – ---------------- = ----------1⁄3 2   ˜2  ˜4 RT ˜ ˜ ˜4  V1 V – 0.8909q V V1 V

250

4.4 Methods for the measurement of solvent activity of polymer * 2

*

PV ˜ ˜ V1 θ2 1.2045- 0.5055 ˜ )  --------------- ( X 12 – TQ 12 V - + ---------1- ( V – --------------+ ----------– V1 ) 2 4   RT RT ˜ ˜ V V

[4.4.78]

The last term in Equation [4.4.78] is again negligible at normal pressures, which is the case for the calculation of solvent activities of common polymer solutions. The reduced volume of the mixture is to be calculated from the equation of state where the same mixing rules are valid, as given by Equations [4.4.75, 4.4.76] if random mixing is assumed. Equation [4.4.78] is somewhat more flexible than Equation [4.4.74]. Again, entropic parameter Q12 and interaction parameter X12 have to be fitted to experimental data of the mixture. There is not much experience with the model regarding thermodynamic data of polymer solutions because it was mainly applied to polymer blends, where it provides much better results than the simple Flory model. To improve on the cell model, two other classes of models were developed, namely, lattice-fluid and lattice-hole theories. In these theories, vacant cells or holes are introduced into the lattice to describe the extra entropy change in the system as a function of volume and temperature. The lattice size, or cell volume, is fixed so that the changes in volume can only occur by the appearance of new holes, or vacant sites, on the lattice. The most popular theories of such kind were developed by Simha and Somcynsky245 or Sanchez and Lacombe.246-248 The Sanchez-Lacombe lattice-fluid equation of state reads: ˜ ˜ –1 1 P˜ V 1 V ˜ ln ------------------- = --- – 1 – V - – -------˜T ˜ ˜ T˜ r V V

[4.4.79]

where the reduced parameters are given in Equation [4.4.73], but no χ-parameter is included, and the size parameter, r, and the characteristic parameters are related by *

*

P V = ( r ⁄ M )RT

[4.4.80]

where: r M

size parameter (segment number) molar mass

In comparison with Equation [4.4.72], the size parameter remains explicit in the reduced equation of state. Thus, a simple corresponding-states principle is not, in general, satisfied. But, in principle, this equation of state is suitable for describing thermodynamic properties of fluids over an extended range of external conditions from the ordinary liquid to the gaseous state (it gives the correct ideal gas limit) and also to conditions above the critical point where the fluid is supercritical. Equation of state parameters for many liquids and liquid/molten polymers have recently been reported by Sanchez and Panayiotou275 and for polymers by Rodgers262 and by Cho and Sanchez.263 To extend the lattice fluid theory to mixtures, appropriate mixing rules are needed. There is a fundamental difficulty here, because the segment size of any component is not necessarily equal to that of another but the molecular hard-core volume of a component must not change upon mixing. Conse-

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quently, the segment number of a component in the mixture, ri, may differ from that for the 0 pure fluid, r i . But, following the arguments given by Panayiotou,276 the number of segments may remain constant in the pure state and in the mixture. This assumption leads to a simpler formalism without worsening the quantitative character of the model. Thus, the following mixing rules may be applied: *

*

*

P = P 1 ψ 1 + P 2 ψ 2 – ψ 1 ψ 2 X 12 *

*

[4.4.81a]

V = ΣΣψ i ψ j V ij

[4.4.81b]

1 ⁄ r = Σψ i ⁄ r i

[4.4.81c]

*

*

*

where V ii = V i and V ij provides an additional binary fitting parameter and Equation [4.4.80] provides the mixing rule for T*. The final result for the residual solvent activity in a binary polymer solution reads: residual

ln a 1

˜ –1 ˜ –1 ˜ V V 1 ˜ – 1 ) ln V ˜ – 1 ) ln -------------- – ln ----------------- – r 1 ( V = r1 ( V - − 1 ˜ ˜ ˜ V1 V V1

˜ –V ˜ ) r1 1 1 X 12 2 r 1 P˜ 1 ( V 1 − -----  ---- – ------ + r 1  -------- ψ 2 + ------------------------------ V ˜T ˜T V ˜  ˜ V ˜ 1 1 1

[4.4.82]

The last term in Equation (4.4.82) is again negligible at normal pressures. Various other approximations were given in the literature. For example, one can assume random mixing of contact sites rather than random mixing of segments,277,278 as well as non-random mixing.277,279 The model is applicable to solutions of small molecules as well as to polymer solutions. Like the Prigogine-Flory-Patterson equation of state, the lattice-fluid model and its variations have been used to correlate the composition dependence of the residual solvent activity.277,279 These studies show that entropic parameter Q12 and interaction parameter X12 have to be fitted to experimental data of the mixture to provide better agreement with measured solvent activities. The model and its modifications have been successfully used to represent thermodynamic excess properties, VLE and LLE for a variety of mixtures, as summarized by Sanchez and Panayiotou.275 In addition to mixtures of polymers with normal solvents, the model can also be applied to polymer-gas systems, Sanchez and Rodgers.280 In lattice-hole theories, vacant cells or holes are introduced into the lattice, which describe the major part of thermal expansion, but changes in cell volume are also allowed which influence excess thermodynamic properties, as well. The hole theory for polymeric liquids as developed by Simha and Somcynsky245 provides a very accurate equation of state that works much better than the Prigogine-Flory-Patterson equation of state or the Sanchez-Lacombe lattice-fluid model with respect to the precision how experimental PVT-data can be reproduced. However, the Dee-Walsh equation of state, Equation [4.4.77], with its more simple structure, works equally well. The Simha-Somcynsky equation of state must be solved simultaneously with an expression that minimizes the partition

252

4.4 Methods for the measurement of solvent activity of polymer

function with respect to the fraction of occupied sites and the final resulting equations for the chemical potential are more complicated. Details of the model will not be provided here. Characteristic parameters for many polymers have recently been given by Rodgers262 or Cho and Sanchez.263 The model is applicable to solutions of small molecules as well as to polymer solutions. Binary parameters have to be fitted to experimental data as with the models explained above. Again, one can assume random mixing of contact sites rather than random mixing of segments as well as non-random mixing, as was discussed, for example, by Nies and Stroeks281 or Xie et al.282,283 Whereas the models given above can be used to correlate solvent activities in polymer solutions, attempts also have been made in the literature to develop concepts to predict solvent activities. Based on the success of the UNIFAC concept for low-molecular liquid mixtures,284 Oishi and Prausnitz285 developed an analogous concept by combining the UNIFAC model with the free-volume model of Flory, Orwoll and Vrij.236 The mass fraction based activity coefficient of a solvent in a polymer solution is given by: comb

ln Ω 1 ln ( a 1 ⁄ w 1 ) = ln Ω 1 where:

Ω1 comb Ω1 res Ω1 fv Ω1

res

fv

+ ln Ω 1 + ln Ω 1

[4.4.83]

mass fraction based activity coefficient of solvent 1 at temperature T combinatorial contribution to the activity coefficient residual contribution to the activity coefficient free-volume contribution to the activity coefficient

Instead of the Flory-Huggins combinatorial contribution, Equation [4.4.68], the Staverman relation228 is used. comb

ln Ω 1

θ ψ1 M1 ψj Mj ψ z - -----------= ln -----1- + --- q 1 ln -----1- + I 1 – ------------w1 2 ψ1 w1  wj

[4.4.84]

j

where the segment fractions ψ i and the surface area fractions θ i have to be calculated according to ψ i = ( w i r i ⁄ M i ) ⁄ ( Σw k r k ⁄ M k )

[4.4.85a]

θi = ( wi qi ⁄ Mi ) ⁄ Σ ( wk qk ⁄ Mk )

[4.4.85b]

and the Ii-parameter is given by Ii = ( z ⁄ 2 ) ( ri – qi ) – ( ri – 1 )

[4.4.85c]

where: i, j z qi Mi wi ri

components in the solution lattice coordination number (usually = 10) surface area of component i based on Bondi's van-der-Waals surfaces molar mass of component i (for polymers the number average is recommended) mass fraction of component i segment number of component i based on Bondi's van-der-Waals volumes

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The molecules must be divided into groups as defined by the UNIFAC method. The segment surface areas and the segment volumes are calculated from Bondi's tables264 according to (i)

 νk

ri =

R k and q i =

k

(i)

 νk

Qk

[4.4.86]

k

where: k number of groups of type k in the solution νk number of groups of type k in the molecule i Rk Van-der-Waals group volume parameter for group k Qk Van-der-Waals group surface parameter for group k

The residual activity coefficient contribution for each component is given by res

ln Ω i

=

(i)

 νk

(i)

[ ln Γ k – ln Γ k ]

[4.4.87]

where: Γk (i) Γk

the residual activity coefficient of group k in the defined solution the residual activity coefficient of group k in a reference solution containing pure component i only

The residual activity coefficient of group k in the given solution is defined by   a km    Λ m exp  – --------      a mk   T  -  –   ----------------------------------------- ln Γ k = Q k 1 – ln   Λ m exp  – ------m  T  m   a pm    Λ p exp  – -------    T 

[4.4.88]

p

where: amn and anm Λm

group interaction parameter pair between groups m and n group surface area fraction for group m

The group surface area fraction Λm for group m in the solution is given by Qm Xm Λ m = ------------------Q X  p p p

where: Xm

group mole fraction for group m

The group mole fraction Xm for group m in the solution is given by

[4.4.89a]

254

4.4 Methods for the measurement of solvent activity of polymer (j)

 νm wj ⁄ Mj j X m = ------------------------------------(j)   νp wj ⁄ Mj j

[4.4.89b]

p

The residual activity coefficient of group k in reference solutions containing only (i) component i, Γ k is similarly determined using Equations [4.4.88, 4.4.89], with the exception that the summation indices k, m, p refer only to the groups present in the pure component and the summations over each component j are calculated only for the single component present in the reference solution. The group interaction parameter pairs amn and anm result from the interaction between the groups m and n. These parameters are unsymmetrical values that have to be fitted to experimental VLE-data of low-molecular mixtures. They can be taken from UNIFAC tables, e.g., Refs.2,284,286-289 and, additionally, they may be treated as temperature functions. The free-volume contribution, which is essential for nonpolar polymer solutions, follows, in principle, from Equation [4.4.74] with parameter X12 = 0 as applied by Raetzsch and Glindemann,290 or in a modified form from Equation [4.4.90] as introduced by Oishi and Prausnitz and used also in Danner's Handbook.2 ˜ 1 ⁄ 3 – 1 ˜ –V ˜  V  V fv 1 1 - – c 1  ----------------------------- ln Q 1 = 3c 1 ln  ------------------˜ 1 ⁄ 3 – 1 ˜ (1 – V ˜ 1 ⁄ 3 ) V V 1

[4.4.90]

where: c1

external degree of freedom parameter of the solvent 1, usually fixed = 1.1

To get a predictive model, the reduced volumes and the external degree of freedom parameter are not calculated from Flory's equation of state, Equation [4.4.72], but from some simple approximations as given by the following relations:2 υ spez, i M i ˜ = ---------------------V i 0.01942r i

[4.4.91a]

 υspez, i wi

i ˜ = --------------------------------------------V 0.01942  r i w i ⁄ M i

[4.4.91b]

i

where:

υ spez, i ri Mi wi

specific volume of component i in m3/kg segment number of component i based on Bondi's van-der-Waals volumes molar mass of component i (for polymers the number average is recommended) mass fraction of component i

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There has been a broad application of this group-contribution UNIFAC−fv concept to polymer solutions in the literature. Raetzsch and Glindemann290 recommended the use of the real free-volume relation from the Flory-Orwoll-Vrij model to account for realistic PVT-data. Problems arise for mixtures composed from chemically different components that posses the same groups, e.g., mixtures with different isomers. Kikic et al.291 discussed the influence of the combinatorial part on results obtained with UNIFAC−fv calculations. Gottlieb and Herskowitz292,293 gave some polemic about the special use of the c1−parameter within UNIFAC−fv calculations. Iwai et al.294,295 demonstrated the possible use of UNIFAC−fv for the calculation of gas solubilities and Henry's constants using a somewhat different free-volume expression. Patwardhan and Belfiore296 found quantitative discrepancies for some polymer solutions. In a number of cases, UNIFAC−fv predicted the occurrence of a demixing region during the calculation of solvent activities where experimentally only a homogeneous solution exists. Price and Ashworth297 found that the predicted variation of residual solvent activity with polymer molecular mass at high polymer concentrations is opposite to that measured for polydimethylsiloxane solutions. But, qualitative correct predictions were obtained for poly(ethylene glycol) solutions with varying polymer molecular mass.298-300 However, UNIFAC−fv is not capable of representing thermodynamic data of strongly associating or solvating systems. Many attempts have been made to improve the UNIFAC−fv model which cannot be listed here. A comprehensive review was given by Fried et al.301 An innovative method to combine the free-volume contribution within a corrected Flory-Huggins combinatorial entropy and the UNIFAC concept was found by Elbro et al.302 and improved by Kontogeorgis et al.303 These authors considered the free-volume dissimilarity by assuming different van der Waals hard-core volumes (again from Bondi's tables264) for the solvent and the polymer segments 1⁄3

fv

1⁄3

Vi = qi ( Vi fv

– V i, vdW )

fv

3

[4.4.92a]

fv

ϕi = xi Vi ⁄  xj Vj

[4.4.92b]

j

where: qi xi Vi Vi,vdW

surface area of component i based on Bondi's van der Waals surfaces mole fraction of component i molar volume of component i van der Waals hard-core molar volume of component i

and introduced these free-volume terms into Equation [4.4.68] to obtain a free-volume corrected Flory-Huggins combinatorial term: fv

fv

fv

ln γ i = ln ( ϕ i ⁄ x i ) + 1 – ( ϕ i ⁄ x i ) fv

fv

fv

ln Ω i = ln ( ϕ i ⁄ w i ) + 1 – ( ϕ i ⁄ x i )

[4.4.93a] [4.4.93b]

To obtain the complete activity coefficient, only the residual term from the UNIFAC model, Equation [4.4.87], has to be added. An attempt to incorporate differences in shape

256

4.4 Methods for the measurement of solvent activity of polymer

between solvent molecules and polymer segments was made by Kontogeorgis et al.302 by adding the Staverman correction term to obtain: fv

fv

ϕ i zq i  ψ i ψ ϕi fv - + 1 – ------ – ------- ln ----- + 1 – -----i ln γ i = ln -----2  θi xi xi θi 

[4.4.93c]

where the segment fractions ψ i and the surface area fractions θi have to be calculated according to Equations [4.4.85a+b]. Using this correction, they get somewhat better results only when Equation [4.4.93] leads to predictions lower than the experimental data. Different approaches utilizing group contribution methods to predict solvent activities in polymer solutions have been developed after the success of the UNIFAC−fv model. Misovich et al.304 have applied the Analytical Solution of Groups (ASOG) model to polymer solutions. Recent improvements of polymer-ASOG have been reported by Tochigi et al.305-307 Various other group-contribution methods including an equation-of-state were developed by Holten-Anderson et al.,308,309 Chen et al.,310 High and Danner,311-313 Tochigi et al.,314 Lee and Danner,315 Bertucco and Mio,316 or Wang et al.,317 respectively. Some of them were presented in Danner's Handbook.2 4.4.4.2 Fugacity coefficients from equations of state Total equation-of-state approaches usually apply equations for the fugacity coefficients instead of relations for chemical potentials to calculate thermodynamic equilibria and start from Equations [4.4.2 to 6]. Since the final relations for the fugacity coefficients are usually much more lengthy and depend, additionally, on the chosen mixing rules, only the equations of state are listed below. Fugacity coefficients have to be derived by solving Equation [4.4.6]. After obtaining the equilibrium fugacities of the liquid mixture at equilibrium temperature and pressure, the solvent activity can be calculated from Equation [4.4.1]. The standard state fugacity of the solvent can also be calculated from the same equation of state by solving the same equations but for the pure liquid. Details of this procedure can be found in textbooks, e.g., Refs.318,319 Equations of state for polymer systems that will be applied within such an approach have to be valid for the liquid as well as for the gaseous state like lattice-fluid models based on Sanchez-Lacombe theory, but not the free-volume equations based on PrigogineFlory-Patterson theory, as stated above. However, most equations of state applied within such an approach have not been developed specially for polymer systems, but, first, for common non-electrolyte mixtures and gases. Today, one can distinguish between cubic and non-cubic equations of state for phase equilibrium calculations in polymer systems. Starting from the free-volume idea in polymeric systems, non-cubic equations of state should be applied to polymers. Thus, the following text presents some examples of this class of equations of state. Cubic equations of state came later into consideration for polymer systems, mainly due to increasing demands from engineers and engineering software where three-volume-roots equations of state are easier to solve and more stable in computational cycles. About ten years after Flory's development of an equation of state for polymer systems, one began to apply methods of thermodynamic perturbation theory to calculate the

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thermodynamic behavior of polymer systems. The main goal was first to overcome the restrictions of Flory's equation of state to the liquid state, to improve the calculation of the compressibility behavior with increasing pressure and to enable calculations of fluid phase equilibria at any densities and pressures from the dilute gas phase to the compressed liquid including molecules differing considerably in size, shape, or strength of intermolecular potential energy. When more sophisticated methods of statistical mechanics were developed, deeper insights into the liquid structure and compressibility behavior of model polymer chains in comparison to Monte Carlo modeling results could be obtained applying thermodynamic perturbation theory. Quite a lot of different equations of state have been developed up to now following this procedure; however, only a limited number was applied to real systems. Therefore, only a summary and a phenomenological presentation of some equations of state which have been applied to real polymer fluids are given here, following their historical order. The perturbed-hard-chain (PHC) theory developed by Prausnitz and coworkers in the late 1970s320-322 was the first successful application of thermodynamic perturbation theory to polymer systems. Since Wertheim's perturbation theory of polymerization323 was formulated about 10 years later, PHC theory combines results from hard-sphere equations of simple liquids with the concept of density-dependent external degrees of freedom in the Prigogine-Flory-Patterson model for taking into account the chain character of real polymeric fluids. For the hard-sphere reference equation, the result derived by Carnahan and Starling324 was applied, as this expression is a good approximation for low-molecular hard-sphere fluids. For the attractive perturbation term, a modified Alder's325 fourth-order perturbation result for square-well fluids was chosen. Its constants were refitted to the thermodynamic equilibrium data of pure methane. The final equation of state reads: 2 mA nm PV 4y – 2y -------- = 1 + c --------------------3- + c   -------------RT ˜ m˜n (y – 1) n m V T

where: y c V0 Anm

[4.4.94]

packing fraction with y = V/(V0τ) and t = (π/6) = 20.5 = 0.7405 (please note that in a number of original papers in the literature the definition of y within this kind of equations is made by the reciprocal value, i.e., τV0/V) degree of freedom parameter, related to one chain-molecule (not to one segment) hard-sphere volume for closest packing empirical coefficients from the attractive perturbation term

The reduced volume is again defined by V = V/V0 and the reduced temperature by * T˜ = T ⁄ T . The coefficients Anm are given in the original papers by Beret320,321 and are considered to be universal constants that do not depend on the chemical nature of any special substance. The remaining three characteristic parameters, c, T* and V0, have to be adjusted to experimental PVT-data of the polymers or to vapor-liquid equilibrium data of the pure solvents. Instead of fitting the c-parameter, one can also introduce a parameter P* by the relation P* = cRT*/V0. In comparison with Flory's free-volume equation of state, PHC-equation of the state is additionally applicable to gas and vapor phases. It fulfills the ideal gas limit, and it describes the PVT-behavior at higher pressures better and without the need of temperature and/or pressure-dependent characteristic parameters, such as with

258

4.4 Methods for the measurement of solvent activity of polymer

Flory's model. Values for characteristic parameters of polymers and solvents can be found in the original literature. A review for the PHC-model was given by Donohue and Vimalchand,326 where a number of extensions and applications also are summarized. Application to mixtures and solutions needs mixing rules for the characteristic parameters and introduction of binary fitting parameters322,327,328 (details are not given here). Examples for applying PHC to polymer solutions are given by Liu and Prausnitz328 or Iwai, Arai, and coworkers.329-331 The chain-of-rotators (COR) equation of state was developed by Chao and coworkers332 as an improvement of the PHC theory. It introduces the non-spherical shape of molecules into the hard-body reference term and describes the chain molecule as a chain of rotators with the aim of an improved model for calculating fluid phase equilibria, PVT and derived thermodynamic properties, at first only for low-molecular substances. Instead of hard spheres, the COR-model uses hard dumbbells as reference fluid by combining the result of Boublik and Nezbeda333 with the Carnahan-Starling equation for a separate consideration of rotational degrees of freedom; however, still in the sense of Prigogine-FloryPatterson regarding the chain-character of the molecules. It neglects the effect of rotational motions on intermolecular attractions; however, the attractive portion of the final equation of state has an empirical dependence on rotational degrees of freedom given by the prefactor of the double sum. For the attractive perturbation term, a modified Alder's fourth-order perturbation result for square-well fluids was chosen, additionally improved by an empirical temperature-function for the rotational part. The final COR equation reads: 2

2

PV 4y – 2y α – 1 3y + 3αy – ( α + 1 )-------- = 1 + --------------------- + c  ------------ -----------------------------------------------+ 3 3  RT 2  (y – 1) (y – 1) mA nm c +  1 + --- { B 0 + B 1 ⁄ T˜ + B 2 T˜ }   -------------  2 ˜ m˜n n m V T where:

[4.4.95]

packing fraction with y = V/(V0τ) and τ = (π/6)20.5 = 0.7405 (please note that in a number of original papers in the literature, the definition of y within this kind of equations is made by its reciprocal value, i.e., τV0/V) c degree of freedom parameter, related to one chain-molecule (not to one segment) hard-sphere volume for closest packing V0 empirical coefficients from the attractive perturbation term Anm B0, B1, B2 empirical coefficients for the temperature dependence of the rotational part α accounts for the deviations of the dumbbell geometry from a sphere y

As can be seen from the structure of the COR equation of state, the Carnahan-Starling term becomes very small with increasing chain length, i.e., with increasing c, and the rotational part is the dominant hard-body term for polymers. The value of c is here a measure of rotational degrees of freedom within the chain (and related to one chain-molecule and not to one segment). It is different from the meaning of the c-value in the PHC equation. Its exact value is not known a priori as chain molecules have a flexible structure. The value of α for the various rotational modes is likewise not precisely known. Since α and c

Christian Wohlfarth

259

occur together in the product c(α − 1), the departure of real rotators from a fixed value of a is compensated for by the c-parameter after any fitting procedure. As usual, the value of α is assigned a constant value of 1.078 calculated according to the dumbbell for ethane as a representative for the rotating segments of a hydrocarbon chain. The coefficient Anm and the three parameters B0, B1, B2 were refitted to the thermodynamic equilibrium data of pure methane, ethane, and propane.332 Both Anm matrices for PHC and COR equation of state contain different numerical values. The remaining three characteristic parameters, c, T* and V0, have to be adjusted to experimental equilibrium data. Instead of fitting the cparameter, one can also introduce a parameter P* by the relation P* = cRT*/V0. Characteristic parameters for many solvents and gases are given by Chien et al.332 or Masuoka and Chao.334 Characteristic parameters for more than 100 polymers and many solvents are given by Wohlfarth and coworkers,335-348 who introduced segment-molar mixing rules and group-contribution interaction parameters into the model and applied it extensively to polymer solutions at ordinary pressures as well as at high temperatures and pressures, including gas solubility and supercritical solutions. They found that it may be necessary sometimes to refit the pure-component characteristic data of a polymer to some VLE-data of a binary polymer solution to calculate correct solvent activities because otherwise demixing was calculated. Refitting is even more necessary when high-pressure fluid phase equilibria have to be calculated using this model. A group-contribution COR equation of state was developed Pults et al.349,350 and extended into a polymer COR equation of state by Sy-Siong-Kiao et al.351 This equation of state is somewhat simplified by replacing the attractive perturbation term by the corresponding part of the Redlich-Kwong equation of state. 2

2

a(t) PV 4y – 2y α – 1 3y + 3αy – ( 1 + α )-------- = 1 + --------------------- + c  ------------ -----------------------------------------------– ----------------------------------- [4.4.96] 3 3   RT [ V + b ( T ) ] RT 2 (y – 1) (y – 1) where: a b c y α

attractive van der Waals-like parameter excluded volume van der Waals-like parameter degree of freedom parameter, related to one chain-molecule (not to one segment) packing fraction accounts for the deviations of the dumbbell geometry from a sphere

Exponential temperature functions for the excluded volume parameter b and the attractive parameter a were introduced by Novenario et al.352-354 to apply this equation of state also to polar and associating fluids. Introducing a group-contribution concept leads to segment-molar values of all parameters a, b, c which can easily be fitted to specific volumes of polymers.351,354 The statistical associating fluid theory (SAFT) is the first and the most popular approach that uses real hard-chain reference fluids, including chain-bonding contributions. Its basic ideas have been developed by Chapman et al.256-258 Without going into details, the final SAFT equation of state is constructed from four terms: a segment term that accounts for the non-ideality of the reference term of non-bonded chain segments/monomers as in the equations shown above, a chain term that accounts for covalent bonding, and an association term that accounts for hydrogen bonding. There may be an additional

260

4.4 Methods for the measurement of solvent activity of polymer

term that accounts for other polarity effects. A dispersion term is also added that accounts for the perturbing potential, as in the equations above. A comprehensive summary is given in Praunsitz's book.49 Today, there are different working equations based on the SAFT approach. Their main differences stem from the way the segment and chain terms are estimated. The most common version is the one developed by Huang and Radosz,355 applying the fourth-order perturbation approach as in COR or PHC above, but with new refitted parameters to argon, as given by Chen and Kreglewski,356 and a hard-sphere pair-correlation function for the chain term as following the arguments of Wertheim. The HuangRadosz-form of the SAFT-equation of state without an association term reads:355 2

mD nm u 5y – 2 PV 4y – 2y - -------------- = 1 + r --------------------3- + ( 1 – r ) ------------------------------------- + r   -------------( y – 1 ) ( 2y – 1 ) RT ˜ m kT (y – 1) V

[4.4.97]

n m

where: empirical coefficients from the attractive perturbation term Boltzmann's constant chain segment number

Dnm k r

In comparison to the PHC equation of state, the new term between the CarnahanStarling term and the double sum accounts for chain-bonding. The terms are proportional to the segment number, r, of the chain molecule. However, the hard-sphere volume, V0, is now a slight function of temperature which is calculated according to the result of Chen and Kreglewski:356 00

V 0 = V [ 1 – 0.12 exp ( – 3u 0 ⁄ kT ) ] where:

V00 u0

3

[4.4.98]

hard-sphere volume at T = 0K well-depth of a square-well potential u/k = u0/k(1 + 10K/T) with 10K being an average for all chain molecules.

The ratio u0/k or u/k is analogous to the characteristic parameter T* in the equations above. There are two additional volume and energy parameters if the association is taken into account. In its essence, the SAFT equation of state needs three pure component parameters which have to be fitted to equilibrium data: V00, u0/k, and r. Fitting of the segment number looks somewhat curious to a polymer scientist, but it is simply a model parameter, like the c-parameter in the equations above, which is also proportional to r. One may note additionally that fitting to specific volume PVT-data leads to a characteristic ratio r/M (which is a specific r-value), as in the equations above, with a specific c-parameter. Several modifications and approximations within the SAFT-framework have been developed in the literature. Banaszak et al.357-359 or Shukla and Chapman360 extended the concept to copolymers. Adidharma and Radosz361 provide an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers355,357-359,361-368 Sadowski et al.369 applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component character-

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istic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. Groß and Sadowski370 developed a “Perturbed-Chain SAFT” equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT- and VLEbehavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh.371 They also state that characteristic SAFT parameters for polymers from PVT-data lead to wrong phase equilibrium calculations and, therefore, also to wrong solvent activities from such calculations. Some ways to overcome this situation and to obtain reliable parameters for phase equilibrium calculations are provided in Ref.,371 together with examples from the literature that will not be repeated here. The perturbed-hard-sphere-chain (PHSC) equation of state is a hard-sphere-chain theory that is somewhat different to SAFT. It is based on a hard-sphere chain reference system and a van der Waals-type perturbation term using a temperature-dependent attractive parameter a(T) and a temperature-dependent co-volume parameter b(T). Song et al.259,260 applied it to polymer systems and extended the theory to fluids consisting of heteronuclear hard chain molecules. The final equation for pure liquids or polymers as derived by Song et al. is constructed from three parts: the first term stems (as in PHC, COR or SAFT) from the Carnahan-Starling hard-sphere monomer fluid, the second is the term due to covalent chain-bonding of the hard-sphere reference chain and the third is a van der Waals-like attraction term (more details are given also in Prausnitz's book49): 2 1 – η ⁄ 2  r2 a ( T ) 4η – 2η PV ------------------------- = 1 + r --------------------( 1 – R ) – 1 +   – --------------3 3 RT (1 – η) (1 – η)  RTV

where:

η a r

[4.4.99]

reduced density or packing fraction attractive van der Waals-like parameter chain segment number

The reduced density or packing fraction η is related to an effective and temperaturedependent co-volume b(T) by η = rb(T)ρ/4, with ρ being the number density, i.e., the number of molecules per volume. However, PHSC-theory does not use an analytical intermolecular potential to estimate the temperature dependence of a(T) and b(T). Instead, empirical temperature functions are fitted to experimental data of argon and methane (see also49). We note that the PHSC equation of state is again an equation where three parameters have to be fitted to thermodynamic properties: σ, e /k and r. These may be transformed into macroscopic reducing parameters for the equation of state by the common relations T* = ε/k, P* = 3ε/2πσ3 and V* = 2πrσ3/3. Parameter tables are given in Refs.86,260,372-374 PHSC was successfully applied to calculate solvent activities in polymer solutions, Gupta and Prausnitz.86 Lambert et al.374 found that it is necessary to adjust the characteristic parameters of the polymers when liquid-liquid equilibria should correctly be calculated. Even with simple cubic equations of state, a quantitative representation of solvent activities for real polymer solutions can be achieved, as was shown by Tassios and

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4.4 Methods for the measurement of solvent activity of polymer

coworkers.375,376 Using generalized van der Waals theory, Sako et al.377 obtained a threeparameter cubic equation of state which was the first applied to polymer solutions: PV V – b + bc a(T) -------- = ------------------------- – -------------------------RT V–b RT ( V + b )

[4.4.100]

where: a b c

attractive van der Waals-like parameter excluded volume van der Waals-like parameter 3c is the total number of external degrees of freedom per molecule

When c = 1, Equation [4.4.100] reduces to the common Soave-Redlich-Kwong (SRK) equation of state.378 Temperature functions and combining/mixing rules for parameters a, b, c are not discussed here because quite different approximations may be used. Problems, how to fit these parameters to experimental PVT-data for polymers, have been discussed by several authors.375-380 Orbey and Sandler380 applied the Peng-Robinson equation of state as modified by Stryjek and Vera381 (PRSV): PV V a(T) -------- = -----------– -----------------------------------------------RT V – b RT ( V 2 + 2bV – b 2 )

[4.4.101]

to calculate solvent activities in polymer solutions using Wong-Sandler mixing rules382 that combine the equation of state with excess energy models (EOS/GE-mixing rules). They have shown that a two-parameter version can correlate the solvent partial pressure of various polymer solutions with good accuracy over a range of temperatures and pressures with temperature-independent parameters. Harrismiadis et al.379 worked out some similarities between activity coefficients derived from van der Waals-like equations-of-state and Equations (4.4.92 and 93), i.e., the Elbro−fv model. Zhong and Masuoka383 combined SRK equation of state with EOS/GE-mixing rules and the UNIFAC model to calculate Henry's constants of solvents and gases in polymers. Additionally, they developed new mixing rules for van der Waals-type two-parameter equations of state (PRSV and SRK) which are particularly suitable for highly asymmetric systems, i.e., also polymer solutions, and demonstrated that only one adjustable temperature-independent parameter is necessary for calculations within a wide range of temperatures.384 In the following paper,385 some further modifications and improvements could be found. Orbey et al.386 successfully proposed some empirical relations for PRSV-equation-of-state parameters with polymer molar mass and specific volume to avoid any special parameter fitting for polymers and introduced a NRTL-like local-composition term into the excess energy part of the mixing rules for taking into account of strong interactions, for example, in water + poly(propylene glycol)s. They found infinite-dilution activity coefficient data, i.e., Henry's constants, to be most suitable for fitting the necessary model parameter.386 Orbey et al.387 summarized three basic conclusions for the application of cubic equations of state to polymer solutions: (i) These models developed for conventional mixtures can be extended to quantitatively describe VLE of polymer solutions if carefully selected parameters are used for the

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pure polymer. On the other hand, pure-component parameters of many solvents are already available and VLE between them is well represented by these cubic equations of state. (ii) EOS/GE-mixing rules represent an accurate way of describing phase equilibria. Activity coefficient expressions are more successful when they are used in this format than directly in the conventional gamma-phi approach. (iii) It is not justifiable to use multi-parameter models, but it is better to limit the number of parameters to the number of physically meaningful boundary conditions and calculate them according to the relations dictated by these boundary conditions. 4.4.4.3 Comparison and conclusions The simple Flory-Huggins χ-function, combined with the solubility parameter approach may be used for a first rough guess of solvent activities of polymer solutions if no experimental data are available. Nothing more should be expected. This also holds true for any calculations using the UNIFAC-fv or other group-contribution models. For a quantitative representation of solvent activities of polymer solutions, more sophisticated models have to be applied. The choice of a dedicated model, however, may depend on the nature of the polymer-solvent system and its physical properties (polar or non-polar, association or donor-acceptor interactions, subcritical or supercritical solvents, etc.), on the ranges of temperature, pressure and concentration one is interested in, on the question whether a special solution, special mixture, special application is to be handled or a universal application is to be found or a software tool is to be developed, on numerical simplicity or, on the other hand, on numerical stability and physically meaningful roots of the non-linear equation systems to be solved. Finally, it may depend on the experience of the user (and sometimes it still seems to be a matter of taste). There are deficiencies in all of the theories given above. These theories fail to account for long-range correlations between polymer segments which are important in dilute solutions. They are valid for simple linear chains and do not account for effects like chain branching, rings, dendritic polymers. But, most seriously, all of these theories are of the mean-field type that fail to account for the contributions of fluctuations in density and composition. Therefore, when these theories are used in the critical region, poor results are often obtained. Usually, critical pressures are overestimated within VLE-calculations. Two other conceptually different mean-field approximations are invoked during the development of these theories. To derive the combinatorial entropic part correlations between segments of one chain, that are not nearest neighbors, are neglected (again, mean-field approximations are therefore not good for a dilute polymer solution) and, second, chain connectivity and the correlation between segments are improperly ignored when calculating the potential energy, the attractive term. Equation-of-state approaches are preferred concepts for a quantitative representation of polymer solution properties. They are able to correlate experimental VLE data over wide ranges of pressure and temperature and allow for physically meaningful extrapolation of experimental data into unmeasured regions of interest for the application. Based on the experience of the author regarding the application of the COR equation-of-state model to many polymer-solvent systems, it is possible, for example, to measure some vapor pres-

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4.4 Methods for the measurement of solvent activity of polymer

sures at temperatures between 50 and 100oC and concentrations between 50 and 80 wt% polymer by isopiestic sorption together with some infinite dilution data (limiting activity coefficients, Henry's constants) at temperatures between 100 and 200oC by IGC and then to calculate the complete vapor-liquid equilibrium region between room temperature and about 350oC, pressures between 0.1 mbar and 10 bar, and solvent concentration between the common polymer solution of about 75-95 wt% solvent and the ppm-region where the final solvent and/or monomer devolatilization process takes place. Equivalent results can be obtained with any other comparable equation of state model like PHC, SAFT, PHSC, etc. The quality of all model calculations with respect to solvent activities depends essentially on the careful determination and selection of the parameters of the pure solvents, and also of the pure polymers. The pure solvent parameter must allow for the quantitative calculation of pure solvent vapor pressures and molar volumes, especially when equation-ofstate approaches are used. Pure polymer parameters strongly influence the calculation of gas solubilities, Henry's constants, and limiting solvent activities at infinite dilution of the solvent in the liquid/molten polymer. Additionally, the polymer parameters mainly determine the occurrence of a demixing region in such model calculations. Generally, the quantitative representation of liquid-liquid equilibria is a much more stringent test for any model, what was not discussed here. To calculate such equilibria, it is often necessary to use some mixture properties to obtain pure-component polymer parameters. This is necessary because no single theory is able to describe correctly the properties of a polymer in both the pure molten state and in the highly dilute solution state. Therefore, characteristic polymer parameters from PVT-data of the melt are not always meaningful for the dilute polymer solution. Additionally, characteristic polymer parameters from PVT-data also may lead to wrong results for concentrated polymer solutions because phase equilibrium calculations are much more sensitive to variations in pure component parameters than polymer densities. All models need some binary interaction parameters that have to be adjusted to some thermodynamic equilibrium properties since these parameters are a priori not known (we will not discuss results from Monte Carlo simulations here). Binary parameters obtained from data of dilute polymer solutions as second virial coefficients are often different from those obtained from concentrated solutions. Distinguishing between intramolecular and intermolecular segment-segment interactions is not as important in concentrated solutions as it is in dilute solutions. Attempts to introduce local-composition and non-random-mixing approaches have been made for all the theories given above with more or less success. At least, they introduce additional parameters. More parameters may cause a higher flexibility of the model equations but lead often to physically senseless parameters that cause troubles when extrapolations may be necessary. Group-contribution concepts for binary interaction parameters in the equation of state models can help to correlate parameter sets and also data of solutions within homologous series.

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4.4.5 THE MOST CURRENT APPLICATIONS

George Wypych ChemTec Laboratories, Toronto, Canada An analytical equation permits calculation of the solvent activity of aqueous ternary electrolyte solutions of different compositions.389 The experimental data corresponding to 23 ternary systems were compared with model predictions showing an excellent fitting capability of the proposed equation.389 Further developments permit prediction of the solvent activity of ternary solutions with electrolytic and molecular components (polyols, sugars, etc.).390 This equation was derived on the basis of the Figure 4.4.20. Dependencies of solvent activity (a1) on sum of contributions from short and long range interactions to the excess Gibbs free molality of both components for the system sodium chloride (2) – sorbitol – water (1) at 298.15 K. Dots: energy of solution and calculation results experimental data; surface: correlation with equation. [Adapted, by permission, from F. J. Passamonti, M. R. were compared with experimental data corGennero de Chialvo, A. C. Chialvo, Fluid Phase Equil., responding to 20 aqueous ternary sys388, 118-22, 2015.] tems.390 Figure 4.4.20 shows an example of results obtained.390 Water activity is an important thermodynamic property of aqueous polymer solutions. It is closely related to the other thermodynamic properties such as vapor pressure, osmotic coefficient, and activity coefficient.391 The water activity in an aqueous solution of poly(N-vinylcaprolactam) having different molecular weights was measured by the isopiestic method at T=308.15 K.391 The water activity and vapor pressure of poly(N-vinylcaprolactam) solution increases with increasing the molecular weight.391 Out of the FloryHuggins model, the modified Flory-Huggins model and Freed Flory-Huggins equation + NRTL model, the Freed Flory-Huggins + NRTL model gave the best correlation with experimental results.391 Molecular weight, density, chemical structures of polymer and solvent, and concentration of polymer solution were input parameters of the model and the solvent activity was an output parameter. The experimental data correlated with the data calculated using a model with an average error of less than 3%.392 The combination of a thermodynamic model and molecular simulation calculates solvent activity directly using the pairwise interaction energy of functional groups obtained from molecular simulation.393 The solvent activities of a large variety of polymer solutions were estimated using the Helmholtz energy of mixing, based on the modified double lattice model with 3.9% of average total deviation in solvent activity estimation.393 A specified group-contribution method was used to estimate vapor-liquid equilibria of ordinary and associated binary polymer solutions.394 The van der Waals energy parame-

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4.4 Methods for the measurement of solvent activity of polymer

ters for dispersion and polar forces for ordinary systems without hydrogen bonding were determined.394 The model gives good correlation with experimental data in solvent activity estimations for ordinary and associated binary polymer solution.394 Sorption equilibrium and diffusion coefficients in the binary systems of poly(vinyl acetate)-methanol and poly(vinyl acetate)-toluene were determined using a magnetic suspension balance.395 The solvent activity was calculated using the Flory-Huggins and UNIFAC-FV models and the diffusion coefficient based on the free-volume theory.395 It is suggested that a simplification in this research field should take place by reduction of the number of equations and the theory parameters but the use of a few parameters fitted to reliable experimental data.395 Solvent solubility was predicted using the group-contribution lattice fluid equationof-state, GCLF-EOS, model, and compared with previously used UNIFAC-FV model.396 The GCLF-EOS model provide better accuracy.396 The UNIFAC-FV model assumes the ideal mixing for estimating reduced volume to determine the free volume term and ignores the influence of excess volume.396 The GCLF-EOS model has the feature of an equationof-state and its predictions show good correspondence with the experiment.396 The model provides a practical tool to design membranes to remove VOC from emissions and suggests suitable operating conditions.396 The solubilities of pharmaceutical compounds in a solvent (water) and co-solvents (ethanol, methanol, and 1,4-dioxane) were predicted using a one-parameter Wilson activity coefficient model.397 The pharmaceutical compounds tested included salicylic acid, acetaminophen, benzocaine, acetanilide, and phenacetin.397 The Wilson equation was used to calculate activity coefficients, as follows397 n

  ln γ i = – ln   x j Λ ij + 1 –   j–1

n

x k Λ ki

 -------------------n k=1  x j Λkj

[4.4.102]

j=1

Λ ij = where:

γ x L V λ R T i, j

L λ ij – λ ii Vj ------L- exp  – ---------------- RT  Vi

activity coefficient liquid mole fraction liquid molar volume binary interaction parameters of Wilson equation gas constant absolute temperature components

The model requires only solubility data in a pure solvent and physical property data of the solutes and solvents.397 The Wilson model enables prediction of the solubility of solutes in a mixed solvent with qualitative prediction accuracy.397

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The liquid-liquid equilibrium data in fluorous solvent (perfluorohexane and Galden® HT-135) mixtures were measured for environmentally benign reaction solvents.398 The experimental results for the liquid-liquid equilibrium were represented using the NRTL activity coefficient model.398 The experimental liquid-liquid equilibrium data correlated well with the NRTL model.398 The manipulation of drug thermodynamic activity (via supersaturation) to enhance drug permeation has been reported by a number of researchers but few reports have investigated the influence of solvent/vehicle thermodynamic activity on drug permeation.399 The influence of the degree of saturation of oxybutynin on permeation from octyl salicylate or propylene glycol vehicles was investigated, in vitro, in human skin.399 The findings emphasize the importance of maintaining the drug in solution in order to achieve effective permeation from dermal and transdermal formulations.399 The decrease in the percentage drug permeation was a result of the decrease in both drug and solvent activity with a degree of saturation.399 To use biodiesel effectively as an absorption solvent, it is important to determine the activity coefficients at infinite dilution.400 A detailed investigation of VLE (vapor-liquidequilibrium) of three volatile organic compounds of industrial significance, benzene, toluene, and 1,2-dichloroethane has been carried out in order to determine their infinite dilution activity coefficients in biodiesel.400 Headspace gas chromatography was used as an experimental method.400 This technique provided a reliable, accurate and sensitive method for measuring infinite dilution activity coefficients of volatile compounds in non-volatile solvents.400 The infinite dilution activity coefficients compared well with the UNIFAC predictions representative for methyl oleate, which is the major component in biodiesel.400 Knowledge of the activity coefficients of solutes under temperature and pressure ranges of interest is generally required for calculations of the physicochemical properties of aqueous multicomponent electrolyte solutions such as seawater.401 Zdanovskii's rule (the molal concentrations of many mixed solutions at constant solvent activity vary in a linear manner or, in another word, when solutions of single electrolyte having the same solvent activity are mixed in any proportion the solvent activity remains unchanged), described originally almost a century ago but widely neglected, provides a fundamentally sound method for calculating the properties of mixed electrolyte solutions.401 Stronger solute-solute interactions, described by the equilibrium constants, can then easily be coupled in a thermodynamically consistent manner.401 The Hansen solubility parameters are typically used for selecting suitable solvents for polymer binders.402 The well-known Flory-Huggins model captures several of the characteristics of polymer solutions.402 A methodology was presented in which the Hansen solubility parameters were incorporated in the Flory-Huggins model.402 The resulting model yields good predictions of solvent activity coefficients at infinite dilution for several acrylate and acetate polymers.402 The knowledge of molecular structures is not required in this Hansen/Flory-Huggins model.402 The only inputs in the proposed FloryHuggins/Hansen model are the pure-component densities and Hansen solubility parameters.402 The model makes use of Hansen solubility parameters, which are tabulated for many solvents, pigments, and polymers.402

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4.4 Methods for the measurement of solvent activity of polymer

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4.4 Methods for the measurement of solvent activity of polymer A. A. Patwardhan, L. A. Belfiore, J. Polym. Sci., Pt. B Polym. Phys., 24, 2473 (1986). G. J. Price, A. J. Ashworth, Polymer, 28, 2105 (1987). M. T. Raetzsch, D. Glindemann, E. Hamann, Acta Polymerica, 31, 377 (1980). E. L. Sorensen, W. Hao, P. Alessi, Fluid Phase Equil., 56, 249 (1990). M. Herskowitz, M. Gottlieb, J. Chem. Eng. Data, 30, 233 (1985). J. R. Fried, J. S. Jiang, E. Yeh, Comput. Polym. Sci., 2, 95 (1992). H. S. Elbro, A. Fredenslund, P. A. Rasmussen, Macromolecules, 23, 4707 (1990). G. M. Kontogeorgis, A. Fredenslund, D. P. Tassios, Ind. Eng. Chem. Res., 32, 362 (1993). M. J. Misovich, E. A. Grulke, R. F. Blanks, Ind. Eng. Chem. Process Des. Dev., 24, 1036 (1985). K. Tochigi, S. Kurita, M. Ohashi, K. Kojima, Kagaku Kogaku Ronbunshu, 23, 720 (1997). J. S. Choi, K. Tochigi, K. Kojima, Fluid Phase Equil., 111, 143 (1995). B. G. Choi, J. S. Choi, K. Tochigi, K. Kojima, J. Chem. Eng. Japan, 29, 217 (1996). J. Holten-Andersen, A. Fredenslund, P. Rasmussen, G. Carvoli, Fluid Phase Equil., 29, 357 (1986). J. Holten-Andersen, A. Fredenslund, P. Rasmussen, Ind. Eng. Chem. Res., 26, 1382 (1987). F. Chen, A. Fredenslund, P. Rasmussen, Ind. Eng. Chem. Res., 29, 875 (1990). M. S. High, R. P. Danner, Fluid Phase Equil., 53, 323 (1989). M. S. High, R. P. Danner, AIChE-J., 36, 1625 (1990). M. S. High, R. P. Danner, Fluid Phase Equil., 55, 1 (1990). K. Tochigi, K. Kojima, T. Sako, Fluid Phase Equil., 117, 55 (1996). B.-C. Lee, R. P. Danner, Fluid Phase Equil., 117, 33 (1996). A. Bertucco, C. Mio, Fluid Phase Equil., 117, 18 (1996). W. Wang, X. Liu, C. Zhong, C. H. Twu, J. E. Coon, Fluid Phase Equil., 144, 23 (1998). J. M. Smith, H. C. Van Ness, M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, 5th Ed., McGraw-Hill, Singapore, 1996. S. M. Walas, Phase equilibria in chemical engineering, Butterworth, Boston, 1985. S. Beret, J. M. Prausnitz, AIChE-J., 21, 1123 (1975). S. Beret, J. M. Prausnitz, Macromolecules, 8, 878 (1975). M. D. Donohue, J. M. Prausnitz, AIChE-J., 24, 849 (1978). M. S. Wertheim, J. Chem.Phys., 87, 7323 (1987). N. F. Carnahan, K. E. Starling, J. Chem.Phys., 51, 635 (1969). B. J. Alder, D. A. Young, M. A. Mark, J. Chem.Phys., 56, 3013 (1972). M. D. Donohue, P. Vimalchand, Fluid Phase Equil., 40, 185 (1988). R. L. Cotterman, B. J. Schwarz, J. M. Prausnitz, AIChE-J., 32, 1787 (1986). D. D. Liu, J. M. Prausnitz, Ind. Eng. Chem. Process Des. Dev., 19, 205 (1980). M. Ohzono, Y. Iwai, Y. Arai, J. Chem. Eng. Japan, 17, 550 (1984). S. Itsuno, Y. Iwai, Y. Arai, Kagaku Kogaku Ronbunshu, 12, 349 (1986). Y. Iwai, Y. Arai, J. Japan Petrol. Inst., 34, 416 (1991). C. H. Chien, R. A. Greenkorn, K. C. Chao, AIChE-J., 29, 560 (1983). T. Boublik, I. Nezbeda, Chem. Phys. Lett., 46, 315 (1977). H. Masuoka, K. C. Chao, Ind. Eng. Chem. Fundam., 23, 24 (1984). M. T. Raetzsch, E. Regener, Ch. Wohlfarth, Acta Polymerica, 37, 441 (1986). E. Regener, Ch. Wohlfarth, M. T. Raetzsch, Acta Polymerica, 37, 499, 618 (1986). E. Regener, Ch. Wohlfarth, M. T. Raetzsch, S. Hoering, Acta Polymerica, 39, 618 (1988). Ch. Wohlfarth, E. Regener, Plaste & Kautschuk, 35, 252 (1988). Ch. Wohlfarth, Plaste & Kautschuk, 37, 186 (1990). Ch. Wohlfarth, B., Zech, Makromol. Chem., 193, 2433 (1992). U. Finck, T. Heuer, Ch. Wohlfarth, Ber. Bunsenges. Phys. Chem., 96, 179 (1992). Ch. Wohlfarth, U. Finck, R. Schultz, T. Heuer, Angew. Makromol. Chem., 198, 91 (1992). Ch. Wohlfarth, Acta Polymerica, 43, 295 (1992). Ch. Wohlfarth, Plaste & Kautschuk, 39, 367 (1992). Ch. Wohlfarth, J. Appl. Polym. Sci., 48, 1923 (1993). Ch. Wohlfarth, Plaste & Kautschuk, 40, 272 (1993). Ch. Wohlfarth, Plaste & Kautschuk, 41, 163 (1994). Ch. Wohlfarth, Macromol. Chem. Phys., 198, 2689 (1997). J. C. Pults, R. A. Greenkorn, K. C. Chao, Chem. Eng. Sci., 44, 2553 (1989). J. C. Pults, R. A. Greenkorn, K. C. Chao, Fluid Phase Equil., 51, 147 (1989). R. Sy-Siong-Kiao, J. M. Caruthers, K. C. Chao, Ind. Eng. Chem. Res., 35, 1446 (1996). C. R. Novenario, J. M. Caruthers, K. C. Chao, Fluid Phase Equil., 142, 83 (1998).

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C. R. Novenario, J. M. Caruthers, K. C. Chao, Ind. Eng. Chem. Res., 37, 3142 (1998). C. R. Novenario, J. M. Caruthers, K. C. Chao, J. Appl. Polym. Sci., 67, 841 (1998). S. H. Huang, M. Radosz, Ind. Eng. Chem., 29, 2284 (1990). S. S. Chen, A. Kreglewski, Ber. Bunsenges. Phys. Chem., 81, 1048 (1977). M. Banaszak, Y. C. Chiew, M. Radosz, Phys. Rev. E, 48, 3760 (1993). M. Banaszak, Y. C. Chiew, R. O.Lenick, M. Radosz, J. Chem. Phys., 100, 3803 (1994). M. Banaszak, C. K. Chen, M. Radosz, Macromolecules, 29, 6481 (1996). K. P. Shukla, W. G. Chapman, Mol. Phys., 91, 1075 (1997). H. Adidharma, M. Radosz, Ind. Eng. Chem. Res., 37, 4453 (1998). S.-J. Chen, M. Radosz, Macromolecules, 25, 3089 (1992). S.-J. Chen, I. G. Economou, M. Radosz, Macromolecules, 25, 4987 (1992). C. J. Gregg, S.-J. Chen, F. P. Stein, M. Radosz, Fluid Phase Equil., 83, 375 (1993). S.-J. Chen, M. Banaszak, M. Radosz, Macromolecules, 28, 1812 (1995). P. Condo, M. Radosz, Fluid Phase Equil., 117, 1 (1996). K. L. Albrecht, F. P. Stein, S. J. Han, C. J. Gregg, M. Radosz, Fluid Phase Equil., 117, 117 (1996). C. Pan, M. Radosz, Ind. Eng. Chem. Res., 37, 3169 (1998) and 38, 2842 (1999). G. Sadowski, L. V. Mokrushina, W. Arlt, Fluid Phase Equil., 139, 391 (1997). J. Groß, G. Sadowski, Fluid Phase Equil., 168, 183m (2000). C. F. Kirby, M. A. McHugh, Chem. Rev., 99, 565 (1999). R. B. Gupta, J. M. Prausnitz, Ind. Eng. Chem. Res., 35, 1225 (1996). T. Hino, Y. Song, J. M. Prausnitz, Macromolecules, 28, 5709, 5717, 5725 (1995). S. M. Lambert, Song, J. M. Prausnitz, Macromolecules, 28, 4866 (1995). G. M. Kontogeorgis, V. I. Harismiadis, A. Fredenslund, D. P. Tassios, Fluid Phase Equil., 96, 65 (1994). V. I. Harismiadis, G. M. Kontogeorgis, A. Fredenslund, D. P. Tassios, Fluid Phase Equil., 96, 93 (1994). T. Sako, A. W. Hu, J. M. Prausnitz, J. Appl. Polym. Sci., 38, 1839 (1989). G. Soave, Chem. Eng. Sci., 27, 1197 (1972). V. I. Harismiadis, G. M. Kontogeorgis, A. Saraiva, A. Fredenslund, D. P. Tassios, Fluid Phase Equil., 100, 63 (1994). N. Orbey, S. I. Sandler, AIChE-J., 40, 1203 (1994). R. Stryjek, J. H. Vera, Can. J. Chem. Eng., 64, 323 (1986). D. S. H. Wong, S. I. Sandler, AIChE-J., 38, 671 (1992). C. Zhong, H. Masuoka, Fluid Phase Equil., 126, 1 (1996). C. Zhong, H. Masuoka, Fluid Phase Equil., 126, 59 (1996). C. Zhong, H. Masuoka, Fluid Phase Equil., 144, 49 (1998). H. Orbey, C.-C. Chen, C. P. Bokis, Fluid Phase Equil., 145, 169 (1998). H. Orbey, C. P. Bokis, C.-C. Chen, Ind. Eng. Chem. Res., 37, 1567 (1998). ASTM E1719 - 12 Standard Test Method for Vapor Pressure of Liquids by Ebulliometry ASTM E2071 - 00(2015) Standard Practice for Calculating Heat of Vaporization or Sublimation from Vapor Pressure Data A. Ricardini, F. Passamonti, A. C. Chialvo, Fluid Phase Equil., 345, 23-7, 2013. F. J. Passamonti, M. R. Gennero de Chialvo, A. C. Chialvo, Fluid Phase Equil., 388, 118-22, 2015. M. Foruotan, M. Zarrabi, J. Chem. Thermodyn., 41, 4, 448-51, 2009. A. A. Tashvigh, F. Z. Ashtiani, M. Karimi, A. Okhovat, Calphad, 51, 35-41, 2015. Y. D. Yi, Y. C. Bae, Fluid Phase Equil., 385, 275-89, 2015. B. H. Chang, Y. C. Bae, Fluid Phase Equil., 207, 247-61, 2003. I. Mamaliga, W. Schabel, M. Kind, Chem. Eng. Process.: Process Intensification, 43, 6, 753-63, 2004. B.-G. Wang, Y. Miyazaki, T. Yamaguchi, S.-i. Nakao, J. Membrane Sci., 164, 1-2, 25-35, 2000. H. Matsuda, K. Kaburagi, K. Kurihara, K. Tochigi, K. Tomono, Fluid Phase Equil., 290, 1-2, 153-7, 2010. H. Matsuda, Y. Hirota, K. Kurihara, K. Tochigi, K. Ochi, Fluid Phase Equil., 357, 71-5, 2013. P. Santos, A.C. Watkinson, J. Hadgraft, M.E. Lane, Int. J. Pharm., 384, 1-2, 67-72, 2010. K. Bay, H. Wanko, J. Ulrich, Chem. Eng. Res. Design, 84, 1, 22-8, 2006. P. M. May, Marine Chem., 99, 1-4, 62-9, 2006. T. Lindvig, M. L. Michelsen, G. M. Kontogeorgis, Fluid Phase Equil., 203, 1-2, 247-60, 2002.

5

Solubility of Selected Systems and Influence of Solutes 5.1 EXPERIMENTAL METHODS OF EVALUATION AND CALCULATION OF SOLUBILITY PARAMETERS OF POLYMERS AND SOLVENTS. SOLUBILITY PARAMETERS DATA. Valery Yu. Senichev, Vasiliy V. Tereshatov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia

5.1.1 EXPERIMENTAL EVALUATION OF SOLUBILITY PARAMETERS OF LIQUIDS The value of solubility parameter can be calculated from the evaporation enthalpy of liquid at any given temperature:1 ΔH p – RT 1 ⁄ 2 δ =  ----------------------  V where:

ΔHp V

[5.1.1]

latent heat of vaporization molar volume

5.1.1.1 Direct methods of evaluation of the evaporation enthalpy For measurement of the evaporation enthalpy of volatile substances, adiabatic apparatuses were developed. They require significant quantities of highly purified substances. The accuracy is determined to a large degree by equipment design and precision of measurement. Most calorimeters measure a latent heat of vaporization work under isobaric conditions. The measurement of a latent heat of vaporization requires monitoring heat input into calorimeter and the amount of liquid evaporated during measurement time.2-4 In calorimeters of a flowing type,5-6 a liquid evaporates from a separate vessel of a calorimeter. The vapors are directed into the second calorimeter where the thermal capacity of the gas is measured. The design of such calorimeters ensures a precise measurement of the stream rate. Heaters and electrical controls permit control of heat flow with high

278

5.1 Experimental methods of evaluation and calculation of solubility parameters of polymers

precision and highly sensitive thermocouples measure the temperature of the gas. There are no excessive thermal losses, thus single-error corrections for the heat exchange can be used to increase the precision of measurement. The calorimeters used for the measurement of the heat of reaction can also be used for the measurement of the latent heat of vaporization. These are calorimeters for liquids, microcalorimeters, mass calorimeters, and double calorimeters.7 The calorimeters with carrier gas are also used.8-9 Evaporation of substance is accelerated by a stream of gas (for example, nitrogen) at reduced pressure. The heat loss by a calorimeter, due to evaporation, is compensated by an electrical current to keep the temperature of calorimeter constant and equal to the temperature of the thermostatic bath. 5.1.1.2 Indirect methods of evaluation of evaporation enthalpy Because the calorimetric methods of measurement of enthalpy of vapor formation are very difficult, the indirect methods are used, especially for less volatile substances. The application of generalized expression of the first and second laws of thermodynamics to the heterogeneous equilibrium between a condensed phase at isobaric-thermal conditions is given by the Clausius-Clapeyron equation that relates enthalpy of a vapor formation to the vapor pressure, P, and temperature, T. For one component system, the Clausius-Clapeyron equation has the following form:7 dP ⁄ dT = – Δ H p ⁄ TΔV where:

ΔV

[5.1.2]

difference between molar volumes of vapor and liquid

The ratio that neglects volume of a condensed phase with the assumption that vapor at low pressure is ideal can be derived from the above equation: d ln P ⁄ d1 ⁄ T = ΔH p ⁄ TΔV

[5.1.3]

After integration: ln P = – ΔH p ⁄ RT + const

[5.1.4]

Introducing compressibility factors of gas and liquids, ΔZ, the Clausius-Clapeyron equation can be written as: d ln P ⁄ d ( 1 ⁄ T ) = – ΔH p ⁄ RΔZ where:

ΔZ

[5.1.5]

difference between compressibility factors of gas and liquids

The value ΔZ includes corrections for the volume of liquid and non-ideality of a vapor phase. The simplifying assumptions give the equation: lnP = A + B/T

[5.1.6]

Approximate dependence of a vapor pressure on inverse temperature is frequently linear but the dependence may also be non-linear because of changing ratio of ΔHp/ΔZ on heating. The mathematical expressions of the dependence lnP on 1/T of real substances in

Valery Yu. Senichev, Vasiliy V. Tereshatov

279

a wide range of temperatures should be taken into account. If ΔHp/ΔZ = a + bT, it results in an equation with three constants: lnP = A + B/T + ClnT

[5.1.7]

In more complicated dependencies, the number of constants may further increase. Another convenient method is based on empirical relation of ΔHp at 25oC with the normal boiling point, Tb, of nonpolar liquids:1 2

ΔH p = T b + 23.7T b – 2950

[5.1.8]

Methods of evaluation of vapor pressure may be divided into static, quasi-static, and kinetic methods. 5.1.1.3 Static and quasi-static methods of evaluation of pressure Manometric method10 consists of thermostating with a high precision (0.01K) and vapor pressure measurement by a level of mercury with the help of a cathetometer or membrane zero-manometer. The accuracy of measurement is 0.1-0.2 mm Hg. Ebulliometric method11 is used for a simultaneous measurement of the boiling and condensation temperature that is required for evaluation of purity of a substance and its molecular mass. 5.1.1.4 Kinetic methods These methods were developed based on the molecular kinetic theory of gases. The Langmuir method is based on the evaporation of substance from a free surface into a vacuum. The Knudsen method is based on the evaluation of the outflow rate of a vapor jet from a mesh. The basic expression used in Langmuir method12 is: Δm 2πRT P =  ---------  --------------- Stα M

1⁄2

[5.1.9]

where: m S t

mass of an evaporated substance surface of evaporation time of evaporation.

The Knudsen method13 is based on a measurement of the mass rate of the vapor outflow through a hole. Knudsen proposed the following expression: Δm 2πRT 1 ⁄ 2 P k =  -----------  ---------------  S h tβ  M  where:

Δm Sh t β M

mass output of substance surface area of the hole time of vaporization Clausing parameter molecular mass

[5.1.10]

280

5.1 Experimental methods of evaluation and calculation of solubility parameters of polymers

The method uses special effusion cameras with holes of a definite form, maintaining a high vacuum in the system. The method is widely applied to the measurements of a vapor pressure of low volatile substances. The detailed comparative evaluation of experimental techniques and designs of equipment used for determination of enthalpy of evaporation can be found in the appropriate monographs.7,14 Values of solubility parameters of solvents are presented in Subchapter 4.1. 5.1.2 METHODS OF EXPERIMENTAL EVALUATION AND CALCULATION OF SOLUBILITY PARAMETERS OF POLYMERS It is not possible to determine solubility parameters of polymers by direct measurement of evaporation enthalpy. For this reason, all methods are indirect. The underlining principles of these methods are based on the theory of regular solutions that assumes that the best mutual dissolution of substances is observed at the equal values of solubility parameters (see Chapter 4). Various properties of polymer solutions involving the interaction of the polymer with solvent are studied in a series of solvents having different solubility parameters. A value of a solubility parameter is related to the maximum value of an investigated property and is equated to a solubility parameter of the polymer. This subchapter is devoted to the evaluation of one-dimensional solubility parameters. The methods of the evaluation of components of solubility parameters in multidimensional approaches are given in the Subchapter 4.1. According to Gee,15 a dependence of an equilibrium swelling of polymers in solvents on their solubility parameters is expressed by a curve with a maximum where the abscissa is equal to the solubility parameter of the polymer. For exact evaluation of δ, a swelling degree is represented by the equation resembling the Gaussian function: 2

Q = Q max exp [ – V 1 ( δ 1 – δ 2 ) ]

[5.1.11]

where: Qmax V1 δ1, δ2

the degree of swelling at the maximum on the curve molar volume of solvent solvent and polymer solubility parameters.

Then 1 Q max 1 ⁄ 2 δ2 = δ1 − +  ------ ln ------------ V1 Q

[5.1.12]

The dependence [(1/V1)ln(Qmax/Q)]1/2 = f(δ1) is expressed by a direct line intersecting the abscissa at δ1 = δ2. This method is used for calculation of the parameters of many crosslinked elastomers.16-19 The Bristow-Watson method is based on the Huggins equation deduced from a refinement of the lattice approach:20

Valery Yu. Senichev, Vasiliy V. Tereshatov

χ = β + ( V 1 ⁄ RT ) ( δ 1 – δ 2 ) where:

β z m

2

281

[5.1.13]

= (1/z)(1-1/m) a coordination number the chain length.

β may be rewritten as χS entropy contribution to χ (see Chapter 4). Accepting that Eq. [5.1.12] represents a valid means of an assignment of a constant δ2 to the polymer, the rearrangement of this equation gives: 2

2

2δ δ1 δ2 χS χ ------- – ------ =  -------2- δ 1 – ------- – -----  RT RT V 1 RT V 1

[5.1.14]

Figure 5.1.1. Dependence for equilibrium swelling of crosslinked elastomer on the base of polyether urethane. [Adapted, by permission, from V.Yu. Senichev in Synthesis and properties of crosslinked polymers and compositions on their basis. Russian Academy of Sciences Publishing, Sverdlovsk, 1990, p.16]

Now it is assumed that χS is of the order of magnitude suggested above and that, in accordance with the Huggins equation, it is not a function of δ2. Therefore χS/V1 is only 2 about 3% or less of δ 2 /RT for reasonable values of δ2 of 10-20 (MJ/m3)1/2. Hence Eq. [5.1.14] gives δ2 from the slope and intercept on a plot against δ1 (see Figure 5.1.1). This method was improved21 by using calculations that exclude strong deviations of χ. When ( χ S RT ⁄ V 1 ≈ const ), Eq. [5.1.14] is close to linear (y = A + Bx), where 2 2 y = δ 1 – χ S ( RT ⁄ V 1 ) , A = – χ S ( RT ⁄ V 1 ) – δ 2 , B = 2δ 2 , x = δ1. But δ2 enters into the expression for a tangent of a slope angle and intercept which is cut off on the ordinates axes. This can be eliminated by the introduction of a sequential approximation of χS(RT/V1) and grouping of experimental points in areas characterized by a definite interval of values χS(RT/V1). Inside each area χ S ( RT ⁄ V 1 ) → const .

282

5.1 Experimental methods of evaluation and calculation of solubility parameters of polymers

The intervals of values χS(RT/V1) are reduced in the course of computations. For n experimental points, the files X (x1, x2,.... xn) and Y(y1, y2,.... yn) are gathered. The tangent of the slope angle is defined by the method of least squares and the current value (at the given stage) of a solubility parameter of a polymer is: n

n



n

x  y – n  xy

i=1 i=1

i=1

δ 2j = -----------------------------------------------2 n  n  2   x – n  x i = 1  i=1

[5.1.15]

where: j

a stage of computation

χS(RT/V1) is then calculated using equation derived from Eqs. [5.1.13] and [5.1.14]:  χ RT -------- = – y i – δ 22j + 2x i δ 2j  S V1  j where:

[5.1.16]

value of δ2 at the given stage of computation

δ2j

Table 5.1.1. Modification of δ 2j values during stages of computation Polymer

polydiene urethane epoxide polydiene urethane poly(butylene glycol) urethane poly(diethylene glycol adipate) urethane

j=1

j=2

j=3

j=4

δ 2j , (MJ/m )

3 1/2

17.64

17.88

17.78

17.8

17.72

18.17

17.93

17.82

19.32

18.89

18.95

18.95

19.42

19.44

19.44

-

By sorting all experimental points into a defined amount of intervals (for 30-50 points it is more convenient to take 5-6 intervals), it is possible to calculate δ2 for each interval separately. The current average weighted value (contribution of δ2 is defined), obtained for each interval, is proportional to the number of points in the interval according to the following formula: δ 2j

i = ----M

k

 δ 2k mk k=1

where: k mk M j

= 1, 2,.... k, number of intervals number of points in k-interval the total number of points stage of computation.

[5.1.17]

Valery Yu. Senichev, Vasiliy V. Tereshatov

283

The shaping of subarrays of points is made in the following order, ensuring that casual points are excluded: 1. the account is made of a common array of points of δ2 and χS(RT/V1)i 2. partition of a common array into a population of subarrays of χS(RT/V1) in limits defined for the elimination of points not included in intervals and points which do not influence consequent stages of computation 3. reductions of intervals in each of the subarrays (this stage may be repeated in some cases). At each stage, the sequential approximation to the constant value of χS(RT/V1) is produced in a separate form, including the maximum number of points. The procedure gives a sequence of values δ2j as shown in Table 5.1.1. In still other methods of evaluation,22 the solvents are selected so that the solubility parameter of polymer occupies an intermediate position between solubility parameters of solvents. The assumption is being made that the maximum polymer swelling occurs when the solubility parameters of the solvent mixture and polymer are equal. This is the case when the solubility parameter of the polymer is lower than the solubility parameter of the primary solvent and the solubility parameter of the secondary solvent is higher. The dependence of the swelling ratio on the composition of the solvent mixture has a maximum (see Figure 5.1.2). Such mixed solvents are Figure 5.1.2. Dependence of equilibrium swelling of called symmetric liquids. The reliability of crosslinked elastomer of polyester urethane (1) and polybutadiene nitrile rubber (2) on the volume fraction the method is examined by a narrow interof acetone in the toluene-acetone mixture. [Adapted, by val of change of the solubility parameter of permission, from V.V. Tereshatov, V.Yu. Senichev, A.I. a binary solvent. The data obtained by this Gemuev, Vysokomol. soed., B32, 412 (1990)]. method for various mixtures differ by no more than 1.5% compared with the data obtained by other methods. Examples of results are given in Tables 5.1.2, 5.1.3. Table 5.1.2. Values of solubility parameters for crosslinked elastomers from swelling in symmetric liquids. [Adapted, by permission, from V.V. Tereshatov, V.Yu. Senichev, A.I. Gemuev, Vysokomol. soed., B32, 412 (1990).] Elastomer Polyether urethane

Symmetric liquids Toluene(1) − acetone (2) Cyclohexane (1) − acetone (2)

Ethylene-propylene rubber Hexane (1) − benzene (2) Toluene (1) − acetone (2)

H

ϕ 2 at Qmax δp, (MJ/m3)1/2 0.11 0.49

18.4 18.2

0.38 0.32

16.2 18.9

284

5.1 Experimental methods of evaluation and calculation of solubility parameters of polymers

Table 5.1.2. Values of solubility parameters for crosslinked elastomers from swelling in symmetric liquids. [Adapted, by permission, from V.V. Tereshatov, V.Yu. Senichev, A.I. Gemuev, Vysokomol. soed., B32, 412 (1990).] Elastomer

H

ϕ 2 at Qmax δp, (MJ/m3)1/2

Symmetric liquids

Butadiene-nitrile rubber

Ethyl acetate (1) − acetone (2) Benzene (1) − acetone (1)

0.22 0.27

19.1 19.1

Polyester-urethane

Toluene (1) − acetone (2) o-Xylene (1) − butanol-1 (2)

0.62 0.21

19.6 19.5

Butyl rubber

Octane (1) − benzene (2)

0.26

16.1

Table 5.1.3. Values of solubility parameters of crosslinked elastomers from swelling in individual solvents and symmetric liquids. [Adapted, by permission, from V.V. Tereshatov, V.Yu. Senichev, A.I. Gemuev, Vysokomol. soed., B32, 412 (1990).] Symmetric liquids

Elastomer

Individual solvents Gee method

Bristow-Watson method 3 1/2

(MJ/m ) Polyether-urethane Ethylene-propylene rubber

18.3 ± 0.1

17.8, 18.4, 19.4

19.2

16.2

16.1-16.4

-

19.0 ± 0.1

18.9-19.4

18.7

Polyester-urethane

19.5-19.6

19.3, 19.9

19.5

Polyester-urethane

16.1

15.9-16.6

14.9

Butadiene-nitrile rubber

The calculations were made using the equation: 2

2

δ p = δ mix = [ δ 1 ( 1 – ϕ'' 1 ) + δ 2 ϕ'' 1 – ΔH mix ⁄ V 12 ] where:

ϕ'' 1 ΔHmix V12

1⁄2

[5.1.18]

the volume fraction of a solvent in a binary mixture of solvents causing a maximum of equilibrium swelling experimental value of the mixing enthalpy of components of binary solvent. It can be taken from literature23-24 the molar volume of binary solvent

If there is no volume change, V12 can be calculated using the additivity method: V 12 = V 1 ϕ 1 + V 2 ϕ 2

[5.1.19]

Attempts25 were made to relate intrinsic viscosity [η] to solubility parameters of mixed solvents. The δ2 of polymer was calculated from the equation: [η] = f(δ1). It was assumed that the maximum value of [η] was when δ1 = δ2 of the polymer. However, studying [η] of polymethylmethacrylate in fourteen liquids, a large scatter of experimental

Valery Yu. Senichev, Vasiliy V. Tereshatov

285

points was found and a curve was drawn to find a diffusion maximum. The precision of δ2 values was affected by 10% scatter in experimental data. This method was widely used by Mangaray et al.26-28 The authors have presented [η] as the Gaussian function of (δ1 − δ2)2. Therefore, dependence {(1/V1)ln[η]max/[η]}1/2 = f(δ1) can be expressed by a straight line intersecting the abscissa at a point for which δ1=δ2. In the case of natural rubber and polyisobutylene, the paraffin solvents and ethers containing alkyl chains of a large molecular mass were studied.26 For polystyrene, aromatic hydrocarbons were used. For polyacrylate and polymethacrylate esters (acetates, propionates, butyrates) were used.27,28 The method was used for determination of δ2 of many polymers.29-31 In all cases, the authors observed extrema for the dependence of [η]=f(δ1), and the obtained values of δ2 coincided well with the values determined by other methods. But for some polymers, it was not possible to obtain extrema for the dependence of [η] = f(δ1).32 A method of the evaluation [η] in one solvent at different temperatures was used for polyisobutylene33 and polyurethanes.34 For polymers soluble in a limited range of solvents, more complex methods utilizing [η] relationship are described.35-37 In addition to the above methods, δ2 of the polymer can be determined from a threshold of sedimentation38 and by critical opalescence.39 The method of inverse gas-liquid chromatography has also been used to evaluate δ2 of polymers, including Hansen's parameters.40-43 One may use some empirical ratios relating solubility parameters of polymers with some of their physical properties, such as surface tension44-46 and glass transition temperature.47 The solubility parameters for various polymers are given in Table 5.1.4. Table 5.1.4. Solubility parameters of some polymers36,48 Polymer

δ (cal/cm3)1/2 (MJ/m3)1/2

Polymer

Butyl rubber

7.84

16.0

Polydimethylsiloxane

Cellulose diacetate

10.9

22.2

Polydimethylphenyleneoxide

Cellulose dinitrate

10.6

21.6

Polyisobutylene

Polyamide-66

13.6

27.8

Natural rubber

8.1

Neoprene Cellulose nitrate

δ (MJ/m3)1/2

(cal/cm3)1/2

9.53

19.5

8.6

17.6

7.95

16.2

Polymethylmethacrylate

9.3

19.0

16.5

Polymethylacrylate

9.7

19.8

8.85

18.1

Polyoctylmethacrylate

8.4

17.2

11.5

23.5

Polypropylene

8.1

16.5

Polyacrylonitrile

14.5

29.6

Polypropylene oxide

7.52

15.4

Polybutadiene

8.44

17.2

Polypropylene sulfide

9.8

19.6

Poly-n-butylacrylate

8.7

17.8

Polypropylmethacrylate

8.8

18.0

Polybutylmethacrylate

8.7

17.8

Polystyrene

8.83

18.0

Polybutyl-tert-methacrylate

8.3

16.9

Polyethylene

7.94

16.2

286

5.1 Experimental methods of evaluation and calculation of solubility parameters of polymers

Table 5.1.4. Solubility parameters of some polymers36,48 Polymer

δ 3 1/2

(cal/cm )

3 1/2

Polymer

(MJ/m )

δ 3 1/2

(MJ/m )

(cal/cm3)1/2

Polyvinylacetate

9.4

19.2

Polyethyleneterephthalate

Polyvinylbromide

9.55

19.5

Polyethylmethacrylate

Polyvinylidenechloride

12.4

25.3

Polybutadienenitrile (82:18)

8.7

17.8

Polyvinylchloride

9.57

19.5

Polybutadienenitrile (75:25)

9.38

19.2

Polyhexyl methacrylate

8.6

17.6

Polybutadienenitrile (70:30)

9.64

19.7

Polyglycol terephthalate

10.7

21.8

Polybutadienenitrile (61:39)

10.3

21.0

Polydiamylitaconate

8.65

17.7

Polybutadienevinylpyridine (75:25)

9.5

19.1

Polydibutylitaconate

8.9

18.2

Polybutadienestyrene (96:4)

10.5

21.4

Polybutadienestyrene (87.5:12.5)

6.2

12.7

Polybutadienestyrene (85:15)

8.5

17.4

Polychloroacrylate

10.1

20.6

Polybutadienestyrene (71.5:28.5)

8.33

17.0

Polycyanoacrylate

14.0

28.6

Polybutadienestyrene (60:40)

8.67

17.7

Polyethylacrylate

9.3

19.0

Chlorinated rubber

9.4

19.2

7.95

16.2

Ethylcellulose

10.3

21.0

Polysulfone Polytetrafluorethylene

Polyethylenepropylene

10.7

21.8

9.1

18.6

8.1

16.5

8.31

17.0

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

J.H. Hildebrand and R.L. Scott, Solubility of non-electrolytes. 3rd ed., Reinhold, New-York, 1950. J. Mathews, J. Amer. Chem. Soc., 48, 562 (1926). A. Coolidge, J. Amer. Chem. Soc., 52, 1874 (1930). N. Osborn and D. Ginnings, J. Res. Nat. Bur. Stand., 49, 453 (1947). G. Waddington, S. Todd, H. Huffman, J. Amer. Chem. Soc., 69, 22 (1947). J. Hales, J. Cox, E. Lees, Trans. Faraday Soc., 59, 1544 (1963). Y. Lebedev and E. Miroshnichenko, Thermochemistry of vaporization of organic substances, Nauka, Moscow, 1981. F. Coon and F. Daniel, J. Phys. Chem., 37, 1 (1933). J. Hunter, H. Bliss, Ind. Eng. Chem., 36, 945 (1944). J. Lekk, Measurement of pressure in vacuum systems, Mir, Moscow, 1966. W. Swietoslawski, Ebulliometric measurement, Reinhold, N.-Y., 1945. H. Jones, I. Langmuir, G. Mackay, Phys. Rev., 30, 201 (1927). M. Knudsen, Ann. Phys., 35, 389 (1911). Experimental thermochemistry, Ed. H. Skinner, Intersci. Publ., 1962. G. Gee, Trans. Faraday Soc., 38, 269 (1942). R.F. Boyer, R.S. Spencer, J. Polym. Sci., 3, 97 (1948). R.L. Scott, M. Magat, J. Polym. Sci., 4, 555(1949). P.I. Flory, I. Rehner, J. Chem. Phys., 11, 521 (1943). N.P. Apuhtina, E.G. Erenburg, L.Ya. Rappoport, Vysokomol. soed., A8, 1057 (1966). G.M. Bristow., W.F. Watson, Trans. Faraday Soc., 54, 1731 (1959). V.Yu. Senichev in Synthesis and properties of crosslinked polymers and compositions on their basis. Russian Academy of Sciences Publishing, Sverdlovsk,1990, pp.16-20. V.V.Tereshatov, V.Yu. Senichev, A.I. Gemuev, Vysokomol. soed., B32, 412(1990). V.P. Belousov, A.G. Morachevskiy, Mixing heats of liquids, Chemistry, Leningrad, 1970. V.P. Belousov, A.G. Morachevskiy, Heat properties of non-electrolytes solutions. Handbook, Chemistry, Leningrad, 1981.

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287

T. Alfrey, A.I.Goldberg, I.A. Price, J. Colloid. Sci., 5, 251 (1950). D. Mangaray, S.K. Bhatnagar, Rath S.B., Macromol. Chem., 67, 75 (1963). D. Mangarey, S. Patra, S.B. Rath, Macromol. Chem., 67, 84 (1963). D. Mangarey, S. Patra, P.C. Roy, Macromol. Chem., 81, 173 (1965). V.E. Eskin, U. Guravlev, T.N. Nekrasova, Vysokomol. soed., A18, 653 (1976). E. G. Gubanov, S.V. Shulgun, V.Sh. Gurskay, N.A. Palihov, B.M. Zuev, B.E. Ivanov, Vysokomol. soed., A18, 653 (1976). C.I. Scheehan, A.L. Bisio, Rubber Chem. Technol., 39, 149 (1966). A.A. Tager, L.K. Kolmakova, G. Ya. Shemaykina, Ya.S. Vigodskiy, S.N. Salazkin, Vysokomol. soed., B18, 569 (1976). W.R. Song, D.W. Brownawell, Polym. Eng. Sci., 10, 222 (1970). Y.N. Hakimullin, Y.O. Averko-Antonovich, P.A. Kirpichnikov, M.A. Gasnikova, Vysokomol. soed., B17, 287 (1975). F.P. Price, S.G. Martin, I.P. Bianchi, J. Polymer Sci., 22, 49 (1956). G.M. Bristow, W.F. Watson, Trans. Faraday Soc., 54, 1731, 1742 (1958). T.G. Fox, Polymer, 3, 11 (1962). K.W. Suh, D.H. Clarke, J. Polymer Sci., A-1, 4, 1671 (1967). V.E. Eskin, A.E. Nesterov, Vysokomol. soed., A8, 1051 (1966). S.K. Ghosh, Macromol. Chem., 143, 181 (1971). A.G. Grozdov, B.N. Stepanov, Vysokomol. soed., B17, 907(1975). K. Adamska, R. Bellinghausen, A. Voelkel, J. Chrom. A, 1195, 146 (2008). J.-C. Huang J. Appl. Polym. Sci., 91, 2894 (2004). A.A. Berlin, V.E. Basin, Fundamentals of adhesion of polymers, Chemistry, Moscow, 1974. S.M. Ygnaytskaya, S.S. Voutskiy, L. Y. Kapluynova, Colloid J., 34, 132 (1972). R.M. Koethen, C.A. Smolders, J. Appl. Polym. Sci., 19, 1163 (1975) R.A. Hayes, J. Appl. Polym. Sci., 5, 318, (1961). E.S. Lipatov, A.E. Nesterov, T.M. Gritsenko, R.A Veselovski, Handbook on polymer chemistry. Naukova dumka, Kiev, 1971. Z.Grubisic-Gallot, M. Picot, Ph. Gramain, H. Benoit, J. Appl. Polym. Sci., 16, 2931(1972). H.-R. Lee, Y.-D. Lee, J. Appl. Polym. Sci., 40, 2087(1990).

288

5.2 Prediction of solubility parameters

5.2 PREDICTION OF SOLUBILITY PARAMETERS Nobuyuki Tanaka Department of Biological and Chemical Engineering, Gunma University, Kiryu, Japan

5.2.1 SOLUBILITY PARAMETER OF POLYMERS To search for suitable solvents for a polymer, the solubility parameter of polymers, δp, is defined as:1-11 δp = (h0/v)1/2

[5.2.1]

where: h0 v

the cohesive enthalpy per molar structural unit for a polymer (cal/mol) the volume per molar structural unit for a polymer (cm3/mol)

because δp is equivalent to the solubility parameter of solvents, δs, that shows the minimum of the dissolution temperature7 or the maximum of the degree of swelling1,2 for the polymer. For δs, h0 is the molar energy of vaporization that is impossible to measure for polymers which are decomposed before the vaporization at elevated temperatures, and v is the molar volume of a solvent. The measurements of the dissolution temperature and the degree of swelling are only means to find the most suitable solvents for a polymer by trial and error. To obtain the exact value of δp at a temperature, T, the δp prediction from the thermal transition behavior such as glass transition temperature and the melting point has been discussed.9-11 Consequently, it was found that the sum of their transition enthalpies gave h0 in equation [5.2.1] approximately: for crystalline polymers, h0 ≈ hg + hx + hu

T ≤ Tg

[5.2.2]

h0 ≈ hx + hu

Tg < T < Tm

[5.2.3]

T ≤ Tg

[5.2.4]

for amorphous polymers, h0 ≈ hg + hx where: hg hu hx Tg Tm

the glass transition enthalpy per molar structural unit for a polymer the heat of fusion per molar structural unit for a polymer the transition enthalpy per molar structural unit due to ordered parts in the amorphous regions the glass transition temperature; here the onset temperature of heat capacity jump at the glass transition the melting temperature

Nobuyuki Tanaka

289

In the following sections, the physical meanings of hg and hx are presented in the theoretical treatments of the glass transition temperature, and for several polymers, δp is predicted using these thermodynamic quantities. 5.2.2 GLASS TRANSITION IN POLYMERS At Tg, polymers are frozen glasses, and the molecular motions are restricted. However, the actual states of glasses are dependent on the cooling rate; if the cooling rate is rapid, the glasses formed are imperfect, such as liquid glasses or glassy liquids.12-14 The annealing of imperfect glasses results in the enthalpy relaxation from imperfect glasses to perfect glasses. At Tg in the heating process, the strong restriction of molecular motions by intermolecular interactions is removed and then the broad jump of heat capacity, Cp, is observed.15 Annealing the glasses, the Cp jump curve becomes to show a peak.15,16 5.2.2.1 Glass transition enthalpy For polymer liquids, the partition function, Ω, normalized per unit volume is given by10,14,17,18 2 3Nx ⁄ 2

N

Ω = ( Z ⁄ N! ) ( 2πmkT ⁄ h )

( q ⁄ vf )

Nx

exp { – Nxh

int

⁄ RT }

[5.2.5]

with vf = qv exp{-hint/RT}

where:

hint h k m N q R vf x Z

the intermolecular cohesive enthalpy per molar structural unit for a polymer Planck's constant Boltzmann's constant the mass of a structural unit for a polymer the number of chains the packing factor of structural units for a polymer the gas constant the free volume per molar structural unit for a polymer the degree of polymerization the conformational partition function per a chain

From equation [5.2.5], the enthalpy and the entropy per molar chain for polymer liquids, Hl and Sl, are derived:10 H1 = RT2dlnZ/dT + (3/2)RxT − RxT2d lnvf/dT+ xhint

[5.2.6]

S1 = (RlnZ + RTdlnZ/dT) + (3/2)Rx − x(Rlnvf + RTdlnvf/dT) + xSd

[5.2.7]

with Sd = (3R/2)ln(2πmkT/h2) − (1/x)(R/N)lnN! + Rlnq The first terms on the right hand side of equations [5.2.6] and [5.2.7] are the conformational enthalpy and entropy per molar chain, xhconf and xsconf, respectively.19 Assuming that chains at Tg are in quasi-equilibrium state, the criteria on Tg are obtained: f flow ( = h flow – T g s flow ) ≈ 0

[5.2.8]

and s flow ≈ 0 (hence h flow ≈ 0 )

[5.2.9]

with hflow = Hl/x − 3RTg/2 and sflow = Sl/x − 3R/2

290

5.2 Prediction of solubility parameters

Figure 5.2.2. State models for an amorphous polymer at each temperature range of (a) T ≤ T g , (b) T g < T ≤ T e , and (c) Te < T, where hatching: glass parts, crosses: ordered parts, and blank: flow parts. The arrows show the mobility of ordered parts [after reference 10].

From equations [5.2.8] and [5.2.9], which show the conditions of thermodyFigure 5.2.1. Schematic curves of Ha and Cp in the vicin- namic quasi-equilibrium and freezing for ity of Tg for an amorphous polymer. Two lines of short polymer liquids, the conformational and long dashes show Ha for a supercooled liquid and Cp enthalpy and entropy per molar structural for a superheated glass (hypothesized), respectively. Te conf conf and s g are derived, unit at Tg, h g is the end temperature of Cp jump [after reference 10]. respectively: conf

hg

conf

sg

2

2

int

{ = RT g ( d ln Z ⁄ dT ⁄ x ) } = RT g d ln v f ⁄ dT – h g

[5.2.10]

{ = (RlnZ + RT g d ln Z ⁄ dT ⁄ x } = R ln v f + RT g d ln v f ⁄ dT – S d

[5.2.11]

Rewriting equation [5.2.10], the glass transition enthalpy per molar structural unit, int conf h g = h g + h g is obtained: 2

2

h g = RT g d ln v f ⁄ dT ≈ RT g ⁄ c 2

[5.2.12]

with c ≈ φ g ⁄ β where:

int

hg c2 β φg

hint at Tg the constant in the WLF equation20 the difference between volume expansion coefficients below and above Tg the fractional free volume at Tg

The WLF equation on the time-temperature superposition of viscoelastic relaxation phenomena is given by:20 log aT = −c1(T − Tg)/(c2 + T − Tg) where: aT c1

the shift factor constant

[5.2.13]

Nobuyuki Tanaka

291

Figure 5.2.1 shows the schematic curves of Ha and Cp for an amorphous polymer, where Ha is the molar enthalpy for an amorphous polymer. Substituting Hl/x for Ha, Ha at Tg corresponds to 3RTg/2, because of hflow = 0. At Tg, the energy of hg is given off in the cooling process and absorbed in the heating process. int conf Table 5.2.1 shows the numerical values of hg (= h g + h g ) and c2 from equation conf conf 12,16 int h g , h g , and s g for several polymers. As the values [5.2.12], together with Tg, int of h g , the molar cohesive energy of main residue in each polymer, e.g., −CONH− for N6 and N66, −CH(CH3)− for iPP, −CH(C6H5)− for iPS, and −C6H4− for PET, was used.21 The predicted values of c2 for PS and PET are close to the experimental values, 56.6 and 55.3K, respectively.20,22 The standard values of c1 and c2 in equation [5.2.13] are 17.44 and 51.6K, respectively.20,23 Table 5.2.1 Polymer N6

int

conf

conf

T K

cal/mol

cal/mol

cal/(k mol)

hg* cal/mol

c2 K

313

8500

475

11.2

8980

21.7

hg

hg

sg

N66

323

17000

976

22.6

17980

11.5

iPP

270

1360

180

0.98

1540

94.1

iPS

35916

4300

520

2.03

4820 (4520)

53.1 (56.6)

PET

342

3900

282

7.10

4180 (4200)

55.6 (55.3)

int

conf

* hg = hg + hg

The numerical values in parentheses are the experimental values20,22 of c2 and hg (from c2). N6: polycaproamide (nylon-6), N66: poly(hexamethylene adipamide) (nylon-6,6), iPP: isotactic polypropylene, iPS: isotactic polystyrene, PET: poly(ethylene terephthalate).

5.2.2.2 Cp jump at the glass transition temperature The mechanism of Cp jump at the glass transition temperature could be illustrated by the melting of ordered parts released from the glassy states.10 Figure 5.2.2 shows the state models for an amorphous polymer below and above Tg. The ordered parts are generated near Tg in the cooling process; in the glasses, the ordered parts are contained. During the heating process, right after the glassy state was removed at Tg, the melting of ordered parts starts and continues up to Te, keeping an equilibrium state between ordered parts and flow parts. In this temperature range, the free energy per molar structural unit of polymer liquids containing ordered parts, fm, is given by10 fm = fxXx + fflow(1 − Xx) where: fx fflow Xx

the free energy per molar structural unit for ordered parts the free energy per molar structural unit for flow parts the mole fraction of ordered parts

[5.2.14]

292

5.2 Prediction of solubility parameters

From (dfm/dXx)p = 0, an equilibrium relation is derived: fm = fx = fflow

[5.2.15]

Whereas, Cp is defined as: C p = ( dh p ⁄ dT ) p

[5.2.16

with hq = fq − T(dfq/dT)p, q = m, x or flow From equations [5.2.15] and [5.2.16], it is shown that Cp of ordered parts equals to that of flow parts. Therefore, hx is given by10 h x ≈ h g + Δh

[5.2.17]

Te

 ΔCp dt

with Δh =

conf

and { RT g ln ( Z g ⁄ Z 0 ) } ⁄ x ≤ Δh ≤ T g { s g

– ( R ln Z 0 ) ⁄ x }

Tg

where:

ΔCp

the difference in the observed Cp and the hypothesized superheated glass Cp at the glass transition the conformational partition function per a chain at Tg the component conformational partition function per chain regardless of the temperature in Z the conformational entropy per molar structural unit at Tg

Zg Z0 conf

sg

The hx is also obtained by rewriting the modified Flory's equation, which expresses the melting point depression as a function of the mole fraction of the major component, X, for binary random copolymers:24-27 h x ≈ 2h u ( 1 – 1 ⁄ a )

[5.2.18] 0

with a = – h u ( 1 ⁄ T m ( X ) – 1 ⁄ T m ) ⁄ ( R ln X ) where: Tm(X)

the melting temperature for a copolymer with X

Tm

the melting temperature for a homopolymer of major component

0

Table 5.2.2 Polymer

hu cal/mol

hx (eq. [5.2.17]) hx (eq. [5.2.17]) − hu hx (eq. [5.2.18]) cal/mol cal/mol cal/mol

hx from δp cal/mol

N6

5100

9590 (10070)

4490 (4970)

4830

−

N66

10300

19300 (20280)

9000 (9980)

9580

10070

iPP

1900

1600 (1780)

−

1470

1420

Nobuyuki Tanaka

293

Table 5.2.2 hx (eq. [5.2.17]) hx (eq. [5.2.17]) − hu hx (eq. [5.2.18]) cal/mol cal/mol cal/mol

hx from δp cal/mol

Polymer

hu cal/mol

iPS

239012

5030 (5550)

2640 (3160)

−

2410-5790

PET

5500

5380 (5670)

−

6600

6790

The numerical values in parentheses were calculated using equation [5.2.17] with the second term of conf T g { s g – ( R ln Z 0 ) ⁄ x } .

Table 5.2.2 shows the numerical values of hx from equations [5.2.17] and [5.2.18], and from the reference values7,8 of δp using equations [5.2.1] ~ [5.2.4], together with the values12,28,29 of hu, for several polymers. The second term on the right hand side of equation [5.2.17] was calculated from {RTgln(Zg/Z0)}/x. The numerical values in parentheses, which were calculated using equation [5.2.17] with the second term of conf T g { s g – ( R ln Z 0 ) ⁄ x } , are a little more than in the case of {RTgln(Zg/Z0)}/x. The relationship of hx (eq.[5.2.17]) >> hu found for N6 and N66 suggests two-layer structure of ordered parts in the glasses, because, as shown in the fourth column, hx (eq.[5.2.17]) − hu is almost equal to hx ( ≈ h u ) from equation [5.2.18] or δp (= 13.6 (cal/cm3)1/2). For iPP, hx (eq.[5.2.17]) is a little higher than hx from equation [5.2.18] or δp (= 8.2 (cal/cm3)1/2), suggesting that the ordered parts in glasses are related closely to the helical structure. For iPS, hx (eq.[5.2.17]) and hx (eq.[5.2.17]) − hu are in the upper and lower ranges of hx from δp (=8.5~10.3 (cal/cm3)1/2), respectively. For PET, hx (eq.[5.2.17]) is almost equal to hu, but hx from equation [5.2.18] or δp (= 10.7 (cal/cm3)1/2) is a little more than hu, resulting from glycol bonds in bulk crystals distorted more than in ordered parts.10,25,30 5.2.3 δ p PREDICTION FROM THERMAL TRANSITION ENTHALPIES Table 5.2.3 shows the numerical values of δp predicted from equations [5.2.1] ~ [5.2.4] usr ing the results of Tables 5.2.1 and 5.2.2, together with hx, hu, hg, h0, and δ p (reference valr 7,8 ues) for several polymers. The predicted values of δp for each polymer are close to δ p . Table 5.2.3 r

hx cal/mol

hu cal/mol

hg cal/mol

h0 cal/mol

δp (cal/cm3)1/2

N6

9590* (10070) 4830**

− − 5100

8980 8980 8980

18570 (19050) 18910

13.4 (13.6) 13.5

− −

N66

19300* (20280) 9580**

− − 10300

17980 17980 17980

37280 (38260) 37860

13.4 (13.6) 13.5

13.6 13.6 13.6

iPP

1600* (1780) 1470**

1900 1900 1900

− − −

3500 (3680) 3370

8.4 (8.6) 8.3

8.27 8.27 8.27

Polymer

δp

(cal/cm3)1/2

294

5.2 Prediction of solubility parameters

Table 5.2.3 r

hx cal/mol

hu cal/mol

hg cal/mol

h0 cal/mol

δp (cal/cm3)1/2

(cal/cm3)1/2

iPS

5030* (5550)

− −

4820 4820

9850 (10370)

9.9 (10.2)

8.5-10.3 8.5-10.3

PET

5380* (5670) 6600**

5500 5500 5500

4180 4180 4180

15060 (15350) 16280

10.2 (10.3) 10.6

10.7 10.7 10.7

Polymer

δp

The numerical values with * and ** are hx from equations [5.2.17] and [5.2.18], respectively. The numerical valconf ues in parentheses were calculated using equation [5.2.17] with the second term of T g { s g – ( R ln Z 0 ) ⁄ x }

For atactic polypropylene (aPP) that could be treated as a binary random copolymer composed of meso and racemic dyads,26,27,31 δp is predicted as follows. For binary random copolymers, hg is given by: int

conf

hg = hg + hg int

( XA )

int

[5.2.19] int

int

with h g = h g ( 1 ) – ( h g ( 1 ) – h g ( 0 ) ) ( 1 – X A ) where:

conf

hg

( XA )

int hg ( 1 ) int hg ( 0 )

XA

the conformational enthalpy per molar structural unit for a copolymer with XA at Tg the intermolecular cohesive enthalpy per molar structural unit for a homopolymer of component A (XA = 1) at Tg the intermolecular cohesive enthalpy per molar structural unit for a homopolymer of component B (XA = 0) at Tg the mole fraction of component A

Further, hx is obtained from equation [5.2.17], but Zg is the conformational partition function for a copolymer with XA at Tg and Z0 is the component conformational partition function for a copolymer with XA regardless of the temperature in Z. Whereas for binary random copolymers, Tg is given by:32,33 int

conf

Tg = Tg ( 1 ) ( hg + hg

int

conf

( XA ) ) ⁄ { hg ( 1 ) + hg

conf

( 1 ) – Tg ( 1 ) ( sg

conf

( 1 ) – sg

( XA ) ) }

[5.2.20] where:

conf

hg

( 1 ) the conformational enthalpy per molar structural unit for a homopolymer (XA = 1) at Tg

conf sg ( 1 ) conf sg ( X A )

the conformational entropy per molar structural unit for a homopolymer (XA = 1) at Tg

Tg(1)

the glass transition temperature for a homopolymer (XA = 1)

the conformational entropy per molar structural unit for a copolymer with (XA = 1) at Tg

Thus, using equations [5.2.19] and [5.2.20], δp for binary random copolymers, including aPP, could be predicted.

Nobuyuki Tanaka

295

Table 5.2.4 Tg K

hg cal/mol

hx cal/mol

0

270

1540

0.05

265

0.1

261

0.15 0.2

1− XA

h0, cal/mol

δp, (cal/cm3)1/2

T > Tg

T < Tg

T > Tg

T < Tg

1600 (1780)

3500 (3680)

5040 (5220)

8.42 (8.62)

10.10 (10.23)

1480

1510

3410

4900

8.31

9.95

1450

1470

3370

4830

8.26

9.88

259

1440

1460

3360

4790

8.24

9.85

257

1430

1440

3340

4770

8.23

9.83

0.3

255

1420

1440 (1500)

3340 (3400)

4760 (4820)

8.22 (8.29)

9.82 (9.87)

0.4

254

1420

1450

3350

4770

8.23

9.83

0.5

255

1440

1470

3370

4810

8.26

9.86

0.6

256

1450

1490

3390

4840

8.28

9.90

0.7

258

1470

1520

3420

4890

8.32

9.95

0.8

262

1500

1560

3460

4960

8.37

10.02

0.85

264

15010

1580

3480

4990

8.39

10.05

0.9

266

1520

1600

3500

5030

8.42

10.09

0.95

268

1540

1620

3520

5060

8.45

10.12

1

270

1550

1650 (1840)

3550 (3740)

5100 (5300)

8.48 (8.69)

10.16 (10.34)

The numerical values in parentheses were calculated using equation [5.2.17] with the second term of conf T g { S g – ( R ln Z 0 ) ⁄ x } .

Table 5.2.4 shows the numerical values of δp for aPP, together with Tg, hg, hx, and h0, which give the concave type curves against 1 − XA, respectively. Where XA is the mole fraction of meso dyads. As hu of crystals or quasi-crystals in aPP, 1900 cal/mol was used, because hu (= 1900 cal/mol) of iPP28 should be almost equal to that of syndiotactic PP (sPP); hconf + hint ≈ 1900 cal/mol at each Tm for both PP, where hconf = 579.7 cal/mol at Tm = 457K28 for iPP, hconf = 536.8 cal/mol at Tm = 449K34 for sPP, and hint = 1360 cal/mol for both PP. Here quasi-crystals are ordered parts in aPP with 1 − XA ≈ 0.30 ~ 0.75, which do not satisfy the requirements of any crystal cell. As Tg of iPP and sPP, 270K was used for both PP.12,35 The experimental values of Tg for aPP are less than 270K.36-41 In this calculation, for aPP with 1 − XA = 0.4, the minimum of Tg, 254K, was obtained. δp in T>Tg showed the minimum, 8.22 (cal/cm3)1/2, at 1 − XA = 0.3, which is 0.20 less than 8.42 (cal/cm3)1/2 of iPP, and δp in T < Tg showed the minimum, 9.82 (cal/cm3)1/2, at 1 − XA = conf 0.3 and 10.10 (cal/cm3)1/2 for iPP. Substituting T g { s g – ( R ln Z 0 ) ⁄ x } for the second 42,43 the numerical values of hx, h0, and δp become a little more term in equation [5.2.17],

296

5.2 Prediction of solubility parameters

than in the case of {RTgln(Zg/Z0)}/x, as shown in Table 5.2.4. However, the increase of hx for iPP led Te (= 375K) near the experimental values,35 e.g., 362K and 376K, where Te was approximated by: 0

T e ≈ 2 ( h x – h g ) ⁄ ΔC p + T g where:

0

ΔC p

[5.2.21]

the difference in liquid Cp and glass Cp before and after the glass transition; 4.59 cal/(K mol) for iPP12

Thus, we can browse the solvents of aPP which satisfy δp = δs. Equations [5.2.2], [5.2.3] and [5.2.4] are available as tools to predict thermal transition behaviors. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

M. Barton, Chem. Rev., 75, 731(1975). G. M. Bristow and W. F. Watson, Trans. Faraday Soc., 54, 1742 (1958). W. A. Lee and J. H. Sewell, J. Appl. Polym. Sci., 12, 1397 (1968). P. A. Small, J. Appl. Chem., 3, 71 (1953). M. R. Moore, J. Soc. Dyers Colourists, 73, 500 (1957). D. P. Maloney and J. M. Prausnity, J. Appl. Polym. Sci., 18, 2703(1974). A. S. Michaels, W. R. Vieth, and H. H. Alcalay, J. Appl. Polym. Sci., 12, 1621 (1968). J. Brundrup and E. H. Immergut, Polymer Handbook, Wiley, New York, 1989. N. Tanaka, Sen-i Gakkaishi, 44, 541 (1988). N. Tanaka, Polymer, 33, 623 (1992). N. Tanaka, Current Trends in Polym. Sci., 1, 163 (1996). B. Wunderlich, Thermal Analysis, Academic Press, New York, 1990. N. Tanaka, Polymer, 34, 4941 (1993). N. Tanaka, Polymer, 35, 5748 (1994). T. Hatakeyama and Z. Liu, Handbook of Thermal Analysis, Wiley, New York, 1998. H. Yoshida, Netsusokutei, 13 (4), 191 (1986). N. Tanaka, Polymer, 19, 770 (1978). N. Tanaka, Thermodynamics for Thermal Analysis in Chain Polymers, Kiryu Times, Kiryu, 1997. A. E. Tonelli, J. Chem. Phys., 54, 4637 (1971). J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1960. C. W. Bunn, J. Polym. Sci., 16, 323 (1955). H. Sasabe, K. Sawamura, S. Sawamura, S. Saito, and K. Yoda, Polymer J., 2, 518 (1971). S. Iwayanagi, Rheology, Asakurashoten, Tokyo, 1971. N. Tanaka and A. Nakajima, Sen-i Gakkaishi, 29, 505 (1973). N. Tanaka and A. Nakajima, Sen-i Gakkaishi, 31, 118 (1975). N. Tanaka, Polymer, 22, 647 (1981). N. Tanaka, Sen-i Gakkaishi, 46, 487 (1990). A. Nakajima, Molecular Properties of Polymers, Kagakudojin, Kyoto, 1969. L. Mandelkern, Crystallization of Polymers, McGraw-Hill, New York, 1964. N. Tanaka, Int. Conf. Appl. Physical Chem., Warsaw, Poland, November 13-16, 1996, Abstracts, Warsaw, 1996, p.60. N. Tanaka, 36th IUPAC Int. Symp. Macromolecules, Seoul, Korea, August 4-9, 1996, Abstracts, Seoul, 1996, p.780. N. Tanaka, Polymer, 21, 645 (1980). N. Tanaka, 6th SPSJ Int. Polym. Conf., Kusatsu, Japan, October 20-24, 1997, Preprints, Kusatsu, 1997, p.263. J. Schmidtke, G. Strobl, and T. Thurn-Albrecht, Macromolecules, 30, 5804 (1997). D. R. Gee and T. P. Melia, Makromol. Chem., 116, 122 (1968). F. P. Reding, J. Polym. Sci., 21, 547 (1956). G. Natta, F. Danusso, and G. Moraglio, J. Polym. Sci., 25, 119 (1957). M. Dole and B. Wunderlich, Makromol. Chem., 34, 29 (1959). R. W. Wilkinson and M. Dole, J. Polym. Sci., 58, 1089 (1962).

Nobuyuki Tanaka 40 41 42 43

F. S. Dainton, D. M. Evans, F. E. Hoare, and T. P. Melia, Polymer, 3, 286 (1962). E. Passaglia and H. K. Kevorkian, J. Appl. Phys., 34, 90 (1963). N. Tanaka, AIDIC Conference Series, 4, 341 (1999). N. Tanaka, 2nd Int. and 4th Japan-China Joint Symp. Calorimetry and Thermal Anal., Tsukuba, Japan, June 1-3, 1999, Preprints, Tsukuba, 1999, pp.92-93.

297

298

5.3 Methods of calculation of solubility parameters of solvents and polymers

5.3 METHODS OF CALCULATION OF SOLUBILITY PARAMETERS OF SOLVENTS AND POLYMERS Valery Yu. Senichev, Vasiliy V. Tereshatov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia The methods of calculation of solubility parameters are based on the assumption that energy of intermolecular interactions is additive. Thus, the value of an intermolecular attraction can be calculated by addition of the contributions of cohesion energy of atoms or groups of atoms incorporated in the structure of a given molecule. Various authors use different physical parameters for contributions of individual atoms. Dunkel proposed to use a molar latent heat of vaporization1 as an additive value, describing intermolecular interactions. He represented it as a sum of the contributions of latent heat of vaporization of individual atoms or groups of atoms at room temperature. Small's method2 received the greatest interest. Small has used the data of Scatchard3 showing that the square root of a product of cohesion energy of substance and its volume is a linear function of a number of carbon atoms in a molecule of the substance. He also proposed additive constants for various groups of organic molecules that permit calculation of (EV)1/2 value. He named these constants as molar attraction constants, Fi: ( EV )

1⁄2

=

 Fi

[5.3.1]

i

Cohesion energy and solubility parameters could then be estimated for any molecule:  F 2  Fi   i i i -, δ = ---------E = -----------------V V

[5.3.2]

where: V

molar volume of solvent or a repeating unit of polymer

The molar attraction constants were calculated by Small based on literature data for a vapor pressure and latent heat of vaporization of liquids. The values of these constants are given in Table 5.3.1. Table 5. 3.1. Molar attraction constants Group >C
CH−

28

68.5

86.0

−CH2−

133

137

131.5

Valery Yu. Senichev, Vasiliy V. Tereshatov

299

Table 5. 3.1. Molar attraction constants Group −CH3

Small2

Van Krevelen5

Hoy7

F, (cal/cm3)1/2 mol-1 214

205.5

−CH(CH3)−

242

274

(234.3)

−C(CH3)2−

335

411

(328.6)

>C=CH−

130

148.5

206.0

−CH=CH−

222

217

243.1

(344)

354

(354.3)

−

676.5

633.0

−C(CH3)=CH− Cyclopentyl

148.3

−

813.5

720.1

Phenyl

735

741.5

683.5

1,4-Phenylene

658

673

704.9

−O−

70

125

115.0

−OH

−

368.5

225.8

−CO−

275

335

263.0

−COO−

310

250

326.6

−COOH

−

318.5

(488.8)

−O−CO−O−

−

375

(441.6)

−CO−O−CO−

−

375

567.3

−CO−NH−

−

600

(443.0)

−O−CO−NH−

−

725

(506.6)

−S−

225

225

209.4

−CN

410

480

354.6

−CHCN−

(438)

548.5

(440.6)

−F

(122)

80

41.3

−Cl

270

230

205.1

−Br

340

300

257.9

−I

425

−

−

Cyclohexyl

The Scatchard equation is correct only for nonpolar substances because they have only dispersive interactions between their molecules. Small eliminated from his considerations the substances containing hydroxyl, carboxyl and other groups able to form hydrogen bonds. This method has received its further development due to Fedors' work,4 who extended the method to polar substances and proposed to represent as an additive sum not only the attraction energy but also the molar volumes. The lists of such constants were

300

5.3 Methods of calculation of solubility parameters of solvents and polymers

published in several works.5-8 The most comprehensive set of contributions to cohesion energy can be found elsewhere.9 Askadskii has shown10 that Fedors' supposition concerning the additivity of contributions of the volume of atoms or groups of atoms is not quite correct because the same atom in an environment of different atoms occupies different volume. In addition, atoms can interact with other atoms in different ways depending on their disposition and this should be taken into account for computation of cohesion energy. Therefore, a new scheme of the solubility parameters calculation was proposed that takes into account the nature of an environment of each atom in a molecule and the type of intermolecular interactions. This approach is similar to that described in the work of Rheineck and Lin.6     ΔE i  i - δ =  ----------------------   N A  ΔV i   i

1⁄2

[5.3.3]

where: NA ΔEi ΔVi

Avogadro's number increment (contribution) to cohesion energy of atom or group of atoms increment to the van der Waals volume of atom

The volume increment ΔVi of an atom under consideration is calculated as a volume of a sphere of an atom minus volumes of spherical segments, which are cut off from this sphere by the adjacent covalently-bound atoms: 4 3 1 3 ΔV 1 = --- πR –  --- πh i ( 3R – h i ) 3 3

[5.3.4]

where: R hi

van der Waals (intermolecular) radius of considered atom a height of segment calculated from the formula: 2

2

2

R + di – Ri h i = R – ----------------------------2d i

[5.3.5]

where: di Ri

bond length between two atoms van der Waals radius of the atom adjacent to the covalently-bonded atoms under consideration

The increments to the van der Waals volume for more than 200 atoms in various neighborhoods are available elsewhere.11 Using data from Tables 5.3.2 and 5.3.3, van der Waals volumes of various molecules can be calculated. The increments to the cohesion energy are given in Table 5.3.4. An advantage of this method is that the polymer density, that is important for estimation of properties of polymers, that have not yet been synthesized, does not need to be known.

Valery Yu. Senichev, Vasiliy V. Tereshatov

301

The calculation methods of the solubility parameters for polymers have an advantage over experimental methods that they do not have any prior assumptions regarding interactions of polymer with solvents. The numerous examples of good correlation between calculated and experimental parameters of solubility for various solvents support the assumed additivity of intermolecular interaction energy. The method has further useful development in the calculation of components of solubility parameters based on principles of Hansen's approach.12 It may be expected that results will also come from analysis of donor and acceptor parameters used in TDMapproach (see Chapter 4). In Table 5.3.5, the increments required to account for contributions to solubility parameters related to the dipole-dipole interactions and hydrogen bonds are presented.13 Table 5.3.6 contains Hansen's parameters for some common functional groups. Further improvements in calculation methods can be obtained using statistical approaches.14,15 Table 5.3.2. Intermolecular radii of some atoms Atom C

R, Å 1.80

Atom F

R, Å 1.5

Atom Si

R, Å 2.10

Atom P

R, Å 1.90

H

1.17

Cl

1.78

Sn

2.10

Pb

2.20

O

1.36

Br

1.95

As

2.00

B

1.62

N

1.57

I

2.21

S

1.8

Table 5.3.3. Lengths of bonds between atoms Bond

di, Å

Bond

di, Å

Bond

di, Å

Bond

di, Å

C−C

1.54

C−F

1.34

C−S

1.76

N−P

1.65

C−C

1.48

C−F

1.31

C=S

1.56

N−P

1.63

arom

C−C

1.40

C−Cl

1.77

H−O

1.08

S−S

2.10

C=C

1.34

C−Cl

1.64

H−S

1.33

S−Sn

2.10

C≡C

1.19

C−Br

1.94

H−N

1.08

S−As

2.21

C−H

1.08

C−Br

1.85

H−B

1.08

S=As

2.08

C−O

1.50

C−I

2.21

O−S

1.76

Si−Si

2.32

C−O

1.37

C−I

2.05

O−Si

1.64

P−F

1.55

C=O

1.28

C−P

1.81

O−P

1.61

P−Cl

2.01

C−N

1.40

C−B

1.73

N−O

1.36

P−S

1.81

C−N

1.37

C−Sn

2.15

N−N

1.46

B−B

1.77

C=N

1.31

C−As

1.96

O=N

1.20

Sn−Cl

2.35

C=N

1.27

C−Pb

2.20

O=S

1.44

As−Cl

2.16

C−Narom

1.34

C−Si

1.88

O=P

1.45

As−As

2.42

C≡N

1.16

C−Si

1.68

N−Parom

1.58

302

5.3 Methods of calculation of solubility parameters of solvents and polymers

*

Table 5.3.4. Values of ΔE i for various atoms and types of intermolecular interaction required to calculate solubility parameters according to equation [5.3.3] Adapted from refs. 10, 11 Atom and type of intermolecular interaction

*

Label

ΔE i , cal/mol

*

C

ΔE C

H

* ΔE H * ΔE O * ΔE N * ΔE F * ΔE S * ΔE Cl * ΔE Br * ΔE I * ΔE = * ΔE d * ΔE a, N * ΔE a, S

O N F S Cl Br I Double bond Dipole-dipole interaction Dipole-dipole interaction in nonpolar aprotic solvents of amide type Dipole-dipole interaction in nonpolar aprotic solvents as in dimethylsulfoxide

550.7 47.7 142.6 1205.0 24.2 1750.0 -222.7 583 1700 -323 1623 1623 2600

*

Aromatic ring

713

ΔE ar

Hydrogen bond Specific interactions in the presence of =CCl2 group Specific interactions in 3-5 member rings in the presence of O atom Isomeric radicals

* ΔE h * ΔE = CCl 2 * ΔE O, r * ΔE i

3929 2600 2430 -412

Table 5.3.5 Increments of atoms or groups of atoms required in equation [5.3.3] Atoms or their groups

ΔVi, Å3

Atoms or their groups

ΔVi, Å3

−CH3

23.2 (22.9)

>CH

11.0 (10.7, 10.4)

=CH2

21.1

−CH=

15.1 (14.7)

3.4 (2.7, 2.1)

−OH

10.3 (9.9)

−O− >CO− −NH2 −F

>CH2 C

18.65 (18.35, 18.15) −NH−

17.1 (16.8, 16.4) 5.0 (4.7, 4.5)

8.8 (8.5)

16.1

−CN

25.9

9.0 (8.9)

−Cl

19.9 (19.5)

The values in brackets correspond to one and two neighboring aromatic carbon atoms. In other cases values are given for the aliphatic neighboring carbon atoms.

Valery Yu. Senichev, Vasiliy V. Tereshatov

303

Table 5.3.6. Hansen's parameters12 2

Vδ h , cal/mol

ΔV, cm /mol

Vδp, (cal cm/mol)1/2

aliphatic

aromatic

−F

18.0

12.55 ± 1.4

~0

~0

−Cl

24.0

12.5 ± 4.2

100± 200

100 ± 20

>Cl2

26.0

6.7 ± 1.0

165 ± 10

180 ± 10

−Br

30.0

10.0 ± 0.8

500 ± 10

500± 100

−I

31.5

10.3 ± 0.8

1000± 200

-

−O

3.8

53 ± 13

1150± 300

1250± 300

>CO

10.8

36 ± 1

800± 250

400± 125

Atom (group)

3

>COO

18.0

14 ± 1

1250± 150

800± 150

−CN

24.0

22 ± 2

500± 200

550± 200

−NO2

33.5

15 ± 1.5

400 ± 50

400 ± 50

−NH2

19.2

16 ± 5

1350± 200

2250± 200

>NH

4.5

22 ± 3

750± 200

-

−OH

10.0

25 ± 3

4650± 400

4650± 500

(−OH)n

n 10.0

n (17 ± 2.5 )

n (4650± 400 )

n (4650± 400 )

−COOH

28.5

8 ± 0.4

2750± 250

2250± 250

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

M. Dunkel, Z. Phys. Chem., A138, 42 (1928). P.A. Small, J. Appl. Chem., 3, 71 (1953). G. Scatchard, J. Amer. Chem. Soc., 56, 995 (1934). R.F. Fedors, Polym. Eng. Sci., 14, 147(1974). D.W. Van Krevelen, Properties of polymers. Correlations with chemical structure, Elsevier Publishing Comp., Amsterdam-London-New York,1972. A.E. Rheineck and K.F. Lin, J. Paint Technol., 40, 611 (1968). K.L. Hoy, J. Paint Technol., 42, 76 (1970). R.A. Hayes, J. Appl. Polym. Sci., 5, 318 (1961). Y. Lebedev and E. Miroshnichenko, Thermochemistry of evaporation of organic substances. Heats of evaporation, sublimation and pressure of saturated vapor, Nauka, Moscow, 1981. A.A. Askadskii, L.K. Kolmakova, A.A. Tager, et.al., Vysokomol. soed., A19, 1004 (1977). A.A. Askadskii, Yu.I. Matveev, Chemical structure and physical properties of polymers, Chemistry, Moscow, 1983. C. Hansen, A. Beerbower, Solubility parameters. Kirk-Othmer Encyclopedia of chemical technology, 2nd ed., Supplement Vol., 1973, 889-910. H.C. Brown, G.K. Barbaras, H.L. Berneis, W.H. Bonner, R.B. Johannesen, M. Grayson and K.L. Nelson, J. Am. Chem. Soc., 75, 1, (1953). V. Tantishaiyakul, N. Worakul, W. Wongpoowarak, Int. J. Pharm., 325, 8 (2006). M. Weng. J. Appl. Polym. Sci., 133, 43328 (2016).

6

Swelling 6.1 MODERN VIEWS ON KINETICS OF SWELLING OF CROSSLINKED ELASTOMERS IN SOLVENTS E. Ya. Denisyuk and V. V. Tereshatov Institute of Continuous Media Mechanics and Institute of Technical Chemistry, Ural Branch of Russian Academy of Sciences, Perm, Russia 6.1.1 INTRODUCTION Diffusion phenomena encountered in the mass-transfer of low-molecular liquids play an important role in many technological processes of polymer manufacture, processing, and use of polymeric materials. Diffusion of organic solvents in crosslinked elastomers may cause considerable material swelling. In this case, the polymeric matrix experiences strains as large as several hundred percents, while a non-homogeneous distribution of a liquid caused by diffusion results in establishing stress-strain state capable of affecting the diffusion kinetics. The processes of material deformation and liquid diffusion in such systems are interrelated and nonlinear in nature and are strongly dependent on physical and geometrical nonlinearities. Therefore, exact relations of nonlinear mechanics of elasticdeformable continuum are the mainstream of a sequential theory of mass-transfer processes of low-molecular liquids in elastomers. The general principles of the development of nonlinear models of mass transfer in elastically deformed materials were developed in previous studies.1,2 The general formulation of constitutive equations and the use of non-traditional thermodynamic parameters such as partial stress tensors and diffusion forces lead to significant difficulties in attempts to apply the theory to the description of specific systems.3,4 Probably, because of this, the theory is little used for the solution of applied problems. In the paper,5 a theory of mechanical and diffusional processes in hyper-elastic materials was formulated in terms of the global stress tensor and chemical potentials. The approach described elsewhere1,2 was used as the basic principle and was generalized to the case of a multi-component mixture. An important feature of the work5 is that, due to the structure of constitutive equations, the general model can be used without difficulty to describe specific systems. In the paper6 the nonlinear theory5 was applied to steady swelling processes of crosslinked elastomers in solvents. The analytical and numerical treatments reveal three possible mechano-diffusion modes which differ qualitatively. Self-similar solutions obtained for these modes describe asymptotic properties at the initial stage of swelling. These

306

6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents

modes are related to material’s thermodynamic properties. The theoretical predictions have been verified in the experiments conducted on real elastomers. 6.1.2 FORMULATION OF SWELLING OF A PLANE ELASTOMER LAYER Consider an infinite plane elastomer layer of thickness 2h embedded in a low-molecular liquid. Suppose that the elastomer initially does not contain liquid and it is not strained. This state is taken as a reference configuration. Let us introduce the Cartesian coordinates (x,y,z) with the origin placed in the layer center and relate them to a polymer matrix. In the examined problem, the Cartesian coordinates will be used as the material coordinates. With reference to the layer, the x-axis has a transverse direction and the other axes have longitudinal directions. In our approach, we define the problem under consideration as a one-dimensional problem, in which all quantities characterizing the elastomer state depend only on the x-coordinate. On swelling, the layer experiences transversal and longitudinal deformations which can be written as X = X(x,t) Y = ν(t)y Z = ν(t)z

[6.1.1]

where (X,Y,Z) are the spatial Cartesian coordinates specifying the actual configuration of the polymeric matrix. From this, it follows that the relative longitudinal stretch of the layer is λ 2 = λ 3 = ν ( t ) and the relative transversal stretch is λ 1 = λ ( x, t ) = ∂X ⁄ ∂x . The quantity J = λ 1 λ 2 λ 3 = λν

2

[6.1.2]

characterizes local relative changes in the material volume due to liquid absorption. The boundary conditions and the relations describing free swelling of the plane layer in the reference configuration are represented in5 as ∂N ∂N ∂ ---------1 = ------  D ---------1 , N 1 = N 1 ( x, t ) ∂x  ∂x  ∂t

[6.1.3]

∂N 2 ⁄ ∂t = 0

[6.1.4]

∂σ 1 ⁄ ∂x = 0

[6.1.5]

N 1 ( x, 0 ) = 0

[6.1.6]

∂N 1 ( 0, t ) ⁄ ∂x = 0, X ( 0, t ) = 0

[6.1.7]

μ ( h, t ) = 0, σ 1 ( h, t ) = 0

[6.1.8]

 σ 2 ( x, t ) =  σ 3 ( x, t ) = 0

[6.1.9]

where: N1,N2 µ

the molar concentrations of the liquid and the chains of polymeric network of elastomer, respectively, the chemical potential of the liquid dissolved in material

E. Ya. Denisyuk and V. V. Tereshatov σk

307

(k = 1,2,3) are the principal values of the Piola stress tensors.

The angular brackets denote integration with respect to coordinate x: h

 … = h

–1

 … dx 0

Because of a symmetry of the swelling process in a layer, the problem is solved for 0 sc, the swelling mode is of a blow-up nature. The solutions describing these modes are given below. I. Power mode (s < sc): ms n

2m m

u ( x, t ) = M 2 t θ ( ξ ), ξ = x ⁄ M 2 t 2q – 1 q

g1 ( t ) = M1 M2

[6.1.39]

ms r

t , g2 ( t ) = M2 t

[6.1.40]

1⁄d–2 1⁄d–1 1 1 m = ------------, n = -------------------, q = -------------------, r = -------------------sc – s sc – s sc – s d ( sc – s )

[6.1.41]

II. Exponential mode (s = sc): 2

2

u ( x, t ) = exp { M 2 ( t – t 0 ) }θ ( ( ξ ), ξ ) = xM 2 ⁄ exp { s c M 2 ( t – t 0 ) ⁄ 2 } 2

g 1 ( t ) = ( M 1 ⁄ M 2 ) exp { ( s c ⁄ 2 + 1 )M 2 ( t – t 0 ) } 2

g 2 ( t ) = exp { ( s c ⁄ 2 + 1 )M 2 ( t – t 0 ) } III. Blow-up mode (s > sc): 2m

ms

u ( x, t ) = M 2 ( t 0 – t )θ ( ξ ), ξ = x ⁄ M 2 ( t 0 – t ) 2q – 1

g1 ( t ) = M1 M2

q

2r

( t0 – t ) , g2 ( t ) = M2 ( t0 – t )

r

where the exponents are defined by Eqs. [6.1.41] but if s > sc, then m, n, q, r < 0.

E. Ya. Denisyuk and V. V. Tereshatov

313

For power and blow-up swelling modes, θ ( ξ ) is derived from the equation s ( θ θ' )' + n ξθ' – m θ = 0 . For an exponential mode, this equation will be valid if we put n = sc/2 and m = 1. The constants M1 and M2 are evaluated from Eq. [6.1.33] and the constant t0 can be estimated by the order of magnitude from the condition 2d –2 u ( 0, t 0 ) ∼ ψ 0 ∼ ε . For the exponential mode, we have t0 ~ −2d M 2 ln ε , and for the – 2 2d ⁄ m . blow-up mode, t0 ~ M 2 ε It is worth noting that at m = 1/s, which holds only if s = 1/d − 2, a solution of Eq. [6.1.39] is expressed in terms of primary functions and describes the diffusion wave propagating with a constant velocity d: u ( x, t ) = ( 1 – 2d )

1⁄s

( dt – x )

1⁄s

The solution describing the blow-up mode turns into infinity at the finite time. In the global sense, the boundary-value problems admitting such solutions are time unsolvable and are generally applied to the modeling high rate physical-chemical processes.10 It is quite evident that all solutions to the swelling problem for a layer of finite thickness are limited and each of the self-similar solutions presented in this study describes asymptotic properties of diffusion modes at the initial well-developed stage of swelling. At the final swelling stage u ( x, t ) → 1 , an approximate solution to the problem can be obtained by its linearization in the vicinity of equilibrium u = 1. To this end, one needs to introduce a variable v(x, t) = 1 − u(x, t). After transformation we get v t = v xx, v x ( 1, t ) = 0, v ( 0, t ) = 2d  v ( x, t ) By making use of the method of variable separation, we find ∞

v ( x, t ) =

2

 ak exp ( –α k t ) cos [ α k ( 1 – x ) ]

[6.1.42]

k=1

where the values of αk are determined from the equation α k = 2d tan α k

[6.1.43]

Restricting ourselves to the first term of a series Eq. [6.1.42], we can write the final swelling stage of the equation of kinetic curve 2

g 1 ( t ) = 1 – ( a 1 ⁄ α 1 ) exp ( – α 1 t ) sin α k

[6.1.44]

The above expressions allow us to describe the shape of kinetic curves g1(t) in general terms. In particular, as it follows from Eqs. [6.1.39] − [6.1.41] at q < 1, the kinetic curves in the coordinates (t,g1) are upward convex and have the shape typical for pseudonormal sorption. This takes place at s < sc/2 − 1. If s = sc/2 − 1, then q = 1, which corresponds to a linear mode of liquid absorption. At s > sc/2 − 1, the lower part of the kinetic curve is convex in a downward direction and the whole curve becomes S-shaped. Note that in terms of coordinates (t1/2,g1) at s ≥ 0 , all the kinetic curves are S-shaped. Hence,

314

6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents

Figure 6.1.2. Diffusion kinetics of plane layer swelling for diffusion coefficient k(u) = us at ε = 0.1 and d = 2/9; a, b are power swelling modes at s = 1 and s = 2.5, respectively; c − exponential swelling mode (s = 5); d − blow-up swelling mode (s = 5.5). Numerals over curves denote correspond to instants of time. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].

the obtained solutions enable us to describe different anomalies of sorption kinetics observed in the experiments on elastomer swelling in low-molecular liquids. Figure 6.1.26 gives the results of the numerical solution to problems of Eq. [6.1.25] with diffusion coefficient defined by Eq. [6.1.35]. The kinetic curves of swelling at different values of s are depicted in Figure 6.1.3.6 Here, it can be noted that strain dependence of the diffusion coefficient described by Eq. [6.1.36] does not initiate new diffusion modes. The obtained three self-similar solu-

E. Ya. Denisyuk and V. V. Tereshatov

315

Figure 6.1.3. Kinetic curves of plane layer swelling at different values of concentration dependence of diffusion coefficient (ε = 0.1,d = 2/9): a − power law mode (1 − s = 0; 2 − s = 1; 3 − s = 1.5; 4 − s = 2.5); b − exponential (5 − s = 5) and blow-up mode (6 − s = 5.5). [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].

tions hold true. Only critical value sc is variable and it is defined by expression s c = ( 2 – p ) ⁄ d – 4 . This fact can be supported by a direct check of the solutions. 6.1.4 EXPERIMENTAL STUDY OF ELASTOMER SWELLING KINETICS The obtained solutions can be applied to an experimental study of the diffusive and thermodynamic properties of elastomers. In particular, with the relation s = 2 ⁄ d – 4 – (1 ⁄ d – 1) ⁄ q

[6.1.45]

following from Eqs. [6.1.38] and [6.1.41] we can estimate the concentration dependence of the diffusion coefficient of a liquid fraction in the elastomer. According to Eq. [6.1.40] the parameter q is determined from the initial section of the kinetic swelling curve. Experimental estimates of the parameter r can be obtained from the strain curve l(t) using Eqs. [6.1.31] and [6.1.40]. Then by making use of the formula d =1 − q/r

[6.1.46]

following from Eq. [6.1.41] we can evaluate the parameter d which characterizes the strain dependence of the equilibrium swelling ratio of elastomer under symmetric biaxial extension in Eq. [6.1.45]. Generally, the estimation of this parameter in tests on equilibrium swelling of strained specimens proves to be a tedious experimental procedure. The value of diffusion coefficient in an equilibrium swelling state can be determined from the final section of the kinetic swelling curve using Eq. [6.1.44], which is expressed in terms of dimensional variables as 2

2

g 1 ( t ) = 1 – C exp ( – α 1 D 0 t ⁄ h )

[6.1.47]

where α1 is calculated from Eq. [6.1.43). For d = 2/9, α 1 ≈ 1.222 . Note that all these relations are valid only for sufficiently high values of elastomer swelling ratio.

316

6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents

Figure 6.1.4. Kinetic (a) and strain (b) curves of elastomer swelling in toluene: 1 − PBU-3; 2 − PBU-4; 3 − PBU-1; 4 − PBU-2. [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., A42, 74 (2000)].

The obtained theoretical predictions have been verified in experiments on real elastomers. The elastomers tested in these experiments were amorphous polybutadiene urethanes (PBU) with polymer network of different density: 0.3 kmol/m3 (PBU-1), 0.05 kmol/m3 (PBU-2), 0.2 kmol/m3 (PBU-3), 0.1 kmol/m3 (PBU-4). Oligooxypropylene triol − Laprol 373 was used as a crosslinking agent for curing of the prepolymer of oligobutadiene diol. The elastomer specimens were manufactured in the form of disks, 35 mm in diameter, and 2 mm thick. The kinetics of specimen swelling was determined in lowmolecular liquids: toluene, dibutyl sebacate (DBS), dioctyl sebacate (DOS). The typical kinetic and strain curves of free swelling are given in Figure 6.1.4.6 The S-shape of the kinetic swelling curves in terms of coordinates (t1/2, g1) is indicative of abnormal sorption. The values of parameters q and r were obtained from kinetic and strain curves using the regression method. The values of correlation coefficient were 0.997− 0.999 and 0.994-0.998 respectively. The obtained data and Eqs. [6.1.45], [6.1.46] were then used to calculate s and d. The diffusion coefficients were defined by the kinetic curves in terms of Eq. [6.1.47] under the assumption that d = 2/9. The obtained results were summarized in Table 6.1.1.6 The analysis of these data shows that swelling of the examined elastomers is of power-mode type. The concentration dependence of the liquid diffusion coefficient defined by the parameter s is rather weak. For elastomers under consideration, no exponential or blow-up swelling modes have been observed. Table 6.1.1. Experimental characteristics of elastomer swelling kinetics6 ε

q

r

s

d

D0, cm2/s

PBU-1/toluene

0.278

0.68

0.84

0

0.19

1.4×10-6

PBU-2/toluene

0.093

0.83

1.09

0.8

0.24

4.9×10-7

PBU-3/toluene

0.230

0.78

1.02

0.5

0.24

1.3×10-6

PBU-4/toluene

0.179

0.71

0.97

0

0.27

1.4×10-6

PBU-1/DBS

0.345

0.67

0.92

0

0.27

6.2×10-8

Elastomer/Liquid

E. Ya. Denisyuk and V. V. Tereshatov

317

Table 6.1.1. Experimental characteristics of elastomer swelling kinetics6 ε

q

r

s

d

D0, cm2/s

PBU-2/DBS

0.128

0.78

1.04

0.5

0.25

2.5×10-8

PBU-3/DBS

0.316

0.67

0.83

0

0.19

6.6×10-8

PBU-4/DBS

0.267

0.69

0.88

0

0.21

7.4×10-8

PBU-1/DOS

0.461

0.67

0.81

0

0.17

1.8×10-8

PBU-4/DOS

0.318

0.63

0.81

0

0.22

3.4×10-8

Elastomer/Liquid

It is of interest to note that experimental values of the parameter d characterizing the strain dependence of equilibrium swelling ratio for elastomers subjected to uniform biaxial extension closely approximate the theoretical values. It will be recalled that this parameter is specified by Eq. [6.1.21]. Moreover, the Flory theory defines it as d = 2/9 = 0.22(2), whereas the des Cloizeaux law provides d ≈ 0.205 , which suggests that the proposed model of elastomer swelling performs fairly well. 6.1.5 CONCLUSIONS A geometrically and physically nonlinear model of swelling processes was developed for an infinite plane elastomeric layer. The approximate solutions describing different stages of swelling at large deformations of a polymeric matrix were obtained. The strain-stress state of the material is caused by diffusion processes and its influence on the swelling kinetics can be analyzed. A non-stationary boundary regime initiated by deformations arising in elastomer during swelling and increasing a thermodynamical compatibility of elastomer with a liquid are the main reasons for swelling anomalies observed in the experiments. Anomalies of sorption kinetics turn out to be a typical phenomenon observable to a certain extent in elastic swelling materials. The theory predicts the possibility of qualitatively different diffusion modes of free swelling. A particular mode is specified by a complex of mechanical, thermodynamical, and diffusion material properties. The results of analytical and numerical solutions for a plane elastomer layer show that the swelling process may be governed by three different laws resulting in the power, exponential, and blow-up swelling modes. Experimentally, it has been determined that in the examined elastomers the swelling mode is governed by the power law. The existence of exponential and blow-up swelling modes in real materials is still an open question. Methods have been proposed, which allow one to estimate the concentration dependence of liquid diffusion in elastomer and strain dependence of equilibrium swelling ratio under conditions of symmetric biaxial elastomer extension in terms of kinetic and strain curves of swelling. REFERENCES 1 2 3 4

A E Green, P M Naghdi, Int. J. Eng. Sci., 3, 231 (1965). A E Green, T R Steel, Int. J. Eng. Sci., 4, 483 (1966). K R Rajagopal, A S Wineman, MV Gandhi, Int. J. Eng. Sci., 24, 1453 (1986). M V Gandhi, K R Rajagopal, AS Wineman, Int. J. Eng. Sci., 25, 1441 (1987).

318 5 6 7 8 9 10

6.1 Modern views on kinetics of swelling of crosslinked elastomers in solvents E Ya Denisyuk, V V Tereshatov, Appl. Mech. Tech. Phys., 38, 913 (1997). E Ya Denisyuk, V V Tereshatov, Vysokomol. soed., A42, 74 (2000) (in Russian). P J Flory, Principles of polymer chemistry, Cornell Univ. Press, New York, 1953. V A Vasilyev, Yu M Romanovskiy, V G Yahno, Autowave Processes, Nauka, Moscow, 1987 (in Russian). P G De Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca, 1980. A A Samarskiy, V A Galaktionov, S P Kurdyumov, A P Mikhaylov, Blow-up Modes in Problems for Quasilinear Parabolic Equations, Nauka, Moscow, 1987 (in Russian)

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319

6.2 EQUILIBRIUM SWELLING IN BINARY SOLVENTS Vasiliy V. Tereshatov, Valery Yu. Senichev, E. Ya Denisyuk Institute of Continuous Media Mechanics and Institute of Technical Chemistry, Ural Branch of Russian Academy of Sciences, Perm, Russia Depending on the purposes and operating conditions of polymer material processing, the differing demands regarding the solubility of low-molecular-mass liquids in polymers exist. Polymeric products designed for use in contact with solvents should be stable against adsorption of these liquids. On the contrary, the well-dissolving polymer solvents are necessary to produce polymer films. The indispensable condition of the creation of the plasticized polymer systems (for example, rubbers) is the high thermodynamic compatibility of plasticizers with the polymer matrix. Hence, it immediately follows the statement of the problem of regulation of thermodynamic compatibility of polymers with low-molecular-mass liquids in a wide range of its concentration in the polymer material. The problem of compatibility of crosslinked elastomers with mixed plasticizers and volatile solvents is thus of special interest. Depending on ratios between solubility parameters of solvent 1, δ1, solvent 2, δ2, and polymer, δ3, solvents can be distinguished as “symmetric” liquids and “non-symmetric” ones. The non-symmetric liquids are defined as a mixture of two solvents of variable composition, solubility parameters δ1 and δ2 which are larger or smaller than solubility parameter of polymer (δ2 > δ1 > δ3, δ3 > δ2 > δ1). The symmetric liquid (SL) with relation to polymer is the mixture of two solvents, whose solubility parameter, δ1, is smaller, and parameter, δ2, is larger than the solubility parameter of polymer, δ3. The dependence of equilibrium swelling on the non-symmetric liquid composition does not have a maximum, as a rule.1 Research on swelling of crosslinked elastomers in SL is of particular interest in the regulation of thermodynamic compatibility of network polymers and binary liquids. Swelling in such liquids is characterized by the presence of maximum on the curve of the dependence of network polymer equilibrium swelling and composition of a liquid phase.2,3 The extreme swelling of crosslinked polymers of different polarity in SL was discussed elsewhere.3 The following elastomers were used as samples: a crosslinked elastomer of ethylene-propylene rubber SCEPT-40 [δ3 = 16 (MJ/m3)1/2, (ve/V0)x = 0.24 kmol/m3], crosslinked polyester urethane, PEU, from copolymer of propylene oxide and trimethylol propane [δ3 = 18.3 (MJ/m3)1/2, (ve/V0)x = 0.27 kmol/m3], crosslinked polybutadiene urethane, PBU, from oligobutadiene diol [δ3 = 17.8 (MJ/m3)1/2, (ve/V0)x = 0.07 kmol/m3] and crosslinked elastomer of butadiene-nitrile rubber [δ3 = 19 (MJ/m3)1/2, (ve/V0)x = 0.05 kmol/m3]. The samples of crosslinked elastomers were swollen to equilibrium at 25oC in 11 SLs containing solvents of different polarity. The following regularities were established. With the decrease in the solubility parameter value of component 1 (see Table 6.2.1) in SL (δ1 < δ3), the maximum value of equilibrium swelling, Q, shifts to the field of larger concentration of component 2 in the mixture (Figures 6.2.1 and 6.2.2). On the contrary, with a decrease in the solubility parameter δ2 (see Table 6.2.1) of components 2 (δ2 > δ3), the

320

6.2 Equilibrium swelling in binary solvents

Figure 6.2.1. Dependence of equilibrium swelling of PEU on the acetone concentration in the mixtures: 1 − toluene-acetone, 2 − cyclohexane-acetone, 3 − heptane-acetone. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]

Figure 6.2.2. Dependence of equilibrium swelling of PBU on the DBP (component 2) concentration in the mixtures: 1 − DOS-DBP, 2 − TO-DBP, 3 − decaneDBP. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]

maximum Q corresponds to the composition of the liquid phase enriched by component 1 (Figure 6.2.3). Table 6.2.1. Characteristics of solvents and plasticizers at 298K. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] ρ, kg/m3

V×106, m3

δ, (MJ/m3)1/2

Cyclohexane

779

109

16.8

Heptane

684

147

15.2

Decane

730

194

15.8

Toluene

862

106

18.2

1,4-Dioxane

1034

86

20.5

Acetone

791

74

20.5

Ethyl acetate

901

98

18.6

Amyl acetate

938

148

17.3

Dibutyl phthalate

1045

266

19.0

Solvent/plasticizer

Vasiliy V. Tereshatov, Valery Yu. Senichev, E. Ya Denisyuk

321

Table 6.2.1. Characteristics of solvents and plasticizers at 298K. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] ρ, kg/m3

V×106, m3

δ, (MJ/m3)1/2

Dioctyl sebacate

913

467

17.3

Transformer oil

890

296

16.0

Solvent/plasticizer

Figure 6.2.3. Dependence of equilibrium swelling of the crosslinked elastomer SCEPT-40 on the concentration of component 2 in the mixtures: 1 − heptane-toluene, 2 − heptane-amyl acetate, 3 − heptane-ethyl acetate. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]

Figure 6.2.4. Dependence of equilibrium swelling of the crosslinked elastomer SCN-26 on the concentration of component 2 in the mixtures: 1 − toluene-acetone, 2 − ethyl acetate-dioxane, 3 − ethyl acetateacetone. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.]

Neglecting the change of volume on mixing, the solubility parameter of the mixture of two liquids is represented by: δ 12 = δ 1 ϕ 1 + δ 2 φ 2 where:

ϕ 1 and ϕ 2 volume fractions of components 1 and 2

More exact evaluation of the δ12 value is possible if the experimental data on enthalpy of mixing, ΔH, of components of SL are taken into account:4

322

6.2 Equilibrium swelling in binary solvents 2

2

δ 12 = ( δ 1 ϕ 1 + δ 2 ϕ 2 – ΔH ⁄ V 12 )

1⁄2

With a change in δ1 and δ2 parameters, the SL composition has the maximum equilibrium swelling which corresponds to shifts in the field of the composition of the liquid phase. The δ12 parameter is close or equal to the value of the solubility parameter of the polymer. Such a simplified approach to the extreme swelling of polymers in liquid mixtures frequently works very well in practice. If there is a maximum on the curve of swelling in SL, then the swelling has an extreme character (11 cases out of 12) (Figures 6.2.16.2.4). The parameter of interaction, χ123, between polymer and a two-component liquid can be used as a co-solvency criterion for linear polymers (or criterion of extreme swelling), more general, than the equality (δ12 = δ3):5 χ 123 = χ 13 ϕ 1 + χ 23 ϕ 2 – ϕ 1 ϕ 2 χ 12 where:

χ13 and χ23 χ12

[6.2.1]

parameters of interaction of components 1 and 2 with a polymer, correspondingly parameter of the interaction of components 1and 2 of the liquid mixture

In the equation obtained from the fundamental work by Scott,5 mixed solvents are represented as “a uniform liquid” with the variable thermodynamic parameters depending on composition. If the χ123 value is considered as a criterion of existence of a maximum of equilibrium swelling of polymer in the mixed solvent, a maximum of Q should correspond to the minimum of χ123. For practical use of Eq. [6.2.2], it is necessary to know parameters χ13, χ23, and χ12. The values χ13 and χ23 can be determined from the Flory-Rehner equation, using data on swelling of a crosslinked elastomer in individual solvents 1 and 2. The evaluation of the χ12 value can be carried out with use of results of the experimental evaluation of vapor pressure, viscosity and other characteristics of a binary mixture.6,7 To raise the forecasting efficiency of prediction force of such criterion as a χ123 minimum, the number of performance parameters determined experimentally must be reduced. For this purpose, the following expression for the quality criterion of the mixed solvent (the analogy with an expression of the Flory-Huggins parameter for the individual solvent-polymer system) is used: V 12 s 2 χ 123 = χ 123 + -------- ( δ 3 – δ 12 ) , V 12 = V 1 x 1 + V 2 x 2 RT where: V12 V1, V2 x1, x2 R T s χ 123

molar volume of the liquid mixture molar volumes of components 1 and 2 molar fractions of components 1 and 2 in the solvent universal gas constant temperature, K. constant, equal to 0.34

[6.2.2]

Vasiliy V. Tereshatov, Valery Yu. Senichev, E. Ya Denisyuk

323 s

s

The values of entropy components of parameters χ 13 and χ 23 (essential for quality prediction)8 were taken into account. Using the real values of entropy components of s s interaction parameters χ 13 and χ 23 , we have: V1 s 2 χ 13 = χ 13 – -------- ( δ 3 – δ 1 ) RT

[6.2.3]

V 2 s χ 23 = χ 23 – -------2- ( δ 3 – δ 2 ) RT

[6.2.4]

the quality criterion of the solvent mixture is represented by3 V 12 s s 2 χ 123 = χ 13 ϕ 1 + χ 23 ϕ 2 + -------- ( δ 3 – δ 12 ) RT

[6.2.5]

The values of parameters χ13 and χ23 were calculated from the Flory-Rehner equation, using data on swelling of a crosslinked polymer in individual solvents, the values s s χ 13 , χ 23 , and χ123 were estimated from Eqs. [6.2.3-6.2.5). Then the equilibrium swelling of elastomer in SL was calculated from the equation similar to Flory-Rehner equation, considering the mixture as a uniform liquid with parameters χ123 and V12 variable in composition. The calculated ratios of components of mixtures, at which the extreme swelling of elastomers is expected, are given in Table 6.2.2. Table 6.2.2. The position of a maximum on the swelling curve of crosslinked elastomers in binary mixtures. [Adapted, by permission, from V. V. Tereshatov, M. I. Balashova, A. I. Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch of AS USSR Press, Sverdlovsk, 1989, p. 3.] Elastomer PEU

PBU

SCN-26

Binary mixture

Components ratio, wt% Calculation

Experiment

toluene-acetone

90/10

90/10

cyclohexanone-acetone

40/60

50/50

heptane-acetone

30/70

25/25

decane-DBP

30/70

30/70

TO-DBP

40/60

40/60

DOS-DBP

60/40

50/50

−

−

ethyl acetate-acetone

70/30

70/30

ethyl acetate-acetone

70/30

70/30

ethyl acetate-1,4-dioxane

Results of calculation of the liquid phase composition at the maximum swelling of elastomer correlate with the experimental data (see Table 6.2.2). The approach predicts the existence of an extremum on the swelling curve. This increases the forecasting efficiency of the prediction.

324

6.2 Equilibrium swelling in binary solvents

The application of “approximation of the uniform liquid” (AUL) for prediction of extreme swelling of crosslinked elastomers is proven under the condition of coincidence of composition of a two-component solvent in a liquid phase and in the swollen elastomer. Results of a study of total and selective sorption by crosslinked elastomers of components of SLs are given below.3 Crosslinked PBU [(ve/V0) = 0.20 kmol/m3] and crosslinked elastomer of butadienenitrile rubber SCN-26 [(ve/V0) = 0.07 kmol/m3] were used in this study. The tests were carried out at 25±0.10oC in the following mixtures: n-nonane-tributyl phosphate (TBP), nhexane-dibutyl phthalate (DBP), n-hexane-dibutyl maleate (DBM), and dioctyl sebacate (DOS)-diethyl phthalate (DEP). A crosslinked elastomer SCN-26 was immersed to equilibrate in amyl acetate-dimethyl phthalate mixture. Liquid phase composition was in range of 5 to 10%. A sol-fraction of samples (plates of 0.9×10-2 m diameter and in 0.3×10-2 m thickness) was preliminarily extracted with toluene. For high accuracy of the analysis of binary solvent composition, a volatile solvent, hexane, was used as a component of SL in most experiments. Following the attainment of equilibrium swelling, the samples were taken out of SL and held in the air until the full evaporation of hexane, that was controlled by the constant mass of the sample. A content of a nonvolatile component of SL in elastomer was determined by the difference between the amount of liquid in the swollen sample and the amount of hexane evaporated. In the case of SL with nonvolatile components (such as, DBP or DOS) the ratio of SL components in the swollen PBU was determined by the gas-liquid chromatography, for which purpose toluene extract was used. The volume fractions of components 1 and 2 of SL in a liquid phase ϕ1 and ϕ2 were calculated on the basis of their molar ratio and densities ρ1 and ρ2. The volume fraction of polymer, υ 3 , in the swollen sample was calculated from the equation: 1 υ 3 = ---------------Qv + 1 where: QV

volume equilibrium swelling of elastomer in SL.

Volume fractions ϕ1 and ϕ2 of components 1 and 2 of low-molecular-mass liquids inside the swollen gel were determined from the equation: υi - , (i = 1,2) φ i = ------------1 – υ3 where:

ϕi

volume fraction of i-component related to the total volume of its low-molecular-mass part (not to the total volume of three-component system)

The results of a study of sorption of two-component liquids in PBU and in crosslinked elastomer SCN-26 are shown in Figures 6.2.5-6.2.8, as dependencies of Qv on the volume fraction ϕ2 of component 2 in a liquid phase and on the volume fraction φ2 of component 2 of SL that is a part of the swollen gel. The data vividly show that extremum

Vasiliy V. Tereshatov, Valery Yu. Senichev, E. Ya Denisyuk

Figure 6.2.5. Dependence of equilibrium swelling of PBU on the ϕ2 value for DEP in the liquid phase (1) and the φ2 value inside the gel (1') swollen in the mixture DOS-DEP.

Figure 6.2.7. Dependence of equilibrium swelling of PBU on the ϕ2 value for TBP in the liquid phase (1) and the φ2 value in the gel (1') swollen in the mixture: nonane-TBP.

325

Figure 6.2.6. Dependence of equilibrium swelling of PBU on the ϕ2 value for DEP in the liquid phase (curves 1 and 2) and the φ2 value inside the swollen gel (curves 1' and 2') in the mixtures: 1,1'-hexane(1)DBM(2), 2,2'- hexane(1)-DBP(2).

swelling of crosslinked elastomers in SL can be observed in all investigated cases. At the maximum value of Qv, the compositions of SL in the liquid phase and in the swollen elastomer practically coincide ( ϕ 2 ≈ φ 2 ). The total sorption can be determined by the total content of the mixed solvent in the swollen skin9 or in the swollen elastic network (these results). The dependencies of Qv on ϕ2 (Figures 6.2.5-6.2.8) reveal the influence of liquid phase composition on the total sorption. The total sorption of the binary solvent by the polymer can also be measured by the value of the volume fraction of polymer in the swollen gel9 because the value of υ3 is unequally related to the volume fraction of the absorbed liquid, υ 3 = 1 – ( υ 1 + υ 2 ) . At the fixed total

326

6.2 Equilibrium swelling in binary solvents

Figure 6.2.8. Dependence of equilibrium swelling of crosslinked elastomer SCN-26 on the ϕ2 value for DMP in the liquid phase (1) and the φ2 value in the gel (1'), swollen in the mixture: amyl acetate-DMP.

Figure 6.2.9. Experimental dependence of the preferential sorption ε on the volume fraction ϕ2 of component 2 in the liquid phase: 1 − DOS(1)-DEP(2)PBU(3), 2 − hexane(1)-DBP(2)-PBU(3), 3 − hexane(1)-DBM(2)-PBU(3), 4 − amyl acetate(1)DMP(2)-SCN-26(3), 5 − nonane(1)-TBP(2)-PBU(3).

sorption (Qv or υ3 = const), the preferential sorption, ε, and be found from the following equation: ε = φ1 – ϕ1 = ϕ2 – φ2 At the same values of Qv difference between coordinates on the abscissa axes of points of the curves 1-1' , 2-2' (Figures 6.2.5-6.2.8) are equal to ε (Figure 6.2.9). As expected,10 preferential sorption was observed, with the essential distinction of molar volumes V1 and V2 of components of the mixed solvent (hexane-DBP, DOS-DEP). For swelling of the crosslinked elastomer SCN-26 in the mixture of components, having similar molar volumes V1 and V2 (e.g., amyl acetate-dimethyl phthalate), the preferential sorption of components of SL is practically absent. Influence of V1 and V2 and the influence of double interaction parameters on the sorption of binary liquids by crosslinked elastomers was examined by the method of mathematical experiment. Therewith the set of equations describing swelling of crosslinked elastomers in the binary mixture, similar to the equations obtained by Bristow6 from the Flory-Rehner theory11 and from the work of Schulz and Flory,12 were used: 2

2

2

ln ϕ 1 + ( 1 – I )ϕ 2 + χ 12 ϕ 2 = ln υ 1 + ( 1 – I )υ 2 + υ 3 + χ 12 υ 2 + χ 12 υ 3 + + ( χ 12 + χ 13 – Iχ 23 )υ 2 υ 3 + ( ν e ⁄ V 3 )V 1  υ 3 

1⁄3

2 – --- υ 3 f 

[6.2.6]

Vasiliy V. Tereshatov, Valery Yu. Senichev, E. Ya Denisyuk –1

2

–1

327 –1

ln ϕ 2 + ( 1 – I )ϕ 1 + 1 χ 12 ϕ 1 = ln υ 2 + ( 1 – I )υ 1 + υ 3 + 2

–1

1⁄3

2

+ I [ χ 12 υ 1 + Iχ 23 υ 3 + ( χ 12 + Iχ 23 – χ 13 )υ 1 υ 3 ] + ( ν e ⁄ V 3 )V 2 υ 3

2 – --- υ 3 f

[6.2.7]

where: = V1/V2 functionality of a network

l f

The analysis of calculations from Eqs. [6.2.6] and [6.2.7] has shown that if V1 < V2, the preferential sorption is promoted by the difference in parameters of interaction when χ12 > χ13. The greater χ12 value at V 1 ≠ V 2 , the more likely preferential sorption takes place with all other parameters being equal. The same applies to the diluted polymer solutions. To improve calculations of the preferential sorption in the diluted solutions of polymers, the correction of Flory's theory is given in the works9,13-15 by introduction of the parameter of three-component interaction, χT, into the expression for free energy of mixing and substitution of χT by qT.14 This approach is an essential advancement in the analysis of a sorption of two-compoFigure 6.2.10. Experimental data and calculated depennent liquids by polymer. On the other hand, dence of equilibrium fraction of components υ1 (1), the increase in the number of experimental υ2 (2), and υ3 (3) in PBU sample swollen in the hexaneDBP mixture on the ϕ2 value for DBP in the liquid parameters complicates the task of predicphase: lines − calculation, points − experimental. tion of the preferential sorption. In the swelling crosslinked elastomers, the preferential sorption corresponds to the maximum Qv value, and compositions of a swollen polymer and a liquid phase practically coincide (Figures 6.2.5-6.2.8). This observation can be successfully used for an approximate evaluation of the preferential sorption. Assuming that ϕ1 = φ1 and ϕ2 = φ2 at extremum of the total sorption (φ = φmin), AUL5 e can be used to calculate the effective value of χ 12 from the expression for χ123.16 e χ 12

m

χ 123 V 1 χ 13 χ 23 V 1 - + ------------- – ---------------------= -----m m m m m ϕ 2 ϕ 1 V 2 V 12 ϕ 1 ϕ 2

[6.2.8]

where: m e χ 12

the index for the maximum of sorption. the value, calculated from the equation [6.2.8], substitutes χ12 from the Eqs. [6.2.6] and [6.2.7]

328

6.2 Equilibrium swelling in binary solvents

Figure 6.2.11. Dependence of equilibrium fraction of components υ1 (1), υ2 (2), and υ3 (3) in SCN-26 sample swollen in the amyl acetate-DMP mixture on the ϕ2 value for DMP in the liquid phase: lines − calculation, points − experimental.

Figure 6.2.12. Dependence of equilibrium φ2 value on the ϕ2 value in the liquid phase: 1 − amyl acetate(1)DMP(2)-SCN-26(3), 2 − hexane(1)-DBM(2)-PBU(3), 3 − nonane(1)-TBP(2)- PBU (3); lines − calculation, points − experimental.

The results of calculations are presented as dependencies of volume fractions, υ1, υ2, and υ3 of the triple system components (swollen polymer) vs. the volume fraction ϕ2 (or ϕ1) of the corresponding components of the liquid phase (Figures 6.2.10 and 6.2.11). For practical purposes, it is convenient to represent the preferential sorption as the dependence of equilibrium composition of a binary liquid (a part of the swollen gel) vs. composition of the liquid phase. These calculated dependencies (solid lines) and experimental (points) data for three systems are given in Figure 6.2.12. The results of calculations based on AUL, are in the satisfactory agreement with experimental data. Hence the experimentally determined equality of concentrations of SL components in the swollen gel and in the liquid phase allows one to predict the composition of the liquid, whereby polymer swelling is at its maximum, and the preferential sorption of components of SL. To refine dependencies of φ1 on ϕ1 or φ2 on ϕ2, correction can be used, for example, minimization of the square-law deviation of calculated and experimental data on the total sorption of SL by the polymer. Thus, it is necessary to account for the proximity of the compositions of solvent in the swollen gel and the liquid phase. REFERENCES 1 2 3 4

A Horta, Makromol. Chem., 182, 1705 (1981). V V Tereshatov, V Yu Senichev, A I Gemuev, Vysokomol. Soedin., 32B, 422 (1990). V V Tereshatov, M I Balashova, A I Gemuev, Prediction and regulating of properties of polymeric materials, Ural Branch. of AS USSR Press, Sverdlovsk, 1989, p. 3. A A Askadsky, Yu I Matveev, Chemical structure and physical properties of polymers, Chemistry,

Vasiliy V. Tereshatov, Valery Yu. Senichev, E. Ya Denisyuk

5 6 7 8 9 10 11 12 13 14 15 16

Moscow, 1983. R L Scott, J. Chem. Phys., 17, 268 (1949). C M Bristow, Trans. Faraday Soc., 55, 1246 (1959). A Dondos, D Patterson, J. Polym. Sci., A-2, 5, 230 (1967). L N Mizerovsky, L N Vasnyatskaya, G M Smurova, Vysokomol. Soedin., 29A, 1512 (1987). J Pouchly, A Zivny, J. Polym. Sci., 10, 1481 (1972). W R Krigbaum, D K Carpenter, J. Polym. Sci., 14, 241 (1954). P J Flory, J Rehner, J. Chem. Phys., 11, 521 (1943). A R Shulz, P J Flory, J. Polym. Sci., 15, 231 (1955). J Pouchly, A Zivny, J. Polym. Sci., 23, 245 (1968). J Pouchly, A Zivny, Makromol. Chem., 183, 3019 (1982). R M Msegosa, M R Comez-Anton, A Horta, Makromol. Chem., 187, 163 (1986). J Scanlan, J. Appl. Polym. Sci., 9, 241 (1965).

329

330

6.3 Swelling data on crosslinked polymers in solvents

6.3 SWELLING DATA ON CROSSLINKED POLYMERS IN SOLVENTS Vasiliy V. Tereshatov, Valery Yu. Senichev Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Data on equilibrium swelling of selected crosslinked elastomers in different solvents are presented in Table 6.3.2. All data were obtained in the author's laboratory during 5 years of experimental work. The network density values for these elastomers are given in Table 6.3.1. The data can be used for the quantitative evaluation of the thermodynamic compatibility of solvents with elastomers and for calculation of ΔZ, the thermodynamic interaction parameter. These data can be recalculated to the network density distinguished by the network density value, given in Table 6.3.1, using Eq. [4.2.9]. Network density values can be used for calculation of the interaction parameter. It should be noted that each rubber has a specific ratio for the equilibrium swelling values in various solvents. This can help to identify rubber in the polymeric material. Temperature influences swelling (see Subchapter 4.2). Equilibrium swelling data at four different temperatures are given in Table 6.3.3. The samples were made from industrial rubbers. The following polyols were used for the preparation of polyurethanes: butadiene diol (M~2000) for PBU, polyoxybutylene glycol (M~1000) for SCU-PFL, polyoxypropylene triol (M~5000) for Laprol 5003, polydiethylene glycol adipate (M~2000) for P-9A and polydiethylene glycol adipate (M~800) for PDA. Polyurethanes from these polyols were synthesized by reaction with 2,4-toluene diisocyanate with the addition of crosslinking agent − trimethylolpropane, PDUE, synthesized by reaction of oligobutadiene isoprene diol (M~4500) with a double excess of 2,4-toluene diisocyanate, followed by the reaction with glycidol. Table 6.3.1. Network density values for tested elastomers (data obtained from the elasticity modulus of samples swollen in good solvents) Elastomer

Trade mark

Network density, (kmol/m3)×102

Silicone rubber

SCT (1)

6.0

Butyl rubber

BR (2)

8.9

Polybutadiene rubber

SCDL (3)

40.5

Ethylene-propylene rubber

SCEPT (4)

2.7

Isoprene rubber

SCI-NL (5)

8.9

Butadiene-nitrile rubber

SCN-26 (6)

5.1

Polydiene-urethane-epoxide

PDUE (7)

16.0

Polybutadiene urethane

PBU (8)

20.8

Polyoxybutylene glycol urethane

PFU (9)

10.0

Vasiliy V. Tereshatov, Valery Yu. Senichev

331

Table 6.3.1. Network density values for tested elastomers (data obtained from the elasticity modulus of samples swollen in good solvents) Elastomer Polyoxypropylene glycol urethane

Trade mark

Network density, (kmol/m3)×102

Laprol 5003 (10)

43.0

Polydiethylene glycol adipate urethane P-9A (11)

6.4

Polydiethylene glycol adipate urethane PDA (12)

9.6

Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*

1

2

3

4

5

6

7

8

9

10

11

12

122

78

16

44

4

137

84

16

42

0

101

32

0

7

139

28

1

155

315

39

24

238

3

53

4

0.5

Hydrocarbons Pentane

355

75

Hexane

380

305

Heptane

367

357

Isooctane

380

341

Decane

391

Cyclohexane

677

Transformer oil

47

214

105

586

30

881

10

1020 230

1580

600

3

Toluene

384

1294

435

492

356

134

315

77

31

Benzene

233

511

506

479

359

158

340

175

73

0-Xylene

515

496

356

122

288

53

42

87

2

22

2

41

0.1

Ethers Diamyl

310

Diisoamyl

333

220

889

584

791

Dioctyl

120 85

1,4-Dioxane

248 33

Didecyl Diethyl of diethylene glycol

20

428

180

896

156

702

7

168

11

203

6

242

3

251

23

Tetrahydrofuran

1 54

264

178

782

48

192

848

133

213

88

121

64

40

238

48

35

249

36

Esters of monoacids Heptyl propionate

260

236

Ethyl acetate

20

Butyl acetate

55

Isobutyl acetate

304

382

287

55

562

170 317

251

48

267

210

Amyl acetate

82

343

Isoamyl acetate

74

Heptyl acetate

213

236

100

545

100

Methyl capronate

369

285

115

Isobutyl isobutyrate

328

276

64

22 6 260

36

26

6

6

332

6.3 Swelling data on crosslinked polymers in solvents

Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*

1

2

3

4

5

6

7

8

9

10

11

12

Esters of multifunctional acids Dihexyl oxalate

28

350

73

166

11

9

Diethyl phthalate

6

837

47

93

165

272

496

126

Dibutyl phthalate

9

767

123

154

121

228

47

20

187

9

Dihexyl phthalate

570

Diheptyl phthalate Dioctyl phthalate

37 8

28

189

Dinonyl phthalate

211

181

Didecyl phthalate

1

33

1.4

23

Diamyl maleate

425

Dimethyl adipate

560

Diamyl adipate Dihexyl adipate

197

71

0.5 232

19

14

246

716

6

294

203

88

295

199

42

2

2

126

12

0.6

280

Dioctyl adipate Dipropyl sebacate

8

20

Diamyl sebacate

70

Diheptyl sebacate Dioctyl sebacate

3

29

60 13

160

127

2 118

445

39

Triacetin

34

Tricresyl phosphate

800

Tributyl phosphate

261

162

5.5

15

28

244

238

45 300

74

3 0.4

0.7

489

129

256

93

105

327

523

140

80

Ketones Cyclohexanone Acetone

577 7

44

88

218

99

Alcohols Ethanol

49

Butanol

16

25

72

7

12

Pentanol

28

33

66

10

5

Hexanol

46

34

62

9

4

67

19

Heptanol

36

Nonanol

57

3

Halogen compounds CCl4

2830

284

999

584

Chlorobenzene

234

Chloroform

1565

Fluorobenzene

66 277

114

572

616

205

113

Nitrogen compounds Diethyl aniline

336

Dimethylformamide

52

120

34 918

Vasiliy V. Tereshatov, Valery Yu. Senichev

333

Table 6.3.2 Equilibrium swelling data (wt%) at 25oC. Elastomer number identifies elastomer (see the second column in Table 6.3.1) Solvent\elastomer*

1

2

3

4

5

6

Nitrobenzene

7

8

9

10

11

12

277

298

242

377

799

241

Capronitrile

769

142

Acetonitrile

47

69

115

84

16

323

Aniline

317

423

*See Table 6.3.1 for elastomer’s name

Table 6.3.3 Equilibrium swelling data (wt%) at -35, -10, 25, and 50oC Solvent\Elasto mer

Laprol*

SCU-PFL

P-9A

PBU

SCN-26

Isopropanol

8,12,37,305

8,19,72

8,10,18,28

3,5,18,28

20,23,26,41

Pentanol

27,34,80,119

16,25,78,104

7,9,10,18

8,9,33,52

31,37,49,60

Acetone

80,366,381,-

80,122,132,-

48,73,218,-

56,321,347,-

162,254,269,382

Ethyl acetate

214,230,288,314

113,114,133,138

209,210,210,213

165,171,187,257

324,343,395,407

Butyl acetate

294,304,309,469

119,122,123,125

41,44,64,80

288,293,307,473

404,426,518,536

Isobutyl acetate

259,259,288,-

89,92,100,105

23,28,48,57

210,212,223,348

309,326,357,362

Amyl acetate

315,309,315,426

124,136,144,155

16,18,36,44

285,297,298,364

343,347,358,359

Tetrahydrofuran

91,96,97,119

119,177,192,-

838,840,848,859

45,51,57,80

145,150,166,-

o-Xylene

363,368,389,471

117,121,122,137

24,25,53,60

328,357,369,375

428,440,405,406

Chlorobenzene

522,537,562,-

241,242,242,246

238,244,277,333

517,528,559,698

967,973,985,1256

Acetonitrile

19,21,28,33

23,26,39,41

254,263,323,362

6,10,16,27

47,47,47,82

Hexane

50,52,61,75

2,3,9,14

4,4,4,28

51,56,63,80

−

Toluene

360,366,380, 397

120,122,134,149

50,57,77,85

331,339,372,415

−

*(ve/V) = 0.149 kmol/m3. Network density values for other elastomers correspond to Table 6.3.2

Table 6.3.4 contains swelling data for rubbers.

Table 6.3.4 Swelling data for four rubbers at 25oC. [Adapted, by permission, from E.T. Zellers, D.N. Anna, R. Sulewski, X. Wei. J. Appl. Polym. Sci, 62, 2069 (1996).] Solvent

Percent gain, wt% Butyl

Natural

Neoprene

Nitrile

n-Hexane

115

114

17

6.7

n-Heptane

141

134

17

6.1

Cyclohexane

265

251

69

13

Methylcyclohexane

259

249

57

12

Benzene

114

283

217

156

334

6.3 Swelling data on crosslinked polymers in solvents

Table 6.3.4 Swelling data for four rubbers at 25oC. [Adapted, by permission, from E.T. Zellers, D.N. Anna, R. Sulewski, X. Wei. J. Appl. Polym. Sci, 62, 2069 (1996).] Solvent

Percent gain, wt% Butyl

Natural

Neoprene

Nitrile

Toluene

179

322

227

128

o-Xylene

226

327

272

126

Mesitylene

236

325

259

70

Triethylamine

171

198

69

22

n-Butylamine

81

177

240

174

Diethylamine

119

166

99

45

Dimethylformamide

2.8

11

55

428

Formamide

1.9

6.4

18

14

N-Methyl-2-pyrrolidone

6.7

22

206

798

2-Pyrrolidone

5.2

16

32

304

N,N-Dimethylacetamide

4.9

13

179

548

Acetone

5.1

15

29

163

Methyl ethyl ketone

11

42

85

247

3-Pentanone

22

115

156

251

Cyclohexanone

28

206

307

508

Methyl acetate

9.2

26

41

141

Ethyl acetate

15

60

65

133

Ethyl formate

9.7

29

37

288

Diethylcarbonate

15

64

82

108

Tetrahydrofuran

179

308

291

352

Dioxane

19

135

220

263

Ethyl ether

41

96

44

25

Nitrobenzene

11

99

247

546

Nitromethane

1.4

3.5

7.3

151

2-Nitropropane

5.8

26

55

345

Nitroethane

2.7

9.4

22

320

Butyraldehyde

17

88

155

297

Benzaldehyde

14

104

339

509

Furfural

4.5

9.2

37

458

2-Methoxyethanol

1.5

5.4

13

90

2-Butoxyethanol

6.2

26

42

47

2-Ethoxyethanol

2.3

9.8

23

64

2-(2-Methoxyethoxy)ethanol

1.8

6.4

23

64

Vasiliy V. Tereshatov, Valery Yu. Senichev

335

Table 6.3.4 Swelling data for four rubbers at 25oC. [Adapted, by permission, from E.T. Zellers, D.N. Anna, R. Sulewski, X. Wei. J. Appl. Polym. Sci, 62, 2069 (1996).] Solvent

Percent gain, wt% Butyl

Natural

Neoprene

Nitrile

Acetonitrile

1.3

2.6

7.3

78

Propionitrile

1.9

6

17

162

Butyronitrile

3.5

15

34

226

Benzonitrile

9.5

105

196

521

Methylene chloride

104

343

241

614

Chloroform

339

528

435

887

Carbon tetrachloride

460

691

377

102

1,2,-Dichloroethane

37

196

233

609

1,1,1-Trichloroethane

357

470

311

211

Perchloroethane

578

719

405

72

Trichloroethylene

494

618

387

333

Methanol

1.1

3

13

20

1-Propanol

1.6

7.7

7.2

25

1-Butanol

2.1

11

8.2

27

Ethanol

0.9

3.6

6.1

23

336

6.4 Influence of structure on equilibrium swelling

6.4 INFLUENCE OF STRUCTURE ON EQUILIBRIUM SWELLING Vasiliy V. Tereshatov, Valery Yu. Senichev Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Swelling single-phase elastomers is, with other parameters being equal, limited by the chemical network. Microphase separation of hard and soft blocks can essentially influence swelling of block-copolymers. Hard domains formed in this process are knots of physical network, which can be resistant to an action of solvents.1-4 Swelling of polyurethane block-copolymers with urethane-urea hard segments is investigated. The maximum values of swelling, Qmax, of segmented polyurethane (prepolymer of an oligopropylene diol with functional isocyanate groups) cured with 4,4’-methylene-bis-o-chloroaniline (MOCA) are given in Tables 6.4.1 and 6.4.2. The prepolymer Vibratane B 600 was obtained by the reaction of an oligopropylene diol with 2,4-toluene diisocyanate. The swelling experiments were carried out in four groups of solvents of different polarity and chemical structure.5 The effective molecular mass of elastically active chains, Mc, between network crosslinks was estimated from the Flory-Rehner equation.6 The interaction parameter of solvent with polymer was determined by calculation. In the first variant of calculation, a classical method based on the solubility parameter concept was used with application of Bristow and Watson's semi-empirical relationship for χ1:7 V 2 s χ 1 = χ 1 +  -------1- ( δ 1 – δ p )  RT where:

s

χ1 V1 R1 T δ1 and δp

[6.4.1]

a lattice constant whose value can be taken as 0.34 the molar volume of the solvent the gas constant the absolute temperature the solubility parameters of the solvent and the polymer, respectively

However, to evaluate χ1 from Eq. [6.4.1], we need accurate data for δ1. In some cases, the negative Mc values are obtained (Tables 6.4.1). The reason is that the real values of the entropy component of the χ1 parameter can strongly differ from the 0.34 value.

Vasiliy V. Tereshatov, Valery Yu. Senichev

337

Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Penetrant

Qmax

χ1

Mc

Monocyclic aromatics Benzene

0.71

0.378

630

Toluene

0.602

0.454

790

p-Xylene

0.497

0.510

815

Mesitylene

0.402

0.531

704

Chlorobenzene

1.055

0.347

905

Bromobenzene

1.475

0.347

1248

o-Dichlorobenzene

1.314

0.357

1106

Anisole

0.803

0.367

821

Nitrobenzene

1.063

0.356

835

Aliphatic alcohols Methanol

0.249

1.925

-90

Ethanol

0.334

0.349

172

n-Propanol

0.380

0.421

484

Isopropanol

0.238

0.352

249

n-Butanol

0.473

2.702

-131

2-Butanol

0.33

1.652

-307

2-Methyl-1-propanol

0.389

0.440

535

Isoamyl alcohol

0.414

0.357

398

Chloroform

4.206

Halogenated aliphatics 0.362

3839

Bromoform

5.583

0.435

4694

1,2-Dibromoethane

1.855

0.412

770

1,3-Dibromopropane

1.552

0.444

870

Dichloromethane

2.104

0.34

1179

Trichloroethylene

1.696

0.364

1098

Tetrachlorethylene

0.832

0.368

429

1,2-Dichlorethane

1.273

0.345

728

Carbon tetrachloride

1.058

0.538

860

1,4-Dichlorobutane

0.775

0.348

626

1,1,2,2-Tetrachloroethane

5.214

0.34

6179

338

6.4 Influence of structure on equilibrium swelling

Table 6.4.1. Characteristics of polyurethane-solvent systems at 25oC. [Adapted, by permission, from U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS - Rev. Macromol. Chem. Phys., 30C (1), 43 (1990).] Qmax

χ1

Mc

0.494

0.341

370

Ethyl acetate

0.509

0.422

513

Ethyl benzoate

0.907

0.34

1111

Methyl ethyl ketone

1.261

0.364

2088

Tetrahydrofuran

2.915

0.39

2890

Penetrant

Miscellaneous liquids Methyl acetate

1,4-Dioxane

2.267

0.376

2966

DMF

1.687

1.093

-1184

DMSO

0.890

1.034

-975

Acetonitrile

0.184

0.772

182

Nitromethane

0.302

1.160

5737

Nitroethane

0.463

0.578

382

n-Hexane

0.069

1.62

2192

Cyclohexane

0.176

0.753

287

Benzyl alcohol

4.221

In the second variant of evaluation of Mc, data on the temperature dependence of volume fraction of polymer, ϕ2, in the swollen gel were used. Results of calculations of Mc from the Flory-Rehner equation in some cases also gave negative values. The evaluation of Mc in the framework of this approach is not an independent way, and Mc is an adjustment parameter, as is the parameter χ1 of interaction between solvent and polymer. Previous evaluation of the physical network density of SPU was done on samples swollen to equilibrium in two solvents.2,9,10 Swelling of SPU in toluene practically does not affect hard domains.9,11 Swelling of SPU (based on oligoether diol) in a tributyl phosphate (a strong acceptor of protons) results in the full destruction of the physical network with hard domains.2 The effective network density was evaluated for samples swollen to equilibrium in toluene according to the Cluff-Gladding method.12 Samples were swollen to equilibrium in TBP and the density of the physical network was determined from equation:2,10 ( v e ⁄ V 0 ) dx – ( v e ⁄ V 0 ) x = ( v e ⁄ V 0 ) d

[6.4.2]

Resulting from the unequal influence of solvents on the physical network of SPU, the values of effective density of networks calculated for the “dry” cut sample can essentially differ. The examples of such influence of solvents are given elsewhere.2 SPU samples with oligodiene soft segments and various concentrations of urethane-urea hard blocks were swollen to equilibrium in toluene, methyl ethyl ketone (MEK), tetrahydrofu-

Vasiliy V. Tereshatov, Valery Yu. Senichev

339

ran (THF), 1,4-dioxane and TBP (experiments 1-6, 9, 10, 12). SPU based on oligoether (experiment 7), with urethane-urea hard segments, and crosslinked single-phase polyurethanes (PU) on the base of oligodiene prepolymer with functional isocyanate groups, cured by oligoether triols (experiments 8, 11), were also used. The effective network densities of materials swollen in these solvents were evaluated by the Cluff-Gladding method through the elasticity equilibrium modulus. The data are given in Table 6.4.2 per unit of initial volume. Table 6.4.2. Results of the evaluation of equilibrium swelling and network parameters of PUE. [Adapted, by permission, from E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, and M.A. Makarova, Vysokomol. Soed., 34B, 22 (1992).] #

ρ kg/m3

Qv

ve/V0

Toluene

Qv

ve/V0 THF

Qv

ve/V0

MEK

Qv

ve/V0

Qv

1,4-Dioxane

ve/V0 TBP

1

996

1.56

1.03

0.46

0.77

1.08

0.41

3.76

0.12

5.12

0.06

2

986

2.09

0.53

0.52

0.43

1.40

0.23

6.22

0.04

11.15

0.02

0.73

0.01

3

999

1.74

0.77

0.49

4

1001

2.41

0.44

0.49

5

1003

4.46

0.15

0.47

6

984

2.63

0.40

0.57

7

1140

0.86

1.83

2.06

8

972

2.42

0.35

1.11

0.38

7.88

0.03

18.48

1.75

0.13

14.3

0.02

∞

0.19

3.44

0.14

4.21

3.29

∞

∞

0.39

1.45 1.40

0.73

1.86

0.31

7.22

0.04

1.84

0.36

1.01

0.54

2.08

0.34

1.48

0.35

0.37

9

979

2.26

0.39

1.72

10

990

2.00

0.63

0.47

0.08

0.98

0.54

1.97

0.35

1.62

0.31

0.99

0.55

2.42

0.29

2.19

0.24

11

991

4.11

0.18

2.79

0.18

3.98

0.17

3.42

0.18

2.54

0.17

12

997

2.42

0.50

1.00

0.32

2.68

0.12

4.06

0.13

4.32

0.08

(ve/V0), kmol/m3

The data shows that the lowest values of the network density are obtained for samples swollen to equilibrium in TBP. Only TBP completely breaks down domains of hard blocks. If solvents, which are acceptors of protons (MEK, THF, 1,4-dioxane), are used in swelling experiment intermediate values are obtained between those for toluene and TBP. The network densities of SPU (experiments 8 and 11) obtained for samples swollen in toluene, TBP, 1,4-dioxane and THF coincide (Table 6.4.2).2 To understand the restrictions to swelling of SPU caused by the physical network containing hard domains, the following experiments were carried out. Segmented polybutadiene urethane urea (PBUU) on the base of oligobutadiene diol urethane prepolymer with functional NCO-groups ( M ≈ 2400 ), cured with MOCA, and SPU-10 based on prepolymer cured with the mixture of MOCA and oligopropylene triol ( M ≈ 5000 ) were used. The chemical network densities of PBUU and SPU were 0.05 and 0.08 kmol/m3,

340

6.4 Influence of structure on equilibrium swelling

respectively. The physical network density of the initial sample, (ve/V0)d, for PBUU was 0.99 kmol/m3 and for SPU-10 was 0.43 kmol/m3. Samples of PBUU and SPU-10 were swollen to equilibrium in solvents of different polarity: dioctyl sebacate (DOS), dioctyl adipate (DOA), dihexyl phthalate (DHP), transformer oil (TM), nitrile of oleic acid (NOA), dibutyl carbitol formal (DBCF), and tributyl phosphate (TBP). The values of equilibrium swelling of elastomers in these solvents, Q1, (ratio of the solvent mass to the mass of the unswollen sample) are given in Table 6.4.3. After swelling in a given solvent, samples were swollen in toluene to equilibrium. The obtained data for T swelling in toluene, Q V , indicate that the physical networks of PBUU and SPU-10 do not change on swelling in most solvents. Equilibrium swelling in toluene of initial sample and the sample previously swollen in other solvents are practically identical. Several other observations were made from swelling experiments, including sequential application of different solvents. If preliminary disruption of the physical network of PBUU and SPU-10 by TBP occurs, swelling of these materials in toluene strongly increases. Similarly, samples previously swollen in TBP have higher equilibrium swelling, Q2, when swollen in other solvents. The value of Q2 is likely higher than equilibrium swelling Q1 of initial sample (Table 6.4.3). Q2 for PBUU is closer to the value of equilibrium swelling of a single-phase crosslinked polybutadiene urethane, PBU, having chemical network density, (ve/V0)x = 0.04 kmol/m3. Thus, the dense physical network of polyurethane essentially limits the extent of equilibrium swelling in solvents, which does not break down the domain structure of a material. Table 6.4.3. Equilibrium swelling of SPBUU and SPU-10 (the initial sample and sample after breakdown of hard domains by TBP) and swelling of amorphous PBU at 25oC SPBUU Solvent

Initial structure Q1

-

QT

SPU-10

After breakdown of domains Q2

Initial structure Q1

1.35

After breakdown of domains

PBU

Q2

Q3 5.56

QT 2.10

DOS

0.62

1.34

3.97

0.66

2.09

3.04

DOA

0.68

1.34

4.18

0.84

2.05

3.26

DBP

0.60

1.36

3.24

0.90

2.12

3.38

DHP

0.63

1.34

3.71

0.85

2.10

3.22

4.47

TO

0.57

1.35

2.29

0.58

2.07

1.92

1.99

NOA

0.59

1.36

4.03

0.72

2.10

2.86

4.66

DBCP

0.69

1.37

4.60

0.155

2.96

3.45

5.08

TBP

5.01

7.92*

5.01

4.22

5.43

4.22

* The result refers to the elastomer, having physical network completely disrupted

Vasiliy V. Tereshatov, Valery Yu. Senichev

341

Swelling of SPU can be influenced by changes in elastomer structure resulting from the mechanical action. At higher tensile strains of SPU, a successive breakdown of hard domains as well as microsegregation may come into play causing reorganization.13-15 If the structural changes in the segmented elastomers are accompanied by a breakdown of hard domains and a concomitant transformation of a certain amount of hard segments into a soft polymeric matrix or pulling off some soft blocks (structural defects) out of the hard domains,14 the variation of network parameters is inevitable. It is known4 that high strains applied to SPU cause disruption of the physical network and a significant drop in its density. Table 6.4.4. Equilibrium swelling of SPU-1 samples in various solvents before and after stretching at 25oC (calculated and experimental data). [Adapted, by permission, from V.V. Tereshatov, Vysokomol. soed., 37A, 1529 (1995).] Solvent

ρ1 kg/m3

V1×103 m3/kmol

Qv (ε=0)

χ1 (ε=0)

Qv (ε=700%) calc

exp

T

QV

(ε=700%)

T

QV

(ε=0)

Toluene

862

107

3.54

0.32

5.06

4.87

DBP

1043

266

1.12

0.56

1.47

1.53

4.85

3.49

n-Octane

698

164

0.79

0.75

0.90

0.93

4.94

3.60

Cyclohexane

774

109

1.46

0.60

1.78

1.95

4.99

3.63

p-Xylene

858

124

2.94

0.36

4.17

3.93

4.81

3.52

Butyl acetate

876

133

2.28

0.44

3.13

2.97

5.12

3.69

DOS

912

468

1.21

0.38

1.60

1.71

5.10

3.63

DOA

924

402

1.49

0.32

2.19

2.18

5.00

3.61

DHS

923

340

1.74

0.30

2.55

2.44

5.01

3.59

DHP

1001

334

1.25

0.47

1.71

1.74

4.79

3.47

DBCP

976

347

4.48

4.51

9.92

9.98

The data on equilibrium swelling of SPU-1 with oligodiene soft segments obtained by curing prepolymer by the mixture of MOCA and oligobutadiene diol ( M ≈ 2000 ) with the molar ratio 1/1 are given in Table 6.4.4. The initial density of the SPU-1 network ( v e ⁄ V 0 ) dx = 0.206 kmol/m3, the physical network density ( v e ⁄ V 0 ) d = 0.170 kmol/ m3. After stretching by 700% and subsequent unloading, the value ( v e ⁄ V 0 ) dx = 0.115 kmol/m3 and ( v e ⁄ V 0 ) d = 0.079 kmol/m3. The density of the chemical network ( v e ⁄ V 0 ) x = 0.036 kmol/m3 did not change. Samples were swollen to equilibrium in a set of solvents: toluene, n-octane, cyclohexane, p-xylene, butyl acetate, DBCF, DBP, DHP, dihexyl sebacate (DHS), DOA and DOS (the values of density, ρ1, and molar volume of solvents, V1, are given in Table 6.2.5). The data in Table 6.4.4 shows that, after stretching, the volume equilibrium swelling of samples does not change in DBCP.4 In other solvents, the equilibrium swelling is noticeably increased.

342

6.4 Influence of structure on equilibrium swelling

The swelling experiments of samples previously swollen in solvents and subsequently in toluene have shown that the value of the equilibrium swelling in toluene varies only for samples previously swollen in DBCF. The effective network densities evaluated for SPU-1 samples, swollen in DBCF, and then in toluene, have appeared equal (0.036 and 0.037 kmol/m3, respectively) and these values correspond to the value of the chemical network parameter, (ve/V0)x, of SPU-1. It means that DBCF breaks down the physical network of elastomer; thus, the values of Qv in DBCF do not depend on the tensile strain. In all other cases, swelling of SPU-1 in toluene differs only marginally from the initial swelling of respective samples in toluene alone. Therefore, these solvents are unable to cause the breakdown of the physical network. The calculation of equilibrium swelling of SPU-1 (after its deformation up to 700% and subsequent unloading) in a given solvent was carried out using the Flory-Rehner equation. In calculations, the values of the χ1 parameter of interaction between solvents and elastomer calculated from experimental data of equilibrium swelling of initial sample (ε = 0) in these solvents were used. The difference between calculated and experimental data on equilibrium swelling of SPU-1 samples after their deformation does not exceed 9%. Therefore, the increase in swelling of SPU-1 is not related to the change in the χ1 parameter but it is related to a decrease in the (ve/V0)dx value of its three-dimensional network, caused by restructuring of material by the effect of strain. The change of the domain structure of SPU exposed to increased temperature (~200oC) and consequent storage of an elastomer at room temperature may also cause a change in equilibrium swelling of material.16 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

V.P. Begishev, V.V. Tereshatov, E.N. Tereshatova, Int. Conf. Polymers in extreme environments, Nottingham, July 9-10, 1991, Univ. Press, Nottingham, 1991, pp. 1-6. E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, and M.A. Makarova, Vysokomol. Soed., 34B, 22 (1992). V.V. Tereshatov, E.N. Tereshatova, V.P. Begishev, V.I. Karmanov, and I.V. Baranets, Polym. Sci., 36A, 1680 (1994). V.V. Tereshatov, Vysokomol. soed., 37A, 1529 (1995). U.S. Aithal, T.M. Aminabhavi, R.H. Balundgi, and S.S. Shukla, JMS-Rev. Macromol. Chem. Phys., 30C (1), 43 (1990). P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, 1953. G.M. Bristow, and W.F. Watson, Trans. Faraday. Soc., 54, 1731 (1958). L.N. Mizerovsky, L.N. Vasnyatskaya, and G.M. Smurova, Vysokomol. Soed., 29A, 1512 (1987). D. Cohen, A. Siegman, and M. Narcis, Polym. Eng. Sci., 27, 286 (1987). E. Konton, G. Spathis, M. Niaounakis and V. Kefals, Colloid Polym. Sci., 26B, 636 (1990). V.V. Tereshatov, E.N. Tereshatova, and E.R. Volkova, Polym. Sci., 37A, 1157 (1995). E.E. Cluff, E.K. Gladding, and R. Pariser, J. Polym. Sci., 45, 341 (1960). Yu.Yu. Kercha, Z.V. Onishchenko, I.S. Kutyanina, and L.A. Shelkovnikova, Structural and Chemical Modification of Elastomers, Naukova Dumka, Kiev, 1989. Yu.Yu. Kercha, Physical Chemistry of Polyurethanes, Naukova Dumka, Kiev, 1979. V.N. Vatulev, S.V. Laptii, and Yu.Yu. Kercha, Infrared Spectra and Structure of Polyurethanes, Naukova Dumka, Kiev, 1987. S.V. Tereshatov, Yu.S. Klachkin, and E.N. Tereshatova, Plastmassy, 7, 43 (1998).

Vasiliy V.Tereshatov, Vladimir N.Strelnikov, Marina A.Makarova

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6.5 EFFECT OF STRAIN ON THE SWELLING OF NANO-STRUCTURED ELASTOMERS Vasiliy V.Tereshatov, Vladimir N.Strelnikov, Marina A.Makarova Institute of Technical Chemistry, Ural Branch of Russia Academy of Sciences, Perm, Russia Nano-heterogeneous elastomers with alternating soft and hard segments are used widely as compared with other block-copolymers having H-bonds. These are, for example, segmented polyurethane-ureas, SPUU, segmented polyurethanes, SPU, elastomers on the base of oligodiene urethane epoxides and so on.1-3 A significant difference in polarity leads to the microphase segregation of hard and soft segments with the formation of hard segments' domains. These domains with sizes of 5-50 nm play a role of reinforcing fillers and crosslinking points of specific physical networks stable at elevated temperatures.1,4 Various combinations of physical-chemical and physical-mechanical properties of segmented elastomers, SE, can be achieved by changing the chemical structure of oligomers having terminal functional groups, diisocyanates, and low-molecular-mass chain extenders. It was determined that a dense physical network having crosslinking points forming hard domains is characteristic of segmented polyurethane-urea. This physical network limits swelling of SPUU in organic liquids that cannot dissolve hard domains. Exploitation of elastic products made from SE can be associated with appearing of great local deformations for example during periodical loading. Structure of these polymers can change at high deformations; domains of hard blocks are partially destroyed with the formation of smaller domains; primary orientation takes place not only for soft segments but for hard segments, as well. Some hard segments are drawn out from some domains.5-9 As a result, the density of physical network having crosslinking points forming hard domains can change. Sorption properties of a material in contact with low-molecular liquids can also change. This subchapter is devoted to the effect of strain on the sorption of organic solvents (plasticizers) by SE with various chemical and supramolecular structure. The sorption of liquids was compared using samples before strain and after application of strain. The change in the molecular and supramolecular structure of SPUU samples with soft segments of different polarity was investigated by the FTIR spectroscopy method for the clarification of reasons of the effect of preliminary strain on the sorption of low-molecular-mass liquids, and for analysis of obtained results. Polyether urethane-urea SPUU-T with polytetramethylene oxide soft segments (average molecular mass of soft segments M n =1430 g mol-1), polybutadiene urethane-urea SPUU-D( M n = 2100 g mol-1), and polyurethane-urea SPUU-TD with mixed polybutadiene and polytetramethylene oxide soft segments were investigated. The quantity of polar and non-polar soft segments was uniform for SPUU-TD. Materials were manufactured using a two stage technology. The first stage was reaction of 2,4-toluenediisocyanate and oligodiols: oligobutadienediol OBD ( M n = 2100 g mol-1) and oligotetramethylene oxide diol OTM ( M n = 1430 g mol-1). The ratio NCO/OH

344

6.5 Effect of strain on the swelling of nano-structured elastomers

was 2.03 at this stage. Prepolymers were cured at the second stage by methylene-bisortho-chloroaniline, MOCA, at 90oC for 3 days. The completeness of conversion of NCOgroups was controlled by the FTIR-spectroscopy. The methods of samples manufacturing are given elsewhere.10 Also, single-phase polyurethane PUE-TL was synthesized for comparison of sorption properties of this material and nano-heterogeneous SPUU. PUE-TL was synthesized on the base of prepolymer of OTM cured by mixture of the initial OTM and oligopropylene oxide triol Laprol 373 ( M n = 370 g mol-1). FTIR spectra of samples' surfaces were obtained by the multiple attenuated total reflectance (MATR) method using the IFA-66/S spectrometer and specially designed MATR accessories with 45o KRS-5 trapezoid as the internal reflection element (operating number of reflections 1000). Tests were conducted using samples cut according to crystal size 20 × 40 mm2, thickness 2 mm before and after stretching up to a given strain value. The 20 × 80 mm2 sheets were stretched, then samples for spectra registration were cut off from working parts of sheets. The density of samples was determined by the hydrostatic method using AR-240 balance (Ohaus, Switzerland) with accuracy 2x10-7 kg. The density of physical network, having crosslinking points which were hard domains and the density of chemical network formed by chemical crosslinking points, was determined for SPUU using an approach developed by the authors.11 The total network density Ndx was determined using the compression modulus of samples swollen with toluene. Swelling in this solvent doesn't affect hard domains. The chemical network density Nx was determined testing samples swollen with tributyl phosphate. The physical network density was determined using difference Ndx − Nx = Nd. For single-phase polyurethane Ndx = Nx (Nd = 0). Low-molecular-mass liquids, such as di-2-(ethylhexyl) phthalate, DEHP, and liquid chlorinated paraffin HP-470 ( M n =470 g mol-1) were used to investigate the strain effect on the sorption properties of SE and single-phase elastomer with a similar structure. Parts of samples were preliminarily drawn up to 350%. Cylindrical specimens (5 mm diameter, 2 mm thickness) cut from drawn samples were immersed in the above-mentioned liquids until the constant mass at the temperature 25±1oC was achieved. Parts of non-drawn samples were immersed in these liquids up to equilibrium, as well. The equilibrium swelling Q, wt% and equilibrium concentration Cp wt%, at swelling were determined. Q = 100m1/m0 where: m1 m0

mass of absorbed liquid initial mass of sample

Cp = 100m1/(m1 + m0) Table 6.5.1 contains data values for Q, Cp for three heterogeneous elastomers with urethane urea hard segments and a single-phase polyurethane PUE-TL. The preliminary strain ε = 350% does not practically affect the equilibrium swelling and the equilibrium concentration of this material at swelling in DEHP and HP-470.

Vasiliy V.Tereshatov, Vladimir N.Strelnikov, Marina A.Makarova

345

Table 6.5.1. Swelling data for SPUU and PUE-TL samples in DEHP and HP-470. DEHP Sample

ε = 0%

HP-470 ε = 350%

ε = 0%

ε = 350%

Q, wt% Cp, wt% Q, wt% Cp, wt% Q, wt% Cp, wt% Q, wt% Cp, wt% SPUU-D

62.6

38.5

70.1

41.2

47.5

32.2

53.8

35.0

SPUU-TD

40.6

28.9

53.8

35.0

44.3

30.7

58.7

37.0

SPUU-T

28.4

22.1

40.8

29.0

40.6

28.9

61.2

38.0

PUE-TL

187

65.2

186

65.0

154

60.6

156

60.9

Figure 6.5.1. FTIR-MATR spectra of SPUU-D (a), SPUU-T (b), and SPUU-TD(c).

The effect of strain differs significantly for swelling of SE with non-polar soft segments (SPUU-D) and ones with polar polyether segments (SPUU-T). Intermediate position in swelling value belongs to SPUU-TD with mixed soft segments. Preliminary strain affects equilibrium swelling of SPUU-D only a little. The values Q, and Cp for SPUU-T change significantly after strain.

346

6.5 Effect of strain on the swelling of nano-structured elastomers

The reason for this effect can be found from the qualitative analysis of FTIR MATR spectra for SPUU-D, SPUU-TD, SPUU-T before and after strain up to 350%. (Figure 6.5.1). The integral spectral curve changed little after straining SPUU-D with non-polar soft segments (Figure 6.5.1a). The band intensity of carbonyl at 1640 cm-1 decreases only a little after strain. This band refers to the absorption of hydrogen-bonded, ordered urea carbonyl. Urea groups are usually linked mutually (self-associates of urea groups) and localized in domains of the hard segments. The intensity of this band can be used for comparison of the microphase segregation degree for soft and hard segments.6 It is suggested that the band at 1663 cm-1 (1663-1666 cm-1) refers to the absorption of hydrogen-bonded, disordered urea carbonyls in the soft phase of polymer. The intensity of this band also changes little after the strain of SPUU-D (Figure 6.5.1a). Significant changes in the SPUU-T spectrum are seen after strain up to 350% (Figure 6.5.1b). The intensity of the band at 1642 cm-1 decreases significantly (the band of carbonyl absorption shifts by 2 cm-1 to the side of higher values of the wave number). This suggests decrease in the degree of microphase segregation of hard and soft segments. The concentration of hard phase in a material decreases, as well. The intensity of band at 1729 cm-1 for free urethane carbonyl and band at 1711 cm-1 for hydrogen-bonded, disordered urea carbonyl in the soft phase of polymer increases. Thus, redistribution of intensity of carbonyl absorbance in hard and soft phase of polyurethane urea is evident. The assignment of carbonyl bands is based on results published elsewhere.12-15 The degree of microphase segregation of hard and soft segments in SPUU-TD decreases less than in SPUU-T, but more than in SPUU-D (Figure 6.5.1c). The results of the analysis of FTIR MATR spectra and data regarding the change in physical network density (for network with hard domains playing a role of crosslinking points) after strain of investigated materials correlate (Table 6.5.2). The value Nd for physical network decreases from 1.42 to 1.1 kmol/m3 for SPUU-T, from 1.09 to 0.88 kmol/m3 for SPUUTD, from 0.78 to 0.68 kmol/m3 for SPUU-D. The data permit to explain differences in sorption values for SPUU after strain. Table 6.5.2. Network parameters for SPUU and single-phase polyurethane PUE-TL before strain and after strain up to 350% N, kmol/m3 Material

ρ, kg/m3

Nx

Ndx

Mdx, kg/kmol

Nd

0

350%

0

350%

0

350%

0

350%

SPUU-T

1100

1.42

1.10

0.04

0.04

1.38

1.06

770

1000

SPUU-TD

1041

1.09

0.88

0.04

0.04

1.05

0.84

955

1180

SPUU-D

989

0.78

0.68

0.05

0.05

0.73

0.63

1270

1450

PUE-TL

1056

0.14

0.14

0.14

0.14

0

0

7600

7600

The decrease in the Nd value (for physical network) and data on the spectral analysis show the partial rupture of hard domains. A part of hard segments transfers to the soft

Vasiliy V.Tereshatov, Vladimir N.Strelnikov, Marina A.Makarova

347

phase after straining. As a result, the volume of polymer available for plasticizer molecules increases. Therefore, two factors promote the increase of solubility of SPUU in liquids: decrease in the physical network density and the increase in the volume fraction of soft phase in heterogeneous polymer.These factors affect swelling of SPUU-TD with polyether soft segments to higher degree after straining. The equilibrium swelling Q and concentration of liquid in SPUU change after strain less in the case when some soft polyether segments are replaced by polydiene segments. Lower rupture of hard domains leads to a little change in swelling values for polydieneurethane urea in DEHP and HP-470. An effect of strain on swelling of segmented polyurethane SPU and three polyurethane ureas SPUU-TD, SPUU-1, and SPUU-P was investigated for 11 polar and non-polar solvents (plasticizers). The molecular mass of polytetramethylene oxide soft segments and polypropylene oxide soft segments (Mn) is 1000 g mol-1 in SPUU-1. Polyurethane was synthesized via curing of prepolymer OTM ( M n = 2000 g mol-1) by BD. Synthesis of prepolymer was conducted using diphenylmethane diisocyanate, MDI. The molar ratio NCO/ OH = 0.98. The molar ratio OTM/MDI = 2.2. The methods of sample manufacture are given elsewhere.10 The values of an effective network density Nd for SPU, SPUU-TD, SPUU-1, and SPUU-P were 0.56, 1.05, 1.75, 1.30 kmol/m3, respectively. Samples were swollen at 25±1oC before the strain and after strain up to the value 350% in the following liquids: ethyl acetate, n-octane, p-xylene, toluene, butyl acetate, isoamyl alcohol, DEHP, dibutyl phthalate, DBP, dibutyl sebacate, DBS, di-(2-ethylhexyl) sebacate, DEHS, and tributyl phosphate, TBP. The results show that samples of linear SE are completely solvable in TBP which is a strong acceptor of protons independent of the structure and polarity of soft segments. The physical network with crosslinking points which are hard domains limits equilibrium swelling in many solvents. This is clearly seen from an example of SPUU-1 with high effective density of such network Ndx = 1.75 kmol/m3. The Q value in the majority of solvents is below 50% (Table 6.5.3). The maximum sorption was obtained for segmented polyurethane with lower physical network density. Preliminary strain leads to increase in plasticizer sorption. Thus, determined peculiarities are characteristic for segmented heterogeneous elastomers with urethane urea and urethane hard segments. It is interesting to note that strain affects the swelling of SE in many liquids with the lesser degree in the case of low network density Nd value. This is evidently seen for example of SPU. Table 6.5.3. Equilibrium swelling of segmented polyurethane and polyurethane ureas in solvents (plasticizers). Solvent (plasticizer)

Q, % (ε = 0)

Q, % (ε = 350)

SPUU-TD

SPUU-1

SPU

SPUU-P

SPUU-TD

SPUU-1

SPU

SPUU-P

Ethyl acetate

64

45

120

116

78

60

133

132

Octane

22

6

15

7

28

7

19

8

p-Xylene

89

48

128

−

14

6

146

−

348

6.5 Effect of strain on the swelling of nano-structured elastomers

Table 6.5.3. Equilibrium swelling of segmented polyurethane and polyurethane ureas in solvents (plasticizers). Solvent (plasticizer) Toluene

Q, % (ε = 0)

Q, % (ε = 350)

SPUU-TD

SPUU-1

SPU

SPUU-P

SPUU-TD

SPUU-1

SPU

SPUU-P

106

57

158

74

130

78

174

86

Butyl acetate

71

44

135

94

89

62

142

109

Isoamyl alcohol

24

29

70

−

28

38

73

−

DEHP

41

15

72

7

54

24

77

10

BBP

48

35

−

41

63

53

−

58

DBS

48

26

95

38

65

40

99

48

DEHS

29

10

41

−

39

14

43

−

TBP

∞

∞

872

∞

∞

∞

878

∞

CONCLUSIONS The effect of preliminary strain on the sorption of liquids having various chemical structures of segmented polyurethane and polyurethane ureas was investigated. The swelling degree increased after straining as a result of partial destruction of domain structure and decrease in the effective density of the physical network formed by hard domains. It was demonstrated that the increase in destruction of domain structure of a material leads to further change in solubility of liquids in an elastomer. This effect is less pronounced in low dense networks and disappears at all in absence of such network (for single-phase elastomers). However, in the last case, the effect of limiting swelling in various liquids due the presence of physical network stable to the solvent action decreases or disappears. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Z.S. Petrovic, J.Ferguson, J. Polym. Sci., 16, 695 (1991). D. Randall, S. Lee, The polyurethanes book. Wiley, New York, 2003. T. Thomson, Polyurethanes as specialty chemicals: principles and applications, CRC Press, Boca Raton, 2005. V. V.Tereshatov, V. N.Strel'nikov, M. A. Makarova, V. Yu. Senichev, and E. R.Volkova, Russ. J. Appl. Chem., 83, 1380 (2010). F. Yeh, B.S. Hsiao, B.B. Sauer, S. Michel, H.W. Siesler, Macromolecules, 36, 1940 (2003). E.M. Christenson, J.M. Anderson, A. Hiltner, E. Baer, Polymer, 46, 1744 (2005). G. Muller-Riederer, R. Bonart, Progr. Colloid. Polym. Sci., 62, 99 (1977). R. Bonart, K. Hoffman, Colloid Polym. Sci., 260, 268 (1982). V.V. Tereshatov, Polym. Sci., 37, 946 (1995). V.V. Tereshatov, M.A. Makarova, V.Yu. Senichev, A.I. Slobodinyuk, Colloid Polym. Sci., 290, 641 (2012). V.V. Tereshatov, E.N. Tereshatova, E.R.Volkova, Polym. Sci., 37, 1157 (1995). R.W. Seymor, G.M. Estes, S.L. Cooper, Macromolecules, 3, 579 (1970). L. Ning, W. De-Nung, Y. Sheng-Kang, Macromolecules, 30, 4405 (1997). V.V. Tereshatov, M.A. Makarova, E.N. Tereshatova, Polym. Sci. A., 46, 1332 (2004). C.M. Brunette, S.L. Hsu, W.J. MacKnight, Macromolecules, 15, 71 (1982).

Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, Vladimir N. Strelnikov

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6.6 THE EFFECT OF THERMODYNAMIC PARAMETERS OF POLYMER−SOLVENT SYSTEM ON THE SWELLING KINETICS OF CROSSLINKED ELASTOMERS Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, Vladimir N. Strelnikov Institute of Technical Chemistry Ural Branch of Russian Academy of Sciences, Perm, Russia Swelling of polymeric materials is a special case of mechano-diffusion processes, i.e. cooccurring and interrelated processes of the fluid diffusion and strain of a material. Threedimensional non-linear theory1 of such processes was used to study swelling of elastomeric polymer networks in low-molecular solvents elsewhere.2,3 A mathematical model describing the non-equilibrium swelling process flowing at finite strains was developed for a flat elastomer sample or a polymer gel.2 Regularities of non-equilibrium processes of polymer networks swelling were described at very low swelling degrees4-6 and at high swelling degrees.2-4 However, the actual swelling process is accompanied usually by a finite strain of a material, the amount of which is determined by the quality of a solvent and varies widely. This subchapter presents the results of theoretical and experimental studies on the influence of solvent properties on the nature of the swelling kinetics of elastomeric polymer networks at finite strains of the polymer matrix. Emphasis is focused on the study of the relationship of the asymptotic properties of the swelling kinetic curves with the thermodynamic quality of a solvent. The chemical potential of a solvent in the sample under swelling is given by the following equation:2 2

–1 4 ⁄ 3 –1 –4

μ = RT [ ln ( 1 – φ ) + φ + χφ + Z φ E φ ν ] where:

χ V1, V2 Z = V2/V1 φ φE ν = ν(τ)

[6.6.1]

Flory-Huggins parameter molar volumes of a solvent and the same for subchains of polymer network dimensionless parameter local volume fraction of a polymer in the swollen sample volume fraction of a polymer in the swollen material at equilibrium longitudinal elongation of the sample under swelling.

Equation [6.6.1] is written in the reference configuration. This configuration corresponds to the state of a material at equilibrium swelling. This means that ν = 1 in this state, 1⁄3 and ν = φ E for the initial (unswollen) state. For this reason, h is one half of the sample thickness in the equilibrium swollen state. The reference state is the state of the material, which is considered as unstrained; thereafter a strain is determined with respect to it. In the case of swellable materials, any state of the undistorted material, in which solvent is distributed uniformly over its volume, can be used as a reference configuration.1,2 Equation [6.6.1] describes the dependence of the chemical potential of a solvent absorbed by the sample under symmetrical biaxial stretching and compression. Equating it

350

6.6 The effect of thermodynamic parameters of polymer-solvent system

to zero, we obtain an equation that can be used to calculate the equilibrium swelling 1⁄3 degree of a sample under these conditions. In particular, if ν = φ E , we obtain the following equation 2

–1 –1

ln ( 1 – φ ) + φ + χφ + Z φ

= 0

[6.6.2]

which determines the local swelling degree on the sample surface during the time of immersion in the solvent. When ν = 1, we obtain the well-known Flory-Rehner equation 2

–1 1 ⁄ 3

ln ( 1 – φ E ) + φ E + χφ E + Z φ E

= 0

[6.6.3]

The kinetic curve is an integral characteristic of the swelling process g ( τ ) =  u ( x, τ )

[6.6.4]

which is usually determined by swelling experiments.7 The diffusion kinetics of flat sample swelling depends on the parameters χ and Z. Flory-Huggins parameter χ is a quantitative measure of the thermodynamic quality of a solvent for the given polymer. For good solvents χ < 0.5, and for the bad ones χ > 0.5. The value of χ = 0.5 corresponds to the so-called θ-solvents. As is shown below, the value determines largely the swelling kinetics. The value of Z affects the equilibrium swelling degree of the material. Next, we consider the elastomeric polymer networks and low-molecular-weight solvents for which Z >> 1. The initial part of the kinetic curve is described by the following equation:8 g ( τ ) = Mτ

q

[6.6.5]

Curves of distribution of diffusing liquid on the sample thickness are presented for various times (dimensionless) elsewhere.8 τ = tD/h2, where t − swelling time (with dimension); D − diffusion coefficient; h − one half of the sample thickness. Figure 6.6.1 shows that dimensionless boundary concentration of solvent u1 differs significantly from 1 for a good solvent ( χ < 0.5) and for a θ-solvent ( χ = 0.5), as well. This means that the liquid concentration on the boundary of the sample-liquid contact at the initial swelling stage is significantly less than equilibrium value u = 1. In the case of a poor solvent u 1 ≈ 1 , swelling kinetic curves are described by the law of normal sorption ( χ > 0.5). When χ < 0.5 swelling curves are S-shaped ones. Kinetic curves of swelling of a sample in a good solvent shown in the coordinates ( τ ; g) are Sshaped, and their initial region is described by equation [6.6.1] with the parameter q > 0.5. Figures 6.6.1 and 6.6.2 show the results of the numerical solution of the boundary problem for a variety of solutions of χ . One can see how the nature of the diffusion process and the shape of swelling kinetic curves changes depending on the deterioration of the thermodynamic quality of solvent. Particularly, it can be seen that as the Flory-Huggins parameter increases, the interval of the boundary concentration decreases, and swelling kinetic curves transform to the kinetic curve of the normal sorption. The swelling kinetics of polydiene-urethane epoxide crosslinked elastomer (PDUE) was investigated for the experimental verification of the theoretical analysis. It was pro-

Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, Vladimir N. Strelnikov

351

Figure 6.6.1. Distribution of the fluid during diffusion at different time points τ = tD/h2 for swelling of a plane layer in a good solvent ( χ = 0), in a θ-solvent ( χ = 0.5), and in a poor solvent ( χ = 0.8) 1) τ = 0.01; 2) τ = 0.1; 3) τ = 0.2; 4) τ = 0.4; 5) τ = 0.6; 6) τ = 0.8; 7) τ = 1.0; 8) τ = 1.5. The curves were obtained at Z = V2/V1 = 200. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova, Vysokomolek. Soed., 45A, 1160 (2003).]

vided for solvents with different thermodynamic quality: dioctyl sebacate (DOS), dioctyl adipate (DOA), dibutyl sebacate (DBS), dioctyl phthalate (DOP), CCl4, toluene, dibutylcarbitolformal (DBKF), dimethyl adipate (DMA), and triacetin.8 PDUE elastomer was obtained by curing oligodiene (vinyl-isoprene) urethane epoxide (M = 5×103) by oligodivinyl carboxylate-terminated oligomer SKD-KTR (M = 3×103) at the molar ratio of 1:0.56. Samples of elastomers were cured for 4 days at 80°C.

352

6.6 The effect of thermodynamic parameters of polymer-solvent system

Figure 6.6.2. Theoretical kinetic curves for swelling of a flat layer at different values of the Flory-Huggins parameter and fixed value of Z = V2/V1 = 200: 1) χ = 0; 2) χ = 0.4; 3) χ = 0.5; 4) χ = 0.6; 5) χ = 1.0. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova, Vysokomolek. Soed., 45A, 1160 (2003).]

Figure 6.6.3. The experimental kinetic curves of PDUE samples swelling in solvents of different thermodynamic quality: DOS ( χ = 0), DOA ( χ = 0.02), DBS ( χ = 0.132), DBKF ( χ = 0.46), and DMA ( χ = 0.93).

Molar volume of the polymer network chains V2 was evaluated by the shear modulus G of a sample swollen in toluene to equilibrium. The parameter χ value was estimated for each solvent using equation [6.6.3]. Kinetic curves of swelling were calculated according to the formula g(t) = m(t)/mE, where m(t), mE − current value of the mass of a liquid absorbed by the sample and finite value, respectively. Experiments were carried out by swelling at 25oC. Figure 6.6.3 shows the kinetic curves of the samples PDUE swelling in solvents of different thermodynamic quality. Table 6.6.1 shows the experimental values of the parameters characterizing the swelling kinetics. Table 6.6.1. Parameters of kinetic curves of swelling of PDUE elastomer in solvents of various thermodynamic quality. [Adapted, by permission, from E.Ya. Denisyuk, E.R. Volkova,

Vysokomolek. Soed., 45A, 1160 (2003)]. φE

χ

Z

Δu, %

q

qexp

Dx1011, m2/s

DOS

0.157

0.0

35

64

0.68

0.665

0.81

DOA

0.156

0.02

41

64

0.7

0.665

2.25

DBS

0.161

0.132

49

63

0.7

0.660

3.29

DOP

0.181

0.152

41

61

0.71

0.652

0.71

CCl4

0.0917

0.218

170

69

0.67

0.674

32.8

DBKF

0.291

0.460

47

47

0.58

0.603

1.89

DMA

0.654

0.930

94

4.2

0.52

0.506

2.26

Triacetin

0.943

2.1

87

0.14

0.50

0.500

0.24

Solvent

Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, Vladimir N. Strelnikov

353

Figure 6.6.3 and Table 6.6.1 show that the kinetic curves of elastomer swelling transform when the quality of the solvent decreases. For example, these curves are S-shaped for solvents with χ smaller than 0.5. This is evidenced by the fact that the parameter q > 0.5, and its value is close to the value of 0.7 corresponding to the limited self-similar regime of swelling of a material in good solvents at a constant diffusion coefficient. Sshape of the kinetic curve of swelling in DBKF is defined poorly, but its properties are close to θ-solvents. Kinetic curves of swelling in DMA, which is a poor solvent for a given polymer, have the shape characteristic for the kinetic curves of normal sorption. They have a distinct linear region, and the S-shape is absent. This corresponds to the value of q ≈ 0.5 . As previously shown,8 the determination of the diffusion coefficient D should be provided in analyzing the final section of the kinetic curve of swelling. This curve is described by the universal expression 2 –1

g ( t ) = 1 – C exp ( – α 1 h Dt )

[6.6.6]

where: g (t) t C h D α1

the ratio of the current mass value of an absorbed liquid to the equilibrium one time of swelling constant one half of the sample thickness in the reference configuration diffusion coefficient of a solvent in the material. the first positive root of the equation α n = γtgα n .

The value γ, taking into account the properties of a solvent, is determined using the following equation:8 4 ( 1 – φE ) γ = ---------------------------------------------------------------------------5⁄3 3 [ Zφ E ( 1 – 2χ 1 + 2χ 1 φ E ) + 1 ]

[6.6.7]

In this case, the diffusion coefficient D includes physical parameters and geometric factors associated with the particular mode of the straining process of polymer matrix during swelling. In addition, it depends essentially on the choice of the reference state, which is necessary to fix the description of the swelling process. It was shown that such choice was ambiguous.2 Any undistorted state can be used as the reference state when the material is not subjected to the mechanical stresses, and the fluid is uniformly distributed in volume. However, the situation is simpler in the case of materials with a low swelling degree. Here geometric factors play a minor role and the size of the sample differs slightly in the “dry” state and in the swollen state. The diffusion coefficient D is weakly dependent on the choice of the reference state; it can be approximately regarded as a physical characteristic of the process. The efficiency of the theory is demonstrated for the single-phase crosslinked polyurethane elastomers. At low degrees of swelling of materials in liquids, equation [6.6.6] can be transformed with simplification into the expression:

354

6.6 The effect of thermodynamic parameters of polymer-solvent system 2

kh D = -------2α1

[6.6.8]

where: h α1 ≈ π ⁄ 2 k

one half of the sample thickness in the equilibrium swollen state for poor solvents and materials with low swelling degree2 slope coefficient, calculated on the final sections of the kinetic curves of swelling, plotted in coordinates (t;−ln(1 − g)).

Expression [6.6.8] describes the kinetics of the normal absorption of liquid in the presence of which the spatial polymer network remains unchanged (absence of chemical network destruction). In the case of micro-heterogeneous materials with block structure, such as segmented polyurethanes and polyurethane-ureas, the absorption of the liquid should not lead to the chemical network destruction, and to the destruction of the physical network having crosslinking points forming hard domains. This subchapter presents the results of a study on the absorption kinetics of a number of liquids for segmented polyether urethane urea. Estimation of the diffusion coefficient of liquids was made for crosslinked polymers with a spatial network where crosslinking points are caused by chemical bonds and hard segment domains. The object of the study was a micro-heterogeneous polyurethane urea (PUU) based 3 on the prepolymer SKU-PFL-100 ( M ∼ 1.4 × 10 ), synthesized by the interaction of olig3 otetramethylene oxide diol ( M ∼ 1 × 10 ) with a double excess of 2,4-toluene diisocyanate. MOCA (aromatic diamine: 3,3’-dichloro-4,4’-diaminodiphenyl methane) was used to cure SKU-PFL-100. The NCO/NH2 ratio was 1.2 for this reaction. Prepolymer was degassed at 50 ± 10 oC before the reaction. The reaction mixture was stirred for 3 minutes at 50 ± 1 oC and a residual pressure of 1-2 kPa after injection of melted aromatic diamine. Curing period was 3 days at 80 ± 2 oC. Cured samples were further stored at the room temperature for at least 30 days. Sorption kinetics of elastomer was studied for following liquids: toluene, DBS, DOA, and transformer oil (TO). The study of the kinetics of swelling was conducted using samples manufactured in the form of discs of 35 mm in diameter and 2 mm in thickness. The kinetics of swelling was measured gravimetrically. A sample was immersed in a plasticizer and periodically weighed using analytical balance. The experimental time was determined via the establishment of the equilibrium concentration of a solvent in the sample. Experiments were carried out at 24 ± 1 °C. Determination of spatial network parameters for elastomers was determined before achievement of the value of the equilibrium swelling of the elastomer in the liquid and after it. Total effective network density Ndx of chemical network and physical network of a polymer resulting from its domain structure, and the density of chemical network Nx were determined by the method described elsewhere.9 Properties of used liquids and the network parameters are shown in Table 6.6.2. Estimation of the network parameters for polymer network shows that the values Ndx and Nx remain almost unchanged before swelling of the polymer in organic liquids and after it. This, according to the previous study,10 demonstrates the stability of not only chemical but also the physical network of the polymer to

Vasiliy V. Tereshatov, Elena R. Volkova, Evgeniy Ya. Denisyuk, Vladimir N. Strelnikov

355

the action of the liquids. Based on the data on the total network density, Ndx, and equilibrium swelling of PUU according to the Flory-Rehner equation,11 the estimation of the parameter (polymer-liquid interaction) was made for used liquids. Table 6.6.2. Properties of low-molecular-mass liquids and PUU samples swollen in them.

[Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).] Solvent

Molar vol. V, cm3/mol

−

Eq. swelling Q, % −

Network density, kmol/m3 Ndx

Nx

1.67

0.22

χ1

kx102, s-1

Dx1012, m2/s

−

−

−

TO

300

6.8

1.67

0.22

1.7

0.72

0.53

DOA

399

12.6

1.67

0.22

1.2

0.75

0.61

DBS

336

17.8

1.67

0.22

1.0

0.93

0.83

Toluene

106

46.8

1.67

0.22

0.7

47.1

43.0

Figure 6.6.4. Kinetic curves for swelling of PUU in toluene, DBS, DOA, and TO. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).]

Figure 6.6.5. Dependences for calculation of k coefficient for the final stage of PUU swelling in toluene, DBS, DOA, and TO. [Adapted, by permission, from V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).]

Figure 6.6.4 shows the results of a study of the kinetics of absorption of low-molecular-mass liquid by the polymer. It can be seen that all swelling kinetic curves plotted in the coordinates ( t ; g), have an initial linear stage, i.e., kinetic curves are normal sorption ones. Consequently, the experimental values of the diffusion coefficient D, can be calculated using equation [6.6.8]. Figure 6.6.5 shows the swelling kinetic curves plotted in the coordinates (t;−ln(1 − g)). They take the shape of straight lines with a slope coefficient k at g ≥ 0.4 . Diffusion coefficients for PUU and non-volatile liquids DBS, DOA, TO, and volatile solvent toluene were determined using obtained k values (Table 6.6.2).

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6.6 The effect of thermodynamic parameters of polymer-solvent system

The results of calculations show that the diffusion coefficients of DBS, DOA, and TO in PUU differ only a little. The diffusion coefficient of toluene is many times higher due to the fact that its molar volume V1 is much smaller. Increase in D during swelling of polymer in toluene according to the previous data8 is also a natural consequence of the greater thermodynamic affinity for toluene to PUU comparing with other solvents. This can be seen from the values of parameter χ 1 shown in Table 6.6.2. Results of investigations show that the proposed approach is quite justified to describe the kinetics of swelling of segmented polyurethanes in low-molecular-mass liquids at a small value of the equilibrium swelling ( Q ≤ 50 %) and in the case of the absence of significant effect of a solvent (or plasticizer) on the microphase segregation in the material. In this case, the law of normal sorption of a liquid by a crosslinked polymer is fulfilled. CONCLUSIONS 1. The effect of the thermodynamic quality of solvent on the swelling kinetics of elastomeric polymer networks was theoretically and experimentally studied. Swelling is considered as a set of interrelated processes of diffusion and strain of a material. It is shown that the quality of a solvent, estimated by the Flory-Huggins parameter value, significantly affects the nature of kinetic curves of polymer network swelling. 2. The swelling curves are S-shaped ones for values of the Flory-Huggins parameter less than 0.5. Swelling is described by the law of normal sorption in poor solvents. 3. The determination of the diffusion coefficient was carried to the final stage of the swelling kinetic curve, which was described by a universal asymptotic expression [6.6.6]. The initial stage of the kinetic curve was of little use because it was not possible to obtain a sufficiently accurate and simple analytical expression. 4. The increase in solubility of a liquid in polymer had a positive effect on the diffusion coefficient of the solvent under swelling of crosslinked elastomer. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

E.Ya. Denisyuk, V.V. Tereshatov, Appl. Mechanics Techn. Phys., 38, 113 (1997). E.Ya. Denisyuk, V.V. Tereshatov, Vysokomolek. Soed., 42A, 71 (2000). E.Ya. Denisyuk, V.V. Tereshatov, Vysokomolek. Soed., 42A, 2130 (2000). T. Tanaka, D. Fillmore, J. Chem. Phys., 70, 1214 (1979). A. Peters, S.J. Candau, Macromolecules, 21, 2278 (1988). Y. Li, T. Tanaka, J. Chem. Phys., 92, 1365 (1990). A.Ya. Malkin, A.E. Chalykh, Diffusion and Viscosity of Polymers. Methods of determination (In Russian). Chemistry, Moscow, 1979. E.Ya. Denisyuk, E.R. Volkova, Polym. Sci., 45A, 686 (2003). E.N. Tereshatova, V.V. Tereshatov, V.P. Begishev, M.A. Makarova, Vysokomolek. Soed, 34B, 22(1992). V.V. Tereshatov, V.Yu. Senichev, Influence of structure on equilibrium swelling, in Handbook of Plasticizers, 3rd Edition, ChemTec Publishing, Toronto, 2017. P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, 1953. V.V. Tereshatov, E.R. Volkova, E.Ya. Denisyuk, Plastmassy, 13, No.12, 14 (2004).

7

Solvent Transport Phenomena Many industrial processes rely on the dissolution of raw materials and subsequent removal of solvents by the various drying process. The formation of a solution and the subsequent solvent removal depend on solvent transport phenomena which are determined by the properties of the solute and the properties of the solvent. Knowledge of the solvent movement within the solid matrix by a diffusion process is essential to the design of various products and the technological processes. The quality of various products is frequently determined by the transport phenomena. In many polymeric products, resistance to solvent ingress (solvent resistance) is one of the most important properties. In some other products, such as, for example, in gloves or packaging materials, polymeric material should prevent solvent migration from one side to the other side of a barrier. In still other products, such as membranes, steady and fast flow of solvent through a membrane is an advantage. A similar list of effects of solvent transport phenomena on the technological processes can also be made. Many materials have to be dissolved before application, therefore solvent sorption and transport throughout a material is an important quality for solvent selection. Dissolved materials are then formed to the required shape and then dried to form final products. Solvent removal rate, the effect of the process on material structure, and completeness of solvent removal are important requirements. Many final physical properties, such as tribological properties, mechanical toughness, optical clarity, protection against corrosion, adhesion to substrates and reinforcing fillers, protective properties of clothing, the quality of the coated surface, toxic residues, morphology and residual stress, ingress of toxic substances, chemical resistance, depend not only on the material chosen but also on the regimes of technological processes. For the above-listed reasons, solvent transport phenomena are of interest to modern industry.

7.1 INTRODUCTION TO SOLVENT TRANSPORT PHENOMENA George Wypych ChemTec Laboratories, Toronto, Canada Small molecule diffusion is the driving force behind the movement of small molecules in and out of the solid matrix. Although both swelling and drying rely on diffusion, these processes are affected by the surfaces of solids, the concentration of small molecules in the surface layers, the morphology of the surface, and the interface between phases in

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7.1 Introduction to solvent transport phenomena

which diffusion gradient exists. For these reasons, swelling and drying are treated as specific phenomena. 7.1.1 DIFFUSION The free-volume theory of diffusion was developed by Vrentas and Duda.1 The theory is based on the assumption that movement of a small molecule (e.g., solvent) is accompanied by a movement in the solid matrix to fill the free volume (hole) left by a displaced solvent molecule. Several important conditions must be described to model the process. These include the time scales of solvent movement and the movement of solid matrix (e.g., polymer segments, called jumping units), the size of holes which may fit both solvent molecules and jumping units, and the energy required for the diffusion to occur. The timescale of the diffusion process is determined by the use of the diffusion Deborah number, De, given by the following equation: τM De = ----τD where:

τM τD

[7.1.1]

the molecular relaxation time the characteristic diffusion time

If the diffusion Deborah number is small (small molecular relaxation time or large diffusion time) molecular relaxation is much faster than diffusive transport (in fact, it is almost instantaneous).2 In this case, the diffusion process is similar to simple liquids. For example, diluted solutions and polymer solutions above the glass transition temperature fall into this category. If the Deborah number is large (large molecular relaxation time or small diffusion time), the diffusion process is described by Fickian kinetics and is denoted by an elastic diffusion process.1 The polymeric structure in this process is essentially unaffected and coefficients of mutual and self-diffusion become identical. Elastic diffusion is observed at low solvent concentrations below the glass transition temperature.2 The relationships below give the energy required for the diffusion process and compare the sizes of holes required for the solvent and polymer jumping unit to move within the system. The free-volume coefficient of self-diffusion is given by the equation:2 ˆ* + ω ξV ˆ* ) γ ( ω1 V 1 2 E 2 D 1 = D 0 exp – -------- × exp – ------------------------------------------ˆ RT V FH

[7.1.2]

where: D1 D0 E R T γ ω* ˆ V

self-diffusion coefficient pre-exponential factor energy per molecule required by the molecule to overcome attractive forces gas constant temperature overlap factor introduced to address the fact that the same free volume is available for more than one molecule mass fraction (index 1 for solvent, index 2 for polymer) specific free hole volume (indices the same as above)

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Figure 7.1.1. Temperature dependence of the solvent self-diffusion coefficient. [Adapted, by permission, from D Arnauld, R L Laurence, Ind. Eng. Chem. Res., 31 (1), 218-28 (1992).] ξ ˆ V FH

Figure 7.1.2. Free-volume correlation data for various solvents. [Data from D Arnauld, R L Laurence, Ind. Eng. Chem. Res., 31 (1), 218-28 (1992).]

the ratio of the critical molar volume of the solvent jumping unit to the critical molar the volume of the polymer jumping unit (see equation [7.1.3]) average hole free volume per gram of mixture.

ˆ* ⁄ V ˆ* = V ˆ* M ⁄ V ˆ* M ξ = V 1 2 1 1 2 2 where: M

[7.1.3]

molecular weight (1 − solvent, 2 − polymer jumping unit)

The first exponent in equation [7.1.2] is the energy term and the second exponent is the free-volume term. Figure 7.1.1 shows three regions of the temperature dependence of free-volume: I − above glass transition temperature, II − close to the transition temperature, and III − below the transition temperature. In the region I, the second term of the equation [7.1.2] is negligible and thus diffusion is energy-driven. In the region II, both terms are significant. In the region III, the diffusion is free volume-driven.3 The mutual diffusion coefficient is given by the following equation: D 1 ω 1 ω 2  ∂μ 1  - --------D = ------------------= D1 Q RT  ∂ω 1 T, p

[7.1.4]

where: D μ1 Q

mutual diffusion coefficient chemical potential of a solvent per mole thermodynamic factor.

These equations are at the core of diffusion theory and are commonly used to predict various types of solvent behavior in polymeric and other systems. One important reason for their wide application is that all essential parameters of the equations can be quantified

360

Figure 7.1.3. Parameter ξ vs. solvent molar volume. 1 − methanol, 2 − acetone, 3 − methyl acetate, 4 − ethyl acetate, 5 − propyl acetate, 6 − benzene, 7 − toluene, 8 − ethylbenzene. [Adapted, by permission, from D Arnauld, R L Laurence, Ind. Eng. Chem. Res., 31 (1), 218-28 (1992).]

7.1 Introduction to solvent transport phenomena

Figure 7.1.4. Mutual and self-diffusion coefficients for polystyrene/toluene system at 110oC. [Adapted, by permission, from F D Blum, S Pickup, R A Waggoner, Polym. Prep., 31 (1), 125-6 (1990).]

and then used for calculations and modeling. The examples of data given below illustrate the effect of important parameters on the diffusion processes. Figure 7.1.2 shows the effect of temperature on the diffusivity of four solvents. The relationship between diffusivity and temperature is essentially linear. Only solvents having the smallest molecules (methanol and acetone) depart slightly from a linear relationship due to the contribution of the energy term. The diffusivity of the solvent decreases as temperature decreases. Several other solvents show a similar relationship.3 Figure 7.1.3 shows the relationship between the solvent's molar volume and its activation energy. The activation energy increases as the solvent's molar volume increases then levels off. The data show that the molar volume of a solvent is not the only parameter which affects activation energy. Flexibility and the geometry of solvent molecule also affect activation energy.3 Branched aliphatic solvents (e.g., 2-methyl-pentane, 2,3-dimethyl-butane) and substituted aromatic solvents (e.g., toluene, ethylbenzene, and xylene) show large departures from free volume theory predictions. Many experimental methods such as fluorescence, reflection Fourier transform infrared, NMR, quartz resonators, and acoustic wave admittance analysis are used to study diffusion of solvents.4-11 Special models have been developed to study process kinetics based on experimental data. Figure 7.1.4 shows the effect of concentration of polystyrene on mutual and self-diffusion coefficients measured by pulsed-gradient spin-echo NMR. The data show that the two coefficients approach each other at high concentrations of the polymer as predicted by the theory.4

George Wypych

Figure 7.1.5. Flux vs. time for two solvents. [Adapted by permission from C F Fong, Y Li, De Kee, J Bovenkamp, Rubber Chem. Technol., 71 (2), 285288 (1998).]

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Figure 7.1.6. Absorbance ratio vs. exposure time to water for PMMA of different molecular weights. [Adapted, by permission, from I Linossier, F Gaillard, M Romand, J F Feller, J. Appl. Polym. Sci., 66, No.13, 2465-73 (1997).]

Studies on the solvent penetration of rubber membranes (Figure 7.1.5) show that in the beginning of the process, there is a lag time called breakthrough time. This is the time required for the solvent to begin to penetrate the membrane. It depends on both the solvent and the membrane. Of solvents tested, acetone had the longest breakthrough time in natural rubber and toluene the longest in nitrile rubber. After penetration, the flux of solvent increased rapidly and ultimately leveled off.7 This study is relevant for testing the permeability of protective clothing and protective layers of coatings. Similar observations were made using Figure 7.1.7. Absorbance ratio vs. exposure time to water for PMMA films of different thickness. [Adapted, internal reflection Fourier transform infraby permission, from I Linossier, F Gaillard, M Romand, red to measure water diffusion in polymer J F Feller, J. Appl. Polym. Sci., 66, No.13, 2465-73 films.9 Figure 7.1.6 shows that there is a (1997).] time lag between the beginning of immersion and water detection in the polymer film. This time lag increases as the molecular weight increases (Figure 7.1.6) and film thickness increases (Figure 7.1.7). After an initial increase in water concentration, the amount levels off. Typically, the effect of molecular weight on the diffusion of the penetrant does not occur. High molecular weight polymer

362

Figure 7.1.8. Relative diffusion rate vs. curing time. [Adapted, by permission, from J Chen, K Chen, H Zhang, W Wei, L Nie, S Yao, J. Appl. Polym. Sci., 66, No.3, 563-71 (1997).]

7.1 Introduction to solvent transport phenomena

Figure 7.1.9. Self-diffusion coefficient vs. polystyrene concentration. [Adapted, by permission, from L Meistermann, M Duval, B Tinland, Polym. Bull., 39, No.1, 101-8 (1997).]

has a shift in the absorption peak from 1730 to 1723 cm-1 which is associated with the hydrogen bonding of the carbonyl group. Such a shift does not occur in low molecular weight PMMA. Water can move at a higher rate in low molecular weight PMMA. In some other polymers, this trend might be reversed if the lower molecular weight polymer has end groups which can hydrogen bond with water. Bulk acoustic wave admittance analysis was used to study solvent evaporation during curing.8 Three characteristic stages were identified: in the first stage viscosity increases accompanied by a rapid decrease in diffusion rate; in the second stage the film is formed, the surface appears dry (this stage ends when the surface is dry) and the diffusion rate becomes very low; in the third stage solvent diffuses from the cured film. This is a slow process during which diffusion rate drops to zero. These changes are shown in Figure 7.1.8. The diffusion rate during drying decreases as the concentration of polymer (phenol resin) in varnish increases. Also, the time to reach the slope change point in diffusion/time relationship increases as the concentration of polymer increases.8 Two methods have been used to measure the diffusion coefficient of toluene in mixtures of polystyrenes having two different molecular weights: one was dynamic light scattering and the other, fluorescence recovery after bleaching.10 The data show that the relationship between the diffusion coefficient and polymer concentration is not linear. The crossover point is shown in Figure 7.1.9. Below a certain concentration of polymer, the diffusion rate drops rapidly according to different kinetics. This is in agreement with the above theory (see Figure 7.1.1 and explanations for equation [7.1.2]). The slope exponent in this study was -1.5 which is very close to the slope exponent predicted by the theory of reptation (-1.75). The above analysis of fundamentals of free-volume theory brings us to various practicalities of transport phenomena. It becomes clear that transport processes involve in

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Figure 7.1.10. Diffusion coefficients of 1 butanol (---) and 1-octanol (solid line) vs. crystallinity degree and temperature. [Data from M Limam, L Tighzert, F Fricoteaux, G Bureau, Polym. Test., 24, 395-402 (2005).]

Figure 7.1.11. Sorption profile of 1-butanol in cyclic olefin copolymer at 23oC. [Data from M Limam, L Tighzert, F Fricoteaux, G Bureau, Polym. Test., 24, 395-402 (2005).]

addition to diffusion, also sorption and permeation. Their common similarity is the same driving force, which is a concentration difference between two phases.12 The first Fick’s law of diffusion shows that flux J is proportional to the concentration gradient: ∂c J = – D  ------  ∂x

[7.1.5]

where: D ∂c ⁄ ∂x

diffusion coefficient the concentration gradient

This law describes an ideal case of steady flow which is strongly influenced by the nature of polymer, crosslinks, plasticizers, fillers, nature of penetrant, and temperature.12 Figure 7.1.10 shows the effect of polymer crystallinity and temperature on diffusion coefficients of 1-butanol and 1-octanol in poly(ethylene terephthalate).13 The increase of temperature facilitates diffusion (see also Figure 7.1.1). There is also a difference in diffusion between two penetrants studied. Butanol has higher diffusion rate than octanol, which is easy to understand since butanol has smaller molecular volume (see also Figure 7.1.3). Increase in crystallinity causes a decrease of the diffusion rate of both solvents.13 The strong effect of temperature on diffusion rate is described by the following equation:13 E D = D 0 exp  – -------a- RT where: Ea R T

activation energy perfect gas constant temperature

[7.1.6]

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7.1 Introduction to solvent transport phenomena

Figure 7.1.11 illustrates that both equations ([7.1.5] and [7.1.6]) apply only to the steady state diffusion but they do not describe sorption which is the initial stage of diffusion.13 Diffusion in unswollen and swollen regions are characteristic for two different stages, namely sorption and permeation, with the last characterized by a steady state diffusion.14 Mass transport through polymeric membranes can be described by a three-step process: the sorption of the components on the feed side, the diffusion (permeation) of the components through the membrane and the desorption of the components on the permeate side of the membrane.15 Swelling and sorption contribute to the lifetime of the membrane.16 They can be studied by numerous analytical methods, such as, gravimetric, barometric, vibrational, and spectroscopic (sorption) and dilation (e.g., cathetometer, ultrasonic, and digital camera) and rotational pendulum (swelling).16 Sorption of solvents through the membrane depends much more on Langmuir sorption than on Henry's Law.17 The solubility of solvent in the membrane is usually very small (less than 1%).17 The permeability coefficients of solvents correlate with the longest molecular dimension of solvents.17 The permeation flux through the film is given by the following equation:18 1 J i = --l

φ i, f

 φ i, p

D -----------dφ 1 – φi i

[7.1.7]

where: i component φ volume fraction D mutual diffusion coefficient l membrane thickness φi,f and φi,p volume fraction on feed and permeate side of the membrane

Permeability coefficient of solvent scales with its polarity represented by its surface energy.19 The above data show that theoretical predictions are accurate when modeling diffusion phenomena in both simple and complicated mixtures containing solvents. Some inconsistencies with the classical Stokes-Einstein law for homogeneous media were found in the case of diffusion coefficients of deep eutectic solvents.20 For an ideal liquid, the classical Stokes-Einstein relation predicts that D varies as T/η (where η is the dynamic viscosity of the deep eutectic solvent).20 The diffusion mechanism in the deep eutectic solvents is similar to that in the ionic liquids where a hopping mechanism or hole diffusion explains transport phenomena with the inhomogeneity of the media often considered as the reason for inconsistencies with the assumptions made in the Stokes-Einstein equation.20The diffusion coefficients were very little affected by the charges present on the diffusing molecules in contrast to observations made for ionic liquids.20 The polymethylmethacrylate concentration inversely influenced the solvent uptake in styrene butadiene rubber/polymethylmethacrylate membranes.21 In the case of semiIPNs, the uptake of solvents decreased by 20% when PMMA content increased from 40 to 60% but with full IPNs, the decrease in solvent uptake was 60%.21 This was explained by

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the continuous nature of the PMMA phase.21 Beginning with 50% PMMA content onwards, the PMMA phase in IPN becomes continuous and it determines the ultimate transport behavior of IPN.21 7.1.2 SWELLING Polymers differ from other solids because they may absorb large amounts of solvents without dissolving. They also undergo large deformations when relatively small forces are involved.22 Swelling occurs in a heterogeneous two-phase system a solvent surrounding a swollen body also called gel. Both phases are separated by the phase boundary permeable to solvent.23 The swelling process (or solvent diffusion into to the solid) occurs as long as the chemical potential of solvent is large. Swelling stops when the potentials are the same and this point is called the swelling equilibrium. Swelling equilibrium was first recognized by Frenkel24 and the general theory of swelling was developed by Flory and Rehner.25,26 The general theory of swelling assumes that the free energy of mixing and the elastic free energy in a swollen network are additive. The chemical potential difference between gel and solvent is given by the equation: 0

0

0

( μ 1 – μ 1 ) = ( μ 1 – μ 1 ) mix + ( μ 1 – μ 1 ) el where:

μ1

chemical potential of gel

μ1

the chemical potential of the solvent

0

[7.1.8]

The chemical potential is the sum of the terms of free energy of mixing and the elas0 tic free energy. At swelling equilibrium, μ 1 = μ 1 , and thus the left-hand term of the equation becomes zero. The equation [7.1.8] takes the following form: 0

0

2

( μ 1 – μ 1 ) mix = – ( μ 1 – μ 1 ) el = RT [ ln ( ( 1 – v 2 ) – v 2 – χv 2 ) ]

[7.1.9]

where: v2 n1, n2 V1, V2 R T χ

= n2V2/(n1V1 + n2V2) volume fraction of polymer moles of solvent and polymer, respectively molar volumes of solvent and polymer, respectively gas constant absolute temperature Flory-Huggins, polymer-solvent interaction parameter.

The interaction between the solvent and solid matrix depends on the strength of such intermolecular bonds as polymer-polymer, solvent-solvent, and polymer-solvent. If the interaction between these bonds is similar, the solvent will easily interact with polymer and a relatively small amount of energy will be needed to form a gel.22 The Hildebrand and Scatchard hypothesis assumes that interaction occurs between solvent and a segment of the chain which has a molar volume similar to that of solvent.22 Following this line of reasoning, the solvent and polymer differ only in potential energy and this is responsible for their interaction and for the solubility of the polymer in the solvent. If the potential energies of solvents and polymeric segments are similar they are readily miscible. In crosslinked polymers, it is assumed that the distance between crosslinks is proportional to

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7.1 Introduction to solvent transport phenomena

the molecular volume of the polymer segments. This assumption is the basis for determining molecular mass between crosslinks from results of swelling studies. The result of swelling in a liquid solvent (water) is determined by equation:23 g

∂T  g ⁄ l  -------- ∂w 1 P

 ∂μ  T  ---------1   ∂w 1 T, P = -------------------------g⁄l ΔH 1

[7.1.10]

where: T w1 g l P g μ1

thermodynamic (absolute) temperature mass fraction of solvent in the gel at saturation concentration phase symbol (for gel) symbol for liquid pressure the chemical potential of solvent in gel phase dependent on temperature g⁄l

ΔH 1

g

–1

= H 1 – H 01 is the difference between partial molar enthalpy of solvent (water) in gel and pure liquid solvent (water) in surrounding

Contrast this with the equation for water in the solid state (ice): g

∂T  g ⁄ cr  -------- ∂w 1 P

 ∂μ  T  ---------1   ∂w 1 T, P = -------------------------g ⁄ cr ΔH 1

[7.1.11]

where: cr

phase symbol for crystalline solvent (ice)

A comparison of equations [7.1.10] and [7.1.11] shows that the slope and sign of swelling curve are determined by the quang ⁄ l or cr tity ΔH 1 . Since the melting enthalpy of water is much larger than the transfer enthalpy of water, the swelling curves of gel in liquid water are very steep. The sign of the slope is determined by the heat transfer of the solvent which may be negative, positive, or zero depending on the quality of solvent. The melting enthalpy is always positive and therefore the swelling curve in the presence of crystalline solvent is flat with a positive slope. A positive slope in temperatures below zero (for ice) means that gel has to Figure 7.1.12. Swelling of crosslinked polyurethane in deswell (release water to its surrounding, or water and ice. [Adapted, by permission, from B dry out) as temperature decreases.23 Figure Hladik, S Frahn, W Borchard, Polym. Polym. Com7.1.12 illustrates this. pos., 3, No.1, 21-8 (1995).]

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For practical purposes, simple equations are used to study swelling kinetics. The degree of swelling, α, is calculated from the following equation:27 V1 – V0 α = -----------------V0

[7.1.12]

where: V1 V0

volume of swollen solid at time t=t volume of unswollen solid at time t=0

The swelling constant, K, is defined by: k α K = ----1- = -----------k2 1–α

[7.1.13]

where: k1 k2

rate constant of the swelling process rate constant of the deswelling process

This shows that the swelling process is reversible and in a dynamic equilibrium. The distance of diffusion is time-dependent: dis tan ce ∝ ( time )

n

[7.1.14]

The coefficient n is between 0.5 for Fickian diffusion and 1 for relaxation-controlled diffusion (diffusion of solvent is much faster than polymer segmental relaxation)28 This relationship is frequently taken literally29 to calculate diffusion distance from a measurement of the change of the linear dimensions of the swollen material. The following equation is used to model changes based on swelling pressure measurements: RT n 2 Π = Aϕ = – -------- [ ln ( 1 – ϕ ) + ϕ + χϕ ] v1 where:

Π A ϕ n v1 χ

[7.1.15]

osmotic pressure coefficient volume fraction of polymer in solution = 2.25 for good solvent and = 3 for Θ solvent molar volume of solvent Flory-Huggins, polymer-solvent interaction parameter

The above relationship is used to study swelling by measuring shear modulus.30 Figure 7.1.13 shows swelling kinetic curves for two solvents. Toluene has a solubility parameter of 18.2 and isooctane of 15.6. The degree to which polymers swell is determined by many factors, including the chemical structures of polymer and solvent, the molecular mass and chain flexibility of the polymer, packing density, the presence and density of crosslinks, temperature, and pressure. In the example presented in Figure 7.1.13, the solubility parameter has a strong influence on swelling kinetics.27 The effect of temperature on swelling kinetics is shown in Figure 7.1.14. Increasing temperature

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7.1 Introduction to solvent transport phenomena

Figure 7.1.13. Swelling kinetics of EVA in toluene and isooctane. [Data from H J Mencer, Z Gomzi, Eur. Polym. J., 30, 1, 33-36, (1994).]

Figure 7.1.14. Swelling kinetics of EVA in tetrahydrofuran at different temperatures. [Adapted, by permission, from H J Mencer, Z Gomzi, Eur. Polym. J., 30, 1, 33-36, (1994).]

Figure 7.1.15. Diffusion distance of 1,4-dioxane into PVC vs. time. [Adapted, by permission, from M Ercken, P Adriensens, D Vanderzande, J Gelan, Macromolecules, 28, 8541-8547, (1995).]

Figure 7.1.16. Effect of pH on the equilibrium swelling of hydrogel. [Data from M Sen, A Yakar, O Guven, Polymer, 40, No.11, 2969-74 (1999).]

increases swelling rate. During the initial stages of the swelling process, the rate of swelling grows very rapidly and then levels off towards the swelling equilibrium. In Figure 7.1.15, the diffusion distance is almost linear with time as predicted by equation [7.1.14]. The coefficient n of the equation was 0.91 meaning that the swelling process was relaxation rate controlled.

George Wypych

Figure 7.1.17. The mass uptake of TCE by PEEK vs. time. [Adapted, by permission, from B H Stuart, D R Williams, Polymer, 35, No.6, 1326-8 (1994).]

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Figure 7.1.18. The frequency of carbonyl stretching mode of PEEK vs. temperature. [Adapted, by permission, from B H Stuart, D R Williams, Polymer, 36, No.22, 4209-13 (1995).]

Figure 7.1.16 shows the relationship between hydrogel swelling and pH. Hydrogels are particularly interesting because their swelling properties are controlled by the conditions around them (e.g. pH).31-33 Because they undergo controllable volume changes, they find applications in separation processes, drug delivery systems, immobilized enzyme systems, etc. Maximum swelling is obtained at pH = 7. At this point, there is complete dissociation of the acidic groups present in the hydrogel. The behavior of hydrogel can be modeled using Brannon-Peppas equation.32 Figure 7.1.17 shows the 1,1,2,2-tetrachloroethylene, TCE, uptake by amorphous polyetheretherketone, PEEK, as a function of time.34,35 The swelling behavior of PEEK in this solvent is very unusual − the sample mass is increased by 165% which is about 3 times more than with any other solvent. In addition, the solvent uptake by PEEK results in a change in optical properties of the solution from clear to opaque. A clear solution is typical of amorphous PEEK and the opaque solution of crystalline PEEK. It was previously suggested by Fowkes and Tischler36 that polymethylmethacrylate forms weak complexes with various acid species in solution. This may also explain the unusual swelling caused by TCE. Because of the presence of C=O, C-O-C, and aromatic groups, PEEK acts as an organic base. TCE is an electron acceptor due to electron-deficient atoms in the molecule.34 This interaction may explain the strong affinity of solvent and polymer. Figure 7.1.18 illustrates the effect of crystallization. Below 250oC, the carbonyl frequency decreases. But a more rapid decrease begins below 140oC which is glass transition temperature. Above 250oC, the carbonyl frequency increases rapidly. Above the glass transition temperature there is a rapid crystallization process which continues until the polymer starts to melt at 250oC then it gradually reverts to its original amorphous structure. The presence of solvent aids in the crystallization process.

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7.1 Introduction to solvent transport phenomena

Figure 7.1.19 shows diffusion boundary between swollen and non-swollen matrix of polymethylmethacrylate affected by the presence of methanol.37 Diffusion distance is given by the following equation:37 x D = B ( ( kt + 1 )

1⁄2

– 1)

[7.1.16] where: B k t

material constant constant time

The diffusion rate is gradually slowing down with distance increase instead of following a constant rate.37 This behavior is reflected in Eq. [7.1.16]. Constants B and k change with temperature, solvent type, and polymer type. The diffusion rate also depends on polymer structure which changes under different conditions of sam37 Figure 7.1.19. Incident light micrograph of a cut sample, ple preparation. showing the diffusion boundary between swollen and 7.1.3 DRYING non-swollen matrix. [Adapted, by permission, from M Solvent removal can be accomplished by Zhu, D Vesely, Eur. Polym. J., 43, 4503-15 (2007). one of three means: deswelling, drying, or changes in the material's solubility. The deswelling process, which involves the crystallization of solvent in the surrounding gel, was discussed in the previous section. Here attention is focused on the drying process. The changes due to the material solubility are discussed in Chapter 11. Figure 7.1.1 can be discussed from a different perspective of results given in Figure 7.1.20. There are also three regions here: region 1 which has a low concentration of solid in which solvent evaporation is controlled by the energy supplied to the system, region 2 in which both the energy supplied to the system and the ability of Figure 7.1.20. Solvent concentration vs. drying time. polymer to take up the free volume vacated by solvent are important, and region 3 where the process is free volume-controlled. Regions 2 and 3 are divided by the glass transition temperature. Drying processes in region 3 and, to some extent in region 2, determine the physical properties of a dried material and the amount of residual solvent remaining in the product. A sharp transition between region 2 and 3 (at glass transition temperature) may indicate that drying process is totally homogeneous but it is not and this oversimplifies the real conditions at the end of

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the drying process. The most realistic course of events occurring close to the dryness point is presented by these four stages:38,39 • elimination of the volatile molecules not immobilized by the adsorption onto the polymer •. elimination of adsorbed molecules from the polymer in its rubbery state • evaporation-induced self-association of the polymer with progressive entrapment of adsorbed volatile molecules in the glassy microdomains (during the transition from a rubbery to a glassy state) • elimination of residual molecules entrapped in the polymer. The last two stages are discussed in Chapter 15 which deals with residual solvent. This discussion concentrates on the effect of components on the drying process and the effect of the drying process on the properties of the product. A schematic of the drying process is represented in Figure 7.1.21. The material to be dried is placed on an impermeable substrate. The material consists of solvent and a semicrystalline polymer which contains a certain initial fraction of amorphous and crystalline domains. The presence of crystalline domains complicates the proFigure 7.1.21. Schematic representation of drying a cess of drying because of the reduction in polymer slab. [Adapted, by permission, from M O Ngui, S K Mallapragada, J. Polym. Sci.: Polym. Phys. Ed., 36, diffusion rate of the solvent. Evaporation of No.15, 2771-80 (1998).] solvent causes an inward movement of material at the surface and the drying process may change the relative proportions of amorphous and crystalline domains.40 Equations for the change in thickness of the material and kinetic equations which relate composition of amorphous and crystalline domains to solvent concentration are needed to quantify the rate of drying. The thickness change of the material during drying is given by the equation: ∂v dL v 1 ------- =  D -------1-  ∂x  x = L dt

[7.1.17]

where: v1 L t D x

volume fraction of solvent thickness of slab as in Figure 7.1.21 time diffusion coefficient coordinate of thickness

The rate of change of crystalline volume fraction is given by the equation: ∂v 2c ---------= k1 v1 ∂t

[7.1.18]

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7.1 Introduction to solvent transport phenomena

Figure 7.1.22. Fraction of water remaining in PVA as a function of drying time at 23oC. [Data from M O Ngui, S K Mallapragada, J. Polym. Sci.: Polym. Phys. Ed., 36, No.15, 2771-80 (1998).]

Figure 7.1.23. Water volume fraction vs. drying time for PVA of different crystallinity. [Adapted, by permission, from M O Ngui, S K Mallapragada, J. Polym. Sci. Polym. Phys. Ed., 36, No.15, 2771-80 (1998).]

where: v2c k1

volume fraction of crystalline phase rate change of crystalline phase proportional to folding rate

The rate of change of amorphous volume fraction is given by the equation: ∂v ∂v 2a ∂ ---------= ------  D -------1- – k 1 v 1 ∂x  ∂x  ∂t

[7.1.19]

where: v2a

volume fraction of amorphous phase

The rate of the drying process is determined by the diffusion coefficient: D = D 0 [ exp ( α D v 1 ) ] ( 1 – v 2c ) ⁄ τ

[7.1.20]

where: D0 αD t

initial diffusion coefficient dependent on temperature constant which can be determined experimentally for spin echo NMR studies41 constant equal to 1 for almost all amorphous polymers ( v 2c ≤ 0.05 ) and 3 for semi-crystalline polymers

According to this equation, the coefficient of diffusion decreases as crystallinity increases because the last term decreases and τ increases. Figure 7.1.22 shows that the fraction of solvent (water) decreases gradually as drying proceeds. Once the material reaches a glassy state, the rate of drying rapidly decreases. This is the reason for two different regimes of drying. Increasing temperature increases the rate of drying process.40 Figure 7.1.23 shows that even a small change in the crystallinity of the polymer significantly affects drying rate. An increase in molecular weight has a similar effect (Figure

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Figure 7.1.24. Water volume fraction vs. drying time for PVA of different molecular weight. [Adapted, by permission, from M O Ngui, S K Mallapragada, J. Polym. Sci.: Polym. Phys. Ed., 36, No.15, 2771-80 (1998).]

Figure 7.1.25. Degree of crystallinity vs. PVA drying time at 25oC. [Adapted, by permission, from M O Ngui, S K Mallapragada, J. Polym. Sci.: Polym. Phys. Ed., 36, No.15, 2771-80 (1998).]

Figure 7.1.26. Viscosity vs. fraction of total evaporation of water from waterborne coating. [Data from S Kojima, T Moriga, Polym. Eng. Sci., 35, No.13, 1098-105 (1995).]

Figure 7.1.27. Surface tension vs. fraction of total evaporation of solvent from waterborne coating. [Data from S Kojima, T Moriga, Polym. Eng. Sci., 35, No.13, 1098-105 (1995).]

7.1.24). This effect is due to lower mobility of entangled chains of the higher molecular weight and to the fact that higher molecular weight polymers are more crystalline. Figure 7.1.25 shows that the drying time increases as the degree of polymer crystallinity increases. Increased crystallinity slows down the diffusion rate and thus the drying process.

374

7.1 Introduction to solvent transport phenomena Table 7.1.1. Experimentally determined initial evaporation rates of waterborne coating containing a variety of solvents at 5% level (evaporation at 25oC and 50% RH) Cosolvent

Figure 7.1.28. Initial evaporation rate from waterborne coating vs. relative humidity for two solvent systems. [Data from S Kojima, T Moriga, Polym. Eng. Sci., 35, No.13, 1098-105 (1995).]

Initial evaporation rate, μg cm-2 s-1

none

3.33

methyl alcohol

4.44

ethyl alcohol

3.56

n-propyl alcohol

4.00

n-butyl alcohol

3.67

isobutyl alcohol

3.67

n-amyl alcohol

3.33

n-hexyl alcohol

3.22

ethylene glycol mono-butyl ester

3.22

ethylene glycol

3.33

The physical properties of liquids, such mono-hexyl ester as viscosity (Figure 7.1.26) and surface tenbutyl carbinol 3.11 sion (Figure 7.1.27), also change during the 4.89 evaporation process. The viscosity change methyl-isobutyl ketone for this system was a linear function of the amount of solvent evaporated.42 This study on waterborne coatings showed that the use of a cosolvent (e.g., isobutanol) caused a reduction in overall viscosity. Micelles of smaller size formed in the presence of the cosolvent explain lower viscosity.42 Figure 7.1.27 shows that the surface tension of system containing a cosolvent (isobutanol) increases as the solvents evaporate whereas the surface tension of a system containing only water decreases. The increase of surface tension in the system containing cosolvent is due to the preferential evaporation of the cosolvent from the mixture.42 Table 7.1.1 shows the effect of cosolvent addition on the evaporation rate of the solvent mixture. The initial rate of evaporation of solvent depends on both relative humidity and cosolvent presence (Figure 7.1.28). As relative humidity increases the initial evaporation rate decreases. The addition of cosolvent doubles the initial evaporation rate. In convection drying, the rate of solvent evaporation depends on airflow, solvent partial pressure, and temperature. By increasing airflow or temperature, higher process rates can be achieved but the risk of skin and bubble formation is increased. As discussed above, Vrentas-Duda free-volume theory is the basis for predicting solvent diffusion, using a small number of experimental data to select process conditions. The design of a process and a dryer which uses a combination of convection heat and radiant energy is a

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Figure 7.1.29. Diffusion coefficients for two polyurethanes (A & B) dissolved in N,N-dimethylacetamide vs. temperature. [Data from G A Abraham, T R Cuadrado, International Polym. Process., 13, No.4, Dec.1998, 369-78.]

Figure 7.1.30. Effect of film thickness on evaporation rate. [Adapted, by permission from G A Abraham, T R Cuadrado, International Polym. Process., 13, No.4, Dec.1998, p.369-78.]

more complex process. Absorption of radiant energy is estimated from the Beer's Law, which, other than for the layers close to the substrate, predicts:43 Q r ( ξ ) = I 0 α exp [ – α ( βh – ξ ) ]

[7.1.21]

where: Qr ξ I0 α β h

radiant energy absorption distance from the substrate intensity of incident radiation volumetric absorption coefficient fractional thickness of the absorbing layer next to the substrate thickness

The radiant energy delivered to the material depends on the material's ability to absorb energy which may change as the solvent evaporates. Radiant energy • compensates for energy lost due to the evaporative cooling − this is most beneficial during the early stages of the process • improves the performance of the dryer when changes to either airflow rate or energy supplied are too costly to make. Radiant energy can be used to improve process control. For example, in a multilayer coating (especially wet on wet), radiant energy can be used to regulate heat flow to each layer using the differences in their radiant energy absorption and coefficients of thermal conductivity and convective heat transfer. Experimental work by Cairncross et al.43 shows how a combination dryer can be designed and regulated to increase the drying rate and eliminate bubble formation (more information on the conditions of bubble formation is included in Section 7.2 of this chapter). Shepard44 shows how drying and curing rates in

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7.1 Introduction to solvent transport phenomena

multilayer coating can be measured by dielectric analysis. Khal et al.45 give information on the prediction and practice of evaporation of solvent mixtures. Vrentas and Vrentas papers provide relevant modeling studies.46,47 These studies were initiated to explain the earlier observations by Crank48 which indicated that maintaining a slightly increased concentration of solvent in the air flowing over a drying material may actually increase the evaporation rate. Modeling of the process shows that although the diffusion of solvent cannot be increased by an increased concentration of solvent on the material's surface, an increased concentration of solvent in the air may be beneficial for the evaporation process because it prevents the formation of skin which slows down solvent diffusion. Analysis of solvent evaporation from paint and subsequent shrinkage49 and drying of small particles obtained by aerosolization50 give further insight into industrial drying processes. The two basic parameters affecting drying rate are temperature and film thickness. Figure 7.1.29 shows that the diffusion coefficient increases as temperature increases. Figure 7.1.30 shows that by reducing film thickness, drying time can be considerably reduced.51 Further information on the design and modeling of drying processes can be found in a review paper52 which analyzes drying process in multi-component systems. The residual solvent in purified paclitaxel was effectively removed using microwave-assisted drying.53 The lower the initial concentration of the solvent and the higher the microwave power, the greater the improvement in the efficiency of microwaveassisted drying.53 Solvent drying time influenced bond strength of the dental adhesive.54 When drying time was very short (2 s) bond strength was lower than with longer drying time (10 s) by air drying.54 Effect of coating thickness, the concentration of polymer, and concentration of solvent, have been studied for poly(styrene)-p-xylene and poly(styrene)-ethyl benzene coatings.55 Polymer crosslinking has increased the drying time in for both the polymer-solvent systems.55 The film thickness had a prevailing impact on drying time because the drying process is diffusion-controlled.55 The increase in the solvent evaporation time from 5 to 25 s resulted in statistically higher mean microtensile bond strength of dental adhesives.56 The residual water and/or solvent may compromise the performance of universal adhesives, which may be improved with extended evaporation times.56 The residual solvent (N-N-dimethylformamide) remained in the poly(vinylidene fluoride) matrix even after it was dried for 72 h at 60°C.57 The residual solvent promoted the nucleation of PVDF during its crystallization improving elastic moduli and reinforcing the material.57 By definition, residual solvents in pharmaceutical products provide no therapeutic benefit.58 They are present in drug substances, excipients, and drug products because they cannot be removed completely by practical manufacturing operations.58 The most toxic solvents (Class 1 − benzene, carbon tetrachloride, 1,2,-dichloroethane, and 1,1-dichloroethene) should be avoided, and the use of the least toxic solvents (Class 3, e.g, ethanol) is encouraged.58 The permitted daily exposure to a particular solvent is known for most

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solvents used in pharmaceutical production.58 The exposure limits provide the basis for establishing acceptance criteria for the residual solvents in pharmaceutical products.58 The analysis of the surfaces by atomic force microscopy and vibrational spectroscopy showed that the solvent cleaning deposited hydrocarbon residue on metal (stainless steel and copper) and soda lime glass substrates.59 The residue was formed by to trace impurities with low vapor pressures inevitably present in the bulk liquid, regardless of solvent purity, which was concentrated upon vaporization of the high vapor pressure solvent.59 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

J S Vrentas and J.L. Duda, J. Polym. Sci., Polym. Phys. Ed., 15, 403 (1977); 17, 1085, (1979). J S Vrentas, C M Vrentas, J. Polym. Sci., Part B: Polym Phys., 30 (9), 1005-11 (1992). D Arnauld, R L Laurence, Ind. Eng. Chem. Res., 31 (1), 218-28 (1992). F D Blum, S Pickup, R A Waggoner, Polym. Prep., 31 (1), 125-6 (1990). C Bouchard, B Guerrier, C Allain, A Laschitsch, A C Saby, D Johannsmann, J. Appl. Polym. Sci., 69, No.11, 2235-46 (1998). G Fleischer, J Karger, F Rittig, P Hoerner, G Riess, K Schmutzler, M Appel, Polym. Adv. Technol., 9, Nos.10-11, 700-8 (1998). C F Fong, Y Li, De Kee, J Bovenkamp, Rubber Chem. Technol., 71 (2), 285-288 (1998). J Chen, K Chen, H Zhang, W Wei, L Nie, S Yao, J. Appl. Polym. Sci., 66, No.3, 563-71 (1997). I Linossier, F Gaillard, M Romand, J F Feller, J. Appl. Polym. Sci., 66, No.13, 2465-73 (1997). L Meistermann, M Duval, B Tinland, Polym. Bull., 39, No.1, 101-8 (1997). J S Qi, C Krishnan, J A Incavo, V Jain, W L Rueter, Ind. Eng. Chem. Res., 35, No.10, 3422-30 (1996). S C George, S Thomas, Prog. Polym. Sci., 26, 985-1017, 2001. M Limam, L Tighzert, F Fricoteaux, G Bureau, Polym. Test., 24, 395-402 (2005). D Vesely, Polymer, 42, 4417-22 (2001). Y Cen, C Staudt-Bickel, R N Lichtenthaler, J. Membrane Sci., 206, 341-49 (2002). A M M Pereira, M C Lopes, J M K Timmer, J T F Keurentjes, J. Membrane Sci., 260, 174-180 (2005). J Tang, K K Sirkar, S Majumdar, J. Membrane Sci., 447, 345-54 (2013). H-K Oh, K-H Song, K-R Lee, J-M Rim, Polymer, 42, 6305-12 (2001). S Darvishmanesh, A Buekenhoudt, J Degreve, B Van der Bruggen, J. Membrane Sci., 334, 43-49 (2009). S Fryars, E Limanton, F Gauffre, L Paquin, C Lagrost, P Hapiot, J. Electroanal. Chem., in press, 2018. J James, G V Thomas, K P Pramoda, S Thomas, Polymer, 116, 76-88, 2017. Z Hrnjak-Murgic, J Jelencic, M Bravar, Angew. Makromol. Chem., 242, 85-96 (1996). B Hladik, S Frahn, W Borchard, Polym. Polym. Compos., 3, No.1, 21-8 (1995). J Frenkel, Rubber Chem. Technol., 13, 264 (1940). P J Flory, J Rehner, J. Chem. Phys., 11, 521 (1943). P J Flory, J. Chem. Phys., 18, 108 (1950). H J Mencer, Z Gomzi, Eur. Polym. J., 30, 1, 33-36, (1994). A G Webb, L D Hall, Polymer, 32 (16), 2926-38 (1991). M Ercken, P Adriensens, D Vanderzande, J Gelan, Macromolecules, 28, 8541-8547, (1995). F Horkay, A M Hecht, E Geissler, Macromolecules, 31, No.25, 8851-6 (1998). M Sen, O Guven, Polymer, 39, No.5, 1165-72 (1998). M Sen, A Yakar, O Guven, Polymer, 40, No.11, 2969-74 (1999). Y D Zaroslov, O E Philippova, A R Khokhlov, Macromolecules, 32, No.5, 1508-13 (1999). B H Stuart, D R Williams, Polymer, 35, No.6, 1326-8 (1994). B H Stuart, D R Williams, Polymer, 36, No.22, 4209-13 (1995). F M Fowkes, D O Tischler, J. Polym. Sci., Polym. Chem. Ed., 22, 547 (1984). M Zhu, D Vesely, Eur. Polym. J., 43, 4503-15 (2007). L A Errede, Macromol. Symp., 114, 73-84 (1997). L A Errede, P J Henrich, J N Schroepfer, J. Appl. Polym. Sci., 54, No.5, 649-67 (1994). M O Ngui, S K Mallapragada, J. Polym. Sci.: Polym. Phys. Ed., 36, No.15, 2771-80 (1998). N A Peppas, J C Wu, E D von Meerwall, Macromolecules, 27, 5626 (1994). S Kojima, T Moriga, Polym. Eng. Sci., 35, No.13, 1098-105 (1995). R A Cairncross, S Jeyadev, R F Dunham, K Evans, L F Francis, L Scriven, J. Appl. Polym. Sci., 58, No.8,

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7.1 Introduction to solvent transport phenomena 1279-90 (1995). D C Shepard, J. Coat. Technol., 68, No.857, 99-102 (1996). L Khal, E Juergens, J Petzoldt, M Sonntag, Urethanes Technology, 14, No.3, 23-6 (1997). J S Vrentas, C M Vrentas, J. Polym. Sci., Part B: Polym Phys., 30 (9), 1005-11 (1992). J S Vrentas, C M Vrentas, J. Appl. Polym. Sci., 60, No.7, 1049-55 (1996). J Crank, Proc. Phys. Soc., 63, 484 (1950). L Ion, J M Vergnaud, Polym. Testing, 14, No.5, 479-87 (1995). S Norasetthekul, A M Gadalla, H J Ploehn, J. Appl. Polym. Sci., 58, No.11, 2101-10 (1995). G A Abraham, T R Cuadrado, International Polym. Process., 13, No.4, Dec.1998, 369-78. Z Pakowski, Adv. Drying, 5, 145-202 (1992). J-Y Lee, J-H Kim, Process Biochem., 48, 545-50, 2013. A Sadr, Y Shimada, J Tagami, Dental mater., 23, 114-19, 2007. A Pathania, J Sharma, R K Arya, S Ahuja, Prog. Org. Coat., 114, 78-89, 2018. I V Luque-Martinez, J Perdigão, M A Muñoz, A Sezinando, A Reis, A D Loguercio, Dental Mater., 30, 10, 1126-35, 2014. K Ke, X-F Wei, R-Y Bao, W Yang, Y Luo, B-H Xie, M-B Yang, Polym. Testing, 34, 78-84, 2014. J V McArdle, Residual solvents in Specification of Drug Substances and Products, Elsevier, 2014, pp. 143-54. A J Barthel, J Luo, K S Hwang, J-Y Lee, S H Kim, Wear, 350-351, 21-6, 2016.

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7.2 BUBBLES DYNAMICS AND BOILING OF POLYMERIC SOLUTIONS Semyon Levitsky* and Zinoviy Shulman** *Shamoon College of Engineering, Israel ** A.V. Luikov Heat and Mass Transfer Institute, Belarus

7.2.1 RHEOLOGY OF POLYMERIC SOLUTIONS AND BUBBLE DYNAMICS 7.2.1.1 Rheological characterization of solutions of polymers Solutions of polymers exhibit a number of unusual effects in flows.1 Complex mechanical behavior of such liquids is governed by qualitatively different response of the medium to applied forces than low-molecular fluids. In hydrodynamics of polymers, this response is described by rheological equation that relates the stress tensor, σ, to the velocity field. The latter is described by the rate-of-strain tensor, e 1 ∂v ∂v e ij = ---  -------i + -------j 2  ∂x j ∂x i where:

νi xi

[7.2.1]

components of the velocity vector, ν Cartesian coordinates (i, j = 1, 2, 3)

The tensors σ and e include isotropic, p, ekk and deviatoric, τ, s contributions: 1 1 σ = – pI + τ, p = – --- σ kk, e = --- e kk I + s, e kk = ∇ ⋅ ν 3 3

[7.2.2]

where: I ∇

unit tensor Hamiltonian operator

For incompressible fluid ∇ ⋅ ν = 0, e = s and rheological equation can be formulated in the form of the τ-dependence from e. Compressibility of the liquid must be accounted for in fast dynamic processes such as acoustic wave propagation, etc. For compressible medium the dependence of pressure, p, for the density, ρ, and temperature, T, should be specified by a certain equation p = p(ρ, T), that is called usually as equation of state. The simplest rheological equation corresponds to incompressible viscous Newtonian liquid and has the form τ = 2η 0 e where:

η0

[7.2.3]

viscosity coefficient

Generalizations of the Newton's flow law [7.2.3] for polymeric liquids are aimed to describe in more or less details the features of their rheological behavior. The most important among these features is the ability to accumulate elastic deformation during flow and thus to exhibit the memory effects. At first we restrict ourselves to the case of small deformation rates to discuss the basic principles of the general linear theory of viscoelasticity

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7.2 Bubbles dynamics and boiling of polymeric solutions

based upon thermodynamics of materials with memory.2 The central idea of the theory is the postulate that instantaneous stresses in a medium depend on the deformation history. This suggestion leads to integral relationship between the stress and rate-of-strain tensors t

τ ij = 2

 G1 ( t – t' )sij ( t' ) dt' –∞ t



σ kk = – 3p 0 + 3

t

G 2 ( t – t' )e kk ( t' ) dt' – 3

–∞

where:

θ p0 G1, G2, G3

∂θ

- dt'  G 3 ( t – t' ) ----∂t'

[7.2.4]

–∞

= T - T0 deviation of the temperature from its equilibrium value equilibrium pressure relaxation functions

The relaxation functions G1(t) and G2(t) satisfy restrictions, following from the entropy production inequality ∂G ∂G ---------1 ≤ 0, ---------2 ≤ 0 ∂t ∂t

[7.2.5]

Additional restriction on G1,2(t) is imposed by the decaying memory principle3 that has clear physical meaning: the state of a medium at the present moment of time is more dependent on the stresses arising at t = t2 than on stresses arising at t = t1 if t1 < t2. This 2 principle implies that the inequality ( ∂G 1, 2 ⁄ ∂t ) ≥ 0 must be satisfied. The necessary condition for the viscoelastic material to be a liquid means lim G 1 ( t ) = 0

[7.2.6]

t→∞

Unlike G1(t), the functions G2(t) and G3(t) contain non-zero equilibrium components, such as lim G 2 ( t ) = G 20, lim G 3 ( t ) = G 30

t→∞

t→∞

[7.2.7]

From the physical point of view, this difference between G1 and G2,3 owes to the fact that liquid possesses a finite equilibrium bulk elasticity. Spectral representations of relaxation functions with account to [7.2.5]-[7.2.7], have the form (G10 = 0) ∞

G i ( t ) = G i0 +  F i ( λ ) exp ( – t ⁄ λ ) dλ 0

where:

λ Fi(λ)

relaxation time spectrum of relaxation times (i = 1, 2, 3)

[7.2.8]

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381

Equations [7.2.8] defines the functions Gi(t) for continuous distribution of relaxation times. For a discrete spectrum, containing ni relaxation times, the distribution function takes the form ni

 Gik δ ( λ – λik )

Fi ( λ ) =

[7.2.9]

k=1

where: partial modules, corresponding to ik Dirac’s delta function

Gik δ ( λ – λ ik )

In this case the integration over the spectrum in Equation [7.2.8] is replaced by summation over all relaxation times, λik. For polymeric solutions, as distinct to melts, it is convenient to introduce in the right-hand sides of equations [7.2.4] additional terms, 2η s s ij and 3ρ 0 η v e kk , which represent contributions of shear, ηs, and bulk, ηv, viscosities of the solvent. The result has the form t ∞

τ ij = 2

t – t'

- s ( t' ) dλ dt' + 2η s s ij   F1 ( λ ) exp  – --------λ  ij

[7.2.10]

–∞ 0

p = p 0 – G 20

t

t ∞

–∞

–∞ 0

t – t'

- e ( t' ) dλ dt' +  ekk ( t' ) dt' –   F2 ( λ ) exp  – --------λ  kk

t ∞

t – t' ∂θ ( t' )

- -------------- dλ dt' – ρ 0 η v e kk, p   F3 ( λ ) exp  – --------λ  ∂t'

+ G 30 θ +

= – 1 ⁄ 3σ kk

[7.2.11]

–∞ 0

Equilibrium values of bulk and shear viscosity, ηb and ηp, can be expressed in terms of the relaxation spectra, F1 and F2, as:1 ∞

ηp – ηs =

 λF1 ( λ ) dλ, ηb – ηv 0

=

∞

0 λF2 ( λ ) dλ

[7.2.12]

In the special case, when relaxation spectrum, F1(λ), contains only one relaxation time, λ11, equation [7.2.10] yields t

τ ij = 2G 11

t – t'

- s ( t' ) dt' + 2η s s ij, G 11  exp  – --------λ 11  ij

= ( η p – η s ) ⁄ λ 11

[7.2.13]

–∞

At ηs = 0 the integral equation [7.2.13] is equivalent to the linear differential Maxwell equation

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7.2 Bubbles dynamics and boiling of polymeric solutions

· τ ij + λ 11 τ ij = 2η p s ij

[7.2.14]

Setting ηs = λ2η0/λ1, λ1 = λ11, ηp = η0, where λ2 is the retardation time, one can rearrange equation [7.2.14] to receive the linear Oldroyd equation3 · τ ij + λ 1 τ ij = 2η 0 ( s ij + λ 2 s·ij ), λ 1 ≥ λ 2

[7.2.15]

Thus, the Oldroyd model represents a special case of the general hereditary model [7.2.10] with appropriate choice of parameters. Usually the maximum relaxation time in the spectrum is taken for λ1 in equation [7.2.15] and therefore it can be used for quantitative description and estimate of relaxation effects in non-steady flows of polymeric systems. Equation [7.2.11], written for quasi-equilibrium process, helps to clarify the meaning of the modules G20 and G30. In this case it gives –1

p = p 0 + G 20 ρ 0 ( ρ – ρ 0 ) + G 30 θ

[7.2.16]

Thermodynamic equation of state for non-relaxing liquid at small deviations from equilibrium can be written as follows ∂p ∂p p = p 0 +  ------ ( ρ – ρ 0 ) +  ------ θ  ∂ρ T = T 0  ∂T ρ = ρ0

[7.2.17]

The thermal expansion coefficient, α, and the isothermal bulk modulus, Kis, are defined as4 ∂ρ ∂p α = – ρ 0  ------ , K = ρ 0  ------  ∂T ρ = ρ 0 is  ∂ρ T = T 0

[7.2.18]

Therefore, equation [7.2.17] can be rewritten in the form –1

p = p 0 + K is ρ 0 ( ρ – ρ 0 ) + αK is θ

[7.2.19]

From [7.2.16] and [7.2.18] it follows G20 = Kis, G30 = Kis. In rheology of polymers, complex dynamic modules, Gk*, k = 1,2,3, are of special importance. They are introduced to describe periodic deformations with frequency, ω, and defined according to: ∞ * Gk

=

F k ( λ ) ( ωλ ) ( ωλ + i )dλ

 -----------------------------------------------------2 0

1 + ( ωλ )

[7.2.20]

Equations of motion of the liquid follow from momentum and mass conservation laws. In the absence of volume forces they mean: dv ρ ------ = ∇ ⋅ σ dt

[7.2.21]

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dρ ------ + ρ∇ ⋅ v = 0 dt

[7.2.22]

For polymeric solution, the stress tensor, σ, is defined according to [7.2.10], [7.2.11]. To close the system, it is necessary to add the energy conservation law to equations [7.2.21], [7.2.22]. In case of liquid with memory it has the form2 ∂ k∇ θ – T 0 ---∂t

t

2

 –∞

∂ G 3 ( t – t' )e kk ( t' ) dt' = T 0 ---∂t

t

∂θ

- dt'  G4 ( t – t' ) ----∂t'

–∞

∞

t – t' –1 G 4 ( t – t' ) = G 40 –  F 4 ( λ ) exp  – ---------- dλ, G 40 = ρ 0 c v T 0  λ 

[7.2.23]

0

where: k cv

heat conductivity of the liquid equilibrium isochoric specific heat capacity

Equations [7.2.10], [7.2.11], [7.2.21]-[7.2.23] constitute complete set of equations for linear thermohydrodynamics of polymeric solutions. The non-linear generalization of equation [7.2.4] is not single. According to the Kohlemann-Noll theory for a “simple” liquid,5 a general nonlinear rheological equation for a compressible material with memory may be represented in terms of the tensor functional that defines the relationship between the stress tensor, σ, and the deformation history. The form of this functional determines specific non-linear rheological model for a hereditary medium. Such models are numerous, the basic part of encountered ones can be found elsewhere1,6-8 It is important, nevertheless, that, in most cases, the integral rheological relationships of such a type for an incompressible liquid may be brought to the set of the first-order differential equations.9 Important special case of this model represents the generalized Maxwell's model that includes the most general time-derivative of the symmetrical tensor τ =

τ

(k)

,τ

(k)

+ λ k F abc τ

(k)

= 2η k e

k

Dτ F abc τ = ------- + a ( τ ⋅ e + e ⋅ τ ) + bItr ( τ ⋅ e ) + centr ( τ ) Dt T 1 Dτ ------- = dτ ----- – w ⋅ τ + τ ⋅ w, w = --- ( ∇v – ∇v ) 2 Dt dt

where: D/Dt d/dt tr w T ∇v λk , η k

Jaumann's derivative1 ordinary total derivative trace of the tensor, tr τ = τkk vorticity tensor transpose of the tensor ∇v parameters, corresponding to the Maxwell-type element with the number k

[7.2.24]

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7.2 Bubbles dynamics and boiling of polymeric solutions

At a = −1, b = c = 0 equations [7.2.24] correspond to the Maxwell liquid with a discrete spectrum of relaxation times and the upper convective time derivative.3 For solution of polymer in a pure viscous liquid, it is convenient to represent this model in such a form that the solvent contribution into total stress tensor will be explicit: τ =

τ

(k)

+ 2η s e, τ

k

(k)

(k)

Dτ (k) (k) + λ k ------------- – ( τ ⋅ e + e ⋅ τ ) = 2η k e Dt

[7.2.25]

To select a particular nonlinear rheological model for hydrodynamic description of the fluid flow, it is necessary to account for kinematic type of the latter.7 For example, the radial flows arising from the bubble growth, collapse or pulsations in liquid belong to the elongational type.3 Therefore, the agreement between the experimental and theoretically predicted dependencies of elongational viscosity on the elongational deformation rate should be a basic guideline in choosing the model. According to data10-13 the features of elongational viscosity in a number of cases can be described by equations [7.2.25]. More simple version of equation [7.2.25] includes single relaxation time and additional parameter 1 ⁄ 2 ≤ α ≤ 1 , controlling the input of nonlinear terms:7 τ = τ τ

(2)

(1)

(2)

+τ ,τ

(1)

= 2η ( 1 – β )e

(1)

Dτ (1) (1) + λ ------------- – α ( τ ⋅ e + e ⋅ τ ) = 2ηβe Dt [7.2.26]

Parameter β governs the contribution of the Maxwell element to effective viscosity, η, (Newtonian viscosity of the solution). Equation [7.2.26] is similar to the Oldroyd-type equation [7.2.15] with the only difference that in the former the upper convective derivative is used to account for nonlinear effects instead of partial derivative, ∂ ⁄ ∂t . Phenomenological parameters appearing in the theoretical models can be found from appropriate rheological experiments.6 Certain parameters, the most important being relaxation times and viscosities, can be estimated from molecular theories. According to molecular theory, each relaxation time λk is relative to mobility of some structural elements of a polymer. Therefore, the system as a whole is characterized by the spectrum of relaxation times. Relaxation phenomena, observed at a macroscopic level, owe their origin to the fact that response of macromolecules and macromolecular blocks to different-inrate external actions is described by different parts of their relaxation spectrum. This response is significantly affected by the temperature − its increase “triggers” the motion of more and more complex elements of the macromolecular hierarchy (groups of atoms, free segments, coupled segments, etc). The most studied relaxation processes from the point of view of molecular theories are those governing relaxation function, G1(t), in equation [7.2.4]. According to the Rouse theory,1 a macromolecule is modeled by a bead-spring chain. The beads are the centers of hydrodynamic interaction of a molecule with a solvent while the springs model elastic linkage between the beads. The polymer macromolecule is subdivided into a number of equal segments (submolecules or subchains) within which the equilibrium is supposed to

Semyon Levitsky* and Zinoviy Shulman**

385

be achieved; thus the model does not permit to describe small-scale motions that are smaller in size than the statistical segment. Maximal relaxation time in a spectrum is expressed in terms of macroscopic parameters of the system, which can be easily measured: 6 ( η p – η s )M λ 11 = -----------------------------2 π cR G T

[7.2.27]

where: M c RG

molecular mass of the polymer concentration of polymer in solution universal gas constant

The other relaxation times are defined as λ1k = λ11/k2. In Rouse theory all the modules G1k are assumed to be the same and equal to cRGT/M. In the Kirkwood-Riseman-Zimm (KRZ) model, unlike Rouse theory, the hydrodynamic interaction between the segments of a macromolecular chain is accounted for. In the limiting case of a tight macromolecular globe, the KRZ theory gives the expression for λ11 that is similar to [7.2.27]: 0.422 ( η p – η s )M λ = ----------------------------------------cR G T

[7.2.28]

The differences between other relaxation times in both spectra are more essential: the distribution, predicted by the KRZ model, is much narrower than that predicted by the Rouse theory. The KRZ and Rouse models were subjected to numerous experimental tests. A reasonably good agreement between the theoretical predictions and experimental data was demonstrated for a variety of dilute polymeric solutions.14 Further advances in the molecular-kinetic approach to description of relaxation processes in polymeric systems have brought about more sophisticated models.15,16 They improved the classical results by taking into account additional factors and/or considering diverse frequency, temperature, and concentration ranges, etc. For the aims of computer simulation of the polymeric liquid dynamics in hydrodynamic problems, either rather simple approximations of the spectrum, F1(λ), or the model of subchains are usually used. Spriggs law17 is the most used approximation z

λ 1k = λ 11 ⁄ k , z ≥ 2

[7.2.29]

The molecular theory predicts strong temperature dependence of the relaxation characteristics of polymeric systems that is described by the time-temperature superposition (TTS) principle.18 This principle is based on numerous experimental data and states that with the change in temperature the relaxation spectrum as a whole shifts in a self-similar manner along t axis. Therefore, dynamic functions corresponding to different temperatures are similar to each other in shape but are shifted along the frequency axis by the value aT; the latter is named the temperature-shift factor. With ωaT for an argument it

386

7.2 Bubbles dynamics and boiling of polymeric solutions

becomes possible to plot temperature-invariant curves Re{G1*(ωaT)} and Im{G1*(ωaT)}. The temperature dependence of aT is defined by the formula ρ ( T 0 )T 0 ( η p ( T ) – η s ( T ) ) a T = -----------------------------------------------------------ρ ( T )T ( η p ( T 0 ) – η s ( T 0 ) )

[7.2.30]

The dependence of viscosity from the temperature can be described by the activation theory19 –1

η p = η p0 exp [ E p ( R G T 0 ) ( T 0 ⁄ T – 1 ) ] –1

η s = η s0 exp [ E s ( R G T 0 ) ( T 0 ⁄ T – 1 ) ]

[7.2.31]

where: Ep, Es

activation energies for the solution and solvent, respectively

The Es value is usually about 10 to 20 kJ/mol. For low-concentrated solutions of polymers with moderate molecular masses, the difference between this two activation energies, ΔE = Ep − Es, does not exceed usually 10 kJ/mol.18,20 For low-concentrated solutions of certain polymers in thermodynamically bad solvents negative ΔE values were reported.20 The Newtonian viscosity of solution related to the polymer concentration can be evaluated for example, using Martin equation18 η p ⁄ η s = 1 + c˜ exp ( k M c˜ ), c˜ = c [ η ] where:

c˜ [η]

[7.2.32]

reduced concentration of polymer in the solution intrinsic viscosity

Martin equation is usually valid in the range of reduced concentrations, c˜ ≤ 10 . For evaluation of [η], the Mark-Houwink relationship21 is recommended [η] = KMa

[7.2.33]

where K and a are constants for a given polymer-solvent pair at a given temperature over a certain range of the molecular mass variation. The parameter a (the Mark-Houwink exponent) lies in the range 0.5 to 0.6 for solutions of flexible chain polymers in thermodynamically bad solvents and in the range 0.7-0.8 for good solvents. For the former ones the –2 constant K ≈ 10 (if the intrinsic viscosity [η] is measured in cm3/g), while for the latter –3 K ≈ 10 . Thus, the spectral functions, F1(λ), are comprehensively studied both experimentally and theoretically. The behavior of relaxation functions, G2(t) and G3(t), is still much less known. The properties of the function, G2(t), were mainly studied in experiments with longitudinal ultrasound waves.22-24 It has been found that relaxation mechanisms manifested in shear and bulk deformations are of a similar nature. In particular, polymeric solutions are characterized by close values of the temperature-shift factors and similar relaxation behavior of both shear and bulk viscosity. The data on the function, F3(λ), indicate that

Semyon Levitsky* and Zinoviy Shulman**

387

relaxation behavior of isotropic deformation at thermal expansion can be neglected at temperatures well above the glass-transition temperature.22 7.2.1.2 Dynamic interaction of bubbles with polymeric liquid Behavior of bubbles in liquid at varying external pressure or temperature is governed by cooperative action of a number of physical mechanisms, which are briefly discussed below. Sufficiently small bubbles execute radial motions (growth, collapse, pulsations) retaining their spherical shape and exchanging heat, mass and momentum with the environment. Heat transfer between phases at free oscillations of gas bubbles is caused by gas heating during compression and its cooling when expanding. Due to difference in thermal resistance of liquid and gas, the total heat flux from gas to liquid is positive for the oscillation period. This unbalanced heat exchange is the source of so-called heat dissipation. The magnitude of the latter depends on the relation between the natural time of the bubble (the Rayleigh time) t0 = R0(ρf0/pf0)1/2, governed by the liquid inertia, and the time of temperature leveling in gas (characteristic time of heat transfer in a gas phase), tT = R02/ag, that is from the thermal Peclet number, PeT = tT/t0, where: R ag kg cgp 0 f g

radius of the bubble thermal diffusivity of gas, ag = kg/(pg0cgp) heat conductivity of gas specific heat capacity of gas at constant pressure index, referring to equilibrium state index, referring to liquid index, referring to gas

In the limiting cases, PeT >>1 and PeT 1 and ϖ = ωt0 with being the non-dimensional frequency. At thermodynamic conditions, close to normal ones, the equilibrium vapor content of the bubble can be neglected, but it grows with temperature (or pressure reduction). In the vapor presence, the pressure and/or temperature variations inside the oscillating bubble cause evaporation-condensation processes that are accompanied by the heat exchange.25-27 In polymeric solutions, transition from liquid to vapor phase and conversely is possible only for a low-molecular solvent. The transport of the latter to the bubble-liquid interface from the bulk is controlled by the diffusion rate. In general case the equilibrium vapor pressure at the free surface of a polymeric solution is lower than that for a pure solvent. If a bubble contains a vapor-gas mixture, then the vapor supply to the interface from the bubble interior is controlled by diffusion rate in the vapor-gas phase. The concentration inhomogeneity within the bubble must be accounted for if tDg > t0 or PeDg >1. Fast motions of a bubble surface produce sound waves. Small (but non-zero) compressibility of the liquid is responsible for a finite velocity of acoustic signals propagation and leads to appearance of additional kind of the energy losses, called acoustic dissipation. When the bubble oscillates in a sound field, the acoustic losses entail an additional phase shift between the pressure in the incident wave and the interface motion. Since the bubbles

388

7.2 Bubbles dynamics and boiling of polymeric solutions

are much more compressible than the surrounding liquid, the monopole sound scattering makes a major contribution to acoustic dissipation. The action of an incident wave on a bubble may be considered as spherically-symmetric for sound wavelengths in the liquid lf>>R0. When the spherical bubble with radius R0 is at rest in the liquid at ambient pressure, p, the internal pressure pin differs from pf0 by the value of capillary pressure, that is pin = pf0 + 2σ/R0 where:

σ

[7.2.34]

surface tension coefficient

If the system temperature is below the boiling point at the given pressure, pf0, the thermodynamic equilibrium of bubble in a liquid is possible only with a certain amount of inert gas inside the bubble. The pressure in vapor-gas mixture follows the Dalton law, which suggests that both the solvent vapor and the gas are perfect gases: pin = pg + pv = (ρgBg + ρvBv)Tm = ρmBmTm, ρm = ρg + ρv

[7.2.35]

Bm = (1 − k0)Bg + k0Bv, Bg,v = RG/μg,v where: k0 μg,v v

equilibrium concentration of vapor inside the bubble molar masses of gas and solvent vapor index, referring to vapor

From [7.2.34], [7.2.35] follows the relation for k0: k0 =

1 + B v B g [ ( 1 + 2σ ) ⁄ p v0 – 1 ] , p v0 = p v0 ⁄ p f0, σ = σ ⁄ ( p v0 R 0 ) [7.2.36]

The equilibrium temperature enters equation [7.2.36] via the dependence of the saturated vapor pressure pv0 from T0. Figure 7.2.1 illustrates the relation [7.2.36] for air-vapor bubbles in toluene.28 The curves 1-3 correspond to temperatures T0 = 363, 378, 383.7K (the latter value is equal to the saturation temperature Ts for toluene at pf0 = 105 Pa). It follows from the calculated data that the vapor content dependence on Figure 7.2.1. Dependence of the vapor content of airthe bubble radius is manifested only for vapor bubble in toluene from radius at different temminor bubbles as a result of capillary peratures. [Adapted, by permission from S.P. Levitsky, forces. The effect vanishes for R0 >> 10 and Z.P. Shulman, Dynamics and heat and mass transfer of bubbles in polymeric liquids, Nauka i mkm. For T0 > ηs are presented on the Figure 7.2.3, where: R* τ τ*rr 0

θ1 Q* kg Δpf* h(t)

dimensionless radius of the bubble, R* = R/R0 dimensionless time, τ = t/t0 dimensionless radial component of the extra-stress tensor at the interface, τ*rr = τrr(R, t)/pf0 0 dimensionless temperature at the center of the bubble, θ 1 = Tg(0, t)/T0 dimensionless heat, transferred to liquid from the gas phase in a time, Q* = Q/(R0T0kgt0) heat conductivity of gas dimensionless pressure change in the liquid at initial moment of time, p *f ( ∞ ) = 1 + Δp *f h ( t ), Δp *f = Δp f ⁄ p f0 unit step function

Calculations have been done for the rheological model [7.2.25] with 20 relaxation elements in the spectrum, distributed according to the law [7.2.29] with z = 2. To illustrate the contribution of rheological non-linearity in equation [7.2.25] the numerical coefficient α (α = 1 or 0) was introduced in the term with λk, containing material derivative. The value α = 1 corresponds to non-linear model [7.2.25], while at α = 0, the equation [7.2.25] is equivalent to the linear hereditary model [7.2.10] with a discrete spectrum. Other parameters of the system were chosen as follows: ηp = 2 Pa ⋅ s , ηs = 10-2 Pa ⋅ s , λ1 = 10-5 s, R0 = 50 mkm, Δp *f = 10, pf0 = 105 Pa, ρf0 = 103 kg/m3, T0 = 293 K, σ = 0.05 N/m. Thermodynamic parameters of air were accepted according to the standard data,70 the heat transfer between phases was described within homobaric scheme71 (pressure in the bubble is a function of t only, that is uniform within the volume, while the density and temperature are changed with r and t according to the conservation laws). For the curve 1 ηp = ηs = 2 Pa ⋅ s (pure viscous liquid with Newtonian viscosity of the solution), for curve 2, α=1, Figure 7.2.3. Heat transfer and rheodynamics at non-linear for curve 3, α = 0, that is, the latter two oscillations of a bubble in polymeric liquid. [Adapted, by graphs correspond to viscoelastic solution permission, from S.P. Levitsky, and Z.P. Shulman, with and without account for the rheologDynamics and heat and mass transfer of bubbles in polymeric liquids, Nauka i Tekhnika, Minsk, 1990.] ical non-linearity, respectively.

Semyon Levitsky* and Zinoviy Shulman**

393

It follows from Figure 7.2.3 that relaxation properties of liquid are responsible for amplification of the bubble pulsations and, as a result, they change the heat transfer between phases. Note that examples, given in Figure 7.2.3 show that the characteristic time of the pulsation damping is less than characteristic time of the temperature leveling in gas, tT (for instance, the time moment τ = 2.4 corresponds to t ⁄ t T ≈ 0.1 ). Therefore, after completion of oscillations the temperature in the center of a bubble is reasonably high, and the R* value exceeds the new isothermal equilibrium radius (R1* = 0.453). The manifestation of rheological non-linearity leads to a marked decrease in deviations of the bubble radius from the initial value at the corresponding instants of time. The explanation follows from stress dynamics analysis in liquid at the interface. At the initial stage, the relaxation of stresses in the liquid slows down the rise in the τ*rr value in comparison with similar Newtonian fluid. This leads to acceleration of the cavity compression. Since the stresses are small during this time interval, the rheological non-linearity has only a minor effect on the process. Further on, however, this effect becomes stronger which results in a considerable increase of normal stresses as compared to those predicted by the linear theory. It leads to deceleration of the cavity compression and, as a result, to a decrease both in the maximal temperature of gas in a bubble and in the integral heat loss. More detail information about rheological features in gas bubble dynamics in polymeric solutions can be obtained using linear approach to the same problem that is valid for small pressure variations in the liquid. The equation describing gas bubble dynamics in a liquid with rheological equation [7.2.10] follows from [7.2.41], [7.2.10] and has the form72 ·· + 3 ⁄ 2R· 2 ) = p ( R ⁄ R ) 3γ – p ( ∞ ) – 2σR – 1 – 4η R ⁄ R· – ρ f0 ( RR g0 0 f s ∞

t

  t – t' –1 − 4  F 1 ( λ )   exp  – ---------- R· ( t' )R ( t' ) dt' dλ  λ  0  0

[7.2.42]

Here it is assumed that gas in the bubble follows polytropic process with exponent γ. This equation was solved in linear approximation38 by operational method with aim to analyze small amplitude, natural oscillations of the constant mass bubble in relaxing liquid. It was taken R = R0 + ΔR, ΔR/R0 > 1 by increasing the superheat because of smallness of the corresponding Sn numbers. 7.2.3 BOILING OF MACROMOLECULAR LIQUIDS Experimental investigations of heat transfer at boiling of polymeric liquids cover highly diluted (c = 15 to 500 ppm), low-concentrated (c ~ 1%), and concentrated solutions

404

7.2 Bubbles dynamics and boiling of polymeric solutions

(c>10%). Surveys of the relevant studies, which have been published until 2006, can be found elsewhere.72,148,149 Later contributions, including studies devoted to pool boiling enhancement in nanofluids were reviewed.150,151 The received data represent diversity of physical mechanisms that reveal themselves in boiling processes. The relative contribution of different physical factors can vary significantly with changes in concentration, temperature, external conditions, etc., even for polymers of the same type and approximately equal molecular mass. For dilute solutions this is clearly demonstrated by the experimentally detected both intensification of heat transfer at nucleate boiling and the opposite effect, viz. a decrease in the heat removal rate in comparison with a pure solvent. Macroscopic effects at boiling are associated with changes in the intrinsic characteristics of the process152 (e.g., bubble shape and sizes, nucleation frequency, etc.). Let discuss the existing experimental data in more details. One of the first researches on the effect of water-soluble polymeric additives on boiling was reported elsewhere.153 For a plane heating element a significant increase in heat flux at fixed superheat, ΔT = 10 − 35 K, was found in aqueous solutions of PAA Separan NP10 (M = 106), NP20 (M = 2x106), and HEC (M ~ 7x104 to about 105) at concentrations of 65 to 500 ppm (Figure 7.2.13). The experiments were performed at atmospheric pressure; the viscosity of the solutions did not exceed 3.57x10-3 Pa ⋅ s . The following specific features of boiling of polymer solution were revealed by visual observations: (i) reduction in the departure diameter of bubbles, (ii) more uniform bubble-size distribution, (iii) decrease in the tendency to coalescence between bubbles. The addition of HEC led to faster covering of the heating surface by bubbles during the initial period of boiling and bubbles were smaller in size than in water and aqueous solutions of PAA. Non-monotonous change in the heat transfer coefficient, α, with increasing the concentration of PIB Vistanex L80 (M = 7.2x105) or L100 (M = 1.4x106) in boiling cyclohexane has been reported.154 The results were received in a setup similar to that described earlier.153 It was found that the value of α increases with c in the range 22 < c < 300 ppm and decreases in the range 300 < c < 5150 ppm.

Figure 7.2.13. Effect of the HEC additives on the boiling curve. 1 − pure water; 2, 3 and 4 − HEC solution with c = 62.5, 125 and 250 ppm, correspondingly. [Adapted, by permission, from P. Kotchaphakdee, and M.C. Williams, Int. J. Heat Mass Transfer, 13, 835, 1970.]

Figure 7.2.14. The relation between the relative heat transfer coefficient for boiling PIB solutions in cyclohexane and the Newtonian viscosity of the solutions measured at T = 298 K. ΔT = 16.67 K; • − PIB Vistanex L-100 in cyclohexane, o − PIB Vistanex L-80 in cyclohexane, x − pure cyclohexane. [Adapted, by permission, from H.J. Gannett, and M.C. Williams, Int. J. Heat Mass Transfer, 14, 1001, 1971.]

Semyon Levitsky* and Zinoviy Shulman**

Figure 7.2.15. The average bubble detachment diameter in boiling dilute aqueous solutions of PEO.118 ΔT = 15 K. For curves 1-3 the flow velocity v = 0.5x10-2, and 10-1 m/s, respectively. [Adapted, by permission, from S.P. Levitsky and Z.P. Shulman, Bubbles in polymeric liquids, Technomic Publishing Co., Lancaster, 1995.]

405

Figure 7.2.16. Heat transfer coefficient for nucleate pool boiling of PEO aqueous solutions. (pf0 = 9.8x103 Pa). Curve 1 corresponds to pure water, for curves 2-7 c = 0.01, 0.02, 0.04, 0.08, 0.16 and 1.28%, respectively. [Adapted, by permission, from S.P. Levitsky, and Z.P. Shulman, Bubbles in polymeric liquids, Technomic Publishing Co., Lancaster, 1995.]

Viscosity of the solution, corresponding to αmax value, according to the data80 only slightly exceeds that of the solvent (Figure 7.2.14). Within the entire range of concentrations at supercritical (with respect to pure solvent) superheats, the film boiling regime did not appear up to the maximum attainable value ΔT ~ 60 K. The growth of polymer concentration in the region of “delayed” nucleate boiling led to a considerable decrease in heat transfer. The findings153,154 were confirmed in studies of the nucleate boiling of aqueous solutions of HEC Natrosol 250HR (M = 2x105), 250GR (M = 7x104), and PEO (M ~ (24)x106) at forced convection of the liquid in a tube.155 A decrease in the size of bubbles in the solution and reduction of coalescence intensity were recognized. Similar results were presented also in a study,82 where the increase in heat transfer at boiling of aqueous solutions of PEO WSR-301(M = 2x106) and PAA Separan AP-30 (15 ppm < c < 150 ppm) on the surface of a conical heater was observed. In aqueous solutions of PAA with c > 60 ppm the α value began to decrease. With an increase in c the detachment diameter of bubbles decreased (Figure 7.2.15), the nucleation frequency increased, and the tendency to coalescence was suppressed. Essential increase (up to ~ 200%) in heat transfer coefficient at nucleate pool boiling of water solutions of HEC with concentration up to 500 ppm on a flat surface at subatmospheric pressures was reported elsewhere.156 It was concluded that heat transfer enhancement is a function of HEC concentration, operating temperature and pressure; smaller bubbles and faster vapor nuclei generation were recognized. Boiling of PEO solutions with c = 0.002 to 1.28% at atmospheric and sub-atmospheric pressures was examined158 for subcoolings in the range 0 to 80 K. It was demonstrated that at saturated boiling the dependence of the heat transfer coefficient α on the polymer concentration is non-monotonous: as c grows, α first increases, attaining the maximal value at c ≈ 0.04%, whereas at c = 1.28% the value of α is smaller than in water (α < αs) (Figure 7.2.10). With a decrease in pressure the effect of polymeric additives weakens and for solution with greatest PEO concentration (in the investigated range)

406

7.2 Bubbles dynamics and boiling of polymeric solutions

Figure 7.2.17. Boiling curves for aqueous solutions of PAA Separan AP-30. (a) experimental data; for curves 1-6 ηr = 1.00, 1.01, 1.04, 1.08, 1.16 and 1.32, correspondingly; (b) calculations made with the use of the Rohsenow pool boiling correlation; for curves 1-5 ηr = 1.00, 1.01, 1.04, 1.16 and 1.32, respectively (ηr = ηp/ηs). [Adapted, by permission, from D.D. Paul and S.I. Abdel-Khalik, J. Rheol., 27, 59, 1983.]

the α value increases, approaching αs from below. The critical heat flux densities in PEO solutions are smaller than those for water. In the view of the discussed results, the work159 attracts special attention since it contains data on boiling of dilute solutions, opposite to those reported earlier.153-158 The addition of PAA, PEO and HEC to water in concentrations, corresponding to the viscosity increase up to ηp = 1.32x10-3 Pas, has brought about reduction in the heat transfer. The boiling curve in coordinates q (heat flux) vs. ΔT displaced almost congruently to the region of larger ΔT values with c (Figure 7.2.17, a). It was demonstrated159 that the observed decrease in α with addition of polymer to water can be both qualitatively and quantitatively (with the Rohsenow pool boiling correlation for the heat transfer coefficient)160 associated with the increase in the solution viscosity (Figure 7.2.17, b). The experiments159 were performed using a thin platinum wire with diameter 0.3 mm. Explanation of experimental data needs more detailed discussion of physical factors that can reveal themselves in boiling of polymeric solutions. They include possible changes in capillary forces on interfaces in the presence of polymeric additives; absorption of macromolecules on the heating surface; increase in the number of weak points in the solution, which facilitates increase in the number of nuclei; thermodynamic peculiarities of the polymer-solvent system; the effect of macromolecules on the diffusion mass transfer in evaporation of solvent; hydrodynamics of convective flows in a boiling layer and the motion of bubbles; manifestation of rheological properties of solution. The capillary effects were indicated as one of the reasons for the intensification of heat transfer, since many polymers (in particular, HEC, PEO, etc.),161 similar to lowmolecular surfactants,162 are capable of decreasing the surface tension.163 As a result, decrease of both the work of the nucleus formation Wcr and the critical size of bubble, Rcr 3

W cr = 16 ⁄ 3πσ Φ ( θ ) [ ( dp ⁄ dT )ΔT ( 1 – ρ v ⁄ ρ f ) ] 3

2 –1

Φ ( θ ) = 1 ⁄ 4 ( 2 + 3 cos θ – cos θ ), R cr = 2σ [ ( dp ⁄ dT )ΔT ( 1 – ρ v ⁄ ρ f ) ] [7.2.59]

Semyon Levitsky* and Zinoviy Shulman** where:

θ σ

wetting angle surface tension coefficient

407

Effect of surfactants on the ebullient behavior, diffusion growth of bubbles and their interaction with liquid in a sound field, nucleate boiling enhancement, incipient superheat, bubble nucleation, coalescence of bubbles, and departure dynamics are studied elsewhere;164-176 see also the comprehensive review.148 Typical behavior of surfactant solutions at saturated nuclear pool boiling was described elsewhere,169 where heat transfer enhancement with an increase of Habon G concentration (molecular mass M ~ 500) was observed. The heat transfer enhancement reached a maximum at Habon concentration of about c0 = 530 ppm, corresponding to the critical micelle concentration of the surfactant, and then decreased with further increase of c. The enhancement of nucleate boiling heat transfer was explained by the decrease in surface tension, whereas the deterioration of boiling heat transfer at higher concentration of the additive was related to the solution viscosity increase. However, it should be noted that the integral effect of the heat transfer enhancement, observed in highly diluted solutions of high polymers, as distinct to low-molecular surfactants, cannot be attributed to the capillary phenomenon alone, since the main change in σ occurs in the range of low polymer concentrations157,177 (c < 50 ppm) and further increase in c does not affect the value of σ, whereas the α value continues to grow. Moreover, PAA, for example, does not behave like surfactants at all. It should be noted also that in the presence of polymer not only the value of σ changes, but also the wetting angle, θ, in the formula [7.2.59]. The latter may lead to manifestation of the opposite tendency.178 Absorption of macromolecules onto a heating surface favors the formation of new centers of nucleation. Together with an increase in nucleation sites in the boundary layer of a boiling liquid it explains the general growth in the number of bubbles. Both this factor and reduction in the σ value for solutions of polymers that possess surface activity, are responsible for a certain decrease in superheat needed for the onset of boiling of dilute solutions.154,158 The decrease in the water vapor pressure due to presence of polymer in solution at c~1% can be neglected. However, if the solution has the LCST, located below the heating wall temperature, the separation into rich-in-polymer and poor-in-polymer phases occurs in the wall boundary layer. At low concentration of macromolecules the first of these exists in a fine-dispersed state that was observed, for example, for PEO solutions.158 The rich-in-polymer phase manifests itself in a local buildup of the saturation temperature, which can be significant at high polymer content after separation; in decrease of intensity of both convective heat transfer and motion of bubbles because of the increase in viscosity; and reduction of the bubble growth rate. The so-called “slow” crisis, observed in PEO solutions158 is explained by integral action of these reasons. Similar phenomenon, but less pronounced, was observed also at high enough polymer concentration.155 It is characterized by plateau on the boiling curves for solutions of PIB in cyclohexane, extending into the range of high superheats. The main reason for the decrease in heat transfer coefficient at nucleate boiling of polymeric solutions with c ~ 1% is the increase in liquid viscosity, leading to suppression

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7.2 Bubbles dynamics and boiling of polymeric solutions

Figure 7.2.18. Growth of vapor bubbles on the heating surface at high (a) and low (b) pressures. [Adapted, by permission, from S.P. Levitsky, B.M. Khusid and Z.P. Shulman, Int.J.Heat Mass Transfer, 39, 639, 1996.]

of microconvection and increasing the resistance to the bubbles' rising. In the presence of LCST, located below the boiling temperature, the role of this factor increases because appearance in the boiling layer of the rich-in-polymer phase in fine-dispersed state. Another reason for the decrease of α in the discussed concentration range is the decrease in the bubble growth rate at the thermal stage, when the superheat ΔT > ΔTˆ* (see the section 7.2.2). In highly diluted solutions the change in Newtonian viscosity due to polymer is insignificant, and though the correlation between heat transfer enhancement and increase in viscosity has been noticed, it cannot be the reason for observed changes in α. In hydrodynamics, the effect of turbulence suppression by small polymeric additives is known, and drag reduction up to 80%, when polymer is added even in minute concentration, was reported. Basic experimental results on flow control by soluble polymers, their effect on flow configurations in multiphase flows, and the proposed models, explaining the drag reduction mechanism, were reviewed recently elsewhere.179 However, this effect also cannot be considered as a reason for the discovered changes in the heat transfer coefficient because laminarization of the boundary layer leads to reduction of the intensity of convective heat transfer.180 Nevertheless, the phenomenon of the decrease of hydrodynamic resistance and enhancement of heat transfer in boiling of dilute solutions have a common nature. The latter effect was connected with manifestation of elastic properties of the solution at vapor bubble growth on the heating surface.181 The general character of the bubbles evolution at boiling under atmospheric and subatmospheric pressures, respectively, is clarified schematically in Figure 7.2.18. In the first case (at high pressures), the base of a bubble does not “spread”182 but stays at the place of its nucleation. Under such conditions, the decrease in the curvature of the bubble surface with time, resulting from the increase in bubble radius, R, leads to liquid displacement from the zone between the lower part of the microbubble and the heating surface. This gives rise to the local shear in a thin layer of a polymer solution. A similar shear flow is developed also in the second case (at low pressures), when a microlayer of liquid is formed under a semi-spherical bubble. As known, at shear of a viscoelastic fluid appear not only tangential but also normal stresses, reflecting accumulation of elastic energy in the strained layer (the Weissenberg effect).3 The appearance of these stresses and elastic return of the liquid to the bubble nucleation center is the reason for more early detachment of the bubble from the heating surface, reduction in its size and growth in the nucleation frequency. All this ultimately leads to enhancement of the heat transfer.

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The above discussion permits to explain the experimental results.159 Their reasons are associated with substantial differences in the conditions of boiling on a thin wire and a plate or a tube. Steam bubbles growing on a wire have a size commensurable with the wire diameter (the growing bubble enveloped the wire).159 This results in sharp reduction of the boundary layer role, the same as the role of the normal stresses. The bubble growth rate on a wire is smaller than on a plane (for a wire R ~ tn where n < ¼).182 The elastic properties of the solution are responsible also for stabilization of the spherical shape of bubbles observed in experiments on boiling and cavitation. Similar results were obtained in experiments183 with polymer foaming development, where was concluded that high elasticity of polymeric material hinders bubble formation, reduces the bubble coalescence and stabilizes the growing bubble. A semiempirical method that allows to describe the time evolution of bubble growth, lamella thinning, and plateau border drainage during reactive polymeric foaming was suggested.184 Finally, the observed reduction in a coalescence tendency and an increase in the bubble size uniformity can also be attributed to the effects of normal stresses and longitudinal viscosity in thin films separating the drawing together bubbles. Recent efforts at gaining fundamental understanding of hydrodynamic interactions between particles, drops, or bubbles moving in non-Newtonian liquids, are summarized in a comprehensive review.185 Additional results may be found elsewhere.186,187 The linkage between the enhancement of heat transfer at boiling of dilute polymer solutions and the elastic properties of the system is confirmed by the existence of the optimal concentration corresponding to αmax (see Figure 7.2.14). Such peak performance at saturated pool boiling at atmospheric pressure of water solution of HEC QP-300 with molecular mass M ~ 600 kg/mol was observed also elsewhere;177,188 for instance, up to 45% increase in the boiling heat transfer coefficient, compared to that in pure water, was obtained177 with c = 4.0x10-9 mol/cc. Similar optimal concentration was established at addition of polymers to water to suppress turbulence − the phenomenon that also owes its origin to elasticity of macromolecules.1,3,9 Therefore, it is possible to expect that the factors favoring the chain flexibility and increase in the molecular mass, should lead to strengthening of the effect. The data on boiling of concentrated polymeric solutions20 demonstrate that in such systems thermodynamic, diffusional and rheological factors are of primary importance. The diagram of the liquid-vapor phase equilibrium is characterized by a decrease in the derivative dp/dT with the polymer concentration (dp/dT → 0 at k → 0). This leads to increase in both the nucleation energy and the detachment size of a bubble (see the equation [7.2.59]) and, consequently, to reduction of the bubbles generation frequency. Note that in reality the critical work, Wcr, for a polymeric liquid may exceed the value predicted by the formula [7.2.59] because of manifestation of the elasticity of macromolecules. As known,160 the heat transfer coefficient in the case of developed nucleate boiling of low-molecular liquids is related to the heat flux, q, by the expression α = Aqn where n ≈ 0.6-0.7. For concentrated polymeric solutions the exponent n is close to zero. The decrease in heat transfer is explained by the increase in the viscosity of the solution near the heating surface resulting from the evacuation of the solvent with vapor. Another rea-

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7.2 Bubbles dynamics and boiling of polymeric solutions

son for the decrease of α in such systems is the reduction of the bubble growth rate with lowering k0 and the impossibility to achieve large Ja numbers by rising of the solution superheat. Since in boiling of concentrated polymer solutions the α value is small, the superheat of the wall at a fixed q increases. This can give rise to undesirable phenomena such as burning fast to the heating surface, structure formation, and thermal Figure 7.2.19. Cooling curves for a silver specimen Usually, in this case the decomposition. quenched in a polymer aqueous solution at 20oC. heat transfer is intensified by mechanical [Adapted, by permission, from S.P. Levitsky and agitation. Note that one of the promising Z.P. Shulman, Bubbles in polymeric liquids, Technomic Publishing Co., Lancaster, 1995.] trends in this field may become the use of ultrasound, the efficiency of which should be evaluated with account for considerable reduction in real losses at acoustically induced flows and pulsations of bubbles in viscoelastic media.189,190 Specific features of boiling of high-molecular solutions are important for a number of applications. One of the examples is the heat treatment of metals, where polymeric liquids find expanding employment. The shortcomings of traditionally used quenching liquids, such as water and oil, are well known.191 Quenching in oil, due to its large viscosity and high boiling temperature, does not permit to suppress the perlite transformation in steels. On the other hand, water as a quenching medium is characterized by high cooling rate over the temperature ranges of both perlite and beinite transformations. However, its maximal quenching ability lies in the temperature range of martensite formation that can lead to cracking and shape distortion of a steel article. Besides, the quenching oils, ensuring the so-called “soft” quenching, are fire-hazardous and have ecological limitations. The polymeric solutions in a certain range of their physical properties combine good points of both oil and water as quenching liquids and permit to control the cooling process over wide ranges of the process parameters. For the aims of heat treatment, a number of water-soluble polymers are used, e.g., PVA, PEO, PAA, polymetacryle acids (PMAA, PAA) and their salts, cellulose compounds, etc.192-194 The optimal concentration range is 1 to 40% depending on molecular mass, chemical composition, etc. Typical data194 are presented on the Figure 7.2.19, where curves 1-5 correspond to the solution viscosity ηp = (1.25, 2.25, 3.25, 5, 11)x10-3 Pas, measured at 40oC. The quenchants based on water-soluble polymers sustain high cooling rates during the initial stage of quenching that permits to obtain fine-grained supercooled austenite, and relatively low intensity of heat removal at moderate temperatures, when martensite transformations take place. The main feature of quenching in polymeric solutions is the prolongation of the cooling period as a whole in comparison with water that is explained by extended range of a stable film boiling (Figure 7.2.20). The increase in polymer concentration leads to reduc-

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Figure 7.2.20. Stability diagrams for film boiling.145 Quenching in water (a) and in aqueous polymer solution with ηs = 3.27x10-3 Pas at 40oC; (b): 1, 2 − stable and unstable film boiling, 3 − nucleate boiling, 4 − convection. Tms, Tm1 and Tm2 are the surface temperatures of the specimen, corresponding to the destabilization of the regimes 1-3, respectively. [Adapted, by permission, from S.P. Levitsky and Z.P. Shulman, Bubbles in polymeric liquids, Technomic Publishing Co., Lancaster, 1995.]

tion of α on the stage of nucleate boiling and growth of the temperature, corresponding to the onset of free convection regime. The effect of polymeric additives on the initial stage of the process was the subject of a special investigation.195 Experiments were performed with aqueous polymer solutions of Breox, PEO and some other polymers with M = 6x103 to 6x105 at pressure 0.1 MPa. The platinum heater with short time lag, submerged in solution, was heated-up in a pulsed regime with T· ~ 105 to 106 K/s. The experimental results revealed the existence of a period with enhanced heat transfer (as compared with water) in solutions with c ~ 1%, which lasted for 10 to 100 μs after the onset of ebullition. The sensitivity of heat transfer to the polymer concentration was sufficiently high. After formation of the vapor film the secondary ebullition was observed, which resulted from superheating of the liquid outside the region of concentration gradients near the interface. The mechanism of this phenomenon was described.196 It is associated with the fact that heat transfer has a shorter time lag than mass transfer, and thus the thermal boundary layer in a liquid grows faster than the diffusion one. Quenching experiments with hot solid spheres in dilute aqueous solutions of polyethylene oxide have been conducted197 in order to investigate the physical mechanisms of vapor explosions suppression in polymer solution. It was found that the minimum film boiling temperature in 30°C liquid rapidly decreased from ~700°C for pure water to ~150°C as the polymer concentration was increased up to 300 ppm for a 22.2 mm sphere, and it decreased to 350°C for a 9.5 mm sphere. This trend was observed consistently in the heated pool up to its boiling temperature, while the tests with surfactant solutions do not show an appreciable reduction in the minimum film boiling temperature. The ability of suppression of vapor explosions by dilute polyethylene oxide solutions against an external

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7.2 Bubbles dynamics and boiling of polymeric solutions

trigger pressure was tested by dropping molten tin into the polymer solutions at 25°C. It was found that the explosion was completely suppressed at c ~ 300 ppm. The experimental data and theoretical results on the growth of vapor bubbles and films in polymeric solutions explain the efficiency of quenchants, based on water-soluble polymers. The main reason is stabilization of the film-boiling regime at initial stage of quenching. Such stabilization is connected with elastic properties of the liquid skin layer, adjacent to the interface that is enriched by polymer due to solvent evaporation.198 Appearance of this layer leads to fast growth of longitudinal viscosity and normal stresses, when perturbations of the interface arise, thus increasing the vapor film stability. A similar mechanism is responsible for stabilization of jets of polymeric solutions9 as well as for retardation of bubble collapse in a viscoelastic liquid (see section 7.2.1). In systems with LCST this effect can be still enhanced due to phase separation, induced by interaction of the liquid with high-temperature body. Additional reason that governs the decrease in heat removal rate at quenching is connected with reduction of heat conductivity in aqueous solutions of polymers with growth of concentration of the high-molecular additive. After the body temperature is lowered sufficiently, the film boiling gave way to the nucleate one. According to data, presented in the previous section, over the polymer concentration ranges, typical for high-molecular quenchants, the α value must decrease in comparison with water. In fact, this is normally observed in experiments. Rise of the temperature, characterizing transition from nucleate boiling to convective heat transfer, is associated with the increase in liquid viscosity. ABBREVIATIONS HEC LCST PS PIB PAA PEO POE PVA TTS

hydroxyethylcellulose lower critical solution temperature polystyrene polyisobutylene polyacrylamide polymethyleneoxide polyoxyethylene polyvinyl alcohol time-temperature superposition

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Semyon Levitsky* and Zinoviy Shulman** 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

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8

Solvent Mixtures 8.1 MIXED SOLVENTS Y. Y. Fialkov, V. L. Chumak Department of Chemistry National Technical University of Ukraine, Kiev, Ukraine 8.1.1 INTRODUCTION One of the basic problems in conducting a chemical process in solution is a control of the process parameters. The most important is the yield of the reaction products and process rates. The equilibrium constants and the rate constants of processes in solutions are multifactor dependencies. They depend on temperature and many solvent properties. The realization of the process in individual solvent often complicates such controls, and in some cases makes it completely impossible. At the same time, it is possible to choose properties determining the process characteristics in mixed solvents directly. Such properties relate, first of all, to the density, ρ, viscosity, η, permittivity, ε, and specific solvation energy. In this chapter, the term “mixed solvent” refers to binary solvents − regardless of the relation of their components. The use of mixed solvents in scientific and industrial practice began at the beginning of the 20th century. But systematic theoretical-experimental research began in the sixties, and its intensity has been growing ever since. There are two basic reports on physical properties of mixed solvents. One is the published in four-volume reference edition by Timmermans1 in the fifties and published at that period by Krestov and co-author's monograph.2 The monographic sources related to mixed solvents are referenced under a common citation.3 8.1.2 CHEMICAL INTERACTION BETWEEN COMPONENTS IN MIXED SOLVENTS The developments in physical chemistry and chemical physics of liquid state substantiated common viewpoint that liquids are associated. Assuming this approach as a limit, we may consider the individual solvent as divided into non-associated molecules having the smaller energy of intermolecular interaction than the energy of molecules in thermal motion, and to molecules, having energy higher than kT. 8.1.2.1 Processes of homomolecular association In mixed solvents formed of associated component A and non-associated component B (does not interact with component A), the following equilibrium takes place:

418

8.1 Mixed solvents

mA where: m

B

2Am/2

B

...

B

Am

[8.1.1]

number of molecules A forming the homomolecular associate (in subscript − association degree)

The systems alcohol−carbon tetrachloride or carbon acids−cyclohexane are examples of mixed solvents of this type. Interesting examples of such mixed solvents are the systems formed of liquid tetraammonium salts, R4NA, and various liquids that are solvateinert towards such compounds. The values of homomolecular association constants of alcohols and acids are high, typically in the range of 103−104. Therefore the concentration of component A is rather low, even at a high content of solvate-inert component B, and may be neglected. The relative degree of the decomposition of heteromolecular associates into aggregates of a smaller association degree increases with increased permittivity of the non-associated solvate-inert component. In solutions of an equal concentration of the two mixed solvents, acetic acid−cyclohexane (ε = 1,88) and acetic acid−chlorobenzene (ε = 5,6), the relative degree of acid heteromolecular association is higher in the first system than in the second system. In mixed solvents formed of two associated components in individual states Am and Bn that do not interact with each other in specific solvation, the chemical equilibrium of mixed heteromolecular associates is established, as follows: Am + Bn ↔ x ( Am ⁄ x Bn ⁄ x )

[8.1.2]

where: x

number of molecules of heteromolecular associate

Whether to consider these heteromolecular associates as real chemical adducts is more related to terminology than a chemical problem. In most cases, investigators assume that in systems formed of two alcohols or two carboxylic acids, specific interaction does not exist. In the case of mixed solvents formed of two carbon acids that is true only when components have similar proton affinity as is the case of a system such as acetic acid−propionic acid (see further paragraph 8.1.2.8). 8.1.2.2 Conformic and tautomeric equilibrium. Reactions of isomerization Various conformers of the same compound differ in their dipole moments. Thus, in the mixed solvents A−B, where A is a liquid whose molecules give conformer equilibrium, and B is solvate-inert towards A, the A conformer ratio changes on addition of B component. In the binary solvents A−B where component A can exist in two tautomeric forms A1 and A2, the ratio of concentrations of these forms changes on addition of component B. Common theory of this influence has been worked out by Kabachnic4,5 who proposed the common scheme of equilibrium in systems of such type (scheme [8.1.3]):

Y. Y. Fialkov, V. L. Chumak

A1H + S

I

419

A1HS

II

A1 HS

III

A2HS

IV

A2H + S

IIIa

A1 + HS The scheme [8.1.3] includes the following stages occurring in sequence: I interaction of the first tautomeric form, A1H, with the solvent that leads to the formation of an addition product, A1HS, (the solvate composition may be more complicated) + II ionization of solvate with formation of ionic couple, A 1 HS III ionic couple may decompose into ions (stage IIIa), transfer an ionized complex into a product of solvent addition already in the second tautomeric form IV formation of the free tautomeric form, A2H A2H. The nature of the chemical type of influences on keto-enol equilibrium is obvious: the more basic the solvent, the higher the degree of keto-enol transformation into enol form. If the solvent is indifferent with enough degrees of approximation, the well-defined dependence of the constants of keto-enol equilibrium on solvent permittivity is encountered. The difference in dipole moments of tautomeric forms is the basis of these relationships. In the mixed solvents such as ACR-B, the first component may undergo rearrangement reactions: ACR ↔ ARC

[8.1.4]

These occur under the solvent influence or even with its direct participation:

ACR

+B

...

+B

ARC

[8.1.4a]

8.1.2.3 Heteromolecular association When components of the binary solvent A−B are solvent-active towards one another, the sum of chemical equilibrium is established: mA + nB ↔ A m B n

[8.1.5]

In most scenarios, the interaction proceeds in steps, i.e., equilibrium solution represents the mixture of heteroassociates of different stoichiometry: AB, AB2, A2B, etc. Systems formed by O−, S−, N−, P− bases with various H-donors (e.g., amines-carboxylic acids, esters−carboxylic acids (phenols), dimethylsulfoxide−carboxylic acid) are examples of this type of interaction.

420

8.1 Mixed solvents

The systems having components which interact by means of donor−acceptor bond (without proton transfer) belong to the same type of solvents (e.g., pyridine−chloracetyl, dimethylsulfoxide−tetrachloroethylene, etc.). Components of mixed solvents of such type are more or less associated in their individual states. Therefore, processes of heteromolecular association in such solvents occur along with processes of homomolecular association, which tend to decrease heteromolecular associations. 8.1.2.4 Heteromolecular associate ionization In some cases, rearrangement of bonds leads to the formation of electro-neutral ionic associate in binary solvents where heteromolecular associates are formed: q+

p-

Am Bn ↔ Kp Lq

[8.1.6]

In many cases, ionic associate undergoes the process of ionic dissociation (see paragraph 8.1.2.5). If permittivity of the mixture is not high, the interaction can limit itself to the formation of non-ionogenic ionic associate, as exemplified by the binary solvent anisol−m-cresol, where the following equilibrium is established: C 6 H 5 OCH 3 + CH 3 C 6 H 4 OH ↔ C 6 H 5 OCH 3 • CH 3 C 6 H 4 OH ↔ +

↔ [ C 6 H 5 OCH 3 • H ] • CH 3 C 6 H 4 O

-

8.1.2.5 Electrolytic dissociation (ionic association) In solvents having high permittivity, the ionic associate decomposes into ions (mostly associated) to a variable degree: q+

p-

q+

p-

Kp Lq ↔ Kp – 1 Lq – 1 + K

q+

p-

+ L ↔ … ↔ pK

q+

+ qL

p-

[8.1.7]

The electrolyte solution is formed according to eq. [8.1.7]. Conductivity is a distinctive feature of any material. The practice of application of individual and mixed solvents refers to electrolyte solutions, having conductivities > 10-3Cm/m. Binary systems, such as carbonic acids−amines, cresol−amines, DMSO−carbonic acids, hexamethyl phosphorous triamide acids, and all the systems acids−water, are the examples of such solvents. The common scheme of equilibrium in binary solvents, where components interaction proceeds until ions formation, may be represented by the common scheme [8.1.8]: Am

K m

2Am/2 + 2Bn/2 Bn

K add

AmBn

K i

p-

Kpq+ Lq

pKq+ + qLp-

K n

where: Km , K n Kadd Ki Ka

the constants of homomolecular association; respectively the constant of the process formation of heteromolecular adduct the ionization constant the association constant.

K a

pKq+qLp-

Y. Y. Fialkov, V. L. Chumak

421

The system acetic acid−pyridine4 may serve as an example of binary solvent whose equilibrium constants of all stages of the scheme [8.1.8] have been estimated. 8.1.2.6 Reactions of composition As a result of interaction between components of mixed solvents, profound rearrangement of bonds takes place. The process is determined by such high equilibrium constant that it is possible to consider the process as practically irreversible: mA + nB → pC

[8.1.9]

where: m, n, p C

stoichiometric coefficients compound formed from A and B

Carbonic acid anhydrides−water (e.g., ( ( CH 3 CO ) 2 O + H 2 O → 2CH 3 COOH ), systems isothiocyanates−amines (e.g., C 3 H 5 NCS + C 2 H 5 NH 2 → C 2 H 5 NHCNSC 3 H 5 ) are examples of such binary solvents. It is pertinent that if solvents are mixed at a stoichiometric ratio (m/n), they form individual liquid. 8.1.2.7 Exchange interaction Exchange interaction mA + nB ↔ pC + qD

[8.1.10]

is not rare in the practice of application of mixed solvents. Carbonic acid−alcohol is an example of the etherification reaction. Carbonic acid anhydride−amine exemplifies acylation process ( ( CH 3 CO ) 2 O + C 6 H 5 NH 2 ↔ C 6 H 5 NHCOCH 3 + CH 3 COOH ; carbonic acid−another anhydride participate in acylic exchange: RCOOH + ( R 1 CO ) 2 O ↔ RCOOCOR 1 + R 1 COOH The study of the exchange interaction mechanism gives a forcible argument to believe that in most cases the process goes through the formation of intermediate − “associate”: mA + nB ↔ [ A m B n ] ↔ pC + qD

[8.1.11]

8.1.2.8 Amphoterism of mixed solvent components The monograph of one of the authors of this chapter7 contains a detailed bibliography of works related to this paragraph. 8.1.2.8.1 Amphoterism of hydrogen acids In the first decades of the 20th century, Hanch ascertained that compounds which are typical acids show distinctly manifested amphoterism in water solutions while they interact with one another in the absence of solvent (water in this case). Thus, in binary solvents, H2SO4−CH3COOH and HClO4−CH3COOH, acetic acid accepts proton forming acylonium, CH3COOH2+, cation. Many systems formed by two hydrogen acids are being studied. In respect to one of the strongest mineral acids, CF3SO3H, all mineral acids are bases. Thus, trifluoromethane sulfuric acid imposes its proton even on sulfuric acid, forcing it to act as a base:8

422

8.1 Mixed solvents -

+

CF 3 SO 3 H + H 2 SO 4 ↔ CF 3 SO 3 • H 3 SO 4

Sulfuric acid, with the exception of the mentioned case, and in the mixtures with perchloric acid (no proton transfer), shows acidic function towards all other hydrogen acids. The well-known behavior of an acidic function of absolute nitric acid towards absolute sulfuric acid is a circumstance widely used for the nitration of organic compounds. Trifluoroacetic acid reveals proton−acceptor function towards all strong mineral acids, but, at the same time, it acts as an acid towards acetic and monochloroacetic acids. In the mixed solvents formed by two aliphatic carbonic acids, proton transfer does not take place and interaction is usually limited to a mixed associate formation, according to the equilibrium [8.1.2]. 8.1.2.8.2 Amphoterism of L-acids In binary liquid mixtures of the so-called aprotic acids (Lewis acids or L-acids) formed by halogenides of metals of III-IV groups of the periodic system, there are often cases when one of the components is an anion-donor (base) and the second component is an anionacceptor (acid): +

-

M I X m + M II X n ↔ M I X m – 1 + M II X n + 1

[8.1.12]

The following is an example of eq. [8.1.12]: In the mixture AsCl3−SnCl4, stannous tetrachloride is a base and arsenic trichloride is an acid: +

2-

2AsCl 3 + SnCl 4 ↔ ( AsCl 2 ) • SnCl 6

8.1.2.8.3 Amphoterism in systems H-acid-L-acid Amphoterism phenomenon is the mechanism of acid−base interaction in systems formed by H-acids or two L-acids in binary systems. For example, in the stannous tetrachloride− carboxylic acid system, acid−base interaction occurs with SnCl4 being an acid: SnCl 4 + 2RCOOH ↔ [ SnCl 4 ( RCOO ) 2 ]H 2 The product of this interaction is such a strong hydrogen acid that it is neutralized by the excess of RCOOH: -

+

[ SnCl 4 ( RCOO ) 2 ]H 2 + RCOOH ↔ [ SnCl 4 ( RCOO ) 2 ]H + RCOOH 2

The mechanism of acid−base interaction in binary solvents of the mentioned type depends often on the component relation. In systems such as stannous pentachloride−acetic acid, diluted by SbCl5 solutions, interaction proceeds according to the scheme: -

-

2SbCl 5 + 4HAc ↔ SbCl 3 Ac 2 + SbCl 6 + Cl + 2H 2 Ac

+

In solutions of moderate concentrations, the following scheme is correct: -

2SbCl 5 + 2HAc ↔ SbCl 4 Ac + Cl + H 2 Ac

+

Y. Y. Fialkov, V. L. Chumak

423

8.1.2.8.4 Amphoterism in binary solutions amine-amine If amines differ substantially in their energies of proton affinity, one of them has a protondonor function in binary mixtures of these amines, so that it acts as an acid:

NH + N

N NH

[8.1.13]

N + HN

In the overwhelming majority of cases, this acid−base interaction limits itself only to the first stage − formation of the heteromolecular adduct. Interactions occurring in all stages of the scheme [8.1.13] are typical of binary solvents such as triethylene amine− pyridine or N-diethylaniline. Proton-donor function towards the amine component reveals itself distinctly in the case of diphenylamine. To conclude the section discussing amphoterism in binary solvents, we have constructed a series of chemical equilibria that help to visualize the meaning of amphoterism as a common property of chemical compounds:

base Et3N

+

acid PhNH2

Et3N.PhNH2

PhNH2

+

Ph2NH

PhNH2.Ph2NH

Ph2NH H 2O

+ +

H 2O HAc

...

Ph2NH.H2O H3O + Ac

HAc

+

CF3COOH

...

H2Ac

CF3COOH + + HNO3 + H2SO4

HNO3 H2SO4 CF3SO3H

+

CF3COO

CF3COOH.HNO3 H2NO3 + HSO4 H3SO4 + CF3SO3

*The first stage of absolute sulfuric and nitric acids

8.1.3 PHYSICAL PROPERTIES OF MIXED SOLVENTS 8.1.3.1 The methods of expression of mixed solvent compositions In the practice of study and application of mixed solvents the fractional (percentage) method of composition expression, according to which the fraction, Y, or percentage, Y*100, of i-component in the mixed solvent are equal, is the most common: i=i

Yi = ci ⁄

 ci

[8.1.14]

i=1 i=i

Yi = ci ⁄

 c i × 100% i=1

where: c

a method of composition expression.

[8.1.14a]

424

8.1 Mixed solvents

The volume fraction, V, of a given component in the mixture equals to: i =i

Vi = vi ⁄

 vi

[8.1.15]

i=1

where: v

initial volume of component

Molar fraction, X, equals i=i

X = mi ⁄

 mi

[8.1.16]

i=1

where: m

the number of component moles.

Mass fraction, P, equals to: i=i

P = gi ⁄

 gi

[8.1.17]

i=1

where: g

mass of a component.

It is evident that for a solvent mixture, whose components do not interact: ΣV = ΣX = ΣP = 1

[8.1.18]

and expressed in percent ΣV 100 = ΣX 100 = ΣP 100 = 100

[8.1.19]

Fractions (percentage) [8.1.19] of mixed solvents, since they are calculated for initial quantities (volumes) of components, are called analytical. In the overwhelming majority of cases, analytical fractions (percentages) are used in the practice of mixed solvents application. However, in mixed solvents A−B, whose components interact with the formation of adducts, AB, AB2, it is possible to use veritable fractions to express their composition. For example, if the equilibrium A + B ↔ AB establishes, the veritable mole fraction of A component equals to: N A = m A ⁄ ( m A + m B + m AB ) where: mi

number of moles of equilibrium participants

[8.1.20]

Y. Y. Fialkov, V. L. Chumak

425

In the practice of mixed solvents application, though more seldom, molar, cM, and molal, cm, concentrations are used. Correlations between these various methods of concentration expression are shown in Table 8.1.1. Table 8.1.1. Correlation between various methods of expression of binary solvent A-B concentration (everywhere − concentration of component A) Argument

Fun ction

x

V VθB/(θA−σθV)

x V

xθA/(σθx+θB)

P

xMA/(σMx+MB)

3

PMB/(MA−σMP) cMθB/(10 ρ−cMσM)

VρA/(σPV+ρB)

3

3

3

3

10 x/MB(1−x)

cm

cM

PρB/(ρA−σPP)

10 ρx(σMx+MB) 10 V/θA

cM

P

cm cmMB/103+cmMB)

cMθA/103

cmMBθA/(103θB cmMBθA)

cMMA/103ρ

cmMA/(103+cmMA)

3

+

103ρcm/(103+cmMA)

10 ρP/MA 3

10 θBV/MBθA(1−V) 10 P/MA(1−P)

3

3

10 cM/(10 ρ−MAcM)

σ is the difference between the corresponding properties of components, i.e., σ = yA − yB, ρ is density, and θ is molar volume.

8.1.3.1.1 Permittivity In liquid systems with chemically non-interacting components, molar polarization, PM, according to definition, is an additive value; expressing composition in molar fractions: i=i

PM =

 P Mi xi

[8.1.21]

i=1

where: xi

molar fraction of the corresponding mixture component

In the case of the binary solvent system: P M = P M x + P M ( 1 – x ) = ( P M – P M )x + P M 1

2

1

2

2

[8.1.21a]

where: x

molar fraction of the first component.

Here and further definitions indices without digits relate to additive values of mixture properties and symbols with digits to properties of component solvents. As i

P M = f ( ε )M ⁄ ρ = f ( ε )θ then f ( ε )θ =

 f ( ε i )θi x i

[8.1.22]

1

or for binary solvent f ( ε )θ = f ( ε 1 )θ 1 x + f ( ε 2 )θ 2 ( 1 – x )

[8.1.22a]

426

8.1 Mixed solvents

where: M ρ θ f(ε)

an additive molecular mass density molar volume one of the permittivity functions, e.g., 1/ε or (ε - 1)/(ε +2)

In accordance with the rules of transfer of additive properties from one way of composition expression to another3 based on [8.1.22], it follows that i

f(ε) =

 f ( εi )Vi

[8.1.23]

1

and for a binary system f ( ε ) = f ( ε 1 )V + f ( ε 2 ) ( 1 – V )

[8.1.23a]

where: V

the volume fraction.

Substituting f(ε) function into [8.1.23], we obtain volume-fractional additivity of permittivity i

ε =

 εi Vi

[8.1.24]

1

or for binary solvent ε = ε1 V + ε2 ( 1 – V )

[8.1.24a]

The vast experimental material on binary liquid systems1,2,3 shows that the equation [8.1.24] gives satisfactory accuracy for systems formed of components non-associated in individual states. For example, dielectric permittivity describes exactly systems n-hexanepyridine, chlorobenzene-pyridine by equation [8.1.24a]. For systems with (one or some) associated components, it is necessary to consider fluctuations, which depend on concentration, density, orientation, etc. Consideration of ε fluctuations shows that calculation of dielectric permittivity for a mixture of two chemically non-interacting liquids requires Δεvalues determined from equation [8.1.24a] and substituted to the equation: 2

Δε = ( ε 1 – ε 2 ) ( Δρ ) ⁄ [ ε ( 2 + δ ε ) ] where:

Δρ δε ε1, ε2 εAdd εexp

[8.1.25]

fluctuation of density = ∂ε Add ⁄ ( ∂V ) ⁄ ( ∂ε exp ⁄ ∂V ) dielectric permittivities of individual components additive value experimental value

The Δε value may be calculated from a simplified equation. For equal volume mixtures (V = 0.5) of two solvents:

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427 2

Δε V = 0.5 = 0.043 ( ε 1 – ε 2 ) ⁄ ε V = 0.5

[8.1.25a]

Thus, permittivity of equivolume mixture of two chemically non-interacting solvents can be calculated from the equation ε V = 0.5 = 0.5 ( ε 1 – ε 2 ) + ε 2 – Δε V = 0.5

[8.1.26]

Having ε values of both initial components and the ε value of the mixture, it is not difficult to interpolate these values for mixtures for any given composition. For systems formed of two associated liquids, there are no reliable methods of ε isotherms calculation. An empirical method has been proposed, which is based on the assumption that each associated component mixed with the other associated component that does not interact chemically with the first one introduces the rigorously defined contribution into ε deviation from the volume-fractional additivity. The extent of these deviations for the first representatives of the series of aliphatic carbonic acids and alcohols of normal structure, as well as for some phenols, are given elsewhere.3 The permittivity of mixtures at different temperatures can be calculated with high accuracy from absolute temperature coefficients of permittivity and their values using equations identical in form to [8.1.24]−[8.1.26]. For example, the calculation of temperature coefficients of permittivity, αε, of the equivolume mixture of two chemically noninteracting associated solvents is carried out using the equation identical in its form to [8.1.26]. Δα ε, V = 0.5 = 0.5 ( α ε – α ε ) + α ε – Δα ε, V = 0.5

[8.1.27]

Δα ε, V = 0.5 = 0.043 ( α ε – α ε ) ⁄ α ε, V = 0.5

[8.1.28]

1

2

2

where 1

2

8.1.3.1.2 Viscosity There is a great number of equations available in literature intended to describe viscosity of mixtures of chemically non-interacting components. All these equations, regardless of whether they have been derived theoretically or established empirically, are divided into two basic groups. The first group includes equations relating mixture viscosity, η, to the viscosity of initial components, ηi, and their content in the mixture, c, (c, in this case, is an arbitrary method of concentration expression): η = f ( η 1, η 2, …η i ; c 1, c 2, …c i – 1 )

[8.1.29]

The equations of the second group include various constants k1, k2, etc., found from experiment or calculated theoretically η = f ( η 1, η 2, …η i ; c 1, c 2, …c i – 1 ; k 1, k 2, … )

[8.1.30]

The accuracy of calculation of solvents mixture viscosity from [8.1.30] type of equations is not higher than from equations of [8.1.29] type. We, thus, limit the discussion to equations [8.1.29].

428

8.1 Mixed solvents

The comparison of equations of type [8.1.29] for binary liquid systems3 has shown that, in most cases, viscosity of systems with chemically non-interacting components is described by the exponential function of molar-fractional composition i

η =

xi

∏ ηi

[8.1.31]

1

or for binary solvent: x

1–x

η = η1 η2

[8.1.31a]

where: molar fractions of components of the binary system

xi

Empirical expressions for calculation of viscosity of the system of a given type, which permit more precise calculations, are given in monograph.3 From [8.1.31], it follows that the relative temperature coefficient of viscosity β η = ∂η ⁄ η∂T = ∂ ln η ⁄ ∂T for mixtures of chemically non-interacting liquids is described by the equation: β = xβ η + ( 1 – x )β η 1

2

[8.1.32]

8.1.3.1.3 Density, molar volume According to the definition, a density, ρ, of the system is the volume-additive function of composition: i

ρ =

 ρi Vi

[8.1.33]

1

or for the binary system: ρ = ρ1 V1 + ρ2 ( 1 –V1 )

[8.1.33a]

From [8.1.33], it follows that molar volume of the ideal system is a molar-additive function of composition: i

θ =

 θi xi

[8.1.34]

1

Molar mass of mixture, according to the definition, is a molar-additive function too: i

M =

 Mi xi 1

For a two-component mixture of solvents, these relations are as follows:

[8.1.35]

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θ = θ1 x + θ2 ( 1 – x )

[8.1.36]

M = M1 x + M2 ( 1 – x )

[8.1.37]

Non-ideality of the system leads to relative deviations of density and molar volume, as well as of other volumetric properties, having a magnitude of about 1%. Here, contraction and expansion of solutions are approximately equiprobable. In systems having condition close to separation, considerable contraction is possible. However, two component systems formed from the most common solvents, used in practical applications, form solutions far from separation at usual temperature range. Taking into account the linear density dependence on temperature in equations [8.1.33] and [8.1.34], it is possible to calculate values of density and molar volume at any given temperature. 8.1.3.1.4 Electrical conductivity The high conductivity of solvent mixture formed from chemically non-interacting components may be related to the properties of only one or both components. Very high conductivity of mineral acids, carboxylic acids, some complexes of acids with amines, stannous chloride, and some tetraalkylammonium salts increases conductivity of their mixtures with other solvents.3 Normal practice does not often deal with mixed solvents of such high conductivity. Therefore, the theory of concentration dependence of the conductivity of binary solvents is briefly discussed here.3,10 Two basic factors which influence conductivity of binary solvent mixture are viscosity and permittivity. The influence of these factors on specific conductivity is quantitatively considered in the empirical equation: κ = 1 ⁄ η exp [ ln κ 1 η 1 – L ( 1 ⁄ ε – 1 ⁄ ε 1 ) ] where:

κ L a

[8.1.38]

conductivity (symbols without index belong to the mixture properties, index 1 belongs to electrolyte component) = aε1ε2/(ε1 − ε2) proportionality coefficient

and in the non-empirical equation: ln κ = const 1 + 1 ⁄ ε ( const 2 + const 3 + const 4 ) + 1 ⁄ 2 ln c – ln η where: c consts

[8.1.39]

concentration, mol l-1 calculated from the equations11 based on crystallographic radii of the ions, dipole moments of molecules of the mixed solution, and ε of mixture components

From equations [8.1.38] and [8.1.39], it follows that isotherms of the logarithm of conductivity corrected for viscosity and concentration lnκηc-1/2 have to be a linear function of reciprocal ε. The validity of this assumption is confirmed in Figure 8.1.1. Control of properties of a multi-component mixture of solvents is achieved by methods of optimization based on analytical dependencies of their properties in composition:

430

8.1 Mixed solvents I

I

I

y = f ( y 1, y 2, …c 1, c 2, …c i – 1 ), y where:

yI, yII I II y 1, y 2

II

II

II

= f ( y 1 , y 2 , …c 1, c 2, …c i – 1 )

[8.1.40]

any property of a solvent initial property of a solvent

Concentration dependences of permittivity, viscosity, density (molar volume) and conductivity described here permit proper selection of the composition of mixed solvent, characterized by any value of the mentioned properties. 8.1.3.2 Physical characteristics of the mixed solvents with the chemical interaction between components In this section, we discuss physical characteristic change due to the changes of binary mixed solvent composition in the systems with chemical interactions between components (these systems are the most commonly used in science and technology). Comprehensive discussion of the physical and chemical analysis of such systems, including stoichiometry and stability constants, determination of the formation of heteromolecular associates can be found in a specialized monograph.3 In theory, if the composition of the mixture is known, then the calculation of any characteristic property of the multicomponent mixture can be performed by the classical physical and chemical analysis methods.3 For the binary liquid system, it is possible only if all chemical forms (including all possible associates), their stoichiometry, stability constants, and their individual physical and chemical properties are determined. A large volume of correct quantitative thermodynamic data required for these calculations is not available. Due to these -1/2 Figure 8.1.1. Dependencies lnκηc on 1/ε at 393.15K obstacles, data on permittivity, viscosity for systems containing tetrabutylammoniumbromide and aprotic solvent (1 − nitromethane, 2 − acetonitrile, and other macro-properties of mixed sol3 − pyridine, 4 − chlorobenzene, 5 − benzene). vents with interacting components are obtained by empirical means. Data on empirical physical properties of liquid systems can be found in published handbooks.1,2,10 Principles of characteristic changes due to the compositional change of liquid mixtures with interacting components are discussed here. Assessment of nature of such interactions can only be made after evaluation of the equilibrium constant (energy) of such interactions between solvents. 8.1.3.2.1 Permittivity Permittivity, ε, is the only property of the mixed liquid systems with the chemical interaction between components that has not been studied as extensively as for systems without chemical interaction.10 When the interaction between components is similar to a given in equation [8.1.8], the formation of conductive solutions occurs. Determination of ε for

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Figure 8.1.2. Classification of permittivity isotherms for binary solvents: 1 and 2 − isotherms for systems with interaction and without interaction, respectively.

these solutions is difficult and sometimes impossible. Although more or less successful attempts to develop such methods of permittivity determination are published from time to time, the problem until now has not been solved. Classification of the isotherms ε vs. composition of liquid systems3 is based on deviations of the experimental isotherms, which are then compared with isotherms of the system without chemical interaction between components. The latter isotherms are calculated from equations [8.1.24] - [8.1.26], (Figure 8.1.2). Type I isotherm corresponds to the experimental isotherm with isotherms [8.1.24] or [8.1.26] of the liquid systems without interaction. The additive ε increase is compensated by ε decrease, due to homomolecular association process. The system diethyl ether−mcresol illustrates this type of isotherm. Type II is determined by the negative deviations from isotherm [8.1.26]. This type corresponds to systems with weak heteromolecular interactions between components, but with the strong homomolecular association of one of the components. The system formic acid−anisole is an example of this kind of isotherm. Furthermore, these isotherms are characteristic when non-associating components in pure state form heteromolecular associates with a lower dipole moment, DM, then DM of both components. The average DM for such kind of interaction in mixed systems is lower than correspondent additive value for the non-interacting system. The system 1,2-dichloroethane−n-butylbromide can be referenced as an example of this kind of mixed binary solvent.

432

8.1 Mixed solvents

Type III combines ε isotherms, which are above the isotherm calculated from equation [8.1.26]. This kind of isotherm suggests an interaction between components of the mixed solvent. The variety of such systems allows us to distinguish between five isotherm subtypes. Subtype IIIa is represented by isotherms lying between the curve obtained from eq. [8.1.26] and the additive line. This isotherm subtype occurs in systems with low value of heteromolecular association constant. The system n-butyric acid−water can be mentioned as a typical example of the subtype. Subtype IIIb combines S-shaped ε isotherms. This shape is the result of the coexistence of homo- and heteromolecular association processes. System pyridine−water is a typical example of this subtype. Subtype IIIc combines most common case of ε isotherms − curves monotonically 2 2 convex from the composition axis ( ∂ε ⁄ ∂V ≠ 0, ∂ ε ⁄ ∂V < 0 ). The system water−glycerol can serve as a typical example of the subtype. Subtype IIId is represented by ε isotherms with a maximum. Typically, this kind of isotherm corresponds to systems with a high heteromolecular association constant. Component interaction results in associates with greater values of DM than expected from individual components. Carboxylic acids−amines have this type of isotherms. Finally, subtype IIIe includes rare kind of ε isotherms with a singular maximum, which indicates equilibrium constant with the high heteromolecular association. This kind of isotherm is represented by system SnCl4−ethyl acetate. 8.1.3.2.2 Viscosity Shapes of binary liquid system viscosity − composition isotherms vary significantly. The basic types of viscosity − composition isotherms for systems with interacting components are given in Figure 8.1.3. Type I − viscosity isotherms are monotonically convex in a direction to the composi2 2 tion axis ( ∂η ⁄ ∂x ≠ 0, ∂ η ⁄ ∂x > 0 ). Chemical interaction influences the shape of viscosity isotherm that is typical when experimental isotherm is situated above the curve calculated under the assumption of absence of any interaction (i.e., from equation [8.1.31a]). The means of increasing heteromolecular association and determination of stoichiometry of associates for this type of isotherms were discussed elsewhere.3 Piperidine− aniline system is an example of this kind of interacting system. 2 2 Type II − S-shaped viscosity curves ( ∂η ⁄ ∂x ≠ 0, ∂ η ⁄ ∂x > 0 at the inflection point). This type of isotherm is attributed to systems which have components differing substantially in viscosity but have a low yield of heteromolecular associates to form local maximum in isotherms. Systems such as sulfuric acid−pyrosulfuric acid and diphenylamine−pyridine are examples of this kind of viscosity isotherm. Type III combines viscosity isotherms, which are convex-shaped from composition 2 2 axis as its common attribute, i.e., ∂ η ⁄ ∂x > 0 . In the whole concentration range, we E have positive values of excessive viscosity η = η exp – [ ( η 1 – η 2 )x + η 2 ] , where ηexp is the experimental value of viscosity. It shall be mentioned that, although the term ηE is used in literature, unlike the excessive logarithm of viscosity (lnη)E = lnηexp − (lnη1/η2 + lnη2), it has no physical meaning. Viscosity isotherms of this type for interacting liquid

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Figure 8.1.3. Classification of viscosity isotherms for binary solvents.

systems are most commonly encountered and have shape diversity, which can be divided into three subtypes. Subtype IIIa − isotherms are monotonically convex shaped from composition axis, but without maximum (in the whole composition range ∂η ⁄ ∂x ≠ 0 ). Dependence viscosity-composition of water−monochloroacetic acid can serve as an example. Subtype IIIb − isotherms with “irrational” maximum (i.e., with a maximum which does not correspond to any rational stoichiometric correlation of components in a mixed solvent). This subtype is the most common case of binary mixed solvents with interacting components. System trifluoroacetic acid−acetic acid is a common example. The true stoichiometry determination method for this case was described elsewhere.3 Subtype IIIc − isotherms with a maximum at rational stoichiometry, which corresponds to the composition of a heteromolecular associate. This case can be exhibited by the system pyrosulfuric acid−monochloracetic acid. Occasionally, isotherms with singular maximum can also occur. This behavior is characteristic of the system mustard oil−amine.

434

8.1 Mixed solvents

This classification covers all basic types of viscosity isotherms for binary mixed systems. Although the classification is based on geometrical properties of isotherm, heteromolecular associations determine specific isotherm shape and its extent. The relative level of interactions in binary mixed systems increases from systems with isotherms of type I to systems with type III isotherms. 8.1.3.2.3 Density, molar volume Unlike the dependences of density deviation (from additive values) on system composition, correspondent dependencies of specific (molar) volume deviation from the additive values: Δθ = θ exp – [ ( θ 1 – θ 2 )x + θ 2 ] where:

Δθ θexp θi x

[8.1.41]

departure from of molar volume experimental value of molar volume molar volumes of components molar fraction of the second component

allow us to make a meaningful assessment of the heteromolecular association stoichiometry.3 Classification of volume-dependent properties of binary mixed solvents are based on dependencies of Δθ value (often called “excessive molar volume”, θE). It is evident both from “ideal system” definition and from equation [8.1.36], that for non-interacting systems Δθ ≈ 0 . Interaction is accompanied by the formation of the heteromolecular associates. It can be demonstrated by analysis of volumetric equations for the liquid mixed systems, data on volume compression, i.e., positive density deviation from additivity rule, and hence negative deviations of experimental specific molar volume from partial molar volume additivity rule. There are three basic geometrical types of Δθ isotherms for binary liquid systems with chemically interacting components12 (Figure 8.1.4.). Type I − rational Δθ isotherms indicating that only one association product is formed in the system (or that stability constants for other complexes in the system are substantially lower than for the main adduct). Most often, an adduct of the equimolecular composition is formed, and the maximum on Δθ isotherm occurs at x = 0.5. Fluorosulfonic acid− trifluoroacetic acid system is an example of the type. Type II − irrational Δθ isotherms with maximum not corresponding to the stoichiometry of the forming associate. This irrationality of Δθ isotherms indicates the formation of more than one adduct in the system. In the case of formation of two stable adducts in the system, the Δθ maximum position is between two compositions which are stoichiometric for each associate. If in the system, two adducts AB and AB2 are formed, then Δθ position of maximum is between xA values of 0.5 and 0.33 molar fractions. This type of Δθ isotherm is most common for interacting binary liquid systems, for example, diethylaniline− halogen acetic acids. Type III includes Δθ isotherms with a singular maximum. According to metrical analysis,3 dependencies of this type are typical of systems where adduct formation constant, K f → ∞ . Mustard oil−amine is an example of this behavior.

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Figure 8.1.4. Classification of isotherms of molar volume deviation from additivity for binary solvents.

The relative extent of the interaction increases from systems with Δθ isotherms of type I to systems of type III isotherms. This conclusion comes from analysis of metrical molar volume equations and comparison of binary systems composed of one fixed component and a number of components, having reactivity towards fixed component changing in well-defined direction. 8.1.3.2.4 Conductivity The shape of specific conductivity relation on the composition of the binary mixed solvent depends on the conductivity of the components and some other parameters discussed below. Because of molar conductivity calculation of binary mixed solvent system, the ion associate concentration should be taken into account (eq. [8.1.7]). This quantity is known in very rare instances,13,14 therefore, the conductivity of interacting mixed solvent is most often expressed in specific conductivity terms. Classification of conductivity shapes for binary liquid systems may be based on the initial conductivity of components. Principal geometrical types of the conductivity isotherms are presented in Figure 8.1.5. The type I isotherm includes the concentration dependence of the conductivity of the systems (Figure 8.1.5). These systems are not often encountered in research and technology practice. The type I can be subdivided into subtype Ia − isotherms with a minimum (for example, selenic acid−orthophosphoric acid) and subtype Ib − isotherms with a maximum (for instance, orthophosphoric acid−nitric acid). The type II isotherms describe the concentration dependence of conductivity for binary systems containing only one conductive component. In this case, also, two geometric subtypes may be distinguished. Subtype IIa − has a monotonically convex shape (i.e., without extreme) in the direction of the composition axis. The binary system, selenic acid−acetic acid, can serve as an example of this kind of dependency. Subtype IIb includes isotherms with a maximum (minimum) − most widespread kind of isotherms (for example: perchloric acid−trifluoroacetic acid). The next frequently observed case is separated as subtype IIb-1; these are isotherms with χ = 0 in the middle of concentration range. The system sulfuric acid−ethyl acetate illustrates the subtype IIb-1.

436

8.1 Mixed solvents

Figure 8.1.5.Classification of specific conductivity isotherms for binary solvents.

Geometrically, the conductivity isotherms of I and II types are similar to the χ isotherms for binary liquid systems without interaction (Section 8.1.3.1.4). But conductivity dependences corrected for viscosity vs. the concentration of interacted system differ from the corresponding dependences for non-interacting systems because of the presence of maximum. Also, interacting and non-interacting systems differ based on analysis of the effect of the absolute and relative temperature conductivity coefficients on concentration.3 The relative temperature electric conductivity coefficient, βχ, differs from the electric conductivity activation energy, Eact, by a constant multiplier.15 Systems formed by non-electrolyte components are the most common types of electrolyte systems. The conductivity of the systems results from the interaction between components. This interaction proceeds according to the steps outlined in the scheme [8.1.8]. The conductivity of the mixed electrolyte solution confirms the interaction between components.

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Subtype IIIa isotherms are the most widespread. Such isotherms have one maximum and bring the conductivity to the origin of pure components. Subtype IIIb isotherms have a minimum situated between two maxima. The maximum appears because of the significant increase of the solution viscosity due to the heteromolecular association process. When the conductivity is corrected for viscosity, the maximum disappears. Conductivity of the mixed solvent pyrosulfuric acid−acetic acid is an example of the system. Subtype IIIb-1 isotherms with a curve is a special case of subtype IIIb isotherms. The curve is caused by viscosity influence. Isotherm IIIb turns to subtype IIIb-1 at higher temperatures. A concentration dependence of conductivity for stybium (III) chloride−methanol is an example of the systems. Determination of stoichiometry of interaction between the components of the mixed solvent is discussed elsewhere.3,12 8.1.3.3 Chemical properties of mixed solvents Solvating ability of mixed solvent differs from the solvating ability of individual components. In addition to the permittivity change and the correspondent electrostatic interaction energy change, this is also caused by a number of reasons, the most important of which are discussed in the chapter. 8.1.3.3.1 Autoprotolysis constants Let both components of the mixed solvent, AH−BH, to be capable of autoprotolysis process. +

-

[8.1.42a]

+

-

[8.1.42b]

2HA ↔ H 2 A + A 2BH ↔ H 2 B + B

As Aleksandrov demonstrated,15 the product of the activities of lionium ions sum ( a + + a + ) on the liate activities sum ( a - + a - ) is a constant value in the whole H2 A H2 B A B concentration range for a chosen pair of cosolvents. This value is named as ion product of binary mixed solvent. HA – HB

K ap

= (a

H2 A

+

+a

H2 B

+

)(a

A

-

+ a -) B

[8.1.43]

If components of binary mixed solvent are chemically interacting, then the equilibrium of protolysis processes [8.1.42] is significantly shifting to one or another side. In most such instances, concentrations of lionium ions for one of the components and liate ions for another become so low that correspondent activities can be neglected, that is autoprotolysis constant can be expressed as: HA – HB

K ap

HA – HB

K ap

= a = a

+

+a

+

+a

H2 A

H2 B

B

A

-

[8.1.44a]

-

[8.1.44b]

438

8.1 Mixed solvents

As an example, let us consider mixed solvent water−formic acid. Both components of the system are subject to autoprotolysis: +

+

-

2H 2 O ↔ H 3 O + OH and 2HCOOH ↔ HCOOH 2 + HCOO

+

It is obvious, that in the mixed solvent, concentrations of the HCOOH 2 ions (strongest acid from possible lionium ions in the system) and the OH- ions (strongest base from two possible liate ions) are neglected, because these two ions are mutually neutralized. The equilibrium constant of the direct reaction is very high: +

-

HCOOH 2 + OH ↔ HCOOH + H 2 O Therefore, in accordance with [8.1.44a] autoprotolysis constant for this mixed solvent can be expressed as: HA – HB

K ap

= a

H3 A

+

+a

HCOO

-

Because of lionium and liate ions activities, both mixed solvent components depend on solvent composition, as does autoprotolysis constant value for the mixed solvent. Figure 8.1.6 demonstrates dependencies of pKap values on composition for some mixed solvents. Using the dependencies, one can change the mixed solvent neutrality condition in a wide range. That is, for mixed solvent composed of DMSO and formic acid, neutrality condition corresponds to the concentration of H+ (naturally solvated) of about 3x10-2 g-ion*l-1 at 80 Figure 8.1.6. Dependence of pKap (−logKap) on the mol% formic acid, but only 10-4 g-ion*l-1 at mixed solvent composition: 1 − DMSO−formic acid; 2 − DMSO−acetic acid; 3 − formic acid-acetic acid. 10 mol% acid component. The method of autoprotolysis constant value determination based on electromotive force measurement in galvanic element composed from Pt,H2(1 atm)|KOH(m), KBr(m), solvent|AgBr,Ag was proposed elsewhere.15a The method was used for the polythermal study of autoprotolysis constant of binary mixed solvent 2-methoxyetanol−water. On the basis of ionization constants, polytherms data, and the autoprotolysis process, thermodynamic data were calculated. A large dataset on the electrophilicity parameter ET (Reichardt parameter65) for binary water−non-water mixed solvents was compiled.66

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8.1.3.3.2 Solvating ability Applying the widely-used chemical thermodynamics concept of free energy linearity, it is easy to demonstrate that any characteristic y which linearly depends on free energy or on free activation energy of process in the mixed solvent composed of specifically non-interacting components, shall be a linear function of the components with partial molar concentration x. i

y =

 yi xi

[8.1.44]

1

The formula was developed analytically by Palm.16 In the mixed solvents with chemically interacting components, the function y = f(x) can substantially deflect from the linear form including appearance of extrema. Selection of the mixed solvent components allows us in most cases to provide controlled solvation of all substances, participating in the chemical process performed in solution. Often, it can be achieved by a combination of solvate-active and solvate-inter components. For example, it is obvious that in all compositional range of mixture DMSO− CCl4 (except 100% CCl4) specific solvation of acid dissolved in this mixture is realized by DMSO. Similarly, in mixed solvent formic acid−chlorobenzene, solvation of the dissolved donor substance is performed exclusively by formic acid. Selection of the second (indifferent) component's ε also provides means to control the universal solvation ability of mixed solvent. In the above-mentioned examples, increasing the solvate-inter component concentration results in the decrease of the mixed solvent ε. On the contrary, addition of indifferent component (propylene carbonate) into the systems such as acetic acid−propylene carbonate or propylene carbonate−aniline causes ε to rise. Because in the last two systems acetic acid and aniline were chosen as solvate-active components, it was obviously intended to use these mixtures for specific solvation of the dissolved donor and acceptor compounds respectively. 8.1.3.3.3 Donor−acceptor properties As was demonstrated,17 the parameters ET and Z of the binary mixed solvent 1,2-dibromoethane−1,2-dibromopropane are a strictly additive function of molar composition. For the mixed solvents, having components engaged into specific interaction, dependencies ET=f(x) and Z=F(x) are non-linear and even extremal, as can be seen from the examples in Figure 8.1.7. The method was proposed18 to linearize polarity index of the mixed solvent by introducing a parameter, which connects the ET and Z values with fractional concentrations of components.

8.1.4 MIXED SOLVENT INFLUENCE ON THE CHEMICAL EQUILIBRIUM 8.1.4.1 General considerations The chemical process established in a solvent can be represented in a general form:7 E↔F

[8.1.45]

440

8.1 Mixed solvents

Figure 8.1.7. ET and Z parameters for some mixed solvents. where: E F

all chemical forms of reaction reagents all chemical forms of reaction products

Considering the traditional thermodynamic cycle, we can use the general equation of Gibbs' energy variation because of the process [8.1.45]: ΔG =ΔGsolv, E − ΔGsolv, F − ΔG(v) where:

ΔGsolv, E, ΔGsolv, F

Gibbs' solvation energy of [8.1.45] equilibrium members

ΔG(v) Gibbs' energy of process [8.1.45] in vacuum

[8.1.46]

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The process [8.1.45] takes place in mixed solvent A−B. Solvation energies of equilibrium members are the algebraic sum of those for each of the mixed solvent components (this sum also takes into account the energy of mixed solvates such as EAxBy and FAzBt): ΔG solv, i = ΔG solv, A + ΔG solv, B = σ solv, i

[8.1.47]

Therefore the equation [8.1.46] can be represented in the form: ΔG = σ solv, E – σ solv, F – ΔG

(v)

[8.1.48]

The variation of free energy due to any chemical process consists of both covalent and electrostatic components: ΔG = ΔG

( cov )

– ΔG

( el )

[8.1.49]

Substituting [8.1.49] in [8.1.48], we come to an equation that in general describes the mixed solvent effect on the equilibrium chemical process: ΔG = – ΔG

(v)

( cov )

( cov )

( el )

( el )

+ ( σ solv, E – σ solv, F ) + ( σ solv, E – σ solv, F )

For universal (chemically indifferent) solvents, where σ assumed that ΔG = – ΔG

(v)

( el )

[8.1.50] ( el )

»σ

( el )

+ σ solv, E – σ solv, F

( cov )

, it may be [8.1.51]

Thus the mixed solvent effect on the equilibrium of the chemical process [8.1.45] is determined not only by the vacuum component but also by the solvation energy of each of the chemical forms of equilibrium members. From free energy to equilibrium constants, one can obtain the equation describing the mixed solvent effect on the equilibrium constant of the [8.1.45] process: ln K = [ ΔG

(v)

( cov )

( cov )

( el )

( el )

+ ( σ solv, F – σ solv, E ) + ( σ solv, F – σ solv, E ) ] ⁄ RT

[8.1.52]

In the special case of universal media, i.e., mixed solvent formed by both solvationinert components, this equation can be presented as: ln K

( univ )

= [ ΔG

(v)

( el )

( el )

+ σ solv, F – σ solv, E ] ⁄ RT

[8.1.53]

Because the energy of all types of electrostatic interaction is inversely proportional to permittivity, these equations can be rewritten in the form: ln K = [ ΔG

(v)

( cov )

( cov )

+ ( σ solv, F – σ solv, E ) + ( β solv, F – β solv, E ) ⁄ ε ] ⁄ RT

[8.1.52a]

and ln K

( univ )

= [ ΔG

(v)

+ ( β solv, F – β solv, E ) ⁄ ε ] ⁄ RT

[8.1.53a]

442

8.1 Mixed solvents

where:

β

the multipliers of the magnitudes of reciprocal permittivity in equations of the energy of the main types of electrostatic interactions such as dipole-dipole, ion-dipole, and ion-ion interactions

As follows from [8.1.52a], in the binary mixed solvents formed from solvation-indifferent components (i.e., universal media), equilibrium constants of the [8.1.45] process are exponent dependent on the 1/ε values (i.e., it is a linear correlation between lnK(univ) and 1/ ε magnitudes). The vacuum component of the energy of the [8.1.45] process can be obtained by the assumption of hypothetical media with ε → ∞ and 1 ⁄ ε → 0 : ΔG

(v)

( univ )

= RT ln K 1 ⁄ ε → 0

[8.1.54]

For binary solvents formed by solvation (active component A and indifferent component B) analysis of equation [8.1.52a] demonstrates that there is also a linear correlation between lnK and 1/ε. Such mixed solvents are proposed to be called as conventionally universal. To analyze the solvent effect on the process [8.1.45], it is often convenient to represent the temperature and permittivity dependencies of lnK in the approximated form: 2

2

ln K = a 00 + a 01 ⁄ T + a 02 ⁄ T + … + ( a 10 + a 11 ⁄ T + a 12 ⁄ T + … ) ⁄ ε + i = m j = n 2

2

+ ( a 20 + a 21 ⁄ T + a 22 ⁄ T + … ) ⁄ ε + … =

a ij -------j i ε T 0



[8.1.55]

i = j = 0

For the universal and conventionally-universal media, this dependence described by the equation can be represented in the form: ln K

( univ )

= a 00 + a 01 ⁄ T + a 10 ⁄ ε + a 11 ⁄ ε T

[8.1.56]

8.1.4.2 Mixed solvent effect on the position of equilibrium of homomolecular association process All questions with which this part deals are considered based on the example of a special and wide-studied type of homomolecular association process, namely, monomer-dimer equilibrium: 2E ↔ E 2

[8.1.57]

For this process, equation [8.1.52] can be presented in the form [8.1.58]: ( cov )

( cov )

ln K dim = [ ΔG dim + ΔG solv, E – 2ΔG solv, E + ( β solv, E – 2β solv, E ) ⁄ ε ] ⁄ RT 2

where:

β

2

value at the 1/ε is calculated in accordance with the following equation

Y. Y. Fialkov, V. L. Chumak 3

2

el

μ

443

ΔG d – d = – 120.6μ ⁄ r d – d kJ/mol the dipole moment

Because of the electrostatic component of the process [8.1.57], the free energy is conditioned by dipole-dipole interactions such as dimer-solvent and monomer-solvent. In a mixed solvent, CCl4−C6H5Cl, universal relation to acetic acid (because the mixed solvent components do not enter into specific solvation with the acid), the dimerization constant dependence on the temperature and permittivity in accordance with [8.1.52.a] and [8.1.56] is described by equation:19 ln K dim = – 1.72 + 1817.1 ⁄ T + 0.92 ⁄ ε + 1553.4 ⁄ εT The dimer form concentration, cM (mol/l), is related to the initial analytical concentration of dissolved compound and dimerization constant in the equation: 0

0

c M = [ 4K dim c M + 1 – ( 8K dim c M + 1 )

1⁄2

] ⁄ 8K dim

[8.1.59] 0

One can calculate, with the help of this equation, that in hexane at c M = 0.1, half of 3 the dissolved acetic acid is in dimer form ( K dim ≈ 1.5 × 10 ). In nitrobenzene solution 2 ( K dim ≈ 10 ), only a third of analytical concentration of acid is in the dimer form. For phenol, these values are 12% and 2%, respectively. Therefore, the composition variation of universal mixed solvents, for instance, using hexane−nitrobenzene binary solvent, is an effective method to control the molecular composition of dissolved compounds able to undergo homomolecular association, in particular, through H-bonding. Typically, in specific solvents, the process of monomer formation [8.1.57] is characterized by considerably lower dimerization constants, as compared with those in universal media. In fact, acetic acid dimerization constant in a water-dioxane binary solvent, the components of which are solvation-active in respect to the acid, vary in the 0.05-1.2 range. Replacing the solvent is often the only method to vary the molecular association state of the dissolved compound. To achieve dimer concentration in 0.1 M solution of phenol in nhexane equal to dimer concentration in nitrobenzene solution (50% at 25oC), it would be necessary to heat the solution to 480oC, but it is impossible under ordinary experimental conditions. 8.1.4.3 Mixed solvent influence on the conformer equilibrium Equilibrium took place in solutions Conformer I ↔ Conformer II

[8.1.60]

and the special case, such as Cis-isomer ↔ Trans-isomer

[8.1.61]

when investigated in detail. But the concentration-determining methods of equilibrium [8.1.60, 8.1.61] members are often not very precise. Dielcometry, or in our measurement the mean dipole moment, can be used only for the low-polar solvents. The NMR methods allowed us to obtain the equilibrium constants of processes by the measurement of chemical dislocation and constants of spin-spin interactions of nucleuses, which are quite pre-

444

8.1 Mixed solvents

cise but only at low temperatures (that is why the numerous data, on conformer and isomerization equilibrium, in comparison with other types of equilibria, are in solutions at low temperatures). It is evident that the accuracy of the experimental definition of equilibrium constants of the investigated process is insufficient. Thus, the summarization of experimental data on solvent effect on [8.1.60, 8.1.61] equilibrium encounters several difficulties. As a rule, the differences in conformer energies are not very high and change from one-tenth to 10-12 kJ/mol. This is one order value with dipole-dipole interaction and specific solvation energies, even in low-active solvents. Moreover, the dipole moments of conformer highly differ one from another, so ε is one of the main factors which affects equilibrium, such as in equations [8.1.60, 8.1.61]. If equations of processes are identical to that of the scheme [8.1.45] in the form and maintenance, it is possible to apply the equations from Section 8.1.4.1 to calculate the equilibrium constants of the investigated process. Abrahem20 worked out details of the solvent effect theory on changing the equilibrium. This theory also accounts for the quadruple interactions with media dipoles. It demonstrates that the accuracy of this theory equations is not better than that obtained from an ordinary electrostatic model. Because of low energy of [8.1.60, 8.1.61] processes, it is not possible to assign any solvents strictly to a universal or specific group. That is why only a limited number of binary solvents can be used for the analysis of universal media influence on conformer equilibrium constants. It is interesting to note that over the years, the real benzene basicity in liquid phase has not been sufficiently investigated. There were available conformer equilibrium constants in benzene, toluene, etc., highly differing from those in other lowpolar media. Such phenomenon is proposed to be called the “benzene effect”.21 Sometimes rather than equilibrium constants, the differences in rotamer energies − for example, gosh- and trans-isomers − were calculated from the experiment. It is evident that these values are linearly proportional to the equilibrium constant logarithm. Different conformers or different intermediate states are characterized by highly distinguished values of dipole moments.22 Indeed, the media permittivity, ε, change highly influences the energy of dipole-dipole interaction. Therefore, according to [8.1.53a], it is expected that conformer transformation energies and energies of intermediate processes in universal solvents are inversely proportional to permittivity. But equilibrium constants of reactive processes are exponent dependent on 1/ε value, i.e., there is a linear correlation between lnKconf and reciprocal permittivity: E conf ( turning ) = A + B ⁄ ε

[8.1.62]

ln K conf ( turning ) = a + b ⁄ ε

[8.1.63]

The analysis of experimental data on conformer and intermediate equilibrium in universal media demonstrates that they can be described by these equations with sufficient accuracy not worse than the accuracy of the experiment.

Y. Y. Fialkov, V. L. Chumak

445

The differences in rotamer energies of 1-fluoro-2-chloroethane in mixed solvents such as alkane−chloroalkane can be described by equation:20 ΔE = E gosh – E trans = – 2.86 + 8.69 ⁄ ε, kJ ⁄ mol According to equation [8.1.51], the permittivity increase leads to decreasing the absolute value of electrostatic components of conformer transformations free energies in universal solvents. For instance, the conformer transformation free energy of α-bromocyclohexanone in cyclohexane (ε = 2) is 5.2 kJ/mol, but in acetonitrile (ε = 36) it is −0.3 kJ/ mol. Specific solvation is the effective factor which controls conformer stability. The correlation between equilibrium constants of the investigated processes [8.1.60] and [8.1.61] and polarity of solvation-inert solvents is very indefinite. For instance, diaxial conformer of 4-methoxycyclohexanone in acetone (as solvent) (ε = 20.7) is sufficiently more stable than in methanol (ε = 32.6). But the maximum stability of that isomer is reached in lowpolar trifluoroacetic acid as solvent (ε = 8.3). Formation of the internal-molecular H-bonding is the cause of the increasing conformer stability, often of gosh-type. Therefore solvents able to form sufficiently strong external H-bonds destroy the internal-molecular H-bonding. It leads to change of conformer occupation and also to decrease of the internal rotation barrier. Due to sufficiently high donority, the benzene has a comparatively high degree of conformer specific solvation (“benzene effect”). This leads to often stronger stabilization of conformer with a higher dipole moment in benzene than in substantially more polar acetonitrile. In a number of cases, the well-fulfilled linear correlation between conformer transformation constants and the parameter ET of mixed solvent exists (see Section 8.1.3.4.3). It is often the solvent effect that is the only method of radical change of relative contents of different conformer forms. Thus, with the help of the isochore equation of chemical reaction, the data on equilibrium constants and enthalpies of dichloroacetaldehyde conformer transformation allow us to calculate that, to reach the equilibrium constant of axial rotamer formation in cyclohexane as solvent (it is equal to 0.79) to magnitude K=0.075 (as it is reached in DMSO as solvent), it is necessary to cool the cyclohexane solution to 64K (−209oC). At the same time, it is not possible because cyclohexane freezing point is +6.5oC. By analogy, to reach the “dimethylsulfoxide” constant to the value of “cyclohexane”, DMSO solution must be heated to 435K (162oC). 8.1.4.4 Solvent effect on the process of heteromolecular association Solvent effect on the process of heteromolecular association mE + nF ↔ E m F n

[8.1.64]

has been studied in detail.22,23 In spite of this, monographs are mainly devoted to individual solvents. In universal media formed by two solvate-inert solvents according to equation [8.1.53a], equilibrium constants of the process of heteromolecular adduct formation depend exponentially on reciprocal permittivity; thus

446

8.1 Mixed solvents

ln K add = a + b ⁄ ε

[8.1.65]

The process of adduct formation of acetic acid (HAc) with tributyl phosphate (TBP) nHAc • TBP in the mixed solvent n-hexane−nitrobenzene7 can serve as an example of the [8.1.65] dependence validity. Equilibrium constants of the mentioned above adducts in individual and some binary mixed solvents are presented in Table 8.1.2. Table 8.1.2. Equilibrium constants of adduct ( nHAc • TBP ) formation in the mixed solvent n-hexane − nitrobenzene (298.15K) and coefficients of equation [8.1.65] Kadd

Solvent

HAc • TBP

2HAc • TBP

3HAc • TBP 5

4HAc • TBP

Hexane (ε=2.23)

327

8002

6.19 × 10

1.46 × 10

H+NB (ε=9.0)

28.1

87.5

275

1935

H+NB (ε=20.4)

19.6

45.0

88.1

518

Nitrobenzene (ε=34.8)

17.4

36.2

60.8

337

a

2.69

3.28

3.58

5.21

b

5.82

10.73

18.34

21.22

–7

Coefficients of equation [8.1.65]

The concentration of adduct EF cM is related to constant Kadd and initial concentra0 tion of the components c M by equation 0

0

c M = [ 2K add c M + 1 – ( 4K add c M + 1 )

1⁄2

] ⁄ 2K add

[8.1.66]

When stoichiometric coefficients are equal to m and n (equation [8.1.64]), Kadd expression is an equation of higher degree relative to cM KE

n

0

m Fn

0

= c M ⁄ ( c M, E – nc M ) ( c M, F – mc M )

m

[8.1.67]

Let us consider an example of the interaction between acetic acid and tributyl phosphate (the change of permittivity of universal solvent permits us to change essentially the output of the reaction product). When initial concentration of the components equals to 0 c M = 0.1 mol/l, the output (in %) of complexes of different composition is listed in the table below:

1:1

2:1

3:1

4:1

in hexane

84

in nitrobenzene

43

46

32

22

13

4.5

2

Y. Y. Fialkov, V. L. Chumak

447

Relative concentration changes the more extensively, the larger the value of the elecel tro-static component of the process free energy, ΔG ε = 0 . Just as in the previous cases, the solvent use, in this case, is an effective means of process adjustment. To reduce the output of adduct HAc • TBF in nitrobenzene to the same value as in hexane solution, nitrobenzene solution must be cooled down to −78oC (taking into account that the enthalpy of adduct formation equals 15 kJ/mol).24 Naturally, the process is not possible because the nitrobenzene melting point is +5.8oC. Let us consider the effect of specific solvation on equilibrium constant of the heteromolecular association process as an example of the associate formation with the simplest stoichiometry: E + F ↔ EF

[8.1.68]

Only when A is a solvate-active component in the mixed solvent A−B, in the general case, both A and B initial components undergo specific solvation: E + A ↔ EA

[8.1.69]

F + A ↔ FA

[8.1.70]

where: EA, FA

solvated molecules by the solvent (it is not necessary to take into account solvation number for further reasoning)

Since specific solvation of the adduct EF is negligible in comparison with specific solvation of initial components, A−B interaction in the solvent can be presented by the scheme: EA + FA ↔ EF + 2A

[8.1.71]

i.e., the heteromolecular association process in the specific medium is a resolvation process, since both initial components change their solvative surrounding. That is why equilibrium constants of the heteromolecular association process, calculated without consideration of this circumstance, belong indeed to the [8.1.71] process but not to the process [8.1.68]. Let us develop a quantitative relation between equilibrium constants for the process [8.1.68] K EF = [ EF ] ⁄ [ E ] [ F ]

[8.1.72]

and for the resolvation process [8.1.71] K us = [ EF ] ⁄ [ EA ] [ FA ]

[8.1.73]

The concentration of the solvate-active solvent or the solvate-active component A of a mixed solvent in a dilute solution is higher than the initial concentration of equilibrium components [E]0 and [F]0. Then activity of equilibrium components is equal to their concentrations. Then, equations of material balance for components A and B can be set down as

448

8.1 Mixed solvents

[ E ] 0 = [ E ] + [ EF ] + [ EA ]

[8.1.74]

[ F ] 0 = [ F ] + [ EF ] + [ FA ]

[8.1.75]

Hence equilibrium constants of the process [8.1.69, 8.1.70] are presented by expressions K EA = [ EA ] ⁄ [ E ] = [ EA ] ⁄ ( [ E ] 0 – [ EF ] – [ EA ] )

[8.1.76]

K FA = [ FA ] ⁄ [ F ] = [ FA ] ⁄ ( [ F ] 0 – [ EF ] – [ FA ] )

[8.1.77]

Definition [8.1.72] is presented in the form K EF = [ EF ] ⁄ ( [ E ] 0 – [ EF ] – [ EA ] ) ( [ F ] 0 – [ EF ] – [ FA ] )

[8.1.78]

and resolvation constant K us = [ EF ] ⁄ ( [ E ] 0 – [ EF ] ) ( [ F ] 0 – [ EF ] )

[8.1.79]

Inserting [8.1.76] in [8.1.77] and [8.1.79] in [8.1.78], we come to the equation relating the equilibrium constants of all considered processes: K EF = K us ( 1 + E A ) ( 1 + F A )

[8.1.80]

A similar form of equation [8.1.80] has been proposed elsewhere.25 If it is impossible to neglect the solvent concentration (or the concentration of solvate component of the mixed solvent) in comparison with [E]0 and [F]0, the equation [8.1.80] is written in the form: A

S

K EF = K us ( 1 + K EA ) ( 1 + K FA )

[8.1.81]

Let E be acidic (acceptor) reagent in reaction [8.1.68], F basic (donor) reagent. Then, if A is acidic solvent, one can neglect specific solvation of the reagent E. Thus equations for equilibrium constant of the process [8.1.68] can be written in the form K EF = K us ( 1 + K FS )

A

K EF = K us ( 1 + K FS )

[8.1.82]

If A is a basic component, the equation [8.1.82] can be re-written to the form K EF = K us ( 1 + K EA )

A

K EF = K us ( 1 + K EA )

[8.1.83]

Equations [8.1.82] and [8.1.83] were developed26-28 for the case of specific solvation. Thus for KEF calculation, one must obtain the equilibrium constant of processes: [8.1.71] − Kus, [8.1.69] − KEA and [8.1.70] − KFS from conductance measurements. The constant KEF is identified in literature as “calculated by taking into account the specific solvation”.29 The value KEF characterizes only the universal solvation effect on the process of heteromolecular associate formation. The approach cited above can be illustrated by equilibrium:

Y. Y. Fialkov, V. L. Chumak

( CH 3 ) 2 SO + o-CH 3 C 6 H 4 OH ↔ ( CH 3 ) 2 SO • CH 3 C 6 H 4 OH

449

[8.1.84]

studied in binary mixed solvents: A) CCl4 − hepthylchloride30 formed by two solvate-inter components [8.1.84] B) CCl4 − nitromethane31 formed by solvate-inter component (CCl4) and acceptor (nitromethane) component C) CCl4 − ethyl acetate32 formed by solvate-inter component (CCl4) and donor (ester) component; The isotherms lnK vs. 1/ε (298.15K) are presented in Figure 8.1.8. These dependencies (lines 1,2,4,5) are required for calculation of equilibrium constants of the heteromolecular association process free from specific solvation effect. It can be seen from Figure 8.1.8 that the values of lnK, regardless of solvent nature, lie on the same line 3, which describes the change of equilibrium constants of the process [8.1.84] in the universal solution CCl4− heptylchloride. The data obtained for equilibrium [8.1.84] in binary mixed solvents of different physical and chemical nature are in need of some explanatory notes. Figure 8.1.8. Dependence of equilibrium constant for the First of all, if solvents are universal formation process of addition product DMSO to o-cresol on permittivity in solution based on heptylchloride (o), or conditionally universal ones, in accorethyl acetate (x) and nitromethane ( • ):1 − resolvation dance with general rules of equilibrium of o-cresol solvated in ethyl acetate in DMSO in mixed constants, the dependence on permittivity solvent CCl4−ethyl acetate; 2 − resolvation of DMSO solvated in nitromethane in o-cresol in mixed solvent and the dependence of K = f(1/ε) in all CCl4−nitromethane; 3 − process [8.1.84] in mixed solcases is rectilinear. vent CCl4−heptylchloride; 4 − solvation of o-cresol in As it appears from the above, specific ethyl acetate; 5 − solvation of DMSO in nitromethane. solvation of one component decreases equilibrium constants in comparison with equilibrium constants in isodielectric universal solvent. The increase of KEF with permittivity increase in DMSO−o-cresol system required supplementary study.33 The method of study of specific solvation effect on the process of heteromolecular association has been described in work34 devoted to study of the following interaction: C 6 H 3 ( NO 2 ) 3 + C 6 H 5 N ( CH 3 ) 2 ↔ C 6 H 3 ( NO 2 ) 3 • C 6 H 5 N ( CH 3 ) 2

[9.85]

450

8.1 Mixed solvents

in the binary liquid solvent formed from a solvate-inert component (heptane) and one of the following solvate-active components: trifluoromethylbenzene, acetophenone or pchlorotoluene. Therefore, trinitrobenzene, TNB, is solvated in initially mixed solvents, so its interaction with donor represents the resolvation process [8.1.85a]. C 6 H 3 ( NO 2 ) 3 • A + C 6 H 5 N ( CH 3 ) 2 ↔ C 6 H 3 ( NO 2 ) 3 • C 6 H 5 N ( CH 3 ) 2 + ( A ) Equation [8.1.62] applied to the process of the heteromolecular association is written in the form: ln K = [ ΔG

(v)

( cov )

( cov )

( cov )

+ ( σG solv, EF – σG solv, E – σG solv, F ) + σβ solv ⁄ ε ] ⁄ RT [8.1.86] ( cov )

But for equilibrium [8.1.85a] in mixed solvents, one can assume σG solv, EF ≈ 0 . That is why the equation [8.1.52] can be converted for the process in conditionally universal media: ln K us = [ ΔG

(v)

( cov )

– σG solv, E + σβ solv ⁄ ε ] ⁄ RT

[8.1.86a]

It follows from equation [8.1.86a] that dependence of lnKus vs. 1/ε will be rectilinear. Experimental data of equilibrium constants for process [8.1.85a] are in agreement with the conclusion. Approximation of data by equation [8.1.65] is presented in Table 8.1.3. It also follows from equation [8.1.86a] that RT, unlike in the cases of chemical equilibrium in universal solvents, describes, not the vacuum component of the process free ( cov ) ( el ) (v) energy, but the remainder ΔG – σG solv, TNB and σG solv, TNB . The values of the remainder as well as an electrostatic component of the free energy for the described chemical equilibrium are summarized in Table 8.1.4. Although the solvate-active components are weak bases, their differences influence ( cov ) ( el ) (v) the values ΔG – σG solv, TNB and σG ε = 1 . The first value characterizes the difference between the covalent components of solvation energy for trinitrobenzene in any solvateactive solvent. It follows from the table, that contributions of the covalent and electrostatic components are comparable in the whole concentration range of the mixed solvents. This indicates the same influence of both donor property and permittivity of the solvent on the [8.1.85a] process equilibrium. Table 8.1.3. Coefficients of equation [8.1.65] equilibrium constants of the [8.1.85a] process at 298.15K (r-correlation coefficient) Solvent

a

b

r

Heptane-trifluoromethylbenzene

−0.80

5.50

0.997

Heptane-acetophenone

−1.49

6.74

0.998

Heptane-chlorotoluene

−2.14

7.93

0.998

Y. Y. Fialkov, V. L. Chumak

451

Table 8.1.4. Free energy components (kJ/mol) of resolvation process [8.1.85a] in mixed solvents at 298.15K ε

−ΔG in system heptane-S, where S is: trifluoromethylbenzene

acetophenone

chlorotoluene

2

6.8

8.3

9.8

4

3.4

4.1

4.9

6

2.3

2.8

3.3

8

1.7

2.1

−

−2.0

−3.7

−5.3

13.6

16.7

19.6

(v)

ΔG – ( el ) σG ε = 1

( cov ) σG solv, TNB

According to the above energy characteristics of the heteromolecular association process (resolvation) in specific media, the solvent exchange affects the products' output (the relationship of output cM and Kus is estimated from the equation [8.1.66]). This shows that the product output (with an initial concentration of reagents 0.1M) can be changed from 34% (pure heptane) to 4% (pure n-chlorotoluene) by changing the binary mixed solvent composition. The processes [8.1.85a] and [8.1.85] can be eliminated completely when the solvate-active component (more basic then chlorotoluene) is used. The possibility of management of the products` output may be illustrated by the data from reaction equilibrium [8.1.84]. As follows from Figure 8.1.8, the maximum equilibrium constant (in investigated solvents) is for pure chloroheptane; the adducts output in this solvent equals to 86% (at initial concentration of reagent 0.1 M). The minimum equilibrium constant of the process is in pure ethyl acetate, where the products` output equals to 18% (at an initial concentration of reagent 0.1 M). Thus the products` output of the reaction [8.1.84] can be changed directionally in the range 90 up to 20% by means of choice of corresponding binary or individual solvent. If the selected solvent is more basic than ethyl acetate or more acidic than nitromethane, the process is not possible. Heteromolecular association process of o-nitrophenol and triethylamine can be an example of the management of products` output. Association constant of this process has been determined for some solvents.35 Use of hexane instead of 1,2-dichloroethane, DHLE, increases products' output from 6% to 93%. When both components of the mixed solvent are solvate-active towards the reagents of equilibrium [8.1.64], the following interactions take place: E + A ↔ EA ; F + A ↔ FA ; E + B ↔ EB ; F + B ↔ FB

[8.1.87]

The process of heteromolecular association [8.1.64] is due to the displacement of the solvent components and formation of completely or partially desolvated adduct: xEA + yFA + ( m – x )EB ↔ E m F n + ( A ) + ( B )

[8.1.88]

It is easy to develop the equation for binary solvent formed from two solvate-active components similar to [8.1.90] by using the above scheme for the binary solvent with one

452

8.1 Mixed solvents

solvate-active component (equations [8.1.76 - 8.1.80]) and introducing equilibrium constant of the process [8.1.88] such as Kus: K EF = K us ( 1 + K EA ) ( 1 + K FA ) ( 1 + K EB ) ( 1 + K FB )

[8.1.89]

where: equilibrium constant of the processes [8.1.87]

Ki

8.1.4.4.1 Selective solvation. Resolvation When component B is added to solution E in solvent A (E is neutral molecule or ion), resolvation process takes place: EA P + qB = EB q + pA

[8.1.90]

The equilibrium constant of this process in ideal solution (in molar parts of the components) equals to: p

K us = m EB m A ⁄ m EA m q

p

q

[8.1.91]

B

where: mi p, q

a number of moles stoichiometric coefficients of reaction

On the other hand, resolvation constant Kus equals to the ratio of equilibrium constants of solvation processes E + pA ↔ EA p ( I ) ; E + qB ↔ EB q ( II ) : K us = K II ⁄ K I

[8.1.92]

The method of Kus determination, based on the differences between free energy values of electrolyte transfer from some standard solvent to A and B, respectively, leads to a high error. If the concentration ratio of different solvative forms is expressed as α, the concentrations A and B are expressed as 1 − xB and xB, respectively, (xB − molar part B), equation [8.1.91] may be presented in the form: p

K us = αx B ⁄ ( 1 – x B )

q

[8.1.91a]

or ln K us = ln a + p ln x B – q ln ( 1 – x B )

[8.1.93]

The last equation permits to calculate a value for the solvent of fixed composition and xB determination at the certain composition of the solvate complexes p and q and resolvation constant Kus. It follows from the equations [8.1.91] and [8.1.91a] (q)

0

(q)

(q)

(q) q

K us = [ m E q ⁄ ( m E – m E ) ] [ x 0 ( 1 – x B ) ] where:

0

mE

a number of moles E in solution

[8.1.91b]

Y. Y. Fialkov, V. L. Chumak (q)

mE

453

a number of moles E solvated by the solvent A

Hence p

q

K us = x' B x B ⁄ [ ( 1 – x' B ) ( 1 – x B ) ]

[8.1.91c]

where: x' B

the molar fraction of B in solvate shell

Figure 8.1.9. Characteristics of solvate shells in the mixed solvent A−B: a − dependence a = EA/EB on composition of the mixed solvent; b − dependence of the solvate shell composition, x' B , on composition xB of the mixed solvent E−A−B.

Equation [8.1.91c] developed for the ideal solution E−A−B permits us to establish the relationship between the composition of mixed solvent xB and the solvate shell composition x' B . For the special case of equimolar solvates, the expression of the resolvation constant is written in the form: K us = αx B ⁄ ( 1 – x B )

[8.1.91d]

It follows that even in an ideal solution of the simplest stoichiometry, α is not a linear function of the mixed solvent composition xB. Dependence of isotherm a on the solvent composition at Kus = 1 is presented in Figure 8.1.9a. Analytical correlation between the composition of solvate shell xB and the mixed solvent composition can be developed: p

q

K us = [ x' B ⁄ ( 1 – x' B ) ] [ x B ⁄ ( 1 – x B ) ]

[8.1.94]

The dependence for Kus = 1 is given in Figure 8.1.9b. As it follows from the analysis of equation [8.1.94] and Figure 8.1.9, the compositions of solvate shell and mixed solvent are different.

454

8.1 Mixed solvents

Figure 8.1.10. Selective solvation of NaI in mixed solvent cyanomethane−methanol (a) and DMFA−methanol (b, curve 1), DMFA − cyanomethane (b, curve 2): xB − composition of mixed solvent; x' B − composition of solvate shell in molar parts of the second component.

A similar approach has been developed for calculation of solvate shell composition Na+ and I- in the mixed solvent formed by the components with close values of permittivity. Such solvent selection permits us to eliminate the permittivity effect on solvation equilibrium. Resolvation constants have been determined from the calorimetric study. The composition of anions solvate complex has been determined from experimental data of electrolyte Bu4NI assuming lack of the cation-specific solvation. Experimental data are presented in Figure 8.1.10. Padova36 has developed this approach to non-ideal solutions. He has proposed an equation based on electrostatic interaction which relates molar fractions of the components (xB − in the mixed solvent and x' B − in the solvate shell) to the activity coefficient of components of the binary solvent: 2

α = ln [ ( 1 – x' B ) ⁄ ( 1 – x B ) ] = ln γ B

[8.1.95]

Strengthening or weakening interaction (ion-dipole interaction or dipole-dipole interaction) of universal solvation leads to re-distribution of molecules in the mixed solvate and to the change of the composition of solvate shell in contrast to the composition of the mixed solvent. The method for determination of average filling of molecules` coordination sphere of dissolved substance by molecules of the mixed solvent (with one solvate-inert component) has been proposed.37 The local permittivity is related to average filling of molecules' coordination sphere expressed by the equation:

Y. Y. Fialkov, V. L. Chumak

455

ε p = ε A x' A + ε B x' B

[8.1.96]

x' A = z A ⁄ ( z A + z B ) ; x' B = z B ⁄ ( z A + z B )

[8.1.97]

where:

where: zA, zB average numbers of A and B molecules in the first solvate shell

The last equations can be used for the development of the next expression permitting to calculate the relative content of B molecules in the solvate shell x' B = ( ε p – ε A ) ⁄ ( ε B – ε A ) where:

εp εA, εB

[8.1.98]

permittivity of binary solvent permittivities of components

Value x' B can be found from the equation linking the location of the maximum of absorption band of IR spectrum with refraction index and ε of the solution. The data on selective solvation of 3aminophthalimide by butanol from butanol− hexane mixture is presented in Figure 8.1.11. The data have been calculated from the equations presented above. Alcohol content in solvate shell has a higher concentration than in solvent composition even at low concentration of alcohol in the solvent. For example, when molar fraction of n-butanol in the mixture was 7%, the relative molar fraction of nbutanol in the solvate shell of aminophthalimide was 30%. The resolvation process completes at n-butanol concentration in solution ≈ 90 %. Mishustin37 proposed a strict and accuFigure 8.1.11. Selective solvation of 3-aminophthalimid (A) by n-butanol (B) from the mixed solvent rate method for selective solvation study. The hexane−n-butanol. method is based on data of free energy transfer of electrolyte from individual solvent A to mixed solvent A−B. The method takes into account non-ideality of the system and allows calculation of the concentration of different solvate forms and their dependence on the mixed solvent composition. An example of the application of this method is in the work.39 Authors have calculated the relative concentration of different solvate forms of Li+ in the mixed solvent ethylenediamine−DMSO and ethylenediamine−DMFA (Figure 8.1.12). Free energy of lithium transfer from DMSO (DMFA) in the mixed solvent has been calculated from the time of spin-lattice relaxation of kernel 7Li. The curves presented in Figure 8.1.12 depict

456

8.1 Mixed solvents

Figure 8.1.12. Dependence of concentration (in molar parts) of solvate forms Li(EDA)mSn on molar fraction, xB, of the second component in the binary solvents ethylenediamine−DMSO (a) and ethylenediamine−DMFA (b): 1 − m = 4, n = 0; 2 − m = n = 2; 4 − m = 0, n = 4.

quantitatively the selectivity of Li+ relative to ethylenediamine, which is a more basic component in contrast to the second components of the mixed solvent, namely DMSO and DMFA. The following systems can serve as examples of the effect of the composition of the mixed solvent on the solvate shell composition: [Cr(NH)S(H2O)m(DMSO)n]3+−H2O−DMSO40 [Be(H2O)m(EG)n]SO4−H2O−ethylene glycol41 [Be(H2O)m(HMPTA)n]SO4−H2O−HMPTA42 [Ni(H2O)mSn]ClO4−H2O−S (where S is methanol, ethanol, propanol, DMSO)43 Data presented in Figure 8.1.13 contain information on the composition of solvate shell as a function of the molar fraction of water in the mixed solvent H2O−other solvents.43 Monograph44 contains a collection of data on resolvation constants of the ions in the mixed solvents. The above-presented dependencies of the composition of solvate shell on the mixed solvent composition as well as resolvation constants permit calculation of the solvate composition by varying solvent Figure 8.1.13. The composition of solvate shell Ni2+ (in composition. The dependence of resolvamolar parts of water) in the mixtures of solvents formed from water and propanol (1), ethanol (2), methanol (3) and DMSO (4). Data from Ref. 43.

Y. Y. Fialkov, V. L. Chumak

457

tion constants on the permittivity of the solvent is discussed in the example of the proton resolvation process. In the mixed solvents water−non-aqueous solvent, in spite of its donor and polar properties, water is a preferred solvating agent. This generalization has some exceptions (solvation in systems Ag+−H2O−acetonitrile, Cr3+−H2O−DMSO, F−H2O−ethylene glycol).45 Solvation energy of proton by donor solvents is very high. The regularities of the proton selective solvation and resolvation processes were studied in more detail in comparison with other ions. Let us consider the changes in the system, when donor component is added to protic acid HA in solvent A. Anion solvation can be neglected if both solvents have donor character. The interaction influences the proton resolvation process eq. [8.1.99]. HA+p + B

HAp-1B

HA+p + qB

+

...

+B

...

HB+p + A

HB+q + pA

The model related to eq. [8.1.99a] was evaluated,46 resulting in the supposition that + + the equilibrium of two forms of a solvated proton ( HA p and HB q ) is important. Solvation stoichiometry was not considered. Both proton solvated forms are denoted as HA+ and HB+. If B is the better donor component (it is a necessary requirement for equilibrium [8.1.99] shift to the right-hand side of equation), the equation from work46 can be simplified to the form:47 A

B

A

K a = K a + ( K a – K a ) { [ K us x B ⁄ ( 1 – x B ) ] ⁄ [ 1 + K us x B ⁄ ( 1 – x B ) ] }

[8.1.100]

where: Ka A B Ka , Ka Kus xB

ionic association constant the ionic association constants of acid in individual solvents A and B a constant of resolvation process molar fraction of B

For the calculation of resolvation constant, one must determine the experimental A constant of HA association in the mixed solvent and determine independently K a and B Ka . When the resolvation process is completed at low concentration of the second component, the change of permittivity of mixed solvent A−B may be ignored. Thus, one may A B assume that K a and K a are constant and calculate Kus from the equation [8.1.100] in the form: A

B

A

B

A

1 ⁄ ( K a – K a ) = 1 ⁄ ( K a – K a ) + { [ ( 1 – x B ) ⁄ x B ] [ 1 ⁄ K us ( K a – K a ) ] } [8.1.101]

458

8.1 Mixed solvents

Thus Kus is calculated as a slope ratio A of coordinates: 1/(Ka − K a ) = (1 − xB)/xB A and (Ka − K a ) remainder is obtained as Yintercept. Dependence of eq. [8.1.101] is presented in Figure 8.1.14. Kus for proton was calculated in a series of mixed solvents. It was shown47 that, when pyridine, dimethylalanine or diphenylamine (resolvating agents with decreasing donor numbers) are added to the solution of trifluoroacetic acid in DMSO, proton decreases consecutively and its values are equal to 2.7x104; 4.2x103 and 35.4, Figure 8.1.14. Dependence of 1/(Ka − KaA) for respectively. CF3COOH on the mixed solvent composition DMSO Consideration of permittivity of the (A)−dimethylalanine at different temperatures. mixed solvent has allowed calculation of proton in the whole concentration range of the mixed solvent DMSO−diphenylamine. The data have been approximated using equation [8.1.55]. ln K us = – 12.2 + 3400 ⁄ T + 453.7 ⁄ ε – 75043 ⁄ εT Equilibrium constants for exchange process of alcohol shell of solvates to water shell were calculated:48 +

+

ROH 2 + H 2 O ↔ H 3 O + ROH

[8.1.102]

The solutions of HCl and HOSO3CH3 in aliphatic alcohol (i.e., CnH2n+1OH) − normal alcohol C1-C5 and isomeric alcohol C3-C5 have been studied. If the components taking part in resolvation process are capable of H-bonding, the anion solvation by these components cannot be neglected. The differences in Kus values for both acids in different solvents may be explained as follows. The dependence of Kus on permittivity and temperature is described by the equation: 2

ln K = a 00 + a 01 ⁄ T + a 02 ⁄ T + ( a 10 + a 11 ⁄ T ) ⁄ ε

[8.1.103]

The coefficients of equation [8.1.103] are presented in Table 8.1.5. Table 8.1.5. Coefficients of the equation [8.1.103] for constants of resolvation process a00

a01x10-2

a02x10-4

a10

a11x10-3

±δ

HCl−n-alcohol

12.4

46.0

56.3

186.8

71.1

0.3

HCl−isomeric alcohol

13.1

5.9

-36.9

318.4

94.7

0.2

HOSO3CH3−n-alcohol

6.3

4.4

-5.4

177.7

60.9

0.3

System

The solvent effect in the following resolvation process was studied:49

Y. Y. Fialkov, V. L. Chumak

459

+

+

ROH 2 + Py ↔ HPy + ROH

[8.1.104]

The solutions of trifluoroacetic acid in ethanol and methanol in the temperature range 273.15-323.15K were investigated. The dependence of Kus on permittivity and temperature is described by the equation: ln K us = 9.44 + 1768 ⁄ T + 77.8 ⁄ ε – 11076 ⁄ εT Unlike the processes considered above, in the case of process [8.1.104] permittivity decrease leads to decreasing Kus. The explanation of the results based on covalent and electrostatic components of resolvation process enthalpy is given.50 The reaction [8.1.104] also has been studied for isodielectric mixtures of alcohol− chlorobenzene with ε = 20.2 (permittivity of pure n-propanol) and ε =17.1 (permittivity of pure n-butanol) to investigate the relative effect of universal and specific solvation on the resolvation process. The mixtures were prepared by adding chlorobenzene to methanol, ethanol, and C1-C3 alcohol. Alcohol is a solvate-active component in these isodielectric solvents. Kus data are given in Table 8.1.6. Table 8.1.6. Equilibrium constants of the process [8.1.104] in isodielectric solvents Kusx10-5

Solvents with ε = 17.1

Kusx10-5

Methanol + 23.5% chlorobenzene

3.9

Methanol + 32.8% chlorobenzene

1.4

Ethanol + 13% chlorobenzene

4.9

Ethanol + 24% chlorobenzene

2.0

n-Propanol

7.3

n-Butanol

4.9

Solvents with ε = 20.2

Insignificant increase of Kus in n-butanol (or n-propanol) solution in comparison to methanol is due to relaxation of the proton−alcohol bond when the distance of ion−dipole interaction increases. The change of donor property of the solvate-active component is not significant. The equations relating Kus to ε permit to divide free energy of resolvation process into the components. Corresponding data are presented in Table 8.1.7. Table 8.1.7. The components of free energy (kJ mol-1) of proton resolvation process at 298.15K σΔGel in process Solvent

ε

[8.1.102]

[8.1.104]

HCl

HOSO3CH3

CF3COOH

Methanol

32.6

3.9

2.0

−3.1

Ethanol

24.3

5.3

2.7

−4.1

n-Propanol

20.1

6.4

3.3

−5.0

n-Butanol

17.1

7.5

3.9

−5.9

n-Pentanol

14.4

8.9

4.6

−

460

8.1 Mixed solvents

Table 8.1.7. The components of free energy (kJ mol-1) of proton resolvation process at 298.15K σΔGel in process ε

Solvent

[8.1.102]

[8.1.104]

HCl

HOSO3CH3

cov

8.2

17.7

−38.1

el

128

66.0

−100.6

−δΔG

– δΔG ε = 1

CF3COOH

In contrast to the processes considered earlier, the vacuum electrostatic component of the resolvation process has high value whereas −δΔGel values are comparable with the covalent component, −δΔGcov. δΔG values according to [8.1.51] are equal to: δΔG = ( ΔG

HB

+

+ ΔG A – ΔG

HA

+

+ ΔG B )

sol

For small additions of B (to component A), (ΔGA)sol = 0 and (ΔGHA)sol = 0, then δΔG = ( ΔG

HB

+

+ ΔG B )

sol

Solvation energy of complex HB+ by solvent A is small because coordination vacancies of the proton are saturated to a considerable extent. Therefore, the interaction energy between A and B significantly influences the value of σΔG. That is why, the mixed solvents (alcohol−water and alcohol−pyridine, for instance) are different because of the proton resolvation process. This can be explained in terms of higher energy of heteromolecular association for the alcohol−water in comparison with alcohol−pyridine. The concept of solvent effect on the proton resolvation process was confirmed by quantum chemical calculations.51 Above phenomena determine the dependence of resolvation constant on physical and chemical properties. Let the resolvation process proceed at the substantial abundance of component A in the mixed solvent and the initial concentrations HA (HA+) and B be equal. The output of the process can be calculated from the equation similar to equation [8.1.66]. The large value of Kus in all considered processes of proton resolvation indicates the effect of permittivity change on the yield of the complex HB+ formation. The output of resolvated proton in the process [8.1.104] proceeding in methanol equals 100%, whereas in the same process in low polarity solvent (e.g., methanol−hexane), with an abundance of the second component, the equilibrium is shifted to the left, resulting in solvate output of less than 0.1%. Kus values in single alcohol solvents are large, thus the output of reaction does not depend on the solvent exchange. + + The process H • DMSO + B ↔ HB + DMSO may be considered as an example of the effect of chemical properties of B on the output of the reaction [8.1.99]. The output of HB+ equals to 98%, if pyridine is included in the process at an initial concentration of 0.1M. Use of diphenylamine, having lower donor properties, decreases the output to 60%.

Y. Y. Fialkov, V. L. Chumak

461

The output differs even more at smaller concentrations of component, such as 10-3 M, which gives yields of 83 and 33%, respectively. 8.1.4.5 Mixed solvent effect on the ion association process The ion association process (or opposite to it − ion dissociation process) has been studied in detail in comparison with other types of chemical equilibrium in solutions. The modern state of the theory of individual solvent effects on equilibrium constant of ion association process (Ka) was described in monographs by Izmailov53 and Busse.54 The formation of free (preferably solvated) ions is due to a successive equilibrium states proceeding in solution [8.1.105]: K

mE + nF

add

EmF n

K i

Catq+pAnp-q

...

K a

pCatq+ + qAnp-

where: Kadd Ki Ka

a constant of adduct formation ionization constant association constant

The true constant of ion association is a ratio of ionic associate concentration q+ pCat p • An q to ion concentration product. If the ionic associate concentration is unknown (as is true in many cases), ion association constant is calculated from the analytical concentration of dissolved substance: q+

p-

q+ p

p- q

K a = { c 0 – p [ Cat ] – q [ An ] } ⁄ [ Cat ] [ An ] where: c0

initial concentration of the electrolyte

The general theory of ionic equilibrium53,54 leads to the conclusion that ion association constant in universal or conditionally universal media, in accordance with the equation [8.1.53a], depends exponentially on reciprocal value of permittivity: ln K a = a 00 + a 01 ⁄ ε

[8.1.106]

where: a00, a01

approximation coefficients

If ion association process has high energy, the solvents are solvate-inert because of large ions, such as (CnH2n+1)4N+, (CnH2n+1)4P+, etc. A solution Figure 8.1.15. Dependence Ka of (C2H5)4NBr on of (C2H5)4NBr in mixed solvents propylene permittivity in mixed solvents formed by propylene carbonate−o-dichlorobenzene and propylcarbonate with o-dichlorobenzene (1,2-o), pyridine (1,2-x) and acetic acid (3) at 298.15K. ene carbonate−pyridine55 serve as an example. The components of these binary solvents (with the exception of inert dichlorobenzene) possess donor properties, though

462

8.1 Mixed solvents

they do not solvate the large anion R4N+ because they are solvate-inert components in relation to the anion. That is why lnKa−1/ε isotherms follow the same line (see Figure 8.1.15). But the lnKa−1/ε isotherm for the solution of propylene carbonate−acetic acid differs from the other two because acetic acid is a solvate-active component in relation to anion Br-. Coefficients of equation [8.1.56] for the various systems are presented in Table 8.1.8. Table 8.1.8. Coefficients of equation [8.1.56] for ionic association of tetraethyl ammonium bromide at 298-323K solvent

−a00

a10

a01

a11

Propylene carbonate−o-dichlorobenzene

5.2

1440

78.8

9523

Propylene carbonate−pyridine

6.3

1850

114

0

Propylene carbonate−acetic acid

7.7

2400

110.5

-11500

The lnKa − 1/ε dependence for universal media is linear in full range of permittivity. The validity of the following equation was evaluated7 for the mixed solvent propylene carbonate−1,4-dioxane in the range of permittivity ε = 65±3 for the solutions Et4NBr: ln K a = 1.32 + 80.05 ⁄ ε Comparison of the free energy of components for ion association process in different solvents permits us to estimate the energy of specific solvation interaction. The electrical component of the change of free energy, depending on ion-ion interaction in accordance with the nature of ion association process, must exceed a sum of vacel uum and covalent components in equation [8.1.52]. σ solv for all above considered systems is higher than 85-90% because of the general change of the process free energy. The components of free energy of association of CH3(C8H17)3NOSO3CH3 in different solvents7 are presented in Table 8.1.9. Table 8.1.9. Components of free energy (kJ mol-1) of ion association of methyl octyl ammonium methyl sulfate in universal solvents at 298.15K Solvent

el

ε

σ solv

Pyridine−DMFA

25.0

7.6

Pyridine−acetonitrile

19.2

9.9

Pyridine−propylene carbonate

16.0

11.9

Nitrobenzene−acetic acid

11.9

16.0

Propylene carbonate−acetic acid

10.6

17.9

Evidently, the change of permittivity of the universal solvent is the most effective method of affecting the ion concentration. Using the equation relating ion concentration * c M for every type of 1-1 electrolyte with Ka and analytical concentration of the electrolyte, cM:

Y. Y. Fialkov, V. L. Chumak

463

0

c M = [ ( 4K a c M + 1 )

1⁄2

– 1 ] ⁄ 2K a

[8.1.107]

one can ascertain, that ε decrease from 185 to 6 changes in the ion concentration of methyl octyl ammonium methyl sulfate in solution from 71 to 0.3%. In a mixed solvent containing propylene carbonate, the ionic concentration of Et4NBr is also changed from 80% (in propylene carbonate) to 3% (in pyridine), and even to 0.8% (in o-dichlorobenzene or acetic acid). Thus, affecting electrolyte strength by solvent choice permits to change a strong electrolyte into non-electrolyte. Table 8.1.10. Coefficients of equations [8.1.56] and [8.1.106] for association constants of salts [8.1.56]

Solvent

a00

a10

[8.1.106] (296K) a01

a11

a00

a01

Lithium bromide (298.15-323.15K) Propylene carbonate−o-dichlorobenzene

3.38

−808

−361

1.53x105

0.67

152.4

Propylene carbonate−pyridine

−5.56

2040

135

−6923

1.29

111.8

Propylene carbonate−acetic acid

−3.55

1617

70.1

−6160

1.87

49.4

Potassium thiocyanate (298.15-348.15K) Acetonitrile−chlorobenzene

3.80

v521

−25.4

3.26x104

2.05

84.0

Propylene carbonate−chlorobenzene

1.88

−229

−1.53

2.60x104

1.11

85.7

−16.7

4

0.88

74.9

DMSO−chlorobenzene

6.18

−1580

2.73x10

A similar phenomenon is observed in conditionally-universal media A−B (A is a solvate-active component, B is a solvate-inert component). Association constant can be calculated from equations [8.1.56] or [8.1.104] for LiBr and KCNS solutions.55,57 The dependence of lnKa and 1/ε (Figure 8.1.16] for LiBr in a mixed solvent [8.1.53] shows an influence of solvateactive component on Ka. The difference of LiBr solvation energy in the presence of pyridine and acetic acid may be evaluated in accordance to [8.1.53], assuming low solvation energy of Li+ by propylene carbonate in comparison with pyridine and negligible value of solvation energy of anion in solvents containing dichlorobenFigure 8.1.16. Dependence of lnKa for lithium bromide zene (DCB) and pyridine. The data presented in Table 8.1.10 on 1/ε in the mixed solvent-based on propylene carbonate at 298.15K. permit us to calculate the components of free energy for ion association processes. To interpret the data, one must take into account:

464

8.1 Mixed solvents

σ

cov

v

= Δσ Cat • An + ( σ sol, Cat • An – σ

sol, Cat

+

–σ

sol, An

-

)

correspondingly: σ

el

= ( β Cat • An – β

Cat

+

–β

An

-

)⁄ε

A small value σcov in all considered systems can be explained by low energy of interaction between the filled orbital of cation and anion. On the contrary, the contribution of ion-ion interaction to the process energy leads to high value of σel in comparison with the covalent component even in media of high permittivity (not to mention media of low permittivities). From [8.1.106], the isodielectric solution formed by two mixed solvents I and II follows the relationship: ln K a, I = ( a 01, I ⁄ a 01, II ) ln K a, II – ( a 01, I ⁄ a 01, II )a 00, II + a 00, I

[8.1.108]

where: 00, 01 I, II

subscripts of coefficients of approximation for dependence on temperature and permittivity subscripts for solvents I and II

The leveling (leveling solvent reduces differences between constants of ion association) or differentiating (differentiating solvent enhances these differences) effect of the first mixed solvent is defined by the ratio of coefficients of equation [8.1.106] or by the el ratio of vacuum electrostatic component of free energy of association process, δΔG ε = 1 . One can calculate ratio a01, PC-DCB/a01, PC-Py = 1.36 using the data from Tables 8.1.10 and 8.1.11 and assess the leveling effect of the solvent propylene carbonate−pyridine on electrolyte strength. The ratio aPC-DCB/aPC-HAc = 3.1 indicates that propylene carbonate− acetic acid has a more pronounced leveling effect on electrolyte strength than propylene carbonate−pyridine. Table 8.1.11. The components of free energy change (kJ mol-1) in ion association process of different salts in conditionally-universal media at 298.15K −σel

Solvent

at max. ε

at min. ε

el

−σcov

σε = 1

Lithium bromide Propylene carbonate−o-dichlorobenzene

5.8

37.7

1.6

377

Propylene carbonate−pyridine

4.2

22.9

3.2

277

Propylene carbonate−acetic acid

1.9

20.0

4.6

122

Potassium thiocyanate Acetonitrile−chlorobenzene

5.7

37.1

5.1

208

Propylene carbonate−chlorobenzene

3.2

37.9

2.7

212

DMSO−chlorobenzene

4.0

33.1

2.2

185

Y. Y. Fialkov, V. L. Chumak

465

The ε change of solvent and universal media affect the ion concentration in solution. The ion concentration in 0.1M solution of LiBr in the mixed solvent propylene carbonate− o-dichlorobenzene varies relative to its analytical concentration from 50% in propylene carbonate to 0.1% in dichlorobenzene. The ion concentration in 0.1M solution of KSCN in the solvent propylene carbonate−chlorobenzene varies from 60% in propylene carbonate to 0.06% in chlorobenzene. The same effect can be obtained by means of solvent heating. For instance, LiBr o solution in o-dichlorobenzene must be heated to ≈ 215 C to reach the same value of association constant as in propylene carbonate at room temperature. For this reason, the solvent may be used as an effective means for tailoring electrolyte strength in conditionally universal media as well. The influence of solvate-active property of components of the mixed solvent is revealed in acid solution. The data for some acids in different mixed solvents are presented in Table 8.1.12.7 Table 8.1.12. The properties of ion association process of H-acids in conditionally universal media at 298.15K

Acid

Solvent

Coefficients of equation [8.1.106] a00

a01 80.6

Components of energy of ion association process, kJ mol-1 σel

el

−σcov

σε = 1

6.2

200

at max. ε

at min. ε

6.1

15.0

CH3SO3H

Methanol−n-hexanol

2.49

HSO3F

Methanol−n-butanol

−1.50

165.0

3.7

408

12.5

23.9

4.86

190.9

12.0

473

15.5

26.7

CF3COOH

−1.82

165

−4.5

408

12.6

23.1

DMSO−CCl4

−1.55

215

−3.8

532

11.4

133

DMSO−o-dichlorobenzene

−1.34

183

−3.3

453

9.7

75.6

DMSO−benzene

0.55

145

1.4

359

7.7

120

DMSO−1,4-dioxane

0.55

129

1.4

319

6.9

80

DMSO−pyridine

1.50

90

3.7

223

4.8

15

Propylene carbonate−DMSO

0.38

146

0.9

361

5.6

7.8

Methanol−n-butanol

−2.06

162

−5.1

401

12.3

22.7

H2SO4*

H2SeO4*

*data for the first constant of ion association

The degree of ion association of acids, as well as ionophores, depends significantly on solvents` permittivity. The influence of the specific solvation by the solvate-active component is pertinent from the comparison lnKa − 1/ε isotherms for acid solutions in conditionally universal media S(1) − S(2), S(1) − S(3)... Figure 8.1.1758 gives lnKa − 1/ε relationships for solutions of sulfuric acid in a binary solvent mixture containing DMSO and CCl4, benzene, dioxane, pyridine. The

466

8.1 Mixed solvents

increase in the second component basic capacity according to [8.1.50] leads to decrease in lnKa. General analysis of the binary solvent mixtures formed by two solvate-active components (these solvents are often used in analytical and electrochemistry) was conducted to evaluate their effect on H-acids.59 The analysis was based on an equation which relates the constant of ion association, Ka, of the solvent mixture and constants of ion association of A B the acid K a and K a of each component of the mixed solvent, using equilibrium constants of scheme [8.1.105] − heteromolecular association constant, Kadd; ionization constant of the adduct, Ki; and resolvation constant, Kus, (e.g., equilibrium constant of process HA n A + B ↔ HA n B + A ), and with molar fractions of components of the mixed solvent xA and xB:

Figure 8.1.18. Dependence of Ka for HSO3F on solvent composition in mixed solvents: A − n-butanol at 298.15K.7 B: 1 − n-hexane; 2 − nitrobenzene; 3 − methanol; 4 − N,N- dimethyl aniline.

Figure 8.1.17. Dependence of Ka of sulfuric acid on 1/ε in mixed solvents based on DMSO at 298.15K. B

B

A

B

K a = K a + ( K a – K a ) [ 1 – ( K a ⁄ ( 1 + K add x B ( 1 + K i ) ) ) ]

[8.1.109]

The equation [8.1.109] changes into equation [8.1.100] when both components of the mixed solvent have donor character, i.e., Kus = 0. The analysis of equation [8.1.100]59 shows that the solvate-active property of components of the mixed solvent A−B has to be changed to influence the dependence of Ka on the composition of the mixed solvent. Some examples of such influence are presented in Figure 8.1.18.

Y. Y. Fialkov, V. L. Chumak

467

8.1.4.6 Solvent effect on exchange interaction processes Chemical processes of exchange interaction, given by the equation: EF + HL ↔ EL + HF

[8.1.110]

are common in research and technology, but the solvent effect on their equilibrium was not frequently studied. Let us systematize the experimental data on these processes.60 Systems with non-associated reagents The process of exchange interaction between bis-(carbomethoxymethyl)mercury and mercury cyanide ( CH 3 OCOCH 2 ) 2 Hg + Hg ( CN ) 2 ↔ 2CH 3 OCOCH 2 HgCN

[8.1.111]

has been studied in the mixed solvent DMSO−pyridine. The components of solvent possess almost equal ability to specific solvation of mercury−organic compounds. This ability is confirmed by equality of the constants of spin−spin interaction 2I(1H−199Hg) for different organic compounds in these solvents. This was also confirmed61 for participants of the equilibrium [8.1.111]. Systems with one associated participant of equilibrium Methanolysis of triphenylchloromethane may serve as an example of such reaction: Ph 3 CCl + CH 3 OH ↔ Ph 3 COCH 3 + HCl

[8.1.112]

This process has been studied in benzene, 1,2-dichloroethane, chloroform, trifluoromethylbenzene and in mixed solvents hexane−nitrobenzene, toluene−nitromethane, toluene−acetonitrile. The low constant of the ion associate formation process of triphenylchloromethane, high constant of the ion association process, and low constant of the heteromolecular association process of HCl (HCl solutions in listed solvents obey the Henry's Law) show that only methanol is an associative participant of the equilibrium.

Systems with two associated participants of equilibrium These systems have been studied by means of the reaction of acidic exchange between acids and anhydrides with different acidic groups: CH 2 ClCOOH + ( CH 3 CO ) 2 O ↔ CH 2 ClCOOCOCH 3 + CH 3 COOH [8.1.113a] CH 3 COOH + ( CH 2 ClCO ) 2 O ↔ CH 2 ClCOOCOCH 3 + CHClCOOH [8.1.113b] in binary mixed solvents formed from tetrachloromethane with chlorobenzene, trifluoromethylbenzene, and nitrobenzene. The system trifluoroacetic acid and methanol, undergoing esterification reaction: CF 3 COOH + CH 3 OH ↔ CF 3 COOCH 3 + H 2 O also belongs to the group.

[8.1.114]

468

8.1 Mixed solvents

The equilibrium process has been studied in binary mixed solvents such as hexane− chloroform, hexane−chlorobenzene, chloroform−chlorobenzene. Also, re-esterification CH 3 COOC 3 H 7 + CX 3 COOH ↔ CX 3 COOC 3 H 7 + CH 3 COOH

[8.1.115]

(where X is F or Cl) has been studied for the full concentration range of propyl acetate−trifluoro- and trichloroacetic acids.62 Esterification process of ethanol by caproic or lactic acids has been studied by these authors.63 The reaction of acetal formation was studied64 RCHO + R'OH ↔ RCH ( OR' ) 2 + H 2 O

[8.1.116]

in systems of isoamyl alcohol−benzaldehyde (a) and ethanol−butyric aldehyde (b). The relationship between the maximum output of the reaction of exchange interaction and associative state of equilibrium [8.1.110] participants follows the Gibbs-DugemMargulis equation: x s d ln a s + Σx i d ln a i = 0

[8.1.117]

where: xS, xi as, ai

molar fractions activity of the solvent and participants of the chemical process, correspondingly

Izmaylov65 showed that maximum output of reaction depends on the initial composition of reagents. Associative and dissociative processes of the chemical system components are accompanied by the change of their chemical potentials if the solvent potential depends on total activity of solution (it depends on concentration in dilute solutions): i

μs =

0 μs

– RT  ln c i

[8.1.118]

i=1

Hence the condition of chemical equilibrium in non-ideal (regular) systems is presented in the following form: ( ∂G ) P, T = ( ∂G S ) P, T + Σ ( ∂G i ) P, T i

∂  ci

[8.1.119] i 0

l

0

 μi v i + n s Δμs

vi ∂ ln K ch ∂ ∂ =1 i = 1 - --------------------- = n s --------------– - ∏ γ i – ------- i---------------------------------------∂V ∂V RT ∂V ∂V

[8.1.120]

i=1

Inserting values of chemical potentials for equilibrium participants [8.1.110] and solvent in equation [8.1.119], one can obtain the equation relating the equilibrium constant, Kch, change to the solvent composition (in volume parts, V), mol number, ns, activity coefficients, γi, stoichiometric coefficients, vi, of process [8.1.110], and chemical potential, 0 μ i , for every participant of equilibrium at concentration 1M.

Y. Y. Fialkov, V. L. Chumak

469

Equation [8.1.120] changes to [8.1.121], if only EF and EL undergo homomolecular association: ∂ ln K ch ∂  1 1  dK ch ---------------- ≈ 2n s c 0EF -------  --------------- – --------------- + ----------dε ∂V  ∂V EL EF K dim K dim

[8.1.121]

where: Kdim

equilibrium constant of homomolecular association

Equations [8.1.120] and [8.1.121] describe the solvent effect on Kch for a non-ideal liquid system. The dependence of lnKch and reciprocal ε is linear: ln K ch = a 00 + a 01 ⁄ ε

[8.1.122]

Coefficients of the equation and some thermodynamic properties of exchange interaction processes are presented in Table 8.1.13. The degree of heteromolecular association of esters in reaction [8.1.121] is higher than for acids when Kdim values are equal. Thus the change of equilibrium constant according to [8.1.121] depends on the electrostatic component. Kch for these reactions also depends on exponentially reciprocal ε. Table 8.1.13. Characteristics of some processes of exchange interaction

Reaction [8.1.111]

Coefficient of equation [8.1.122]

Free energy components, kJ/mol el

a00

−a01

−σcov

σε = 1

σG at max. ε

σG at min. ε

2.40

97.6

5.9

241

5.2

19.0

[8.1.115], a, (F)

1.72

19.6

4.3

48.5

3.1

6.3

[8.1.115], b, (Cl)

2.55

17.1

6.3

42.3

5.1

7.0

[8.1.116], a

1.24

47

3.1

116.4

7.5

9.9

[8.1.116], b

2.47

16.7

6.1

41.3

3.4

4.1

The dependence of the equilibrium constant of reaction [8.1.116] on ε is similar in a concentration range from 0.5 to 1.0 molar fraction of aldehyde if the degrees of homomolecular association for aldehydes and acetals are smaller than for alcohol and water. Kch increase with increasing ε of media is a general property of all processes of exchange interaction presented in the Table 8.1.13. Dependence of lnKch − 1/ε for process [8.1.111] is not linear in all mixed solvents (Figure 8.1.19). Extreme Kch dependence on 1/ε is explained by the chemical effect of solvation (it is explained in detail elsewhere60). Correlations with different empirical parameters of individual solvent parameters are held true for this process. The best of them is a correlation (r=0.977) with parameter ET. The influence of the molecular state of participants of exchange interaction on the process equilibrium is reflected in Kch dependence (processes [8.1.113]) on the mixed sol-

470

8.1 Mixed solvents

vent composition (Figure 8.1.20). The change of Kdim for acetic acid is less pronounced than for monochloroacetic acid, when CCl4 is replaced by chlorobenzene. Thus Kch should increase for reaction [8.1.113a] and it should decrease for reaction [8.1.113b], with ε increasing in accordance to equation [8.1.121]. Correlation of Kdim for acetic and monochloroacetic acids is obtained when chlorobenzene is replaced by nitrobenzene. This leads to decrease of Kdim when ε increases in the case of reaction [8.1.113a], and the opposite is the case for reaction [8.1.113b]. That is why a maximum is observed in the first process (see Figure Figure 8.1.19. Dependence of equilibrium constants 8.1.20 on the left hand side), and a minimum for triphenylchloromethane methanolysis on 1/ε of is observed for the second process. mixed solvent at 298.15K: 1 − hexane−nitrobenzene; At equilibrium [8.1.114] (with three 2 − toluene−nitromethane; 3 − toluene−acetonitrile. associated participants), association degree of associated participants decreases with media polarity increasing. It leads to Kch increasing and to Kadd decreasing in the process of heteromolecular association of acid and alcohol.

Figure 8.1.20. Dependence of Kch on the mixed solvent composition for processes [8.1.113a] and [8.1.113b] at 298.15K: 1 − tetrachloromethane−nitrobenzene; 2 − tetrachloromethane−chlorobenzene.

Y. Y. Fialkov, V. L. Chumak

471

Thus, Kch depends to a low extent on the composition of studied mixed solvents. Vacuum component of free energy of processes of exchange interaction (Table 8.1.13) is low; σGel values are low, too. This indicates, that ε change does not lead to the change of the reaction output. Solvent replacement leads to an essential change of reaction output in the process [8.1.111], characterized by the high value of σel (see Table 8.1.13), from 6% in pyridine to 60% in DMSO (in 0.1M solutions). Kch increase in pyridine solution to its value in DMSO requires cooling to −140oC. 8.1.4.7 Mixed solvent effect on processes of complex formation Non-aqueous solvent effect on equilibrium and thermodynamic of complexation processes are summarized in monographs.67-69 The solvent effect on complex formation processes has two aspects. The first is a change of coordination sphere composition, changing participation of solvent as a chemical reagent [8.1.123]: [MLm]p+

+A

[MLm-1A]p+ + L

...

[MAn]p+ + mL

where: Lm A, B

a ligand in initial complex components of binary solvent

If both components of the mixed solvent are solvate-active, equilibrium [8.1.123] may be presented as [8.1.123a]: [MLm]p+

+A+B

[MLm-2AB]p++ 2L

...

[MAn-qBq]p+ + mL

Coordination solvents A and B taking part in the processes are the same ligands as L. The second aspect of the solvent effect is related to the thermodynamic properties of the complex, such as formation constant. Discussing the problem of solvent effect on complex stability, authors often neglect the change of a complex nature, due to the change in a solvent as follows from equations [8.1.123] and [8.1.123a]. These processes may also be regarded as resolvation processes. When the components of mixed solvate are solvate-inert in relation to the complex, equation [8.1.53a] takes the following form: ln K k = a 00 + a 01 ⁄ ε

[8.1.124]

472

8.1 Mixed solvents

Figure 8.1.21. Dependence of stability constants for cadmium thiocyanate complexes on 1/ε in mixed solvent water-methanol at 298.15K.

Figure 8.1.22. Stability constant of amine complexes of some Ni(NH3)+ in water-organic solvents: 1 − NiEn2+; 2 − [N; NH3]2+; 3 − [CdCH3NH2]2+; 4 − [AgCH3NH2]2+; 5 − [AgEn2]2+; 6 − [NiEn2]2+.

Coefficient a00 has a physical meaning of logarithm of formation constant at ε → ∞ related to the standard ionic strength I = 0. In Figure 8.1.21presents this dependence. Table 8.1.14. Complexation process characteristics for system Cd2+−thiourea in mixed solvent water−methanol at 298.15K

Constant

Coefficient of equation a00

Component σG, kJ/mol Correlation coefficient r

a01

σG

cov

el σε = 1

−σGcov in H2O

in MeOH

K2

−0.42

367.7

0.996

−1.0

910

11.6

27.9

K3

1.07

561.9

0.987

2.6

1390

17.7

42.7

K4

7.79

631.3

0.991

19.3

1563

19.9

47.9

K5

2.72

837.0

0.988

6.7

2072

26.4

63.6

The data for cadmium thiourea complexes in water-methanol mixed solvent70 are presented in Table 8.1.14. Dependence of stability constant on the solvent composition is very complex in the mixed solvents formed by two solvate-active components as defined

Y. Y. Fialkov, V. L. Chumak

473

by the relative activity, L, of A and B. Dependencies of stability constant for some complexes in water−B solution (where B is methyl acetate, methanol, etc.69) are presented in Figures 8.1.21 and 8.1.22 for complex NiEn2+ (En = ethylenediamine) in water−non-aqueous solution (the constants are presented relative to stability constant in water).

8.1.5 THE MIXED SOLVENT EFFECT ON THE CHEMICAL EQUILIBRIUM THERMODYNAMICS In most cases, thermodynamic characteristics of equilibrium processes are determined by the temperature dependence of equilibrium constant K = f(T), according to the classical equation: ΔH = RT2(dlnK/dT) and ΔS = RlnK + T(dlnK/dT) or ΔS = ΔH/T + RlnK. Because the equilibrium constant is a function of both temperature and permittivity [8.1.52a], i.e., K = f ( T, ε )

[8.1.125]

A change of constant during temperature change is a consequence of enthalpy of the process (not equal to zero) and temperature dependence of permittivity. Thus, the change of equilibrium constant with temperature changing depends on both selfchemical equilibrium characteristics (here ΔH) and solvent characteristics (namely, solvent permittivity influence on the equilibrium constant). This is pertinent from Figure 8.1.23, which shows the dependence of equilibrium constant logarithm on reciprocal permittivity (isotherms). Equilibrium Figure 8.1.23. Isotherms lnK − f(ε) for different temperobtained experimentally (dotted constants atures (T1 < T2 < T3). line a−b) correspond to various values of permittivity. The thermodynamic characteristics of a chemical process, calculated from equilibrium constant polytherms, are integral characteristics (ΔHi and ΔSi), i.e., they consist of terms related to process itself (ΔHT and ΔST) and terms depended on permittivity change with temperature changing (ΔHε and ΔSε): ΔH i = ΔH T + ΔH ε

[8.1.126a]

ΔS i = ΔS T + ΔS ε

[8.1.126b]

The thermodynamic description of a process in a solvent has to lead to defined values of ΔHT and ΔST, which are called van't Hoff or original parameters.7 It follows from Figure 8.1.23 that one has to differentiate the equilibrium constant of polytherms corresponding to isodielectric values of the solvent on temperature (e.g., to equilibrium constant values of c−d dotted line).

474

8.1 Mixed solvents

Division of equation [8.1.126] into the constituents must be done with full assurance to maintain the influence of different solvents. For this reason, it is necessary to have a few isotherms of equilibrium constant dependencies on permittivity (K = f(ε)T). We have developed an equation of a process depicted by scheme [8.1.45] after approximating each isotherm as lnK vs. 1/ε function and by following an approximation of these equations for ε-1, ε-2, ε-3...ε-j conditions. We, then, can calculate the integral value of process entropy by differentiating relationship [8.1.55] versus T, e.g., ΔG= −RTlnK: i = m

i = m

j = n

ΔS i = R

j = n i i



( 1 – i )a ji ( T ε ) – j ( d ln ε ⁄ dT ) ⁄ ε

j–1



i = 0

i = 0

j = 0

j = 0

a ji ⁄ T

i–1

⁄ε

i

[8.1.127]

Here, the first term of the sum in brackets corresponds to ΔST/R value and the second term to ΔS/R. We can determine “van't Hoff's” (original) constituents of the process entropy if all the terms containing dlnε/dT are equal to zero: i = m j = n

ΔS T = R



i i

( 1 – i )a ji ⁄ ( T ε )

[8.1.128]

i = 0 j = 0

Van't Hoff's constituent of enthalpy is determined in analogous manner as ΔH=ΔG+TΔS (ΔHT): i = m j = n

ΔH T = – R



a ji ⁄ ( T

i–1 j

ε)

[8.1.129]

i = 0 j = 0

Such approach may be illustrated by dependence of formic acid association constant on temperature and permittivity in mixed solvents: water−ethylene glycol,72 which is approximated by equation 2

ln K = a 00 + a 01 ⁄ T + a 02 ⁄ T + a 11 ⁄ ( εT ) where: a00 a01 a02 a10 a11

= 40.90 = −2.17x104 = 3.11x106 = −425.4 = 2.52x105

Hence ΔH i = – R [ a 01 + 2a 02 ⁄ T + a 11 ⁄ ε + T ( d ln ε ⁄ dT ) ( a 10 T + a 11 ) ⁄ ε ]

Y. Y. Fialkov, V. L. Chumak

475

ΔS i = R [ a 00 – a 02 ⁄ T + a 10 ⁄ ε – ( d ln ε ⁄ dT ) ( a 10 T + a 11 ) ⁄ ε ] and consequently, ΔH T = – R ( a 01 + 2a 02 ⁄ T + a 11 ⁄ ε ) ΔS T = R ( a 00 – a 02 ⁄ T + a 10 ⁄ ε ) Comparison of ΔHi with ΔHT and ΔSi with ΔST shows that integral values of thermodynamic characteristics of the ionic association process for HCOOH are not only less informative than van't Hoff's characteristics, but they contradict the physical model of the process in this case. Indeed, corresponding dependencies of compensative effect are described by equations: ΔHi = −0.704ΔSi + 22.87 kJ/mol ΔHT = 0.592ΔST − 22.22 kJ/mol Thus, if the compensative effect for integral thermodynamic functions is interpreted, one should conclude that characteristic temperature (this is tanα = ΔH/ΔS) is a negative value, but that is, of course, devoid of physical sense. In common cases, when the dependence [8.1.125] is approximated using equation [8.1.56], “van't Hoff's” (original) thermodynamic constituents of equilibrium process are equal to: ΔH T = – R ( a 01 + a 11 ⁄ ε )

[8.1.130]

ΔS T = R ( a 00 + a 10 ⁄ ε )

[8.1.131]

As it is evident from [8.1.130] and [8.1.131], the original thermodynamic characteristics of the process are summarized by the terms where the first of them does not depend, and the second one depends, on permittivity. These terms accordingly are called covalent and electrostatic constituents of the process in solution, i.e., cov

= – Ra 01 and ΔH

cov

= Ra 00 and ΔS

ΔH ΔS

el

el

= – Ra 11 ⁄ ε

= Ra 10 ⁄ ε

[8.1.132] [8.1.133]

It should be emphasized that ΔGT values are substantially more informative than integral thermodynamic values for thermodynamic analysis of chemical equilibrium in solutions of mixed solvents. Indeed, in frequent cases of equilibrium constant polytherm characterized by an extreme (i.e., sign of ΔHi changes), one may arrive at the wrong conclusion that the process nature changes greatly at a temperature of extreme value. As has been shown,71 the appearance of the extreme value of equilibrium constant polytherms is caused in the majority of cases by temperature change of solvent permittivity. The condition of extreme appearance for the process described by equation [8.1.55] is: a 01 exp ( αT extr + γ ) + αa 11 T extr ( a 10 T extr + a 11 ) = 0

[8.1.134]

476

8.1 Mixed solvents

where:

α, γ γ Textr

the coefficients of lnε = αT+ γ equation activity coefficient temperature corresponding to extremum of isotherm of equilibrium constant

Let us illustrate the principle of integral thermodynamic characteristics of chemical equilibrium in mixed solvent based on the example of ionic association process of methylsulfuric acid HSO3CH3 and its tetraalkylammonium salt CH3(C8H17)3N + OSO3CH3 in mixed solvent: methanol−n-butanol.73 The dependencies of ionic association constants for these electrolytes on temperature and permittivity are described by equations based [8.1.56] the relationship: K a, acid = 14.53 – 3436 ⁄ T – 130.28 ⁄ ε + 5.84 × 10 ⁄ εT K a, salt = 11.8 – 2514 ⁄ T – 198.70 ⁄ ε + 7.79 × 10 ⁄ εT Thermodynamic characteristics of these systems, calculated based on [8.1.130][8.1.133] equations, are given in Tables 8.1.15 and 8.1.16. Table 8.1.15. Thermodynamic characteristics of ionic association process of HSO3CH3 in mixed solvent: methanol−n-butanol (298.15K) (ΔHcov = 28.56 kJ/mol, ΔScov = 120.8 J/(mol*K)) BuOH mol%

ε

60.39 51.60

ΔH, kJ/mol

ΔS, J/(mol K)

ΔHi

ΔHT

ΔHel

ΔSi

ΔST

ΔSel

20

20.62

4.29

−24.28

121.4

66.6

−54.1

22

20.90

6.50

−22.07

119.9

71.6

−49.2

37.24

24

21.19

9.89

−20.23

118.8

75.7

−45.1

25.32

26

21.49

8.34

−18.67

118.0

79.1

−41.7

15.82

28

21.79

11.22

−17.34

117.6

82.1

−38.7

8.76

30

22.09

12.38

−16.18

117.3

84.7

−36.1

Table 8.1.16. Thermodynamic characteristics of ionic association process of CH3(C8H17)3N + OSO3CH3 in mixed solvent: methanol−n-butanol (298.15K) (ΔHcov=20.90 kJ/mol, ΔScov= 98.1 J/(mol K))f BuOH mol%

ε

60.39

20

ΔH, kJ/mol

ΔS, J/(mol K)

ΔHi

ΔHT

ΔHel

ΔSi

ΔST

ΔSel

3.85

−11.23

−32.13

66.1

15.5

−82.6

51.60

22

5.00

−8.31

−29.21

67.7

23.0

−75.1

37.24

24

6.00

−5.88

−26.78

69.1

29.3

−68.8

25.32

26

6.90

−3.82

−24.72

70.5

34.6

−63.5

15.82

28

7.70

−2.05

−22.95

71.8

39.1

−59.0

8.76

30

8.45

−0.52

−21.42

73.1

43.0

−55.1

George Wypych

477

The analysis of data leads to the conclusion that ΔHi depends weakly on permittivity for both acids and salts. This contradicts the nature of the process. In contrast, the rate of ΔHT change is large enough. The analogous observations can be made regarding the character of ΔSi and ΔST values changes along with permittivity change. If the considerable endothermic effect of the ionic association for acid can be explained by desolvation contribution of ionic pair formation (i.e., a solvated molecule of acid), the endothermic effect of ionic pair formation by such voluminous cations contradicts the physical model of the process. Estimation of desolvation energy of ionic pair formation of salt ions according to the equation74 shows that this energy is two orders of magnitude lower than the energy of heat movement of solvent molecules. For this reason, the process of ionic association of salt ions is exothermal, as seen from ΔHT values. The exothermal character increases with permittivity decreasing, i.e., with an increase of ionion interaction energy. Dependencies ΔHi on ΔSi for salt and acid are not linear, i.e., the compensative effect is not fulfilled. Consequently, the substantial change of the ionic association process is due to change of solvent composition. Considering the same chemical characteristics of mixed solvent components, this conclusion is wrong because the compensative effect if fulfilled for van't Hoff's components is: ΔHT = 0.448 ΔST − 28.5 kJ/mol ΔHT = 0.389 ΔST − 17.3 kJ/mol The smaller the magnitude of the characteristic temperature for salt (389K), in comparison to acid, the smaller the barrier of the ionic pairs formation process. That is true because the association process in the case of acid is accompanied by energy consumption for desolvation.

8.1.6 RESULTS OF STUDIES

George Wypych ChemTec Laboratories, Toronto, Canada A solvent mixture composed of o-dichlorobenzene and chloroform was used for inkjet-printed semiconductor.75 Its crystalline structure was investigated as a function of the mixing ratio of the component solvents to improve the reproducibility of the deposition process and the structural quality of the final films.75 The poor uniformity of inkjet printed films is mainly caused by the so-called “coffee-stain” effect caused by a convective flow occurring inside Figure 8.1.24. Schematic representation of the sessile drop from its center towards the edges, competing convective and inward (Marangoni) flows taking place in an inkjet printed where the evaporation rate is higher.75 The liquid droplet. [Adapted, by permission, from Grimaldi, I.A, Barra, M., De Girolamo Del flows towards the edges to make up for the evaporation losses.75 A possible approach to reduce the Mauro, A., Loffredo, F., Cassinese, A., Villani, F., Minarini, C., Synth. Metals, “coffee-stain” effect is based on the use of mixtures 161, 23-24, 2618-22, 2012.] of solvents having different boiling points and sur-

478

8.1 Mixed solvents

Figure 8.1.25. Polarized optical images and corresponding 2D profiles of perylene diimide drops on bare SiO2 substrates. The drops are inkjet printed by using o-dichlorobenzene:chloroform mixtures at different volume mixing ratios and substrate temperature: (a, e) 1:0 @ T = 90°C; (b, f) 4:1 @ T = 90°C; (c, g) 3:2 @ T = 90°C; (d, h) 1:4 @ T = 35°C. [Adapted, by permission, from Grimaldi, I.A, Barra, M., De Girolamo Del Mauro, A., Loffredo, F., Cassinese, A., Villani, F., Minarini, C., Synth. Metals, 161, 23-24, 2618-22, 2012.]

face tensions.75 The temperature and surface tension gradients can be generated producing a Marangoni flow from droplet rim to the center (Figure 8.1.24) which balances the “coffee-stain” effect providing a uniform spatial redistribution of the material.75 Figure 8.1.25 shows the effect of mixed solvent selection and temperature on uniformity of distribution of N,N′-bis(n-octyl)-1,6dicyanoperylene-3,4:9,10bis(dicarboximide) in film deposited after drying.75 The optical images and the related profilometric analyses revealed that the best condition can be achieved using 3:2 o-dichlorobenzene:chloroform mixture (Figure 8.1.25c and g).75 At this condition, the substrate region was fully covered by the material, without the presence of empty zones.75 Further increase Figure 8.1.26. AFM image and longitudinal axis cross-section pro- of the chloroform content (1:4; file of the CA fibers obtained from different DCM/Acetone, A, Figure 8.1.25d) leads to the formaratio: (A), (B) 10% (w/v) CA in 1/1 DCM/A; (C), (D) 10% CA in 2/1 DCM/A; (E), (F) 10% CA in 3/1 DCM/A; (G), (H) 7.5 CA in 9/ tion of small crystallites which 1 DCM/A. [Adapted, by permission, from Celebioglu, A., Uyar, T., spread over the printed drop Mater. Lett., 65, 14, 2291-4, 2011.]

George Wypych

479

region and separated from each other with marked empty regions.75 A comparative study of racemic 9-(2,3-dihydroxypropyl)adenine palmitoylation, a potential prodrug, catalyzed by several lipases in dimethylformamide/co-solvent mixtures and in pure organic solvent was performed.76 An enhancement in the substrate conversion could be achieved with DMF/hexane (4:1) co-solvents as the reaction medium instead of pure organic solvent with immobilized Candida antarctica B lipase.76 The extraction yield of tomato waste carotenoids in different solvents and solvent mixtures was studied to optimize the extraction conditions for maximum recovery.77 A mixture of ethyl acetate and hexane gave the highest carotenoid extraction yield.77 The optimized conditions for maximum carotenoid yield (37.5 mg kg-1 dry waste) were 45% hexane in the solvent mixture, the solvent mixture to waste ratio of 9.1:1 (v/w) and particle size 0.56 mm.77 Electrospun porous cellulose acetate fibers were produced from highly volatile binary solvent system, dichloromethane/acetone.78 The fiber surfaces were much rougher and more porous with higher depth when the dichloromethane content was increased.78 The depth of the pores was around 10-15 nm for CA fibers obtained from 1/1 (v/v) dichloromethane/acetone whereas the depth of the pores increased up to around 50 nm for 9/1 (v/v) dichloromethane/acetone ratio (Figure 8.1.26).78 The morphology of fluorescent polyfluorene derivatives has strong effects on their electroluminescent performance.79 The polyfluorene copolymer films from chlorobenzene:toluene solvent mixtures formed more crystalline α-phase polyfluorene upon thermal

Figure 8.1.27. The film-forming process of doped polyfluorene prepared with pure solvent or solvent mixture. [Adapted, by permission, from Liu, L., Wu, K., Ding, J., Zhang, B., Xie, Z., Polymer, 54, 22, 6236-41, 2013.]

480

8.1 Mixed solvents

annealing than those prepared from pure toluene or chlorobenzene solvents.79 The evaporation rate difference of solvent mixtures assisted the formation of crystal nuclei and enhanced the polyfluorene crystallinity after thermal annealing.79 Figure 8.1.27 shows the difference in the film-forming process for single solvent and solvent mixture.79 The solvent mixture-processed fluorescent polyfluorene-based white emissive polymer showed more efficient blue emission and had a more balanced electron and hole transport.79 The light-emitting efficiency of the light-emitting diodes based on polyfluorene-based white emissive polymer was greatly enhanced.79 A true molecular dissolution of cellulose in binary mixtures of common polar organic solvents with ionic liquid have been accomplished.80 Structural information on the dissolved chains (average molecular weight ~5×104 g/mol; gyration radius ~36 nm, persistence length ~4.5 nm), indicate the absence of significant aggregation of the dissolved chains and the calculated value of the second virial coefficient ~2.45×10-2 mol ml/g2 indicates that this solvent system is a good solvent for cellulose.80 The power conversion efficiency of organic solar cells is an important prerequisite for production of low cost photovoltaics manufactured with high throughput.81 The combination of high volatile solvents with the less volatile host solvent (indane) permits an increased fabrication speed due to a reduction of the overall drying time and formation of films with a good light absorption behavior and a high polymer crystallinity.81 Produced from the solvent mixture toluene-indane, the solar cell performance is comparable to the o-dichloroFigure 8.1.28. Schematic phase diagram of the binary benzene reference device indicating that the solvent. The phase separation temperature, Ts, varies as a function of the concentration of 3-methylpyridine; for mixture is a suitable replacement for T>Ts the mixture features two phases (blue-shaded increased productivity.81 area), while for T 51

log (K1/K2) = −0.0959 ET + 4.60

6

0.85

ET < 52

log K1K2 = 1.31 log PM + 1.81

6

0.91

log PM > −1.0

8.2.3.2 Surface tension In the development of the basic phenomenological model, eq. [8.2.23], we derived a relationship for the surface tension of the solvation shell. Combining eqs. [8.2.16] and [8.2.18] yields

Kenneth A. Connors

493 2

K 1 x 1 x 2 + 2K 1 K 2 x 2 γ = γ 1 + γ' -----------------------------------------------------2 2 x1 + K1 x1 x2 + K1 K2 x2

[8.2.26]

where γ' = γ 2 – γ 1 /2. Now if we identify the solute-solvation shell system with the airsolvent interface, we are led to test eq. [8.2.26] as a description of the composition dependence of surface tension in mixed solvent systems, air playing the role of the solute. Figures 8.2.3 and 8.2.4 show examples of these curve-fits.14

Figure 8.2.3. Surface tension of 2-propanol-water mixtures. The smooth line is drawn with eq. 8.2.26. [Adapted, by permission, from D. Khossravi and K.A. Connors, J. Solution Chem., 22, 321 (1993).]

Figure 8.2.4. Surface tension of glycerol-water mixtures. The smooth line is drawn with eq. 8.2.26. [Adapted, by permission, from D. Khossravi and K.A. Connors, J. Solution Chem., 22, 321 (1993).]

When K2 = 0, eq [8.2.26] gives the 1-step model, eq. [8.2.27], where γ' = γ 2 – γ 1 . K1 x2 γ = γ 1 + γ' ----------------------x1 + K1 x2

[8.2.27]

We had earlier15 published an equation describing the dependence of surface tension on composition, and a comparison of the two approaches has been given;14 here we will restrict attention to eqs. [8.2.26] and [8.2.27]. Suppose we set K1 = 2 and K2 = 1/2 in eq. [8.2.26]. This special condition converts eq. [8.2.26] to

γ = γ1 x1 + γ2 x2

[8.2.28]

494

8.2 The phenomenological theory of solvent effects in mixed solvent systems

which corresponds to ideal behavior; the surface tension is a linear function of x2. The restriction K1 = 2, K2 = 1/2 is, however, a unique member of a less limited special case in which K1 = 4K2. This important condition (except when it happens to occur fortuitously) implies the existence of two identical and independent binding sites.16 Inserting K2 = K1/4 into eq. [8.2.26] yields, upon simplification, eq. [8.2.29], where γ' = γ 2 – γ 1 .

( K1 ⁄ 2 ) x2 γ = γ 1 + γ' ----------------------------------x1 + ( K1 ⁄ 2 ) x2

[8.2.29]

Eq. [8.2.29] will be recognized as equivalent to eq. [8.2.27] for the 1-step model. The interpretation is as follows: the 2-step model, eq. [8.2.26], can always be applied, but if the result is that K 1 ≈ 4K 2 the 1-step model will suffice to describe the data. Moreover, if K 1 ≈ 4K 2 from the 2-step treatment, no physical significance is to be assigned to the second parameter. These considerations are pertinent to real systems. Table 8.2.4 lists K1 and K2 values obtained by applying eq. [8.2.26] to literature data.15 Several systems conform reasonably to the K 1 ≈ 4K 2 condition. Recall that ideal behavior requires the special case K1 = 2, K 2 = 1 ⁄ 2 . The less restrictive condition K 1 ≈ 4K 2 we call “well-behaved.” Figure 8.2.3 shows a well-behaved system; Figure 8.2.4 shows one that is not well-behaved. The distinction is between a hyperbolic dependence on x2 (well-behaved) and a non-hyperbolic dependence. Table 8.2.4. Solvation parameter estimates for surface tension data according to eq. [8.2.26] Cosolvent

K1

K2

K1/K2

Methanol

19.8

2.9

6.8

2-Propanol

130

29.4

4.4

1-Propanol

232

50

4.6

t-Butanol

233

65

3.6

Acetic acid

115

2.7

42.6

Acetone

138

7.1

19.4

Acetonitrile

33.4

14.5

2.3

Dioxane

62.1

7.4

8.4

THF

136

25.9

5.3

Glycerol

22.7

0.80

28.4

DMSO

12.3

1.43

8.6

Formamide

5.52

2.57

2.1

Ethylene glycol

9.4

2.62

3.6

A further observation from these results is that some of the K1 values are much larger than those encountered in solubility studies. Correlations with log PM have been shown.14

Kenneth A. Connors

495

8.2.3.3 Electronic absorption spectra The energy of an electronic transition is calculated from the familiar equation hc E T = h ν = -----λ

[8.2.30]

where h is Planck's constant, c is the velocity of light, ν is frequency, and λ is wavelength. If λ is expressed in nm, eq. [8.2.31] yields ET in kcal mol-1. 4

E T = 2.859 × 10 ⁄ λ

[8.2.31]

The phenomenological theory has been applied by Skwierczynski to the ET values of the Dimroth-Reichardt betaine,13 a quantity sensitive to the polarity of the medium.17 The approach is analogous to the earlier development. We need only consider the solvation effect. The solute is already in solution at extremely low concentration, so solute-solute interactions need not be accounted for. The solvent cavity does not alter its size or shape during an electronic transition (the Franck-Condon principle), so the general medium effect does not come into play. We write ET of the mixed solvent as a weighted average of contributions from the three states: E T ( x 2 ) = F WW E T ( WW ) + F WM E T ( WM ) + F MM E T ( MM )

[8.2.32]

where the symbolism is obvious. Although ET(WW) can be measured in pure water and ET(MM) in pure cosolvent, we do not know ET(WM), so provisionally we postulate that ET(WM) = [ET(WW) + ET(MM)]/2. Defining a quantity Γ by E T ( x 2 ) – E T ( WW ) Γ = --------------------------------------------------E T ( MM ) – E T ( WW )

[8.2.33]

we find, by combining eqs. [8.2.9], [8.2.10], and [8.2.32], 2

K1 x1 x2 ⁄ 2 + K1 K2 x2 Γ = -----------------------------------------------------2 2 x1 + K1 x1 x2 + K1 K2 x2

[8.2.34]

The procedure is to fit Γ to x2. As before, a 1-parameter version can be obtained by setting K2 = 0: K1 x2 Γ = ----------------------x1 + K1 x2

[8.2.35]

Figure 8.2.5 shows a system that can be satisfactorily described by eq. [8.2.35], whereas the system in Figure 8.2.6 requires eq. [8.2.34]. The K1 values are similar in magnitude to those observed from solubility systems, with a few larger values; K2, for those systems requiring eq. [8.2.34], is always smaller than unity. Some correlations were obtained of K1 and K2 values with solvent properties. Figure 8.2.7 shows logK1 as a function of logPM, where PM is the partition coefficient of the pure organic solvent.

496

8.2 The phenomenological theory of solvent effects in mixed solvent systems

Figure 8.2.5. Dependence of ET on composition for the methanol-water system. The smooth line was drawn with eq. 8.2.35. [Adapted, by permission, from R.D. Skwierczynski and K.A. Connors, J. Chem. Soc., Perkin Trans. 2, 467 (1994).]

Figure 8.2.6. Dependence of ET on composition for the acetone-water system. The smooth line was drawn with eq. 8.2.34. [Adapted, by permission, from R.D. Skwierczynski and K.A. Connors, J. Chem. Soc., Perkin Trans. 2, 467 (1994).]

8.2.3.4 Complex formation. We now inquire into the nature of solvent effects on chemical equilibria, taking noncovalent molecular complex formation as an example. Suppose species S (substrate) and L (ligand) interact in solution to form complex C, K11 being the complex binding constant. K

S + L

11

C

[8.2.36]

It is at once evident that this constitutes a more complicated problem than Figure 8.2.7. A plot of log K1 from the ET data against those we have already considered inaslog PM; the circles represent 1-step solvents (eq. 8.2.35) much as here we have three solutes. We and the squares, 2-step solvents (eq. 8.2.34). [Adapted, begin with the thermodynamic cycles by permission, from R.D. Skwierczynski and K.A. Connors, J. Chem. Soc., Perkin Trans. 2, 467 shown as Figure 8.2.8; these cycles (1994).] describe complex formation in the solid, solution, and gas phases horizontally, and the energy changes associated with the indicated processes. ΔGlatt corresponds to the crystal lattice energy (solute-solute interactions), ΔGcav represents the energy of cavity formation (identical with the general medium effect of Section 8.2.2). ΔGcomp is the free energy of complex formation, which in the solution phase is given by eq. [8.2.37].

Δ G comp ( I ) = – kT ln K 11

[8.2.37]

Kenneth A. Connors

497

Figure 8.2.8. Thermodynamic cycles for bimolecular association. The symbols s, l, g represent solid, liquid, and gas phases; the superscripts refer to substrate S, ligand L, and complex C. [Adapted, by permission, from K.A. Connors and D. Khossravi, J. Solution Chem., 22, 677 (1993).]

Eq. [8.2.37] gives the free energy with respect to a 1M standard state, because the unit of K11 is M-1. To calculate the unitary (mole fraction) free energy change we write, instead of eq. [8.2.37], eq. [8.2.38]: *

Δ G comp ( I ) = – kT ln ( K 11 M ρ )

[8.2.38]

where M* is the number of moles of solvent per kg of solvent and ρ is the solution density. The unitary free energy does not include the entropy of mixing. From cycle gl in Figure 8.2.8 we obtain eq. [8.2.39]. C

C

Δ G comp ( g ) + ( Δ G cav + Δ G solv ) – Δ G comp ( I ) − L

L

S

S

− ( Δ G cav + Δ G solv ) – ( Δ G cav + Δ G solv ) = 0

[8.2.39]

We apply the δM operator to eq. [8.2.39] C

S

L

C

S

δ M Δ G cav – δ M Δ G cav – δ M Δ G cav + δ M Δ G solv – δ M Δ G solv − L

− δ M Δ G solv = δ M Δ G comp ( I )

[8.2.40]

where we have assumed δMΔGcomp(g) = 0, which is equivalent to supposing that the structure of the complex (the spatial relationship of S and L) does not depend upon solvent composition, or that the intersolute effect is composition independent.

498

8.2 The phenomenological theory of solvent effects in mixed solvent systems

Also applying the δM treatment to eq. [8.2.4] gives

δ M Δ G soln = δ M Δ G cav + δ M Δ G solv

[8.2.41]

for each species; recall that ΔGgen med and ΔGcav are identical. Use eq. [8.2.41] in [8.2.40]: C

L

S

δ M Δ G comp ( I ) = δ M Δ G soln – δ M Δ G soln – δ M Δ G soln

[8.2.42]

Eq. [8.2.42] says that the solvent effect on complex formation is a function solely of the solvent effects on the solubilities of reactants (negative signs) and product (positive sign). This is a powerful result, because we already have a detailed expression, eq. [8.2.23], for each of the three quantities on the right-hand side of eq. [8.2.42]. Thus, the problem is solved in principle.18 In practice, of course, there are difficulties. Each of the δMΔGsoln terms contains three adjustable parameters, for nine in all, far too many for eq. [8.2.42] to be practical in that form. We, therefore, introduce simplifications in terms of some special cases. The first thing to do is to adopt a 1-step model by setting K2 = 0. This leaves a six-parameter equation, which, though an approximation, will often be acceptable, especially when the experimental study does not cover a wide range in solvent composition (as is usually the case). This simplification gives eq. [8.2.43]. * δ M Δ G comp

L

C

C

C

S

S

S

( gA γ' – kT ln K 1 ) K 1 x 2 ( gA γ' – kT ln K 1 ) K 1 x 2 - – --------------------------------------------------------= ---------------------------------------------------------− C S x1 + K1 x2 x1 + K1 x2 L

L

( gA γ' – kT ln K 1 ) K 1 x 2 − --------------------------------------------------------L x1 + K1 x2

[8.2.43]

Next, in what is labeled the full cancellation approximation, we assume C S L K 1 = K 1 = K 1 = K 1 and we write ΔgA = gAC − gAS − gAL. The result is

( kT ln K 1 + Δ gA γ' ) K 1 x 2 * δ M Δ G comp = ---------------------------------------------------------x1 + K1 x2

[8.2.44]

and we now have a 2-parameter model. The assumption of identical solvation constants is actually quite reasonable; recall from the solubility studies that K1 is not markedly sensitive to the solute identity. The particular example of cyclodextrin complexes led to the identification of another special case as the partial cancellation approximation; in this case we assume C S L K 1 = K 1 < K 1 , and the result is, approximately.19

( kT ln K 1 – gA γ' ) K 1 x 2 * δ M Δ G comp = -----------------------------------------------------x1 + K1 x2

[8.2.45]

Functionally eqs. [8.2.44] and [8.2.45] are identical; the distinction is made on the basis of the magnitudes of the parameters found. Note that gA in eq. [8.2.45] is a positive

Kenneth A. Connors

499

quantity whereas ΔgA in eq. [8.2.44] is a negative quantity. In eq. [8.2.45] it is understood that gA and K1 refer to L. Eqs. [8.2.44] and [8.2.45] both have the form

( kT ln K 1 + G γ' ) K 1 x 2 * δ M Δ G comp = --------------------------------------------------x1 + K1 x2

[8.2.46]

where G = ΔgA in eq. [8.2.44] and G = −gA in eq. [8.2.45]. Table 8.2.5 shows G and K1 values obtained in studies of α-cyclodextrin complexes.19,20 The assignments are made on the basis of the magnitude of K1; those values substantially higher than typical solubility K1 values suggest that the full cancellation condition is not satisfied. After the assignments are made, G can be interpreted as either ΔgA (full cancellation) or −gA (partial cancellation). Notice in Table 8.2.5 that all full cancellation systems give substantial negative ΔgA values. If g is constant, ΔA = gΔA, and the negative ΔA value leads to a solvophobic driving force of gΔAγ for complex formation. (The dioxane system in Table 8.2.5 is unassigned because its K1 value suggests partial cancellation whereas its G value suggests full cancellation). Table 8.2.5. Parameter values of the 4-nitroaniline/α-cyclodextrin and methyl orange/α-cyclodextrin systems19,20 Cosolvent

K1

Ga

Cancellation assignment

4-Nitroaniline Acetonitrile

55

+3

Partial

2-Propanol

46

−3

Partial

Ethanol

29

−9

Partial

Acetone

10

−57

Full

Methanol

3.1

−68

Full

Methyl orange Acetone

46

−3

Partial

2-Propanol

43

−11

Partial

Acetonitrile

40

−13

Partial

Dioxane

31

−38

(Unassigned)

Ethylene glycol

7.7

−58

Full

DMSO

6.4

−66

Full

Methanol

4.9

−43

Full

a

Units are Å2 molecule-1

8.2.3.5 Chemical kinetics Treatment of the solvent effect on chemical reaction rates by means of the phenomenological theory is greatly facilitated by the transition state theory, which postulates that the ini-

500

8.2 The phenomenological theory of solvent effects in mixed solvent systems

tial and transition states are in (virtual) equilibrium. Thus the approach developed for complex formation is applicable also to chemical kinetics. Again, we begin with a thermodynamic cycle, Figure 8.2.9, where R represents the reactant (initial state) in a + unimolecular reaction, R + is the transition state, and P is the product. From Figure + 8.2.9 we write eq. [8.2.47], where Δ G +rxn ( 1 ) + subsequently written Δ G +rxn , is the free Figure 8.2.9. Thermodynamic cycle for a unimolecular energy of activation in the solution phase. reaction. (Adapted, by permission, from J.M. LePree and K.A. Connors, J. Pharm. Sci., 85, 560 (1996).]

+ + + +   + + + + R R Δ G rxn ( 1 ) = Δ G rxn ( g ) +  Δ G gen med + Δ G solv – ( Δ G gen med + Δ G solv )  

[8.2.47]

Applying the δM operation gives eq. [8.2.48] + +

+ +

+ +

δ M Δ G rxn = Δ G rxn ( x ) – Δ G rxn ( x 2

2 = 0)

[8.2.48]

+

The quantity Δ G +rxn ( g ) disappears in this subtraction, as do other composition-independent quantities. We make use of eq. [8.2.13] and eq. [8.2.19] to obtain a function hav+ + R R ing six parameters, namely K 1 , K 2 , K + , gAR, gA + . This function is made manageable + + R R by adopting the full cancellation approximation, setting K 1 = K +1 = K1 and K 2 = K +2 = K2. We then obtain + + +  + 2 2 2 + + δ M Δ G rxn =  Δ gA γ'K 1 x 1 x 2 + 2 Δ gA γ'K 1 K 2 x 2 ⁄ ( x 1 + K 1 x 1 x 2 + K 1 K 2 x 2 ) [8.2.49]   +

+

where Δg A + = g A + − gAR; this is the difference between the curvature-corrected molecular surface areas of the cavities containing the transition state and the reactant. This quantity may be positive or negative. LePree21 tested eq. [8.2.49] with the decarboxylative dechlorination of N-chloroaminoacids in mixed solvents RCH(NHCl)COOH + H2O → RCHO + NH3 + HCl + CO2

[8.2.50]

For this test, the reaction possesses these very desirable features: (1) the kinetics are first order, and the rate-determining step is unimolecular; (2) the reaction rate is independent of pH over the approximate range 4-13; (3) the rate-determining step of the process is not a solvolysis, so the concentration of water does not appear in the rate equation; and (4) the reaction is known to display a sensitivity to solvent composition. Figures [8.2.10] and [8.2.11] show curve-fits, and Tables 8.2.6 and 8.2.7 give the parameter values obtained in

Kenneth A. Connors

501

Figure 8.2.10. Solvent effect on the decomposition of N-chloroaniline in acetonitrile-water mixtures. The smooth curve is drawn with eq. 8.2.49. [Adapted, by permission, from J.M. LePree and K.A. Connors, J. Pharm. Sci., 85, 560 (1996).]

Figure 8.2.11. Solvent effect on the decomposition of N-chloroleucine in 2-propanol-water mixtures. The smooth curve is drawn with eq. 8.2.49. [Adapted, by permission, from J.M. LePree and K.A. Connors, J. Pharm. Sci., 85, 560 (1996).] +

the curve-fitting regression analysis. Observe that Δg A + is positive. This means that the transition state occupies a larger volume than does the reactant. This conclusion has been independently confirmed by studying the pressure dependence of the kinetics.21,22 Table 8.2.6. Model parameters for solvent effects on the decomposition of N-chloroalanine21 Cosolvent

K1

K2

+

Δg A + , nm2 molecule-1

Methanol

2.8

3.1

0.168

Ethanol

5.7

2.8

0.238

1-Propanol

13.0

3.2

0.22

2-Propanol

5.9

11

0.206

Ethylene glycol

4.4

1.7

0.348

Propylene glycol

5.2

6.0

0.27

Acetonitrile

7.0

2.0

0.42

Dioxane

8.9

4.3

0.55

502

8.2 The phenomenological theory of solvent effects in mixed solvent systems

Table 8.2.7. Model parameters for solvent effects on the decomposition of N-chloroleucine21 +

K1

K2

Δg A + , nm2 molecule-1

Methanol

2.5

4.0

0.193

2-Propanol

2.7

40

0.242

Ethylene glycol

4.4

3.2

0.38

Acetonitrile

7.5

3.9

0.43

Cosolvent

The success shown by this kinetic study of a unimolecular reaction unaccompanied by complications arising from solvent effects on pH or water concentration (as a reactant) means that one can be confident in applying the theory to more complicated systems. Of course, an analysis must be carried out for such systems, deriving the appropriate functions and making chemically reasonable approximations. One of the goals is to achieve a practical level of predictive ability, as for example, we have reached in dealing with solvent effects on solubility. 8.2.3.6 Liquid chromatography In reverse phase high-pressure liquid chromatography (RP HPLC), the mobile phase is usually an aqueous-organic mixture, permitting the phenomenological theory to be applied. LePree and Cancino23 carried out this analysis. The composition-dependent variable is the capacity factor k' , defined by eq. [8.2.51], tR – tM VR – VM - = --------------k' = -------------------VM tM

[8.2.51]

where VR is the retention volume of a solute, tR is the retention time, VM is the column dead volume (void volume), and tM is the dead time. It is seldom possible in these systems to use pure water as the mobile phase, so LePree reversed the usual calculational procedure, in which water is the reference solvent, by making the pure organic cosolvent the reference. This has the effect of converting the solvation constants K1 and K2 to their reciprocals, but the form of the equations is unchanged. For some solvent systems a 1-step model was adequate, but others required the 2-step model. Solvation constant values (remember that these are the reciprocals of the earlier parameters with these labels) were mostly in the range 0.1 to 0.9, and the gA values were found to be directly proportional to the nonpolar surface areas of the solutes. This approach appears to offer advantages over earlier theories in this application because of its physical significance and its potential for predicting retention behavior.

8.2.4 INTERPRETATIONS The very general success of the phenomenological theory in quantitatively describing the composition dependence of many chemical and physical processes arises from the treatment of solvation effects by a stoichiometric equilibrium model. It is this model that pro-

Kenneth A. Connors

503

vides the functional form of the theory, which also includes a general medium effect (interpreted as the solvophobic effect) that is functionally coupled to the solvation effect. The parameters of the theory appear to have physical significance, and on the basis of much experimental work they can be successfully generated or predicted by means of empirical correlations. The theory does not include molecular parameters (such as dipole moments or polarizabilities), and this circumstance deprives it of any fundamental status, yet at the same time enhances its applicability to the solution of practical laboratory problems. Notwithstanding the widespread quantitative success of the theory, however, some of the observed parameter values have elicited concern about their physical meaning, and it is to address these issues, one of which is mentioned in 8.2.3.1, that the present section is included. 8.2.4.1 Ambiguities and anomalies Consider a study in which the solubility of a given solute (naphthalene is the example to be given later) is measured in numerous binary aqueous-organic mixed solvent systems, and eq. [8.2.23] is applied to each of the mixed solvent systems, the solvent effect * δ M Δ G soln being calculated relative to water (component 1) in each case. According to hypothesis, the parameter gA is independent of solvent composition. This presumably means that it has the same value in pure solvent component 1 and in pure solvent component 2, since it is supposed not to change as x2 goes from 0 to 1. And in fact the nonlinear regression analyses support the conclusion that gA is a parameter of the system, independent of composition. But in the preceding paragraph no restriction has been placed on the identity of solvent component 2, so the conclusion must apply to any cosolvent 2 combined with the common solvent 1, which is water. This means that all mixed solvent systems in this study as described should yield the same value of gA. But this is not observed. Indeed, the variation in gA can be extreme, in a chemical sense; see Table 8.2.2. This constitutes a logical difficulty. There is another anomaly to be considered. In nearly all of the nonelectrolyte solubility data that have been subjected to analysis according to eq. [8.2.23], the solute solubility increases as x2, the organic cosolvent concentration, increases, and gA is positive, the physically reasonable result. But in the sucrose-water-ethanol system, the sucrose solubility decreases as x2 increases, and gA is negative. There appears to be no physically reasonable picture of a negative gA value. A further discrepancy was noted in 8.2.3.2, where we saw that some of the solvation constants evaluated from surface tension data did not agree closely with the corresponding numbers found in solubility studies. 8.2.4.2 A modified derivation Recognizing that the original condition that g and A are independent of composition was unnecessarily restrictive, we replace eq. [8.2.18] with eq. [8.2.52], where the subscripts 1 and 2 indicate values in the pure solvents 1 and 2. ˆγ = g A γ + ( g A γ – g A γ ) f gˆ A 1 1 1 2 2 2 1 1 1 2

[8.2.52]

504

8.2 The phenomenological theory of solvent effects in mixed solvent systems

It is important for the moment to maintain a distinction between gA in the original ˆˆ formulation, a composition-independent quantity, and g A in eq. [8.2.52], a compositiondependent quantity. Eq. [8.2.52] combines the composition dependence of three entities ˆγ , which is probably an oversimplification, but it at least generA into a single grouping, gˆ ates the correct values at the limits of x2 = 0 and x2 = 1; and it avoids the unmanageable algebraic complexity that would result from a detailed specification of the composition ˆγ A dependence of the three entities separately. Eq. [8.2.14] now is written ΔGgen med = gˆ and development as before yields eq. [8.2.53] as the counterpart to eq. [8.2.23], where δ M gA γ = g 2 A 2 γ 2 – g 1 A 1 γ 1 . 2

( δ M gA γ ⁄ 2 – kT ln K 1 ) K 1 x 1 x 2 + ( δ M gA γ – kT ln K 1 K 2 ) K 1 K 2 x 2 * - [8.2.53] δ M Δ G soln = ---------------------------------------------------------------------------------------------------------------------------------------------------------2 2 x1 + K1 x1 x2 + K1 K2 x2 Comparison of eqs. [8.2.23] and [8.2.53] gives eq. [8.2.54], which constitutes a specification of the meaning of gA in the original formulation in terms of the modified theory. gA ( γ 2 – γ 1 ) = g 2 γ 2 A 2 – g 1 γ 1 A 1

[8.2.54]

Now, the right-hand side of eq. [8.2.54] is a constant for given solute and solvent system, so the left-hand side is a constant. This shows why gA in the original theory (eq. [8.2.23]), is a composition-independent parameter of the system. Of course, in the derivation of eq. [8.2.23] gA had been assumed constant, and in effect this assumption led to any composition dependence of gA being absorbed into γ. In the modified formulation, we ˆγ is being accounted for A acknowledge that the composition dependence of the product gˆ without claiming that we can independently assign composition dependencies to the separate factors in the product. 8.2.4.3 Interpretation of parameter estimates Eq. [8.2.54] constitutes the basis for the resolution of the logical problem, described earlier, in which different cosolvents, with a given solute, yield different gA values, although gA had been assumed to be independent of composition. As eq. [8.2.54] shows, gA is determined by a difference of two fixed quantities, thus guaranteeing its composition independence, and at the same time permitting gA to vary with cosolvent identity. Eq. [8.2.53] is, therefore, conceptually sounder and physically more detailed than is eq. [8.2.23]. Eq. [8.2.53] shows, however, that in the absence of independent additional information (that is, information beyond that available from the solubility study alone) it is not possible to dissect the quantity (g2γ2A2 − g1γ1A1) into its separate terms. In some cases such additional information may be available, and here we discuss the example of naphthalene solubility in mixed aqueous-organic binary mixtures. Table 8.2.8 lists the values of gA(γ2 − γ1) obtained by applying eq. [8.2.23] to solubility data in numerous mixed solvent systems.8 In an independent calculation, the solubility of naphthalene in water was written as eq. [8.2.55], *

Δ G soln ( x 2 = 0 ) = Δ G cryst + g 1 A 1 γ 1

[8.2.55]

Kenneth A. Connors

505

which is equivalent to eq. [8.2.4]. ΔGcryst was estimated by conventional thermodynamic arguments and ΔGsolv was omitted as negligible,24 yielding the estimate g1A1γ1=4.64x10-20 J molecule-1. With eq. [8.2.54] estimates of g2A2γ2 could then be calculated, and these are listed in Table 8.2.8. Table 8.2.8. Parameter estimates and derived quantities for naphthalene solubility in watercosolvent mixtures at 25oCa Cosolvent

γ2, erg cm-2

1020 gA(γ2 − γ1), J molecule-1 1020 g2A2γ2, J molecule-1

Methanol

22.4

−3.11

1.53

Ethanol

21.8

−2.70

1.94

Isopropanol

20.8

−2.19

2.45

Propylene glycol

37.1

−2.46

2.18

Ethylene glycol

48.1

−2.24

2.22

Acetone

22.9

−3.37

1.27

Dimethylsulfoxide

42.9

−3.67

0.97

a

Data from ref. (8); γ1 = 71.8 erg cm-2, g1A1γ1 = 4.64x10-20 J molecule-1.

Observe that g1A1γ1 and g2A2γ2 are positive quantities, as expected; gA(γ2 − γ1) is negative because of the surface tension difference. It is tempting to divide each of these quantities by its surface tension factor in order to obtain estimates of gA, g1A1, and g2A2, but this procedure may be unsound, as proposed subsequently. 8.2.4.4 Confounding effects Solute-solute interactions It is very commonly observed, in these mixed solvent systems, that the equilibrium solubility rises well above the dilute solution condition over some portion of the x2 range. * Thus solution phase solute-solute interactions must make a contribution to Δ G soln . To some extent, these may be eliminated in the subtraction according to eq. [8.2.22], but this operation cannot be relied upon to overcome this problem. Parameter estimates may, therefore, be contaminated by this effect. On the other hand, Khossravi25 has analyzed solubility data for biphenyl in methanol-water mixtures by applying eq. [8.2.23] over varying ranges of x2; he found that gA(γ2 − γ1) was not markedly sensitive to the maximum value of x2 chosen to define the data set. In this system the solubility varies widely, from x3=7.1x10-7 (3.9 x 10-5 M) at x2 = 0 to x3 = 0.018 (0.43 M) at x2 = 1. Coupling of general medium and solvation effects In this theory, the general medium and solvation effects are coupled through the solvation exchange constants K1 and K2, which determine the composition of the solvation shell surrounding the solute and thereby influence the surface tension in the solvation shell. But the situation is actually more complicated than this, for if surface tension-composition data are fitted to eq. [8.2.26] the resulting equilibrium constants are not numerically the same as the solvation constants K1 and K2 evaluated from a solubility study in the same mixed solvent. Labeling the surface tension-derived constants K' 1 and K' 2 , it is usually

506

8.2 The phenomenological theory of solvent effects in mixed solvent systems

found that K' 1 > K1 and K' 2 > K2. The result is that a number attached to γ at some x2 value as a consequence of a nonlinear regression analysis according to eq. [8.2.23] will be determined by K1 and K2, and this number will be different from the actual value of surface tension, which is described by K' 1 and K' 2 . But of course the actual value of γ is driving the general medium effect, so the discrepancy will be absorbed into gA. The actual surface tension (controlled by K' 1 and K' 2 ) is smaller (except when x2 = 0 and x2 = 1) than that calculated with K1 and K2. Thus gapparent = gtruexγ( K' 1 , K' 2 )/γ(K1, K2). This effect will be superimposed on the curvature correction factor that g represents, as well as the direct coupling effect of solvation mentioned above. The cavity surface area In solubility studies of some substituted biphenyls, it was found (see 8.2.3.1) that gA evaluated via eq. [8.2.23] was linearly correlated with the nonpolar surface area of the solutes rather than with their total surface area; the correlation equation was gA = 0.37 Anonpolar. It was concluded that the A in the parameter gA is the nonpolar surface area of the solute. This conclusion, however, was based on the assumption that g is fixed. But the correlation equation can also be written gA = 0.37 FnonpolarAtotal, where Fnonpolar = Anonpolar/Atotal is the fraction of solute surface area that is nonpolar. Suppose it is admitted that g may depend upon the solute (more particularly, it may depend upon the solute's polarity); then the correlation is consistent with the identities A = Atotal and g = 0.37 Fnonpolar. Thus differences in gA may arise from differences in solute polarity, acting through g. But A may itself change, rather obviously as a result of solute size, but also as a consequence of the change of solvent, for the solvent size and geometry will affect the shape and size of the cavity that houses the solute. The role of interfacial tension In all the preceding discussion of terms having the gAγ form, γ has been interpreted as a surface tension, the factor g serving to correct for the molecular-scale curvature effect. But a surface tension is measured at the macroscopic air-liquid interface, and in the solution case, we are actually interested in the tension at a molecular scale solute-solvent interface. This may be more closely related to an interfacial tension than to a surface tension. As a consequence, if we attempt to find (say) g2A2 by dividing g2A2γ2 by γ2, we may be dividing by the wrong number. To estimate numbers approximating to interfacial tensions between a dissolved solute molecule and a solvent is conjectural, but some general observations may be helpful. Let γX and γY be surface tensions (vs. air) of pure solvents X and Y, and γXY the interfacial tension at the X-Y interface. Then in general,

γ XY = γ X + γ Y – W XY – W YX

[8.2.56]

where WXY is the energy of interaction (per unit area) of X acting on Y and WYX is the energy of Y acting on X. When dispersion forces alone are contributing to the interactions, this equation becomes26 d d 1⁄2

γ XY = γ X + γ Y – 2 ( γ X γ Y )

[8.2.57]

Kenneth A. Connors d

d

507

where γ X and γ Y are the dispersion force components of γX and γY. In consequence, γXY is always smaller than the larger of the two surface tensions, and it may be smaller than either of them. Referring now to Table 8.2.8, if we innocently convert g2A2γ2 values to estimates of g2A2 by dividing by γ2, we find a range in g2A2 from 23 Å2 molecule-1 (for dimethylsulfoxide) to 118 Å2 molecule-1 (for isopropanol). But, if the preceding argument is correct, in dividing by γ2 we were dividing by the wrong value. Taking benzene (γ = 28 erg cm-2) as a model of supercooled liquid naphthalene, we might anticipate that those cosolvents in Table 8.2.8 whose γ2 values are greater than this number will have interfacial tensions smaller than γ2, hence should yield g2A2 estimates larger than those calculated with γ2, and vice versa. Thus, the considerable variability observed in g2A2 will be reduced. On the basis of the preceding arguments, it is recommended that gAγ terms (exemplified by g1A1γ1, g2A2γ2, and gA(γ2 − γ1)) should not be factored into gA quantities through division by γ, the surface tension, (except perhaps to confirm that magnitudes are roughly as expected). This conclusion arises directly from the interfacial tension considerations. Finally, let us consider the possibility of negative gA values in eq. [8.2.23]. Eq. [8.2.54] shows that a negative gA is indeed a formal possibility, but how can it arise in practice? We take the water-ethanol-sucrose system as an example; gA was reported to be negative for this system. Water is solvent 1 and ethanol is solvent 2. This system is unusual because of the very high polarity of the solute. At the molecular level, the solute in contact with these solvents is reasonably regarded as supercooled liquid sucrose, whose surface tension is unknown, but might be modeled by that of glycerol (γ = 63.4 erg cm-2). In these very polar systems capable of hydrogen-bonding eq. [8.2.57] is not applicable, but we can anticipate that the sucrose-water interaction energies (the WXY and WXY terms in eq. [8.2.56] are greater than sucrose-ethanol energies. We may expect that the sucrosewater interfacial tension is very low. Now, gA turned out to be negative because gA(γ2 − γ1), a positive quantity as generated by eq. [8.2.23], was divided by (γ2 − γ1), a difference of surface tensions that is negative. Inevitably gA was found to be negative. The interfacial tension argument, however, leads to the conclusion that division should have been by the difference in interfacial tensions. We have seen that the interfacial tension between sucrose and water may be unusually low. Thus the factor (γ2 − γ1), when replaced by a difference of interfacial tensions, namely [γ(sucrose/ethanol) − γ(sucrose/water)], is of uncertain magnitude and sign. We, therefore, do not know the sign of gA; we only know that the quantity we label gA(γ2 − γ1) is positive. This real example demonstrates the soundness of the advice that products of the form gAγ not be separated into their factors.27,28

508

8.2 The phenomenological theory of solvent effects in mixed solvent systems

8.2.5 PRACTICAL APPLICATIONS AND FINDINGS

George Wypych ChemTec Laboratories, Toronto, Canada The solvent exchange model has been proposed by Bosch and Roses to investigate preferential solvation experimentally.29 This model is an extension of the stepwise solvent exchange model of Connors which derived equations that relate ET values of a solute with the solvent composition.17 The competition between different solvent species to solvate the solute is described by some exchange equilibria in the vicinity of solute.29 An equilibrium constant (named as the preferential solvation parameter) is defined for each exchange reaction, which relates the mole fraction of solvents in solvation shell to that in the bulk mixture.29 The formation of solvating complexes is postulated from solvent-solvent interaction on the microsphere of solvation.29 El-Seoud modified this model by considering the formation of solvating complexes in both cybotactic region and bulk mixture.30 All of the species in the solvation shell are considered in equilibrium with the same species in the bulk mixture.30 Solubility measurement is a laborious and time-consuming procedure and mathematical models could be used as an alternative approach.33 The Jouyban-Acree model is one of the well-established models providing accurate computations for solubility of a solute with respect to temperature and composition of the solvent mixture.33 The solvatochromic properties of the free base and the protonated 5, 10, 15, 20-tetrakis(4-sulfonatophenyl)porphyrin, TPPS, were studied in pure water, methanol, ethanol (protic solvents), dimethylsulfoxide (non-protic solvent), and their corresponding aqueous-organic binary mixed solvents.31 The correlation of the empirical solvent polarity scale (ET) values of a cancer drug in different solvents was analyzed by the solvent exchange model of Bosch and Roses.31 The results from the preferential solvation and solvent-solvent interactions have been successfully applied to explain the variation of equilibrium behavior of protonation of TPPS occurring in aqueous organic mixed solvents of methanol, ethanol, and DMSO.31 Absorption spectra of morin hydrate were studied in pure water, methanol, ethanol, 1-propanol, and 2-propanol and their aqueous binary mixtures.32 Spectral changes were interpreted in terms of specific and non-specific solute-solvent interactions.32 The molar transition energy (ET) at the maximum absorption as a solvatochromic probe was measured for each binary mixture.32 The preferential solvation was found as a non-ideal behavior of ET curve respective to the mole fraction of the alcohols in all the binary mixtures.32

8.2.5 NOTES AND REFERENCES 1 2 3 4 5 6 7

D. Khossravi and K.A. Connors, J. Pharm. Sci., 81, 371 (1992). R.R. Pfeiffer, K.S. Yang, and M.A. Tucker, J. Pharm. Sci., 59, 1809 (1970). J.B. Bogardus, J. Pharm. Sci., 72, 837 (1983). P.L. Gould, J.R. Howard, and G.A. Oldershaw, Int. J. Pharm., 51, 195 (1989). Also, when K1 = 1 and K2 = 1, eq. [8.2.13] shows that ΔGsolv = ΔGWW; in this special case the solvation energy is composition-independent. H.H. Uhlig, J. Phys. Chem., 41, 1215 (1937). J.E. Leffler and E. Grunwald, Rates and Equilibria of Organic Reactions, J. Wiley & Sons, New York,

George Wypych

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

25 26 27

28 29 30 31 32 33

509

1963, p. 22. J.M. LePree, M.J. Mulski, and K.A. Connors, J. Chem. Soc., Perkin Trans. 2, 1491 (1994). The curvature correction factor g is dimensionless, as are the solvation constants K1 and K2. The parameter gA is expressed in Å2 molecule-1 by giving the surface tension the units J Å-2 (where 1 erg cm-2 = 1x10-23 J Å-2). D. Khossravi and K.A. Connors, J. Pharm. Sci., 82, 817 (1993). J.M. LePree, Ph.D. Dissertation, University of Wisconsin-Madison, 1995, p. 29. A. Leo, C. Hansch, and D. Elkins, Chem. Revs., 71, 525 (1971). C. Reichardt, Solvents and Solvent Effects in Organic Chemistry, VCH, Weinheim, 1988. D. Khossravi and K.A. Connors, J. Solution Chem., 22, 321 (1993). K.A. Connors and J.L. Wright, Anal. Chem., 61, 194 (1989). K.A. Connors, Binding Constants, Wiley-Interscience, New York, 1987, pp. 51, 78. R.D. Skwierczynski and K.A. Connors, J. Chem. Soc., Perkin Trans. 2, 467 (1994). K.A. Connors and D. Khossravi, J. Solution Chem., 22, 677 (1993). M.J. Mulski and K.A. Connors, Supramol, Chem., 4, 271 (1995). K.A. Connors, M.J. Mulski, and A. Paulson, J. Org. Chem., 57, 1794 (1992). J.M. LePree and K.A. Connors, J. Pharm. Sci., 85, 560 (1996). M.C. Brown, J.M. LePree, and K.A. Connors, Int. J. Chem. Kinetics, 28, 791 (1996). J.M. LePree and M.E. Cancino, J. Chromatogr. A, 829, 41 (1998). The validity of this approximation can be assessed. The free energy of hydration of benzene is given as −0.77 kJ mol-1 (E. Grunwald, Thermodynamics of Molecular Species, Wiley-Interscience, New York, 1997, p. 290). Doubling this to −1.5 kJ mol-1 because of the greater surface area of naphthalene and repeating the calculation gives g1A1γ1 = 4.88x10-20 J molecule-1, not sufficiently different from the value given in the text to change any conclusions. D. Khossravi, Ph.D. Dissertation, University of Wisconsin-Madison, 1992, p. 141. F.M. Fowkes, Chemistry and Physics of Interfaces; American Chemical Society: Washington, D.C., 1965, Chap. 1. The introduction of the interfacial tension into the cavity term was first done by Yalkowsky et al.,28 who also argue that a separate solute-solvent interaction term is unneeded, as the solute-solvent interaction is already embodied in the interfacial tension. In our theory, we explicitly show the coupling between the solute-solvent and solvent-solvent interactions (eq. [8.2.19]), but this is in addition to the solute-solvent interaction (eq. [8.2.13]). This difference between the two theories is a subtle issue that requires clarification. S.H. Yalkowsky, G.L. Amidon, G. Zografi, and G.L. Flynn, J. Pharm. Sci., 64, 48 (1975). U. Buhvestov, F. Rived, C. Ràfols, E. Bosch, M. Rosés, J. Phys. Org. Chem., 11, 185-92, 1998. E.B. Tada, P.L. Silva, C. Tavares, O.A. El Seoud, J. Phys. Org. Chem., 18, 5, 398-407, 2005. A. Farajtabar, F. Jaberi, F. Gharib, Spectrochim. Acta, Part A: Molec. Biomolec. Spectr., 83, 1, 2013-20, 2011. R. Yazdanshenas, F. Gharib, J. Molec. Liq., 243, 414-9, 2017. M. Mohammadzade, M. Barzegar-Jalali, A. Jouyban, J. Molec. Liq., 206, 110-3, 2015.

9

Acid-base and Other Interactions 9.1 GENERAL CONCEPT OF ACID-BASE INTERACTIONS George Wypych ChemTec Laboratories, Toronto, Canada Acid-base interaction is an important part of research on adsorption of molecules of liquids on the surfaces of solids. The main focus of this research is to estimate the thermodynamic work of adhesion, determine mechanism of interactions, analyze the morphology of interfaces and various surface coatings, develop surface modifiers, study the aggregation of macromolecular materials, explain the kinetics of swelling and drying, understand the absorption of low molecular weight compounds in polymeric matrices, and determine the properties of solid surfaces. In addition to these, there are many other applications. Several techniques are used to determine and interpret acid-base interactions. These include contact angle, inverse gas chromatography, IGC, Fourier transform infrared, FTIR, and X-ray photoelectron spectroscopy, XPS. These methods, as they are applied to solvents, are discussed below. Contact angle measurements have long been used because of common availability of instruments. They have been developed from simple optical devices to the present day precise, sophisticated, computer-controlled instruments with sufficient precision. Van Oss and Good1,2 developed the basic theory for this method. Their expression for surface free energy is used in the following form:

γ = γ where:

γLW γAB γ+ γ-

LW

+γ

AB

= γ

LW

+ -

+2 γ γ

[9.1.1]

Lifshitz-van der Waals interaction acid-base interaction Lewis acid parameter of surface free energy Lewis base parameter of surface free energy.

The following relationship is pertinent from the equation [9.1.1]:

γ

AB

+ -

= 2 γ γ

[9.1.2]

512

9.1 General concept of acid-base interactions

A three-liquid procedure was developed1-3 which permits the determination of the acid-base interaction from three measurements of contact angle: LW LW

+ -

- +

LW LW

+ -

- +

LW LW

+ -

- +

γ L1 ( 1 + cos θ 1 ) = 2 ( γ S γ L1 + γ S γ L1 + γ S γ L1 ) γ L2 ( 1 + cos θ 2 ) = 2 ( γ S γ L2 + γ S γ L2 + γ S γ L2 )

[9.1.3]

γ L3 ( 1 + cos θ 3 ) = 2 ( γ S γ L3 + γ S γ L3 + γ S γ L3 ) Solving this set of equations permits the calculation of solid parameters from equation [9.1.1]. The work of adhesion, Wa, between a solid and a liquid can be calculated using the Helmholtz free energy change per unit area: LW LW

+ -

- +

– Δ G SL = Wa SL = γ S + γ L – γ SL = 2 ( γ S γ L + γ S γ L + γ S γ L )

[9.1.4]

A determination is simple. However, several measurements (usually 10) should be taken to obtain a reliable averages (error is mostly due to the surface inhomogeneity). There is a choice between measuring the advancing or the receding contact angle. Advancing contact angles are more representative of equilibrium contact angles.3 Inverse gas chromatography data are interpreted based on Papirer's equation:4,5 D 1⁄2

RT ln V N = 2N ( γ S )

D 1⁄2

a ( γL )

+c

[9.1.5]

where: R T VN N γD S, L a c

gas constant temperature net retention volume Avogadro's number dispersion component of surface energy indices for solid and liquid, respectively molecular area of the adsorbed molecule integration constant relative to a given column. D

Several probes are used to obtain the relationship between RTlnVN and a γ L . From REF this relationship the reference retention volume, V N , is calculated and used to calculate the acid-base interaction's contribution to the free energy of desorption: VN Δ G AB = RT ln -----------REF VN

[9.1.6]

If data for a suitable temperature range for ΔGAB can be obtained, the acid-base enthalpy, ΔHAB can be calculated using the following equation:

Δ H AB = K a DN + K b AN where: Ka Kb

acid interaction constant base interaction constant

[9.1.7]

George Wypych

513

Figure 9.1.1. Correlation of binding energy and ΔHAB for several polymers. [Adapted, by permission, from J F Watts, M M Chehimi, International J. Adhesion Adhesives, 15, No.2, 91-4 (1995).] DN AN

Figure 9.1.2. Correlation of binding energy and ΔHAB for several solvents. [Adapted, by permission, from J F Watts, M M Chehimi, International J. Adhesion Adhesives, 15, No.2, 91-4 (1995).]

donor number acceptor number

Finally, the plot of ΔHAB/AN vs. DN/AN gives Ka and Kb. Further details of this method are described elsewhere.4-9 It can be seen that the procedure is complicated. The conditions of experiments conducted in various laboratories were sufficiently different to affect correlation of data between laboratories.10 To rectify this situation, a large body of data was obtained for 45 solvents and 19 polymers tested under uniform conditions.10 Fowkes11 showed that the carbonyl stretching frequency shifts to lower values as the dispersion component of surface tension increases. The following empirical relationship was proposed:

ΔHAB = 0.236ΔvAB where:

ΔHAB ΔvAB

[9.1.8]

the enthalpy change on acid-base adduct formation projection of carbonyl stretching frequency on dispersive line.

It should be noted that, as Figure 7.1.18 shows, the change in frequency of carbonyl stretching mode is related to the process of crystallization.12 XPS is emerging as a very precise method for evaluating acid-base interactions based on the works by Chehimi et al.6-9 There is a very good correlation between XPS chemical shift and the change in exothermic enthalpy of acid-base interaction. Drago's equation is used for data interpretation:13

− ΔHAB = EAEB + CACB where: A, B EA, EB CA, CB

subscripts for acid and base, respectively susceptibility of acid or base species to undergo an electrostatic interaction susceptibility of acid or base species to undergo a covalent interaction.

[9.1.9]

514

Figure 9.1.3. Intensity ratio vs DN and AN. [Adapted, by permission, from M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994).]

9.1 General concept of acid-base interactions

Figure 9.1.4. PMMA surface content vs. intensity ratio. [Data from M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994).]

The determination of properties of the unknown system requires that master curve is constructed. This master curve is determined by testing a series of different polymers exposed to a selected solvent. An example of such a relationship is given in Figure 9.1.1. The enthalpy change caused by the acid-base adduct formation is obtained from a study of the same solid with different solvent probes (see Figure 9.1.2). Having this data, coefficients E and C can be calculated from the chemical shifts in any system. Figure 9.1.3 shows that there is a correspondence between DN and AN values of Figure 9.1.5. Thickness of PMMA overlayers vs. intensity ratio. [Data from M L Abel, M M Chehimi, different solvents and Cl(2p)/Cl(LMM) Synthetic Metals, 66, No.3, 225-33 (1994).] intensity ratios.7 Figure 9.1.4 shows that the type of solvent (measured by its Cl(2p)/Cl(LMM) intensity ratio) determines adsorption of basic PMMA on acidic polypyrrole. Figure 9.1.5 shows that also the thickness of PMMA overlayer corresponds to Cl(2p)/Cl(LMM) intensity ratio of solvent. XPS analysis combined with analysis by atomic force microscopy, AFM, determines differences in the surface distribution of deposited PMMA on the surface of polypyrrole depending on the type of solvent used (Figure 9.1.6).6 AFM, in this experiment, permitted the estimation of the surface roughness of polypyrrole. When PMMA was deposited from tetrahydrofuran, a poor solvent, it assumed a surface roughness equivalent to that of poly-

George Wypych

515

Figure 9.1.6. Schematic diagram of surface roughness of polypyrrole and deposition of PMMA from two different solvents. [Adapted, by permission, from M L Abel, J L Camalet, M M Chehimi, J F Watts, P A Zhdan, Synthetic Metals, 81, No.1, 23-31 (1996).]

Figure 9.1.7. Relationship between RT ln VN and number of carbon atoms in n-alkanes. [Adapted, by permission from M M Chehimi, E Pigois-Landureau, M Delamar, J F Watts, S N Jenkins, E M Gibson, Bull. Soc. Chim. Fr., 9 (2) 137-44 (1992).]

Figure 9.1.8. Flory interaction parameter vs. inverse temperature for polyamide. [Adapted, by permission, from L Bonifaci, G Cavalca, D Frezzotti, E Malaguti, G P Ravanetti, Polymer, 33 (20), 4343-6 (1992).]

pyrrole. Whereas PMMA, when deposited from a good solvent − CHCl3,6 developed a smooth surface. The above examples show Figure 9.1.9. Carbonyl stretching frequency vs. dispercontribution to surface tension of solvent. [Adapted, the importance of solvents in coating mor- sion by permission from M M Chehimi, E Pigois-Landureau, phology. M Delamar, J F Watts, S N Jenkins, E M Gibson, Bull. Figure 9.1.7 shows the correlation Soc. Chim. Fr., 129 (2) 137-44 (1992).] between the number of carbon atoms in nalkanes and the net retention volume of solvent using IGC measurements.8 Such a correlation must be established to calculate the acid-base interaction's contribution to the free energy of desorption, ΔGAB, as pointed out in discussion of equations [9.1.5] and [9.1.6].

516

9.1 General concept of acid-base interactions

Figure 9.1.8 shows that the Flory interaction parameter (measured by IGC) increases as the temperature increases. Figure 9.1.9 shows a good correlation between carbonyl stretching frequency as determined by FTIR and the dispersion contribution of the surface tension of the solvent. The above shows a good correspondence between the data measured by different methods. This was also shown by a theoretical analysis of the effect of acidbase interactions on the aggregation of PMMA.14 But there is as yet no universal theory for the characterization of acid-base Figure 9.1.10. Calculated apparent pH for system H2O2− interaction. H2O using eq. [9.1.10]. [Data from J J Kosinski, P Acid-base equilibria can be conveWang, R D Springer, A Anderko, Fluid Phase Equilibria, 256, 34-41 (2007). niently characterized by pH which is a common and experimentally determined characteristic parameter.16 The following model is useful in relating pH to activity coefficients on the mole fraction scale:16 pH = – log x

H

+

– log γ

x H

+

1000 – log ------------MH O

[9.1.10]

2

where: x γx M

mole fraction activity coefficient of the component on a mole fraction basis molecular weight

Figure 9.1.10 shows pH calculated for an H2O2−H2O solvent system using Eq. [9.1.10]. The calculated data are in the perfect agreement with several sets of experimental data.16 An exact evaluation of pKB is not an easy task from direct pH measurement in an acid-base system containing organic cosolvent.17 A new method based on studies of the same acids in water and organic solvents lead to repeatable results.17 More information on optimization of reaction methods based on fundamental concepts of Brönsted–Lowry acids and bases can be found in the monographic source.18 A chapter in another monograph addresses fundamentals of nonaqueous solvent chemistry.19 The p-toluidine oligomer was successfully used as an acid-base indicator for studying solvatochromism in solvents of different polarity.20 The acid solution color sharply turned from pink (acidic medium) to yellow (basic medium) at the endpoint.20

REFERENCES 1 2

C J van Oss, L Ju, M K Chaudhury, R J Good, J. Colloid Interface Sci., 128, 313 (1989). R J Good, Contact Angle, Wetting, and Adhesion, VSP, 1993.

George Wypych 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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K-X Ma, C H Ho, T-S Chung, Antec '99 Proceedings, 1590 and 2212, SPE, New York, 1999. C Saint Flour, E. Papirer, Colloid Interface Sci., 91, 63 (1983). K C Xing, W. Wang, H P Schreiber, Antec '97 Proceedings 53, SPE, Toronto, 1997. M L Abel, J L Camalet, M M Chehimi, J F Watts, P A Zhdan, Synthetic Metals, 81, No.1, 23-31 (1996). M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994). M M Chehimi, E Pigois-Landureau, M Delamar, J F Watts, S N Jenkins, E M Gibson, Bull. Soc. Chim. Fr., 129 (2) 137-44 (1992). J F Watts, M M Chehimi, International J. Adhesion Adhesives, 15, No.2, 91-4 (1995). P Munk, P Hattam, Q Du, A Abdel-Azim, J. Appl. Polym. Sci.: Appl. Polym. Symp., 45, 289-316 (1990). F M Fowkes, D O Tischler, J A Wolfe, L A Lannigan, C M Ademu-John, M J Halliwell, J. Polym. Sci., Polym. Chem. Ed., 22, 547 (1984). B H Stuart, D R Williams, Polymer, 36, No.22, 4209-13 (1995). R S Drago, G C Vogel, T E Needham, J. Am. Chem. Soc., 93, 6014 (1971). S J Schultz, Macromol. Chem. Phys., 198, No. 2, 531-5 (1997). L Bonifaci, G Cavalca, D Frezzotti, E Malaguti, G P Ravanetti, Polymer, 33 (20), 4343-6 (1992). J J Kosinski, P Wang, R D Springer, A Anderko, Fluid Phase Equilibria, 256, 34-41 (2007). B Pilarski, A Dobkowska, H Foks, T Michalowski, Talanta, 80, 1073-80 (2010). B G Cox, Acids and Bases. Solvent Effects on Acid-Base Strength, Oxford University Press, Oxford, 2013. J E House, K A House, in Acids, Bases, and Nonaqueous Solvents. Descriptive Inorganic Chemistry. 3rd Edition, Elsevier, 2015. M S Zoromba, Spectrochim. Acta Part A: Molec. Biomolec. Spectr., 187, 61-7, 2017.

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9.2 ACIDS AND BASES IN MOLTEN SALTS, OXOACIDITY Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov Institute for Scintillation Materials, 60 Nauki Avenue, Kharkov, Ukraine 61001 Modern developments in chemistry and chemical industry result from wide use of different chemical processes in presence of molecular and ionic solvents since their nature efficiently affects the performance of technological processes.1,2 Selection of the most appropriate solvent providing optimal process conditions (expenditures on electricity, heat, reagents, the product yield, etc.) for the desired process is one of the important tasks of chemical technology. It should be noted that in addition to usual room-temperature molecular solvents various ionic solvents receive now the great attention from investigators. They can be divided into two groups: room-temperature ionic liquids which usually consist of complex organic cations and anions and high-temperature molten salts. Each group has advantages and disadvantages. For instance, the use of room-temperature ionic liquids does not require heating and oxygen-free atmosphere, but they became too expensive because of the difficulties in their synthesis and purification.3,4 High-temperature ionic melts have opposite performance characteristics. Although their use means heating and a need for protective atmosphere, the main components of the melts are usual cheap salts, such as KCl, NaCl, NaNO3, Na2SO4 etc. When chemical processes are conducted at elevated temperatures they may result in saving time due to a considerable increase in the process rate. Molten salts are widely used as convenient solvents in different technological processes, such as, surface treatment (etching, fluxes), electrolytic methods of production of metals and alloys, refining, electrochemical deposition of coatings, etc.5-7 Halide melts are starting materials for crystal growth with such widely used crystals as CsI:Tl, NaI:Tl and LaBr3:Ce3+ (scintillators), KCl, NaCl (acoustical) and KBr, CsBr (IR optics), which are grown from the corresponding ionic melts. For several decades, ionic melts have been attracting considerable attention as solvents for treatment of nuclear wastes without production of wastes,8,9 that is especially important from the viewpoint environment ecology. Ionic melts possess a number of properties due to which they compare favorably with the conventional room-temperature solvents. As a rule, they are quantitatively dissociated to the constituent ions, which permits application of high (order of 10 A cm-2) current densities in the electrochemical processes. Halide melts are absent of strong oxidants similar to H+ that makes it possible to obtain final products, which cannot be made from aqueous solutions (i.e., alkali and alkali earth metals, subions etc.). Molten salts are very attractive as green technological solvents. Their use does not cause accumulation of harmful liquid wastes since cooling of used ionic liquids to room-temperature transforms them into solids. Reactions occurring in ionic melts-solvents are considerably affected by impurities contained in the constituents of the melt or formed during their preparation (mainly, at the stage of melting) due to high-temperature hydrolysis or interactions of salts with materials

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of crucibles (alumina, quartz, etc.) as well as aggressive oxygen-containing components of atmosphere (O2, CO2, H2O etc.). The complete list of these impurities is large and includes multicharged cations of transition metals, different complex anions (oxo- or halide anions). The effect of these admixtures on processes in ionic melts depends on the degree of their donor−acceptor interactions with the constituent parts of ionic melts or dopants purposefully added to these solvents. Admixtures of oxygen-containing substances in the majority of molten salts are the most wide-spread and their influence on the technological processes and the parameters of final products is often negative. The negative effect of admixtures is caused by the fixation of reagents of acidic character (cations, polynuclear oxygen-containing anions, gases of acidic character) that favors formation of insoluble (precipitates or suspensions) or slightly dissociated products in the molten medium. This results in the slowing down of process caused by decrease in the equilibrium concentration of starting acidic reagents, appearance of inclusions of oxide particles in electrochemically deposited metals or grown crystals, additional absorption bands in optical single crystals, uncontrolled losses of dopants, reduction of radiation hardness of scintillation materials,10,11 substantial corrosion, and accelerated damage and destruction of contacting constructional materials. Therefore, the information concerning the physicochemical parameters of the reactions of oxide ions and oxo-compounds in high-temperature ionic solvents (melts) is of considerable scientific and applied science importance. Below, we consider the data on both thermodynamics of reactions of oxocompounds in ionic melts and kinetics of purification processes of halide melts from oxide ion traces.

9.2.1 ACID−BASE DEFINITIONS USED FOR DESCRIPTION OF DONOR−ACCEPTOR INTERACTIONS IN MOLTEN SALTS Traditionally, different kinds of donor-acceptor interactions in liquid media are considered as acid−base interactions within the framework of an appropriate acid−base concept or definitions. The last century witnessed the development of a few definitions, which can be conditionally divided to definitions of “carriers” of acidic (basic) properties, definitions considering acid−base reactions in solution in relation to the nature of solvent and principles allowing to predict the direction of different acid−base reactions under various conditions. 9.2.1.1 Pearson's “hard” and “soft” acid−base concept (HSAB) The HSAB concept is now considered as one of the most appropriate instruments used for prognosis of chemical interactions on the basis of properties of outer electron shells of the reacting ions and atoms.12-14 The original classification proposed by Pearson considers metal cations of subgroups “a” of the Periodic Table as “hard” acids, whereas F- and Clanions and ammonia are referred to as “hard” bases. As for the “soft” reagents, it should be mentioned that cations of subgroups “b” of the Periodic Table are intermediate and soft acids. Such anions as CN- and I- are classified as soft bases. According to Pearson, the hardest acid is proton (H+) and the softest one is CH3Hg+, and the hardest bases are OHand F- and the softest ones are I- and H-. The current interpretation of HSAB principle is as follows: small components of weak polarization and high electronegativity are the “hard” reagents, and the “soft”

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reagents are relatively large components possessing stronger polarization and weaker electronegativity. Hard acids are barely reduced, and hard bases are barely oxidized, whereas soft acids can be easily reduced and soft bases are easily oxidized. According to HSAB principle, acid−base interactions result in the preferential formation of “hard acid−hard base” and “soft acid−soft base” final adducts. Any acid or base may be classified as hard or soft acid and base depending on its ability to form adducts with generally accepted “'hard” and “soft” bases and acids. The preferable form of the “hard−hard” and “soft−soft” pairs happens because the interaction between electron orbitals possessing close energies is more thermodynamically favorable. Such interactions lead to the formation of adducts with ionic (“hard” acids and bases, electrostatic interaction) and covalent (“soft” acids and bases) chemical bonds. The list of some hard and soft acids and bases which will be discussed below is presented in Table 9.2.1. It should be noted that attribution of acids and bases to hard and soft ones only on the basis of their ionic radii is incorrect. Indeed, cations Mg2+ and Ni2+ of the same ionic radius (0.074 nm) do not belong to the same class of acids. Table 9.2.1. Pearson's hard and soft acids and bases Acids

Bases Hard

H , Li , Na , K , Cs , Mg , Ca , Sr , Ba , CO2 O2-, NO3-, CO32-, SO42-, F-, Cl-, OH+

+

+

+

+

2+

2+

2+

2+

2+

2+

2+

Intermediate 2+

2+

2+

+

2+

+

Fe , Co , Ni , Cu , Zn , Pb

NO2-, Br-, SO32Soft

Cu , Cd , Ag , Cu

+

I-, H-, CN-

Because of its relative simplicity HSAB principle is widely used to predict directions of different donor−acceptor reactions in liquid media of a different kind. However, in order to obtain correct results, not only the subgroup acids and bases should be taken into account, but also the properties of reagents in a given solvent. If there are no considerable distinctions in the strength of acids or bases, then the use of HSAB principle for estimation is sufficiently correct. If the opposite is the case, a lot of exclusions should be considered. For example, aqueous solutions of mercury (II) chloride are known to interact with potassium iodide, but this interaction proceeds according to the HSAB concept predictions: [9.2.1] (KI and HgCl2 are “hard−soft” and “soft−hard” compounds, respectively, and the products are “hard−hard” KCl and “soft−soft” HgI2 compounds). HgCl2 solution reacts with KOH formed by more “hard−hard” acid and base: [9.2.2]

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It should be noted, however, that the HSAB predictions of acid−base interactions in high-temperature ionic melts is usually more accurate than in the case of room-temperature molecular solvents, because at high temperatures (of the order of 1000K and more) ionic melts favor destruction of solvate shells and therefore, the correlation between electronic structure and acidity becomes straight-forward. 9.2.1.2 Definitions of acid−base pair Donor−acceptor interactions in ionic melts are usually treated as acid−base interactions according to Lewis15 and Lux-Flood16-19 definitions. The former defines acids as acceptors of unshared electron pairs whereas Lewis bases are the donors of unshared electron pairs. Since 1923 this definition was modified and one of the most recent variations defined acids as the electron pair (or anion) acceptors or cation (or proton) donors and bases as the electron pair (or anion) donors or cation (or proton) acceptors.20 Lux-Flood definition is less common than that by Lewis. It is mainly applicable for ionic melts, oxide-containing glasses, and metallurgical slags. It defines acids as acceptors of oxide ion (O2-) and its acceptors are referred to as Lux acids. 9.2.1.2.1 The Lewis definition An acid−base reaction according to Lewis definition may be described by the following principal scheme: [9.2.3] where: A B K

acid the conjugate base the equilibrium constant (pK used below designation means −logK).

For ionic melts, this definition can be used to describe interactions in media containing complex anions capable of heterolytic dissociation. The dissociation process: [9.2.4] where: M B

the central atom of the complex anion the ligand and simultaneously Lewis base

serves as “inner” acid−base equilibrium of a solvent. Typical melts where the Lewis definition can be used for the description of donor-acceptor processes include halogenoaluminates ( AlX 4 ), halogenogallates ( GaX 4 ), fluoroborates ( BF 4 ), etc. Molten alkali metal chloroaluminates containing an excess of aluminum chloride compared with a stoichiometry of MCl−AlCl3 = 1:1 (where M − alkali metal) are promising solvents for obtaining several products which cannot be synthesized using room-tem2+ 3+ perature solvents. They are sub-ions of metals,21 such as Cd+ ( Cd 2 ), Bi+, Bi 5 and excess of AlCl3 in the melt-solvent favors stabilization of similar intermediate oxidation degrees. Tremillon and Letisse,22 Torsi and Mamantov23 investigated acid−base properties of AlCl3−MCl (M = Li, Na, K, Cs) melts containing an excessive amount of AlCl3 compared with MAlCl4 stoichiometry in 175-400°C temperature range. To determine equilibrium concentration of Cl−, a potentiometry was used with the indicator chloride-reversible

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electrode. The solvents undergo the acid−base dissociation according to the following equation: [9.2.5] In chloroaluminate melts, chloride ion donors (e.g., alkali metal chlorides) are bases and substances increasing AlCl3 ( Al 2 Cl 7 ) concentration, in comparison with the initial pure solvent, are acids. The pK values of reaction [9.2.5] in NaAlCl4 melt decrease with the temperature increase from 7.1 (175°C) to 5.0 (400°C). This corresponds to the observation that stability of chloroaluminate decreases with temperature. The increase in the radius of alkali metal cation results in an increase of the pK values, in Li+−Na+−K+−Cs+ sequence it grows as follows: 3.8−5.0−5.8−7.4. The explanation of such a decrease may be obtained within the framework of HSAB principle. Indeed, both chloride ion and alkali metal cations are referred to as hard bases and the “hardness” of the latter decreases from Li+ to Cs+. Therefore, the strength of fixation of chloride ion formed on the right side of reaction [9.2.5] by alkali metal cations decreases with the cation radius increase. According to Le Chatelier principle, the strengthening of Cl− fixation should result in a shift of equilibrium [9.2.5] to the right and reduction of pK that actually takes place. Dioum, Vedel, and Tremillon24 reported a study of “inner” acid−base equilibria in molten potassium halogenogallates, KGaX4 (where X = Cl, I). The obtained data show that the acid−base products of solvents increased from KGaCl4 to KGaI4. The schemes of their self-dissociation processes and the corresponding constants are as follows: , pK=4.25±0.05 , pK=2.60±0.05

[9.2.6] [9.2.7]

A plausible explanation suggests that a change of Lewis base takes place in coordination shell around Ga3+ ion: a hard base (Cl−) is changed by a soft base (I−). Since Ga3+ ion belongs to hard cation acids, the stability of the halide complexes is reduced in the sequence GaCl4− → GaI4−. 9.2.1.2.2 The Lux-Flood definition (oxoacidity) Another definition used in ionic melts concerns donor−acceptor processes with the transfer of oxide ions, O2−. Since 1939, when Lux proposed to define acids as acceptors of O2− and bases as donors of oxide-ion16 and later this kind of acid−base interactions became to be known as “oxoacidity”. The general scheme of a Lux acid−base interaction may be presented by the following equation: [9.2.8] From this scheme, it follows that the Lux-Flood definition is a particular case of more common Lewis definition described above. For the quantitative interpretation of interactions with the transfer of O2−, Lux introduces the “pO” index serving as a measure of basic (acidic) properties of a melt: [9.2.9]

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where: a

O

2-

and m

O

2-

the activity and molality of oxide ion in the studied ionic melt, respectively.

The proposed oxygen index may be considered as an analog of pOH index in roomtemperature aqueous solutions. Measurements of pO during the acid−base reactions of different kinds permits to calculate their thermodynamic characteristics and their equilibrium constants. Due to the absence of reliable experimental data on the activity coefficients of most ions in molten salts and theoretical substantiations of their estimations similar to Debye-Hückel equation in room-temperature molecular solvents, the equilibrium constants are often obtained as concentrations but not thermodynamic parameters. Therefore, the practical pO indices discussed further are the negative logarithms of equilibrium O2− concentrations in the considered melt. Since in most cases, studies concern the diluted solutions of ionic solids or liquids in ionic liquids, i.e., both ingredients are the substances with ionic bonding. The same nature of bond allows considering the formed solutions as close to ideal but not infinitely diluted solutions, as it takes place in solutions of ionic substances in water or other room-temperature molecular liquids. 9.2.1.3 Definitions for solvent system Solvents of various nature (molecular, ionizing, ionic) often serve as media for performing different technological processes, which can be considered as acid−base processes according to the appropriate acid−base definition. The processes are subjected to solvent action that shifts the equilibrium favoring formation of desirable final products or retarding it. The degree of this action depends on acidic or basic properties of the solvent. The same compound may act as an acid or a base in different solvents depending on their nature, mainly, on acid−base properties. For example, acetic acid, CH3COOH, demonstrates relatively weak acidic properties in aqueous solutions: (room temp.)

[9.2.10]

since the selected solvent (water) is not considered acidic. Use of more basic solvents, such as liquid ammonia, results in a considerable strengthening of CH3COOH acidity. The increase in the solvent acidity (e.g., in the case of anhydrous sulfuric acid) causes acetic acid to demonstrate appreciable basic properties as is seen from the following example: [9.2.11] Such solvent-dependent behavior of dissolved substances requires the development of definitions for the solvent system, which will help in dividing substances into acids and bases depending on their activities in the presence of solvents and on the concentration of components formed due to the intrinsic self-dissociation process of a given solvent. The most known definition of such kind is “definition for solvents system” or “solvosystem concept” by Franklin. According to it, the process of self-ionization of an ionizing solvent L can be written as follows: [9.2.12] and the corresponding expression for the mass action law is given as below

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[9.2.13] The majority of widely used room-temperature solvents possess a negligible degree of the self-ionization, therefore, the initial and the equilibrium concentrations of solvent molecules are constant and they are practically the same. The term in the denominator can be entered as the constant K' L , which gives the following final form: [9.2.14] The constant KL is called “ionic product of solvent”; and it is the value that causes the difference in acidity (basicity) parameter units between solutions of strong acids and bases. The pKL value itself defines the extent of acid−base range of an ionizing solvent in logarithm units. Now let us consider the action of different dissolved substances on ratio of l+ and l− concentrations in acidic and basic solutions in solvent L. A substance, which addition leads to increase of the concentration of l+ components in the solution (from Eq. 9.2.14 it means automatically that concentration of l− decreases), is considered an acid according to Lewis definition; on the contrary, addition of a substance causing reduction of l+ concentration as compared with its concentration in a pure solvent, is classified as a base. To illustrate the above discussion, let us consider phosphorus oxochloride, POCl3 as an example of ionizing solvents.25 The self-ionization process of liquid POCl3 may be described by the following equation: [9.2.15] Dissolution of phosphorus pentachloride, PCl5, in this solvent results in an increase of POCl2+ concentration that permits to consider PCl5 as an acid in POCl3: [9.2.16] Addition of NH4Cl to POCl3 causes increase of equilibrium concentration anion components corresponding to the anion product of the self-dissociation process of the solvent [9.2.15]: [9.2.17] hence, NH4Cl demonstrates basic properties in POCl3. From Eq. [9.2.12], it follows, that the solvosystem concept is appropriate for the description of acid−base interaction in any molecular solvent with the relatively small ionic product and, consequently, a low degree of self-ionization. In particular, it may be used for the description of interactions in covalent halide melts and aluminum, zinc and cadmium halides should be mentioned among such solvents. In relation to “acid” and “base” terms, this definition is more common than the definition formulated by Arrhenius or Brønsted-Lowry for proton acidity. Although, there are charge limitations of acidic and basic components of the solvent: the acidic component is a cation component whereas the basic component is mandatory an anion.

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If an acid dissolved in a solvent is stronger than the acid formed from the solvent self-ionization then the leveling of acidic properties takes place. It leads to complete solvolysis of the dissolved acid with the formation of an equivalent quantity of acid from the solvent, therefore the amount of the conjugated base equivalent to initial acid concentration is formed and this base does not reveal basic properties at all. For example, in an aqueous solution of HClO4, the following process takes place: [9.2.18] All above-mentioned remains true for dissolved strong bases. Let us consider several examples of non-aqueous solvents working in complete agreement with the Franklin solvosystem concept. In this relation, antimony (III) chloride and bromide have been studied. Their dissociation occurs as follows:26,27 [9.2.19] [9.2.20] Liquid antimony bromide has relatively low intrinsic electric conductivity which is –5 –1 of the order of 1 × 10 Ω cm.26 As follows from equation [9.2.20], the solutions of such ionic bromides as (CH3)4NBr, NH4Br, KBr, TlBr should show basic properties. This is really so, and three former bases were found to dissociate completely up to concentrations of the order of 10-2 mol kg-1. On the contrary, covalent bromides such as AlBr3, certain Lewis acids of antimony Sb(CH3C6H4SO3)3 and adducts of SbCl3 of SbX2AlCl4, SbX2FeCl4 compositions27 are bromide ion acceptors, therefore, they are referred to as acids, since their addition leads to increase of SbX2+ concentration in the liquid antimony halides as compared with that in the pure solvent. Whitney et al.28 reported that ClF3 and BF5 are promising liquid media for performing fluorination processes and different syntheses of complex fluorides based on alkali metal salts. These solvents are prone to self-ionization according to the following equations: [9.2.21] [9.2.22] Both solvents are characterized by relatively wide temperature ranges of their liquid state: −76.3 ÷ 11.75oC and −61.4 ÷ 40.4oC, respectively. Studies of the reactions of metal fluorides, which demonstrate basic properties in these solvents, show that the degree of their transformation into the corresponding complex fluorides [9.2.23] [9.2.24]

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increases with the atomic number of alkali metals, i.e., with the decrease of “hardness” of cation acids in the sequence Na+→K+→Rb+→Cs+ that causes weakening “Me−F” bond in the above sequence and facilitates the formation of the complex anion. In principle, this fact may be explained by increased insolubilities of the fluorides in the fluoride solvents. As for ClF3, it is a weaker Lewis acid as compared with BrF5 that can be seen from the reaction of these compounds: [9.2.25] and from the behavior of ClF3 in anhydrous HF which is a superacidic solvent: [9.2.26] The weak acidity of ClF3 explains the fact that there are no reactions of the solvent with LiF and NaF, whereas a strong acid BrF5 reacts appreciably with the latter fluoride. As for halogen pentafluorides, their acidities increase in the sequence ClF5→BrF5→IF5. This conclusion can be made also on the basis of the stability of corresponding ammonium salts of the NH4XF6 composition. The considered cases are rather exclusions than the rule. Practical application of the solvosystem concept is not so simple since for the systems similar to [9.2.15] the identification of ions formed at self-ionization and determination of their equilibrium concentrations are often very difficult. These systems possess low values of dielectric constant (relative permittivity) that creates additional obstacles for investigation and their incompleteness of dissociation and formation of ionic associates even in dilute solutions. For example, it is known that in liquid sulfurous anhydride the following acid−base interaction takes place:29 [9.2.27] which supposedly gives the evidence of the self-ionization of SO2 with the formation of two-charged anion and cation at low temperature according to the following equation: [9.2.28] However, the isotopic exchange examination of a liquid SO2 with the use of 18O30 shows that the equilibrium [9.2.28] actually does not take place. From the viewpoint of the mass action law, it means that according to the equation [9.2.28] the ionization degree of liquid SO2 is extremely low and the isotopic exchange cannot be revealed. High-temperature ionic solvents essentially differ from the above-described solvents, because of the considerably higher degree of the self-ionization, and, because in such media, ions, but not molecules, are the main components. Due to this reasoning, the use of the classic solvosystem concept to characterize acid−base equilibria as dependent on self-ionization process in the solvent fails to be successful, excluding some covalent halides of Al, Cd, Zn. Indeed, small additions of the strong acceptor of chloride ions (e.g., LnCl3) to molten KCl cannot change appreciably the equilibrium concentration of Cl−, which is the parameter that serves as a measure of basic properties of this melt according

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to the classic solvosystem concept. Therefore, pCl− ( ≡ −log[Cl−]) values in similar systems will be practically unchanged and insensitive to small concentrations of acids and bases unless these additions lead to appreciable changes in the melt composition. This also concerns the second ion, K+. This melt possesses the unchangeable acid−base properties in relation to K+ and Cl− concentrations. From the viewpoint of the solvosystem concept, the dissociation of the complex ion being a constituent part of the solvent with very low equilibrium constant value, but not only self-ionization, may be considered as “intrinsic” acid-base equilibrium of a solvent. In this case, concentrations of acids and bases can be varied in a very wide range. Such an approach will be more fruitful if it is used to describe donor−acceptor equilibria in ionic media as acid−base ones. A broader understanding of heterolytic dissociation of solvent constituents may be achieved by applying “self-ionization” term rather than “self-dissociation” term, i.e., the process of dissociation of complex components as constituent part of the solvent. This facilitates a choice of “acid” or “base” of solvent in melts containing complex ions (as a rule, they are anions), which are prone to Lewis acid−base dissociation. Processes of their dissociation can be treated as the intrinsic acid−base equilibria of a melt of such kind. In this case, eliminated anion of the simpler composition will be considered as the base of the solvent and the electron-deficient residue will be the acid of the solvent, the division is made on the basis of Lewis definition.15 Melts based on complex halides of gallium (III),24 aluminum (III),31 and boron (III)32,33 may serve as examples of successful use of above approach. Electron-deficient covalent halides (e.g., AlCl3 or BF3) in these melts are the solvent acids, and the corresponding halide ions are the bases of solvents. The dissociation constants of complex halide ions, which are nothing but acid−base self-dissociation constants of the corresponding solvents, are relatively small. Therefore, the equilibrium concentrations of the acids and the bases of solvent will be considerably affected by dissolved substances of acidic and basic character by Lewis. The existence of several acids of the solvent is possible in the melts of such kind and this leads to considerable complication of interpretation of the experimental results regarding acid−base equilibria in these media.34 Ionic melts consisting of salts of oxygen-containing acids (sulfates, carbonates, nitrates) may serve as another case of melt having heterolytic dissociation complex anion. The process of its dissociation results in the formation of oxide ion as the basic component and division substances into acids and bases may be performed according to the above-mentioned Lux-Flood definition. In addition to oxygen-containing melts, this definition is successfully used for the description of reactions between donors and acceptors of oxide ions in oxygenless melts, although these reactions fail to be considered in the framework of the solvosystem concept because the base (O2−) cannot be formed as a product of self-dissociation of the solvent constituents. The effect of molten background on Lux-Flood acid− base interactions is appreciable, and it depends on the strength of interactions between cations and anions in melts and base and acid, respectively. 9.2.1.3.1 Generalized definition of the solvent system. Two kinds of solvents As it has been mentioned above the usability of the classic solvosystem concept is narrowed to a group of solvents able of self-ionization. However, it is pertinent that acid−base interactions can run in solvents, which are not able to form acid and base owing to self-

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9.2 Acids and bases in molten salts, oxoacidity

dissociation processes. Aprotic solvents may serve as a typical example of solvents of such kind; another case of solvents unable to the acid-base self-dissociation takes place if we consider the Lux acid−base equilibria in molten oxygenless media. This means that in relation to any given acid or base, two kinds of solvents exist differing in autodissociation ability leading to formation of acid or base.35,36 The perceived difference between ionic melts and room-temperature molecular solvents can be related to limitations of the solvosystem concept. The division of substances into acids and bases is based on their reactions with the products of the molecular solvent self-dissociation, and the degree of this self-dissociation in a pure solvent is considered negligible. On the contrary, an ionic melt is the case of completely ionized solvent, and this is just the fact that does not give possibility to apply the classic solvosystem concept fruitfully for studies of acid−base interaction in this kind of liquid media. In order to generalize the definition of the solvent system for the case of ionic media, Franklin's definition should be analyzed attentively. At first, it should be noted that the term “self-ionization” in this definition should be substituted by the more appropriate term “self-dissociation” or “intrinsic acid−base equilibrium of a solvent” describing a more common case of heterolytic breakdown of the constituent components of a liquid. Indeed, for molecular or slightly ionized room-temperature solvents the terms “self-ionization” and “intrinsic acid-base equilibrium of the solvent” are related to the same process, whereas for ionic liquids they differ essentially. For instance, although sodium nitrate (NaNO3) is subjected to practically complete ionization in the liquid state according to such an equation: [9.2.29] (self-ionization), its intrinsic acid−base product: [9.2.30] calculated according to the following Lux-Flood acid−base self-dissociation equilibrium: [9.2.31] is too small and it provides the relatively wide range of varying acidic and basic properties of solutions in nitrate melts-solvents. Further, the terms “acid” and “base” cannot be attributed exclusively to cation and anion components formed during the process of self-dissociation of an ionic solvent. This occurs in the case of acid−base self-dissociation of sulfate melts used in the Lux acid−base reactions. Their intrinsic acid−base dissociation equilibrium is presented by the following equation: [9.2.32] Here, only anions are the reaction participants. Both in molten nitrates and in molten sulfates only anions, but not uncharged components of the solvents, are the initial substances undergoing the breakdown into acids and bases.

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So, the behavior of oxygen-containing melts as solvents for acid−base reactions can be described by a manner similar to the solvosystem concept. However, for this purpose, the solvosystem concept should be generalized in some relations. The main object lying in the basis of Franklin's solvosystem concept is a molecular solvent prone to self-ionization with the formation of small concentrations of cations and anions of the solvent. Water, spirits, and some other room-temperature liquids are the typical examples. However, one can imagine hypothetically a solvent being not prone to self-ionization, which possesses its intrinsic acid−base equilibrium without breakdown to ionic components. An example of such a solvent and process of its acid−base self-dissociation may be expressed by the following equation: [9.2.33] (this compound actually exists and it is called borazane which presents itself as the white solid powder melting with the decomposition at ~104°C). These speculations permit to determine the statements of the classic solvosystem concept which should be generalized in the case of non-dissociated and ionic solvents: • the acid and the base of a solvent may be formed not only due to the self-ionization equilibrium but also at any process of heterolytic dissociation of its constituent parts, both molecules and ions; • as for the terms “acid” and “base”, their interpretation should be widened. Cation and anion components of a solvent are not only the case of the acid and the base of solvent. Any Lewis acid may be considered as the acid of the solvent regarding the base of solvent; • in relation to a given definition of acids and bases, solvents should be divided into two kinds: solvents of the first kind and solvents of the second kind taking into account the existence of intrinsic acid−base equilibria in these media. A solvent is referred to as the first kind in the case of the existence of intrinsic acid− base equilibrium in it. In contrast, if a solvent is unable to dissociate with the formation of a given acid or base (for instance, O2− is not a product of dissociation of molten sodium chloride), it belongs to solvents of the 2nd kind. Such solvent will affect acid−base processes only by fixation of acid or base by its basic or acidic components, respectively. It should be emphasized that the classic solvosystem concept considers the self-ionization process to be primary, whereas the resultant substances such as acids and bases are obtained on the basis of their reaction with solvent or its constituent components. However, the practice of investigation of acid−base equilibria in solutions consists of studies of donor−acceptor reactions with the transfer of a definite component (acid or base) in different solvents irrespective of the fact whether it is able to dissociate with the formation of a given acid (base) or remain intact. Therefore, to propose an enhanced formulation of the solvosystem concept, solvents should be divided based on the initially chosen definition of acids and bases. The generalized definition of a solvent system formulated in our works35,36 can be presented in the following form:

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9.2 Acids and bases in molten salts, oxoacidity

the intrinsic acid−base dissociation (self-dissociation) of a solvent is any (excluding redox) reaction of heterolytic dissociation of its constituent parts (molecules or ions), which results in the formation of electron-deficient component-acid and electron-donor component-base. • a solvent belongs to a group of solvents of the first kind in the case of the formation of corresponding acid (base) as a result of its intrinsic dissociation processes in other case it is referred to as solvent of the second kind. (This means that several self-dissociation processes may exist in a solvent simultaneously). The self-dissociation processes of the solvents of the first kind can be described by the following basic scheme: •

[9.2.34] and the equilibrium [9.2.35] has a form of Eq. [9.2.34] and [9.2.36] where: li, lj and lk Al, i and Bl, i

the constituent parts of the solvent L which may be the same the acid of the solvent and the base of the solvent as products of li component dissociation.

There are no limitations of charge on these components. As follows from equations [9.2.34] and [9.2.36], there is a possibility for the simultaneous existence of some different processes of acid−base self-dissociation in the same solvent. Interaction of solvents of the first kind with acids or bases (solvolysis) results in the formation of solvo-acid or solvo-base and solvated conjugate base or acid, respectively:

where: A1 and B1

(solvo-acid)

[9.2.37]

(solvo-base)

[9.2.38]

conjugated acid−base pair

The presented above equation system shows that acidic properties of acids in solvents of the first kind are partially or completely leveled to the properties of Al, ilj, whereas the basic properties of bases are leveled to those of Bl, ilk. To clarify principal differences between solvents of the first kind and solvents of the second kind, let us consider Fig. 9.2.1. Here it is assumed that only one self-dissociation process takes place and it is accompanied by the formation of the acid of the solvent, Al, and the conjugated base, Bl. The solvent of the first kind occupies a definite acid−base range in the common acidity scale, pA (Fig. 9.2.1, I). The position of the standard (1 mol kg-1) solution of strong

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Figure 9.2.1. Acid−base ranges in solvents of different kinds: I − solvent of the first kind, II(base) − solvent of the second kind with defined basic component, II(acid) − solvent of the second kind with defined acidic component. Designations show directions of leveling of the acidic and basic properties.

acid is defined by acidity of Allj components and the position of the standard solution of strong base is shifted to higher pA values. The distance between these solutions is pKl, i.e., the index of the equilibrium constant of [9.2.36]. A pure solvent or neutral solution is characterized by a pAl value equal to 1/2pKl. If an acid stronger than Allj (its acidity is designated as A' ⁄ B' ) is added to the solvent it undergoes solvolysis according to the equation [9.2.37] and acidity of its solution will be equivalent to that of Allj (the leveling process is designated as A in Fig. 9.2.1). Therefore, the strongest acids in the solvent of the first kind cannot differ in measured acidity and they are indiscernible. The similar situation takes place in the case of dissolution of strong bases in the solvent of the first kind: basicity of bases stronger than Bllk, e.g., A'' ⁄ B'' is leveled to the strength of the base of the solvent (Bllk), this process is designated as B in Fig. 9.2.1. It follows that in the solvents of the first kind, one can determine correctly only acidities of acids weaker than Allj and basicities of bases weaker than Bllk. Water as the solvent of the first kind for protic acidity can serve as an example. It is well known that acidities of such strong acids as HClO4, HNO3, HCl are close and they cannot be distinguished only on the basis of pH measurements since because of the solvolysis they form the same quantities of solvated H+ (H5O2+): [9.2.39] Similarly, NaOH and NaH are bases of the same strength since their interaction with water results in the formation of the same amount of solvated OH−: [9.2.40]

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9.2 Acids and bases in molten salts, oxoacidity

From reactions [9.2.39] and [9.2.40], it follows that there are no acids stronger than solvated H+ and no bases stronger than solvated OH− in aqueous solutions. The neutral point of this solvent is located at pH = pOH = 7 at room temperature. The solutions with pH values lower than 7 are acidic, whereas values of pH > 7 are characteristic of basic solutions. Ionic solvents of the first kind can be exhaustively illustrated by nitrate melts such as potassium nitrate KNO3 or its low-melting equimolar mixture with sodium nitrate KNO3− NaNO3 (the melting point ca. 220oC) as solvents for Lux-Flood acid−base processes. The intrinsic acid−base equilibrium in these solvents can be expressed by equation [9.2.31]. Oxide ion is formed as one of the products of NO 3 dissociation, and this permits to consider them as solvents of the first kind. Acidic and basic solutions are defined by their relation to the neutrality point which is pO = 1/2pK. The magnitude of the intrinsic acid−base product of the nitrate melts was estimated by several investigators. Zambonin presented this value for a molten equimolar mixture KNO3−NaNO3 as 10-18 (molality),37 whereas Kust and Duke calculated these values to be 2.7×10-26 at 250oC and 2.7×10-24 at 300oC.38 The phenomenon of the leveling of acidic and basic properties in the nitrate melts can be illustrated by the following examples: (oxo-acid)

[9.2.41] (oxo-base)

[9.2.42] 35,36

and the equation The leveling of acidic properties was proven in our papers [9.2.42] is written taking into account that the strength of a base is leveled to the basic properties of the adduct of O2− to the most acidic cation of the ionic solvent (in KNO3− NaNO3 equimolar mixture this cation is Na+ because of its smaller radius than that of K+). Consequently, the solvents of the first kind may be characterized by the limit of the leveling of acidic properties, equal to pAl = pKa (for a chosen standard solvent pKa is assumed to be 0), by the neutrality point located at pAl = pKa + 1/2 pKl, where Kl is the constant of the intrinsic acid−base dissociation and by the limit of the strength of bases pA = pKa + pKl. As for solvent of the first kind, the measure of the strength of acid (base) is a degree of its interaction with solvent leading to the formation of solvated acid (base) of solvent. Since the equilibrium concentration of the acid (base) of solvent cannot exceed the initial concentration of the added monobasic acid (monoacidic base), for this case, the 0 0 following relation is correct: c A ≥ c A ( c B ≥ c B ). l, j l, i Now let us proceed to consideration of acid−base processes occurring in solvents of the second kind taking into account that acid Al is the “carrier” of acidic properties (the speculations concerning the “carrier” of basicity Bl are similar). The range of varying acidic properties of such a solvent is shown in Fig. 9.2.1, line II (acid). The dissociation process of solvent L occurring according to equation [9.2.34] does not result in the formation of Al acid. If we add an acid (Al) to solvent, the following reaction will take place: [9.2.43]

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This equation shows that one of the constituent parts of solvent, namely li, which fixes the acid, possesses basic properties. Addition of a base to the solvent will result in similar reaction with the participation of constituent parts of the acidic character. However, the addition of a base into the pure solvent L does not lead to the creation of acid Al or reduction of its concentration, since there are no components of such kind in the pure solvent. From Fig. 9.2.1 it follows that in the case of a solvent of the second kind, the acid A' is completely transformed into the conjugated base B' , whereas the acid−base pair A'' ⁄ B'' is not subjected to solvolysis at all. Therefore, the acidic properties of strong acids are leveled to those of Al − li. Although the properties of bases are changed because of the reaction with the constituent parts of solvent, they cannot be leveled to the properties of a common base B. Theoretically, there are no limitations to the strength of bases in solvents of the second kind. Hence, the solvents of the second kind are characterized by the limit of leveling of acidic properties, for standard solutions, it is defined by the relation pAl = pKa; the term “neutrality point” is theoretically senseless since there is no acid Al in the pure solvent. An experimentally determined value of the neutrality point in the real solvent and pAl index depend only on the content and nature of admixtures, which remain in the solvent after its purification and their concentration depends on the purifying ability and thoroughness of the applied variant of the purification. The strength of bases in such a case cannot be expressed via strength of certain common base since it is not produced in solution after addition of another base. In simpler words, the role of bases in the solvents of the second kind is only in fixation of acidic components and increase in pAl of the solution, whereas their addition to the pure solvent does not result in the formation of the solvent's base. Therefore, acidity scales in the solvents of the second kind are limited by the leveling of properties of a “carrier” of acidic (or basic) properties; there are no theoretical limitations on the opposite side of the acidity scale. Aprotic solvents (e.g., benzene or CCl4) as media for protolytic acid−base equilibria belong to the solvents of the second kind, that makes terms “acidic” and “basic” medium to be conditional. In aqueous solution, there are clear boundaries between these media (pH=7), which is located in the middle of the acid−base range of water. It should be noted that authors39 did not show a limit of the leveling of acidic properties in benzene, although this limit should be observed. Indeed, benzene is well-known to add proton in anhydrous sulfuric acid, and this process is widely used in organic synthesis. Hence the acid−base pair C6H7+/C6H6 should be placed on the acidity scale somewhere above H3SO4+/H2SO4 pair since H3SO4+ reacts with benzene forming C6H7+. As for bases, their strength in benzene is not limited theoretically. The generalized solvosystem concept proposed above is applicable to the description of principal features of protolytic and aprotic solvents, although just for this case this does not allow to obtain new results. As for the case of ionic melts, it is more important for the analysis, since the theoretical basis of acid−base interactions in this kind of solvents is not developed so extensively. Nevertheless, there are many results on oxoacidity obtained in

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9.2 Acids and bases in molten salts, oxoacidity

ionic solvents of both the first and the second kind which deserves to be treated in a proper way. The above-considered features of the leveling of acidic and basic properties in solvents of different kinds permit to conclude that the position of each particular solvent in the generalized scale of acidity depends on properties, at least, of one conjugated acidbase pair, in which acid or base is generated as one of the products of solvent self-dissociation. The position of the acid−base range of a solvent in the generalized scale of acidity defines which acids and bases can exist in this solvent and which ones undergo solvolysis. Therefore, determination of the width of the acid−base range of a solvent and its position in the generalized acidity scale is an important practical task of the chemistry of acids and bases. 9.2.1.4 Peculiarities of oxygen-containing and oxygenless melts as media for oxoacidity Now let us consider principal distinctions of two kinds of high-temperature ionic solvents oxygen-containing (primary) and oxygenless (secondary) according to papers.40,41 9.2.1.4.1 Oxygen-containing melts The Lux-Flood acid−base interactions in oxygen-containing ionic melts are studied more extensively than in the solvents of the second kind (mainly, these are melts based on the alkali and alkaline earth metal halides) since melting points of the most studied nitrates and their mixtures (KNO3, KNO3−NaNO3) do not exceed 350°C. The complications taking place in these systems are caused, at first, by the superimposition of their own acid− base equilibrium of melt-solvents (self-dissociation), which, according to the said above, belongs to the solvents of the first kind. As the solvents of the first kind, oxygen-containing ionic melts involve not only oxide ions but also the solvent acid as a product of the intrinsic acid−base dissociation. This reason leads to the two-side limitation of acid−base ranges that gives rise to different specific features of these solvents, such as the leveling of properties of acids, narrowing of acid−base range with the temperature rise, etc. The behavior of the oxoacidic acid−base pairs in these solvents is similar to that of the Brønsted-Lowry acid−base pairs in aqueous solutions. However, oxygen-containing ionic melts possess some distinctive features originating at relatively high temperatures of the liquid state. In some cases, the acid of solvent is volatile or thermally instable16,42 and, being formed as a result of the Lux acid−base process, it is gradually evaporated from the melt. This leads to a loss of acid, and pO of such an acidic solution approaches the value corresponding to the instrumentally measured neutral point of the solvent. Therefore, besides the leveling of acidic properties, the oxygen-containing melts are often characterized by their upper limit of acidity defined either by the limited solubility of the formed gaseous acid in a solvent or by the decomposition temperature of this acid. Such high-acidic oxides as CrO3 and MoO3 were found to decompose molten KNO3 with subsequent evolution of NO2, termination of this decomposition resulted in stabilization of pO values of the melt.43 This value determined by the method of potentiometric titration was found to decrease as the temperature of the melt was considerably increased.

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Such a behavior of acidic solutions in the nitrate melt was explained by the formation of + + nitrogen pentoxide, N2O5 ( NO 2 • NO 3 ), or nitronium cation, NO 2 , in the acidic solutions, together with the corresponding oxoanions of Cr(VI) and Mo(VI). Since the added acids are very strong, their reaction with the melt: [9.2.44] is completely shifted to the right and the strength of such acids is practically determined + by the acidic properties of NO 2 . The thermal stability of the cation is relatively small, and when its concentration exceeds a certain magnitude the reaction of nitronium with nitrate ions: [9.2.45] becomes intense enough. The proposed kinetic methods of the determination of the nitrate melt acidities are based on measurements of the rate of this reaction: the rate of NO2 evolution from the melt depends only on their acidity. Further, during the course of reaction [9.2.45], the concen+ tration of NO 2 cation decreases; this causes a decrease in the rate of NO2 evolution. Finally, the latter becomes so slow that a series of sequential measurements of pO demonstrate that this parameter remains practically constant, i.e., the system passes to quasiequilibrium state. The pO value measured under these conditions is the upper limit of the melt acidity, which is independent of the composition of the added strong acid. This explains the thermal dependence of the upper limit of acidity for nitrate melts observed elsewhere.43 The rise of the melt temperature results not only in the decrease of cation + NO 2 stability but also in the increase of the rate of reaction [9.2.45]. Similarly to the discussed nitrate melts, molten sulfate mixtures are characterized by the upper limit of acidity that is seemingly defined by both the limited solubility of SO3 in these melts at temperatures near 800oC and its instability under these conditions. This conclusion may be obtained from the data found elsewhere.16 There is a shift in pO (or electromotive force of the potentiometric cell, emf) of acidic solution towards the neutrality point of the melt. This process was found by Lux to be caused by evaporation of SO3 from the acidic solutions K2SO4−Na2SO4 equimolar mixture and by its possible decomposition according to the following scheme: [9.2.46] Let us summarize principal features of oxygen-containing ionic melts as the media of the first kind. • These ionic solvents are characterized by the existence of the intrinsic acid−base dissociation, which possesses a constant acid−base product pKl described by an equation similar to [9.2.30]. The ranges of acidic and basic solutions are separated clearly by their neutrality point, which is located at pOl = 1/2 pKl,i. • They are distinguished by the leveling both of acidic and basic properties in these melts due to the solvolysis reactions. The properties of acids are leveled because

536

9.2 Acids and bases in molten salts, oxoacidity

of the formation of the equivalent quantity of acid of the solvent that makes all the strong acids indistinguishable. The properties of strong bases are limited by the basicity of the oxide ion adduct with the most acidic constituent cation of the ionic solvent. The values of equilibrium constants of oxide ion addition may be determined without appreciable distortion only for acids and bases weaker than the acid or the base of the solvent. • Acid−base processes are complicated since they are affected, at least, by one intrinsic acid−base equilibrium of the melt. As a rule, the upper limit of acidity caused by volatility or thermal decomposition of concentrated solutions of the solvent acids is observed experimentally. Therefore, the melts-solvents of the first kind are of interest in the following scientific aspects: determination of the acid−base product of the ionic solvent and estimation of the upper limit of acidity of these solvents (such as nitrates, sulfates). Decrease in stability of the solvent acid can be used for the stepwise decomposition of acidic solutions of cations and synthesis of complex oxide compounds and composites by coprecipitation.44-47 It is possible to obtain complex oxides containing alkali metals by precipitation of multivalent metal oxides with the alkali metal oxide as a strong Lux base, as it was reported by Hong et al., who used 0.59 LiNO3−0.41 LiOH mixed melt to obtain electrochemically active lithium cobaltate, LiCoO2.48 9.2.1.4.2 Oxygenless melts Pure oxygenless melts contain no oxide ions in any form, and because of this the pure melts cannot serve as donors of O2−. The melts, which are solvents of the second kind, can affect acid−base interaction in two manners: by fixation of oxide ions entering melt and by solvation of conjugated acid or base. These ionic solvents are used in practice for research and applied purposes, however, they contain admixtures of oxide ion donors, which are 22formed in the melt from initial admixtures of oxoanions such as SO 4 , CO 3 , OH−. The second way of the appearance of oxide ion admixtures in molten media is characteristic of the melts based on alkali metal halides: the process of high-temperature hydrolysis of the halide melts results in the formation of hydroxide and, after their dissociation, of oxide ions: [9.2.47] The presence of the oxide-containing admixtures in oxygenless melts inevitably leads to their dissociation with formation of oxide ions and conjugated gas-acid, as admixtures of these processes, which are described in ionic form by the following equations: [9.2.48] [9.2.49] [9.2.50] Since concentrations of all these admixtures depend on the purity of salts used for preparation of melts, they are not constant. This means that for each specific melt-solvent,

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the initial pO values fluctuate around a certain value. For example, pure CsI and KCl− NaCl melts are characterized by pO ≈ 4 , whereas for more capricious NaI and KCl−LiCl melts, pO values are lower and usual vary between 3 and 3.7. For a comparison, at 298K, pure water as a solvent is characterized by pH = 7, and this value remains constant after achieving a certain degree of H2O purity. Oxygen admixture solutions differ substantially in the degree of dissociation with the formation of oxide ion. For instance, the addition of even relatively high concentrations of sulfate ions does not result in appreciable changes of O2− concentration in the melt, 2whereas the effect of the addition of CO 3 and OH− on pO values in melts is more pronounced. The investigations carried out on various ionic melts and in a wide temperature range (from 500 to 1100K) permit to arrange the above discussed oxoanions in the follow22ing order SO 4 → CO 3 → OH− in which the basic properties increase. The preliminary thorough purification of oxygenless halide ionic melts from oxygencontaining admixtures may provide the pO values varying within the limits of 3 to 4.5. This is the main cause of errors affecting calculations of thermodynamic parameters, especially at small concentrations of reagents in melts and it is impossible to eliminate this influence by any way. So, in the case of alkali metal halide melts the use of the strongest halogenating agent does not result in essential reduction of oxide ion concentration, since the action of such reagents favor the transformation of oxide ion into weaker bases such as 2CO 3 (at carbohalogenation), and the latter admixture is hardly decomposed in the melt. It is known that earlier studies of oxoacidity in molten salts were performed without detailed analysis of the melts composition and pO of “pure” oxygenless melts yielded the instrumentally determined initial concentration of the residual admixtures, which was often used as a constant of a given solvent.49-52 Proceeding from this assumption, the authors of the mentioned papers constructed empirical scales of acidity of some oxygenless melts and attributed acid−base ranges to these melts. As follows from the above-written, the acid−base ranges in the ionic solvents of the second kind are half-opened, therefore, their length cannot be estimated by a constant value. Features of oxygenless melts as the solvents of the second kind are as follows: • The constituent components of these melts are not susceptible to Lux-Flood acid−base dissociation, therefore, there is no acid in a solvent, whereas the solvent base is adduct of oxide ions to constituent cations of the melt. • They are characterized by leveling basic properties of the strongest bases since they are transformed in the equivalent quantity of the solvent base. There are no limitations of the strength of acids that makes it possible to compare the relative acidic properties of all acids, which are stable in these melts at a definite temperature. • Their acidic and basic regions are determined conditionally with respect to the initial concentration of oxide ions in the melts, which depends on the concentration of oxygen admixtures in the “pure” solvent and, subsequently, on the quality of the melt purification from oxygen-containing impurities. The melt-solvents of the second kind and molten alkali metal halides are widely used in different practical applications (electrochemical deposition of metals,53 alloys, crystal

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9.2 Acids and bases in molten salts, oxoacidity

growth, etc.). Investigations of acidic properties of these solvents permit estimation of stability of various dissolved oxygen-containing impurities, the solubility of constructional materials (alundum, yttria stabilized zirconia, etc.) and to control the mentioned processes to account for changes of the acidity (basicity) of the used melt-solvent. Naturally, the knowledge of the acidic properties of “pure” ionic liquids makes it possible to choose the optimal ionic solvent for performing necessary technological process on the basis of accurate quantitative parameters. Therefore, investigations of acid−base reactions in molten salts for determination of the effect of ionic melt composition on different acid−base equilibria are of importance both from theoretical and applied viewpoints.

9.2.2 THE EFFECT OF THE IONIC SOLVENT COMPOSITION ON ACID−BASE EQUILIBRIA. MELT OXOACIDITY PARAMETERS, Ω AND pI L The interaction between constituent parts of an ionic solvent and dissolved oxide ions occur, mainly, because of the cation components of solvent and they are one of the most important factors defining the effect of the ionic melt composition on the acid−base reactions in it. Such an interaction may be presented by the following principal scheme: [9.2.51] where: li

a constituent component of the solvent of acidic character

The higher the degree of interaction the more complete the oxide ion fixation in complexes that shifts Lux-Flood acid−base reactions to the side corresponding to the destruction of the basic products. This can be found out experimentally by changing the calculated values of equilibrium constants of the acid−base reactions in a given ionic solvent as compared to the corresponding value in the reference (standard) melt. The results concerning the information on the relative acidic properties of ionic solvents will be considered below. Ionic solvents among which molten alkali metal halides and their mixtures with alkaline metal halides are characterized by the absence of constitutional oxygen (i.e., oxide ions). As stated above they are referred to as the solvents of the second kind. This means that there is no the intrinsic acid−base equilibrium in these media and limitations of the strength of Lux acids. Nevertheless, the strength of bases is leveled to the basicity of the complex formed by oxide ions and these cation components of solvent, which demonstrate the strongest acidic properties in a given melt. For example, Tremillon et al.54 on the basis of general considerations concluded that the properties of Lux bases in the KCl−NaCl equimolar mixture are leveled to the basic properties of Na2O, but not to K2O, since the following equilibrium: [9.2.52] in the molten salts of various anion compositions is shifted to the right. Because of this, the bases stronger than Na2O do not exist in melts of KCl−NaCl series subjected to sol-

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volysis. This conclusion54 agrees with the present-day knowledge about the relative acidic properties of K+ and Na+ as Lewis acids in molten salts. The basicity of standard solution ( a 2- = 1 ) of a strong base in a solvent of the secO ond kind depends on the absolute concentration of “free” oxide ions in this solution and it is an important fundamental characteristic of the oxoacidic properties of the said ionic solvent. To estimate the positions of melts within the general oxoacidity scale, it is necessary to determine parameters reflecting the oxoacidic properties of a given melt. This requires to choose the reference melt which acidity will serve as a reference point and to develop methods of acidity estimation. The relative acidity index of this melt should be equal 0. Similar to the approach used for estimation of protic acidity in room-temperature molecular liquids, the use of the primary medium effect of oxide ion, − log γ 2- as a 0, O , L measure of oxoacidic properties, is the most justified. This parameter presents a measure of work of transferring 1 mole of a substance (ion) from the standard solution (c = 1 mol kg-1) in a given solvent L to the standard solution in the reference solvent55 that may be expressed by the following formula: [9.2.53] where: A

* X, O

2-

and A

2-

X, O , L

the work of substance M solvation in the reference and the given solvent, respectively

The values of the primary medium effect of the proton were used by Izmailov to construct the common acidity scale for protolytic solvents and for the solvents more basic than water having negative values of − log γ + , whereas for more acidic solvents these 0, H , L values are positive. It is obvious that for the case of molten salts values of − log γ 20, O , L will be positive for melts possessing weaker acidity than the reference one and they will be negative for more acidic melts. Further, Izmailov proposed to construct common acidity scale for solutions in different solvents using pA index, which is equal to: [9.2.54] where: pHL

the measured pH value in solvent L

This makes pA index practically equivalent to Hammett function H0.56 In the case of . the standard solutions with respect to H+ A similar approach was proposed in several recent works in which authors introduced Ω57,58 (analog of pA or H0) and pIL40 (analog of – log γ 0, O2-, L ) indices for the characterization of oxoacidic properties of solutions in ionic solvents. Their physical sense will be clarified below. First, let us define the primary medium effect of oxide ion by the following formula: [9.2.55]

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9.2 Acids and bases in molten salts, oxoacidity

that corresponds to the transfer of oxide ion from the standard solution in solvent L to the standard solution in the reference melt. Beginning with work of Tremillon, KCl−NaCl equimolar mixture is considered as the reference melt and log γ 2= 0. Recent 0, O , KCl – NaCl investigations59 shows that CsCl−KCl−NaCl eutectic melt could be used as the reference one since it possesses wider temperature range in the liquid state (the melting point of CsCl−KCl−NaCl ternary eutectic is 480°C compared with 658°C for KCl−NaCl). Acidic properties of both melts depend on Na+ cations, therefore, they are very close. Melts containing more acidic cation than Na+, e.g., KCl−LiCl and CaCl2−KCl melts should possess negative values of – log γ 2- since their constituent cations formed oxides which are 0, O , L less able to dissociate than Na2O. Taking into account the above considerations, the sense of Ω function is similar to pA value introduced by Izmailov [9.2.54] and may be expressed as: [9.2.56] where: pOL pIL

the measured pO value in a given melt L the oxobasicity index of solvent L

The latter is introduced as the concentration analog of – log γ 2- since there is no 0, O , L information about the activity coefficients in the literature. For the standard solution of oxide ions in solvent L Ω = pIL. It is seen that Ω can be used as a characteristic of the relative basicity of solution with any concentration of oxide ion in solvent L, whereas pIL index describes the oxoacidic properties of this solvent. Melts or solutions more basic than the standard solution in the reference melt have negative values of Ω and these possessing weaker basicity are characterized by positive Ω values. The more detailed relation between Ω and pIL is pertinent from Fig. 9.2.2. Values of pO in the reference melt are equal to Ω values (see Eq. [9.2.56] and Fig. 9.2.2, line 1). For melts having higher acidity, similar dependences are parallel to the dependence for the reference melt and they are spaced by pIL magnitude (Fig. 9.2.2, line 2). For melts having weaker acidity, Ω − pO are placed below the dependence for the reference melt (Fig. 9.2.2, line 3). For any solution (denoted in Fig. 9.2.2 by a star) value of Ω* can be calculated as a sum of pOL and pIL (vector Ω* equals to the sum of vectors pOL and pIL). So, Ω* is nothing else but the value of pO in the reference melt which has basicity equal to the basicity of a given solution in melt L. In any two melts the difference of Ω between solutions with the same pOL is a constant equal to pIL or −pIL (Fig. 9.2.2 arrow 5). Fig. 9.2.2 gives an illustration of physical sense of the oxobasicity index pIL, which is the value of pO in the reference melt possessing the basicity equal to the basicity of the standard solution in melt L. For example, line 4 shows that the standard solution of O2− (1 mol kg-1, pO = 0) in KCl−LiCl eutectic melt (2) possesses basicity equal to that of molten KCl−NaCl equimolar mixture with concentration of O2− of 3x10-4 mol kg-1 (pO = 3.5). As for less acidic CsI (line 3), it can be found that the standard solution of oxide ion in this melt has basicity of 10 mol kg-1 (pO = −1) of a solution of O2− in KCl−NaCl eutectic melt.

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Figure 9.2.2. Scheme showing relation between Ω, pIL and pOL for different melts: 1 − Ω − pO dependence for the standard solvent, 2, 3 − the similar dependence for more (KCl−LiCl, pIL ~ 3.5) and less (CsI, pIL ~ −1.0) acidic melts, respectively, 4, 4’ − lines of the equal basicity, 5 − solutions in the reference and the studied melts with the same concentration of O2−.

9.2.2.1 Methods of estimation of ionic melt oxoacidity There are several experimental methods, which permit estimation of the oxobasicity indices, pIL, and the oxoacidity function, Ω. They are used for calculation of these indices on the basis of an experimental parameter (equilibrium constant of a preliminary chosen acid−base process, solubility product of metal oxide or simply emf of a certain solution) with the use of a definite non-thermodynamic assumption. One of the earliest attempts of Ω calculation was made by Tremillon et al.57,58 To construct the general acidity scale in molten media the authors proposed to estimate the acidity function for ionic melts determining the constant of the following equilibrium: [9.2.57] in a given melt and in the reference melt. According to this proposition, the common oxoacidity function Ω may be calculated from the following formula: [9.2.58]

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9.2 Acids and bases in molten salts, oxoacidity

and, hence, this oxoacidity function57,58 can be expressed using the equilibrium constant of reaction [9.2.57] in the following way: [9.2.59] It is obvious that the expression in the parentheses by this author is nothing but the primary medium effect of O2− expressed by the difference in values of the equilibrium constants of [9.2.57] for the media compared: the reference KCl−NaCl melt, with pK HCl ⁄ H O equal to 14 at ~700oC and the studied melt. 2 The expediency of using reaction [9.2.57] is substantiated by the fact that in molten ionic chlorides, the mole fraction of chloride ion equals 1 and the activities of HCl and H2O in a chloride melt are proportional to their partial pressures in the atmosphere over this melt. The creation of constant partial pressures of both gases over different ionic solvents is easily achieved by passing an inert gas (N2 or Ar) through aqueous solutions of HCl of a certain concentration kept at a constant temperature. Under these conditions passing this gaseous mixture with the stable composition through different chloride melts gives the possibility to obtain solutions of the same Ω, irrespective of the melt composition. The above-mentioned papers57,58 report determination of the upper limits of basicity, which can be achieved in alkali metal chlorides and the melts containing polyvalent metal chlorides as constituent parts of the melt. Owing to small ionic radii and high charge, these cations demonstrate elevated acidic properties. The increase of the initial molality of oxide ions finally results in precipitation of the solid oxide, formed by such acidic cations, from its saturated solution with oxide ion concentration equal to s 2- . The oxoacidity function O corresponding to this limit can be described by the following equation: [9.2.60] A study of KCl−NaCl+xCeCl3 melts, where x values are within 0.05-0.30 (molar fraction),57 shows that increase in the acidic cation concentration in the melt leads to the rise of the corresponding Ωmin value. Nevertheless, it remains within 13-14, whereas the acidity scale shift (Ω value of the standard solution of a strong base) is within 10-12. Increase in the melt acidity caused by the increase of the mole fraction of CeCl3 in the melt from 0.1 to 0.3 reduces Ce2O3 solubility in the melt from 10-2.3 to 10-1.65. There is no linear correlation between the oxide solubilities and the melt acidities. Similar investigations of KCl−NaCl−MgCl2 and KCl−NaCl−CaCl2 melts with the addition of 20 mol% of the alkaline earth metal chlorides show that, for the former melt, the shift of the acidity scale is approximately equal to 14, in the latter case it is only 9. There are the upper limits of basicity in both melts. In the former melt, Ωmin is approximately equal to 14.7, in the Ca2+−doped melt, Ωmin approaches 11. There is no the upper limit of basicity in the molten KCl−LiCl (0.41:0.59) eutectic mixture and the shift of the acidity scale for the equimolar KCl−NaCl mixture is ca. 8 logarithmic units.57 The processes of pyrohydrolysis of alkali metal halide melts doped with ZnCl2 at ~600oC were studied elsewhere.60,61 The pO scales in the melts were shifted by 3 units in

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the acidic region in comparison with the KCl−LiCl eutectic, so, Zn2+-containing melts possess higher acidity than Li+-containing ones. Concluding the discussion of Tremillon's approach, it should be mentioned that ionic melts were investigated by indirect methods, which excluded the addition of solid base into the melt. All known investigations of the relative acidic properties of ionic melts are based on the determination of the equilibrium concentration of oxide ion as a product of reaction [9.2.57] in these media. The equilibrium parameters and conditions were not checked experimentally, therefore, there may be doubts regarding the correctness of Ω values estimated in such a way. Let us analyze the experimental data on oxoacidity investigations in KCl−LiCl eutectic melts and their agreement with predictions on the basis of Ω value,57 which was estimated as ca. 8. Such a considerable difference in acidities for KCl−NaCl and KCl− LiCl melts is unexpected since the index of the Li2O dissociation constant (pK): [9.2.61] 62

was found to be pK = 3.95 for the equimolar KCl−NaCl mixture. The high acidity of KCl−NaCl−CaCl2 (0.4:0.4:0.2) melt was surprising too, the acidity scale shift was estimated to be approximately 9.57 If Ω values57,58 actually reflect the primary medium effect of O2−, they cause that the above-mentioned melts as extremely aggressive acidic media, likely because of performance of anhydrous sulfuric acid in comparison with water ( H 0 ≈ – log γ + = – 11 ).63 In 0, H particular, such melts should completely dissolve appreciable quantities of solid oxides, e.g., MgO, NiO, etc., up to 1 mol kg-1. For instance, MgO, which is practically insoluble in KCl−NaCl equimolar mixture (pKs = 9.33 ± 0.06 )64,65 can be characterized by pKs ≈ 1 (because 9.33 − 8 ≈ 1) in KCl−LiCl eutectic that corresponds to the value of the solubility product of the order of 10-1. As for the KCl−NaCl−CaCl2 melt, the solubility product value should also be close to 1. On the contrary, most metal oxides slightly soluble in the KCl−NaCl melt were shown by Shapoval, Makogon, and Pertchik66,67 to remain only slightly soluble in KCl−LiCl eutectic. Moreover, these oxides (NiO, CoO) are dissociated incompletely under these conditions.66 The equilibria of high-temperature chloride melt pyrohydrolysis, carbonate ion dissociation, and magnesium oxide solubility in the equimolar CaCl2−KCl mixture at 575oC were studied elsewhere.68 The pK value of equilibrium [9.2.49] was found to be equal 1.4 and the solubility product index of MgO: [9.2.62] was pKs,MgO = 5.3 ± 0.1 . The shift of the indices of these constants compared with those obtained in melts of weaker acidity (e.g., CsCl−KCl−NaCl eutectic or the equimolar KCl− NaCl mixture) was not more than 4, which did not agree with values predicted based on the published Ω values.57,58 The above reasoning shows that the use of equation [9.2.57] yields distorted Ω values, which complicates estimation of molten salt acidity. An important argument for Eq. [9.2.57] is that the use of this equilibrium implies a constant concentration of chloride-ion

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9.2 Acids and bases in molten salts, oxoacidity

in chloride melts. This is true for melts based on alkali chloride, among them, mixed chloride-sulfate and chloride-nitrate melts. However, reaction [9.2.57] cannot be used for estimation of the acidic properties of melts which do not contain chloride ions. Neutral (chargeless) HCl and H2O molecules are “foreign” admixtures for ionic melts as ionic substances in aqueous solutions: in both cases, there are two kinds of principally different interactions: electrostatic (between ions) and Van der Waals or donor−acceptor (between uncharged components). The correctness of reaction [9.2.57] depends on the stability of the partial pressures of HCl and H2O in the atmosphere over the concentrated aqueous solution of HCl, which are used as a source of HCl + H2O gas mixture. Errors arising in the concentrated solutions are sizeable, especially for the solutions with HCl concentration exceeding 30 wt%. It is important to consider the amphoteric character of H2O. The assumption justifying the use of reaction [9.2.57] is the fact that HCl is an acid and H2O is a conjugated base. Water shows appreciable oxoacidic properties in molten salts, it reacts with oxide ions forming hydroxides. Water vapor passed through melt reacted with both oxide ions and other constituent parts of the melt. In melts based on lithium salts, HCl and H2O solubilities do not obey Henry law.69 Under these conditions, we can attribute acidic properties not only to Li+ cations but also to complexes of Li(H2O)n+. The concentration of the latter depends on hygroscopic properties of cations forming melt, therefore, one can expect that melts containing hygroscopic cations, such as Ca2+ and Li+ should have elevated acidity when their oxoacidic properties are estimated on the basis of the reaction [9.2.57].68 Estimation of the oxobasicity index, pIL, on the basis of Lux-Flood indicator of acid− base reactions is part of the oxobasicity evaluation. Let us consider the following scheme: The reference melt, ΔG* = 2.3RT pK*

[9.2.63] The studied melt, ΔGL = 2.3RT pKL Process [9.2.63] takes place in the reference melt and in a given melt and may be characterized by the values of the Gibbs free energies ΔG* and ΔGL, respectively. Rewriting this reaction in such a manner: [9.2.64] where the stoichiometric indices for initial reagents are negative and for the reaction products are positive, we can present common expression of the effect of solvent nature on Lux-Flood acid−base equilibria: [9.2.65)] or

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[9.2.66] Taking into account that there are 3 participants of the reaction: A, O expression [9.2.66] may be presented as follows:

2−

and B, the

[9.2.67] and, finally [9.2.68] The non-thermodynamic assumption, which is the base of the indicator reaction can be expressed as [9.2.69] All the changes of free energies or equilibrium constants can be attributed to resolvation of oxide ion and to the differences in the melts acidities. Homogeneous Lux acid−base equilibria similar to [9.2.8] were not considered earlier as convenient indicator reactions for the determination of the oxobasicity indices of ionic melts. Nevertheless, the equilibrium constants KL, and K* in the reference and the studied melt permit estimation of pIL value: [9.2.70] if the premise of [9.2.69] is correct. Homogeneous equilibria, where A = Cr2O72- or VO3are considered as following this rule. Cr2O72-/CrO42- acid−base pair is especially convenient for acidity estimations of molten alkali metal chlorides since both anions are twocharged components and have larger radii than halide ions. The data on metal oxide solubilities in molten salts are especially suitable for estimations of the oxoacidic properties of molten media. If the process of MeO dissolution in a melt is described by the equation: [9.2.71] the expression for its solubility product, Ks, MeO, can be presented by this equation: [9.2.72] To determine the oxobasicity index, the values of Ks, MeO calculated in molar fraction scale can be used. The expression for pIL is very simple: [9.2.73] Using the solubility method for estimating the acidic properties of melts with the same anion composition is substantiated because the Gibbs energy of MeO precipitated as a solid phase is independent of ionic melt composition. Concerning Me2+ cations, the most

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probable forms of their existence in halide melts are complex anions, having MeX42- composition. Therefore, in the case of the same anion composition, it may be assumed that log γ 2+ ≈ 0 . Taking into account that log γ 0, MeO, L = 0 (see the first sentence of this 0, Me paragraph), the condition [9.2.69] can be considered to be true. Main limitations of the use of the solubility method are due to different stabilities of the metal-halide complexes formed by acidic cations with various halide ions. Therefore, the solubility data can only be used to estimate the oxobasicity indices of ionic solvents of the same anion composition. In the case when the anion composition is changed, the obtained acidity parameters may have considerable errors, because Me2+ designates different anion complexes of different stability, e.g., MeCl42- and MeBr42- complexes formed in chloride and bromide melts, respectively. Aside from the cation composition, the solubility product changes are affected considerably by the anion composition of these solvents at high-temperature ionic solvents. The oxobasicity index of a melt requires an additional subscript for its designation by analogy with the Hammett function. If this value is obtained using the solubility data, then pIL, s designation is to be used (“s” means “solubility”). If an indicator of homogeneous acid−base reaction is used, this designation should be pIL,h, and in the case of reactions with the participation of gaseous acids such as H2O or CO2 it is pIL, g. This additional information is very helpful in practical applications of the oxobasicity indices when estimating equilibrium parameters of the Lux acid−base reactions in melts of different anion and cation compositions. There exists a direct way of measurement of emf in the reference and the studied melts with the same concentration of oxide ions. As it has been mentioned above (Fig. 9.2.2 arrow 5) the difference in acidity in these melts equals pIL. Measurements are performed in the electrochemical concentration cell with an indicator oxygen electrode: [9.2.74] where: YSZ

the solid electrolyte membrane ZrO2 + 10 mol% Y2O3

The non-thermodynamic assumption limiting the use of this method is that the potential of liquid junction equals zero. As it follows from Smirnov’s data,70 this actually takes place in molten salts. However, the use of two gas oxygen electrode makes the cell too cumbersome, therefore, the more convenient way is to perform emf measurements according to Eq. [9.2.74] using a compact reference electrode, for example Ag|Ag+ electrode. Example of such approach can be found elsewhere,71-74 where the cell construction is as follows [9.2.75] If E is the emf value measured in the studied melt and E* is the value obtained in the reference melt and pI* is the oxobasicity index of the reference melt than the oxobasicity index of the studied melt, pIL, is calculated according to the formula:

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[9.2.76] where: k

the slope of E-pO plot obtained by usual calibration of the cell [9.2.75] by a strong Lux-Flood base

To demonstrate the possibilities of the discussed variants of oxoacidity determination, let us consider the corresponding results obtained in Li+−based chloride melts. The method for HCl/H2O acid−base pair yields for KCl−LiCl eutectic value of Ω (pIL) ca. 8, 22whereas the solubility method gives value of 3.475,76 and the use of Cr 2 O 7 ⁄ CrO 4 acid− base pair permits to estimate pIKCl−LiCl as 3.6.77 It is interesting that the oxobasicity index of 2CsCl−LiCl melt is found in the mentioned above paper73 to be ca 3.8. The presented comparison shows that the use of HCl/H2O indicator system leads to overestimation of oxoacidic properties of the chloride melts whereas the results of other approaches are practically coincident. 9.2.2.2 Oxoacidity scales of halide melts at different temperatures

Figure 9.2.3. The common oxoacidity scale of ionic melts KNO3 (1), Li2SO4−K2SO4−Na2SO4 (2) and KCl−NaCl (3). Position of conjugated acid−base pair corresponds to the equimolar KNO3−NaNO3 mixture at 350oC.

The principal shape of the melt oxoacidity scale is presented in Fig. 9.2.3. Solvents of the first kind possess the two-side limited acid−base ranges. The limits of leveling basic properties are determined by acidities of the most acidic cations of melts. The leveling acidic properties in these solvents takes place because of formation in melts of the 1st kind of acidic component, namely NO2+ (nitrates) and S2O72− (sulfates). As for the acid−base pairs subjected to the solvolysis, let us consider the sulfate melt (Fig. 9.2.3, 2). The positions of K+/K2O and Na+/Na2O are situated to the left of Li+/Li2O pair, therefore, properties of K2O and Na2O are leveled to Li2O. The addition of two former substances to Li2SO4−K2SO4−Na2SO4 melt is equivalent to the addition of Li2O and one cannot distinguish solutions of potassium and sodium oxides based only on acidity measurements. Leveling acidic properties is observed for MoO3 and CrO3 as placed to the right of S2O72−/SO42− pair and these acids are completely transformed to MoO42− and CrO42− with formation of the equivalent amount of S2O72− acid.

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9.2 Acids and bases in molten salts, oxoacidity

In solvents of the 2nd kind, only leveling of basic properties is observed (Fig. 9.2.3, 2). From the acidic side, the acid−base range is opened and it means that acidic properties are not leveled and properties of the above mentioned MoO3 and CrO3 acids differ. Table 9.2.2. Solubility products of MgO in several chloride melts at 600oC and their oxobasicity indices (with respect to the CsCl−KCl−NaCl eutectic) Melt/composition

pKs, MgO

pIL, s

Ref.

CsCl−KCl-NaCl (0.455:0.245:0.30)

12.68

0

78

KCl−LiCl (0.41:0.59)

9.45

3.2

79

BaCl2−CaCl2−NaCl (0.235:0.245:0.52)

8.15

4.5

80

CaCl2−NaCl (0.5:0.5), 575oC

7.44

5.2

68

Let us return to the oxoacidic properties of molten ionic halides. Table 9.2.2 includes the information about oxoacidic properties of several chloride melts with solvents of the 2nd kind at 600°C determined by solubility method considering CsCl−KCl−NaCl eutectic melts as the reference melts and data on solubility of MgO in these melts. The oxobasicity indices have been shown above to give exhausting information about the acidic properties of these solvents. The solubility of this oxide in molten CsCl−KCl−NaCl eutectic and the solubilities in other melts with known oxobasicity indices may be predicted with good accuracy. Hence, the oxoacidic properties of the ionic melts based on alkali metal chlorides at 600oC increase in the following order: CsCl−KCl−NaCl → KCl−LiCl → CaCl2− BaCl2−NaCl → CaCl2−NaCl. Several our works are devoted to the investigation of different kinds of acid−base equilibria in ionic melts based on alkali metal halides in order to determine their oxobasicity indices at 700 and 800oC. Unfortunately, there are no necessary experimental data obtained by other investigators. The equimolar KCl−NaCl mixture is chosen in several papers57,58,75 as the reference melt at these temperatures, although its oxoacidic properties differ by less than 0.1 from the CsCl−KCl−NaCl eutectic (see below), i.e., they are practically coincident. The solubilities of 11 metal oxides in the equimolar KCl−NaCl mixture are reported elsewhere.64 Similar investigations in the molten CsCl−KCl−NaCl eutectic show that the solubility products of the same oxide (in molar fraction scale) in both melts are close.81 This means that both melts are suitable as the reference melts not only at 700oC but also at other temperatures at which these media exist in the liquid state. An investigation of oxide solubilities in the molten KCl−LiCl eutectic at 700oC was carried out elsewhere.75,82,83 The oxide solubilities in this melt are considerably higher than in the KCl−NaCl equimolar mixture at the same temperature. The pKs,MgO value shift is ca. 3.4 logarithmic units in comparison with the KCl−NaCl equimolar mixture and this value is the oxobasicity index, pIKCl-LiCl, s = 3.4. It is remarkable that the shifts are so close.

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This demonstrates the applicability of the parameter introduced for the melt acidity estimation, namely for calculation of the oxide solubility parameters. Oxide solubilities were determined in ionic melts consisting of alkali metal chlorides and alkaline earth metal chlorides, the concentrations of latter were close to 0.25 (mole fraction). The compositions of these melts are listed below and the calculated values of the oxobasicity indices are: CaCl2−KCl (0.235:0.765, pIL = 4.05),84 SrCl2−KCl−NaCl (0.22:0.36:0.42, pIL = 1.95),85 BaCl2−KCl−NaCl (0.43:0.29:0.28, pIL = 2.01)86 and BaCl2−KCl (0.26:0.74, pIL = 1.83).87 In CaCl2−KCl melt, the upper limit of basicity is caused by precipitation of CaO from the saturated melt. As follows from Fig. 9.2.4, this limit corresponds to pOL value near 3 and to Ω value equal to 5.4. Practically the same shifts of the solubility product indices for different cation composition of melts were observed from experimental results for all studied oxides. The addition of alkaline earth metal chloride to the melts of weak acidity strengthens their acidic properties causing the oxide solubility to increase. The oxoacidity Figure 9.2.4. Dependence of emf of the potentiometric cell with the membrane oxygen electrode vs. pOL in the increase is observed in the following order: molten CaCl2−KCl equimolar mixture at 700oC. The melt + Ba2+ → melt + Sr2+ → melt + onset of the “plateau” is caused by the precipitation of Li+ → melt + Ca2+, which agrees with the CaO. well-known tendency of strengthening the acidic properties in the same Group of the Periodic Table with the decrease in the ion radius. The solubility data are appropriate for estimation of acidity of ionic melts unless they differ in anion composition. As for iodide melts, their acidities cannot be compared with acidities of KCl−NaCl eutectic in such a manner. To solve this problem, the reactions of oxide ion addition to B4O72− and VO3− anions were studied in the equimolar KCl−NaCl mixture and NaI melt at 700oC (see Table 9.2.3).88 Table 9.2.3. pK values of some acid−base equilibria in the equimolar KCl−NaCl mixture and NaI at 700oC KCl-NaCl

NaI

−

Equilibrium

4.82 ± 0.2

5.02 ± 0.3

2VO3− + O2− = V2O74−

5.23 ± 0.2

5.40 ± 0.2

2−

2−

B2O7 + O = 4BO2

These reactions were considered as indicator reactions. The corresponding pK values are included in Table 9.2.3. Increase of acid strength in iodide melt causes that the pK shifts coincide with both reactions. This magnitude may be treated as the oxobasicity index of molten sodium iodide, pINaI, h equal to −0.2. The negative sign means that the iodide melt possesses weaker acidic properties than the KCl−NaCl equimolar mixture,

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Figure 9.2.5. Oxoacidity scale of melts based on alkali metal halides at 700oC, constructed using pIL, h indices (for chloride melts the pIL, s indices were used). [Data from V. L. Cherginets and T. P. Rebrova, Doklady Physical Chemistry, 394, 42 (2004).]

although the latter consists not only of Na+ cations but also of K+ ones, the latter is a weaker acid than Na+. Molten iodide melts typically demonstrate weaker acidity than molten chlorides of a similar cation composition. All above experiments form a base for construction of the oxoacidity scale of melts based on alkali metal halides at 700oC.76 This scale is presented in Fig. 9.2.5. The studied ionic melts may be divided into three groups. The first group includes melts having weak acidities such as the KCl−NaCl equimolar mixture, the ternary CsCl−KCl−NaCl eutectic having pICsCl-KCl-NaCl, s equal to −0.1, and NaI melt. The second group includes melts based on alkali and alkaline earth metal chlorides such as BaCl2 and SrCl2. This group is characterized by the oxobasicity indices of the order of 2. At similar concentrations, the acidity of Ba2+−containing melts is close to that of Sr2+−containing melt (see Fig. 9.2.5), i.e., the oxobasicity indices of BaCl2−KCl with x 2+ = 0.26 and SrCl2−KCl−NaCl with x 2+ = 0.22 differ by less than 0.1. Ba Sr Increasing concentration of the most acidic constituent cation in an ionic melt results in the rise of oxobasicity indices of the Ba2+−containing melts. The experimental values of the oxobasicity indices, namely: pI BaCl -KCl-NaCl, s = 2.01 and pI BaCl -KCl, s = 1.83 lead to 2 2 the conclusion that when Ba2+ concentration in chloride melts increases as it is presented by an expression: [9.2.77] pIL,s value increases by 0.18. It is thus possible to estimate the oxobasicity index of melts, which differ in the content of the same acidic cation, using the following relation: [9.2.78] where and are the molar fractions of the most acidic cation in the melt with known oxobasicity index (denoted as L) and the melt in question (the subscript is L1), respectively.

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The melts of the highest acidity, which belong to the third group, are the KCl−LiCl eutectic mixture and the CaCl2− KCl eutectic melt. The upper limit of basicity in the latter melt is caused by limited solubility of CaO in it, the addition of O2− over such a limit results in precipitation of CaO from the saturated melt (Fig. 9.2.4). On the contrary, there is no precipitation of alkaline earth metal oxide when melts belong to the second group (Ba2+- and Sr2+0 based chloride melts). The reason for this Figure 9.2.6. The dependence of pO against – log m 2in the KCl−LiCl eutectic melt containing: 0.05 mol Okg-1 is higher solubility of BaO and SrO as of PbCl2 (1) and 0.045 mol kg-1 of CdCl2 (2). The plot compared with CaO. Stronger acidities of obtained in the pure KCl−LiCl (3) is presented for a melts doped with alkaline earth metal catcomparison. ions favor subsequent solubility increase. The second reason is stabilization of oxide ions in these melts by the formation of polynuclear complexes, e.g., Me2O2+ composition, etc. Similar effect should be neglected in conventional solubility investigations, where concentrations of acidic cations under the study do not exceed 0.1 mol kg-1. However, it becomes very important for high-concentrated solutions in ionic melts and chloride melts. Our study of KCl−LiCl eutectic gives an excellent illustration of the leveling of acidic properties by high-acidic melt cations. In Fig. 9.2.6, the results of Pb2+ and Cd2+ titration with KOH are presented. The behavior of the KCl−LiCl eutectic melt doped with 0.05 mol kg-1 of these cations does not differ from that of the “pure” melt. That is, the changes of the oxoacidic properties of solutions as compared with the pure eutectic cannot be detected. It is so because the acidic properties of Pb2+ and Cd2+ cations are not stronger than those of Li+, and the following equilibrium: [9.2.79] is shifted to the right, at least, in diluted solutions of the corresponding chlorides. The dissociation constant of PbO in the KCl−NaCl equimolar mixture at 700oC was determined by potentiometric titration to be 5.13x10-4 (pKPbO = 3.29 ± 0.04 ),64 whereas the pK value of Li2O dissociation in this melt was equal to 3.95.62 This observation proves that the acidity of Li+ cation exceeds that of Pb2+ and Cd2+, and dissociation processes of PbO and CdO in the Li+−based melt are practically complete and its determination by a potentiometric method becomes impossible.64 The leveling of the acidic properties of these cations may be predicted from the known oxobasicity index of the KCl−LiCl eutectic (pIKCl-LiCl, s = 3.5) which exceeds pKPbO = 3.29. Temperatures of the order of 800oC provide essentially broader scope for studying acid−base interactions in molten salts, since practically all single alkali metal halides exist under these conditions in a liquid state (excluding NaCl which has melting point close to 801oC).90 This permits to estimate the oxobasicity indices of several ionic media to trace

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9.2 Acids and bases in molten salts, oxoacidity

Figure 9.2.7. Oxoacidity scale of melts based on alkali metal halides at 800oC, constructed using pIL, s indices.

the effect of the anion composition of alkali metal halide melts on their acidic properties. To achieve this purpose, investigations of some acid−base reactions in molten alkali halide melts were performed. The results of oxide solubility studies (mainly, MgO and CaO) and carbonate ion dissociation are reported in some our papers. The most interesting data concerning oxoacidic properties of sodium chloride and bromide are presented in Fig. 9.2.7. From this Figure, it follows that ionic melts based on chlorides and bromides of alkali metals excluding Li+-containing melts are close (pIL indices are within ±0.5). The oxoacidic properties of an ionic melt can be characterized by the oxobasicity index as the concentration analog of the primary medium effect on oxide ion. The KCl−NaCl equimolar mixture and the ternary CsCl−KCl−NaCl (0.455:0.245:0.30) eutectic are convenient reference melts. The obvious advantage of the latter melt is its low melting point (~480oC). This permits the use of this reference melt in the wider temperature range.

Figure 9.2.8. The united oxoacidity scale of chloride and bromide melts at 700°C constructed using pIL,s indices.

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Recently we have extended the bulk of data on oxide solubilities in some bromide melts at 700°C that gave us the possibility to construct common oxoacidity scale for chlorides and bromides.91 The studied melts were (compositions in mole fractions are given in brackets): KBr−NaBr (0.5:0.5), BaBr2−KCl (0.51:0.49) and KBr−LiBr (0.4:0.6). The common oxoacidity scale is presented in Figure 9.2.8. As is seen, the average difference of the oxobasicity indices of the chloride and bromide melts with close cation compositions does not exceed 0.3 and the oxoacidic properties of bromide melts are somewhat weaker than those of their chloride analogs. It means that the oxide solubilities in 1 mole of the molten KBr−NaBr equimolar mixture are practically equal to the corresponding values referred to 1 mole of the KCl−NaCl melt. Similarly to the KCl−NaCl equimolar mixture which is the reference chloride melt for a number of investigations, the molten KBr−NaBr equimolar mixture can be chosen as the reference point while studying bromide melts. The change of anion in Cl → Br sequence does not result in appreciable changes of oxide solubilities. If we compare the oxobasicity indices of KBr−NaBr and 2CsBr∙KBr melts, we can establish that in the latter melt the average increase of pIL is 0.94 that is approximately equal to 1. This takes place because of leveling oxoacidic properties of KBr−NaBr to those of Na+-based melts whereas the acidic properties of 2CsBr∙KBr melt is determined by acidity of K+ which possesses weaker oxoacidic properties comparing with Na+.

9.2.3 HOMOGENEOUS ACID-BASE REACTIONS IN MOLTEN SALTS 9.2.3.1 Methods of estimations of Lux-Flood acidity in molten salts The literature data show that many methods were used for oxoacidity studies and estimation of the acidic properties of melts. One of the simplest methods consists of the use of indicators.92 Acid−base indicators employed in aqueous solutions for protic acidity measurements were used for acidity studies in molten KNO3−LiNO3 eutectic at 210°C and KSCN at 200°C. The color of indicator solution, relative to acidity, changes during titration of strong Lux bases (sodium hydroxide or peroxide) by potassium pyrosulfate, K2S2O7. The indicators exist in basic form, having an excess of oxide ions, whereas acidic form arises in the melt containing the excess of pyrosulfate. The color transitions are assumed to be connected to the following process: [9.2.80] where: HInd Ind−

the protonized (acidic) form of the acid−base indicator the anionic (basic) form of the indicator

In molten nitrates, such a transition was observed only with phenolphthalein (yellow-purple). Other indicators seemingly were oxidized by melt (the conclusion made elsewhere92 was “insoluble in the melt”). In molten KSCN not possessing oxidizing properties, color transitions were observed for all indicators used (methyl red, thymolphthalein, etc.). The use of the organic indicators for acidity estimation is limited by their thermal instability and tendency to oxidize at high temperatures. Since ionic melts have no constitutional water, the reverse transition of indicator into the protonized form [9.2.80] is hardly possible (the solution of phenolphthalein became yellow at the reverse transition

554

9.2 Acids and bases in molten salts, oxoacidity

“base−acid”).92 Therefore, the use of indicator method is possible only at relatively low temperatures ( SiO2 > Al2O3. However, the use of spectral methods for oxoacidity studies is based on analysis of cooled (quenched) samples and such a routine may distort results because of inconsistency between the solution temperature and that of acidity estimation. The results of the melt basicity estimation by the determination of acidic gases (SO3, CO2, H2O) solubilities are presented elsewhere.97,98 Sulfur trioxide solubility in molten sodium phosphate was determined by thermogravimetric analysis,97 the correlation between the melt basicity and the SO3 solubility was apparent. The use of CO2 and H2O for the oxobasicity estimation was described elsewhere.98 Similar methods may be used only for basic melts since acids displace the acidic gas from the melt. Furthermore, the interaction products of the acidic gas with the melt may be relatively stable, especially in basic solutions, and their formation leads to irreversible changes in the melt properties. The so-called “kinetic method” was used for Lux acidity studies in molten nitrates. The interactions between the nitrate melt KNO3−NaNO3 equimolar mixture and potassium pyrosulfate were studied:99,100 [9.2.81] + NO 2 ,

NO 3

The formed nitronium cation, reacts with according to Eq. [9.2.45]. The latter stage is considerably slower than [9.2.81], hence, data on its rate permit estimation of the melt acidity, which can be presented by the following sum:100

2-

-

The acid−base interaction between Cr 2 O 7 and chlorate ions, ClO 3 , in molten KNO3−NaNO3 equimolar mixture is described by the following equation sequence:101,102 [9.2.82] [9.2.83] From the two above processes, reaction [9.2.83] is the limiting stage, the rate of the chlorine evolution is proportional to the total acidity of the melt: 2+ T A = [ Cl 2 O 7 ] + [ ClO 2 ] The interaction between bromate ( BrO 3 ) and dichromate ions, in nitrate melt has 103 been studied elsewhere. The studies permit estimation of relative acidities of some oxocations.101-103 The acidities increased in order BrO2+→ClO2+→NO2+.

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Slama used the kinetic method to investigate metal cation (Cu2+, Co2+) acidities in molten KNO3−NaNO3 at 325-375°C temperature range.104,105 The cation acidities were estimated on the base of the NO2 evolution rate [9.2.45]. Nitronium cation is formed as a product of the following reaction: [9.2.84] where:

Me2+

Cu2+ or Co2+

Metal cation acidities are comparable to acidic properties of dichromate ion and mentioned above cations.101-103 A potentiometric method, or more accurately, a method of emf measurements with a liquid junction in cells with oxide-reversible electrodes was most advantageous in oxoacidity studies of various melts. The principal construction of electrochemical cells for oxoacidity studies may be presented by the following scheme: [9.2.85] The potential of the liquid junction in electrochemical cells including ionic melts as solvents is usually less than 0.001 that gives possibility to neglect this experimental error in the estimation of the equilibrium constants. The known reference electrodes were metallic (i.e., metal immersed in solution with the definite concentration of the corresponding cation) or gas oxygen electrodes immersed in solutions with definite oxide ion concentrations (concentration cells). 9.2.3.2 Molten nitrates Traditionally, nitrate melts are considered among the most exhaustively studied. Relatively low melting temperatures of both nitrates and their mixtures give the possibility to use simpler experimental techniques. The majority of potentiometric studies yielded the equilibrium constants of various Lux-Flood acid−base processes.43,106-130 These studies were mainly conducted in molten KNO3 at 350°C. Constants of acid−base reactions of Group V highest oxides (P2O5, As2O5, V2O5) with Lux-Flood bases were also investigated by Shams El Din et al.106-111 All oxides break down the nitrate melt, the first stage is the formation of corresponding meta-acid salts and nitronium cation: [9.2.86] where: R

the designation of Group V element

The second step is the redox interaction between nitronium cation and nitrate ion according to [9.2.45], which is shifted to the right at high melt acidity, NO2 evolution takes place until emf values decrease down to −0.5 V, this value corresponds with the upper limit of oxoacidity in molten KNO3. The oxygen index value (pO) for this limit can

556

9.2 Acids and bases in molten salts, oxoacidity

be estimated as 16.106-111 Addition of Na2O, as the strong Lux-Flood base leads to the following acid−base neutralization stages: [9.2.87] and [9.2.88] The oxoacidic properties of the studied oxides increase in order V2O5 < P2O5 < As2O5. In addition to the equilibrium parameters of reactions [9.2.86-9.2.88],109-111 the constants of the following assumed equilibria, with the participation of hydroanions 222HPO 4 , H 2 PO 4, HAsO 4 , and H 2 AsO 4 were also determined: [9.2.89] [9.2.90] Since even pure salts containing hydroanions undergo decomposition at temperatures much lower than 350°C with the formation of the corresponding meta- or pyrosalts,90 equilibria [9.2.89] and [9.2.90] hardly take place in the absence of water vapor in the atmosphere over the melt. The acidic properties of the highest oxides of VI Group elements (Cr, Mo, W) were studied elsewhere.43,111,112 Similarly to Group V oxides, CrO3 and MoO3 decompose 22nitrate melt with formation of Cr 2 O 7 and Mo 3 O 10 , respectively.105-110 After the complete evolution of NO2, emf values are close to 0.5 V, that is in a good agreement with other studies.106-111 The potentiometric titration curves of formed products contained only one bit of emf (or pO). Chromate and molybdate ions are the final products of the neutralization reactions. WO3 was studied elsewhere43,111,112 and it was found to be weaker acid, which did not decompose nitrate melt. Its titration occurs at one stage and results in tungstate ion formation. The acidities of oxides increased in the following order: WO3 < MoO3 < CrO3. The equilibrium constants43,106-112 are considerably distorted since the calculated magnitudes shift in the order of a few pK units. Such phenomenon may take place either because of incorrect determination of reaction participants (stoichiometry) or slope changes in the calibration plot of oxygen electrode Pt(O2) in the acidic region. Relative acidities of different metal cations in molten KNO3 have been investigated by Shams El Din et al. using potentiometric titration of corresponding carbonates by K2Cr2O7114 or NaPO3.115 The titration process can be presented by the following common equation: [9.2.91] Cations can be arranged in the following order: K≈Na>Li≈Ba>Sr>Ca>Pb in which the Lux-Flood acidity increases. The cation order was in a good correlation with the elec-

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

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tronegativity of metals. The proposed method of investigation had an essential problem since the acids used for titration of fixed oxide ions with the simultaneous decomposition of carbonate formed insoluble chromates and phosphates with the majority of cations studied. As it has been shown,101,102 the addition of Ca2+ into nitrate melts leads to the 2shift of interaction Cr 2 O 7 – NO 3 to the formation of nitronium cation and the melt decomposition although solution without Ca2+ is stable. Such a shift is explained by the formation of slightly soluble CaCrO4 in nitrate melt and has no relation to Ca2+ acidity. As to barium position in the sequence it gives evidence of formation of complexes or precipitates, since their acidic properties are substantially weaker than those of Li+. At the formation of the BaCrO4 precipitate Ba2+ acidity approaches that of Li+ acidity. Probably, the same reason affected the arrangement of other alkaline earth metals in this sequence. The relative strength of different Lux bases in nitrate melts was investigated.116,117 The studied bases can be divided into two groups: the oxide ion group (OH−, O2−,O22−) and the carbonate ion group (CO32−, HCO3−, (COO)22− CH3COO−, HCOO−). The bases belonging to the first group are assumed in the mentioned papers116,117 to be completely transformed into O2−. The bases belonging to the second group are weaker than the first group bases. From the thermal data, it may be seen that at the experimental temperature (350°C) all second group bases are completely broken down to carbonates. The differences between single bases may be attributed to reduction properties − organic salts reduce nitrate ions to more basic nitrite ones and favor the accumulation of oxide and carbonate ions in the melt over the stoichiometric ratio. Hence, the use of a majority of the proposed bases for quantitative studies of oxoacidity is not possible, especially for acids having apparent oxidizing properties (chromates, vanadates, etc.). 4Oxide ions in molten nitrates exist as the so-called pyronitrate ions N 2 O 7 which are 2- 118 strong bases with the basicity approximately equal to those of CO 3 . The modern understanding excludes the existence of nitrogen compounds with the coordination number exceeding 3 by oxygen, hence pyronitrate hardly exists under the mentioned conditions. Indeed, other oxoanion studies114 demonstrated the absence of the mentioned ion in basic nitrate solutions. A possible way for the stabilization of O2− in nitrate melts is the formation of alkali metal silicates due to reactions with walls of a crucible (usually it is pyrex). The anomalous behavior of the electrode Pt(O2) has been noted and explained by “peroxide” function of the gas oxygen electrodes (of the first type).120,121 On the contrary to gas electrodes, metal-oxide electrodes (of the second type) were reversible with the slope corresponding to the reaction: [9.2.92] The acid−base equilibria in complex solutions based on nitrates containing phosphates and molybdates were used to produce heteropolyacids in molten nitrates.122,123 The formation of polynuclear complexes was confirmed by cryoscopic examinations reported.124

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9.2 Acids and bases in molten salts, oxoacidity

Some features of potentiometric titration techniques in molten salts have been discussed.125,126 The previous work125 is devoted to “automatic” potentiometric titration in molten nitrates. A rod, prepared as a frozen K2Cr2O7 solution in nitrate melt, was immersed with the constant rate in the melt containing a base. Emf data were recorded by the recording potentiometer. Such a routine may be used only for detection of equivalence points in melts with an accuracy of ~3.5%.125 The equilibrium under these conditions cannot be achieved during so short time after the titrant addition. The effect of acidic oxides on the thermal stability of molten NaNO3 has been investigated by Hoshino et al.127 The increase of oxide acidity results in the decrease of the melt decomposition temperature. This is explained by the reduction of the activation energy of decomposition due to fixing oxide ions by acids. But there was also another explanation: decreasing temperature of melt decomposition is caused by the equilibrium shift towards the oxide-ions and nitrogen oxide formation under the action of an acid. Acidic properties of oxides decrease in the sequence SiO2 > TiO2 > ZrO2 > Al2O3 > MgO. Baraka et al. reported potentiometric investigations of new metal-oxide electrodes consisted of “refractory metal| oxide of this metal” pair (Nb|Nb2O5, Ta|Ta2O5, Zr|ZrO2) for oxoacidity studies in the nitrate melt.128-130 Similarly to Shams El Din, authors128-130 constructed the empirical acidity scale in the molten potassium nitrate at 350°C. The sequence of the studied Lux-Flood acids is as follows: NH4VO3 > NaPO3 > NaH2PO4 > K2Cr2O7 > K2HPO4 > Na4P2O7 > NaHAsO4 > K2CO3 > Na2O2. This sequence includes some acids seldom existing in molten salts. NH4VO3 at 350°C should be completely transformed into V2O5 with a partial reduction of the latter by ammonia formed as one of the decomposition products of NH4VO3. The acidic salts (hydrophosphates and hydroarsenates) decompose to the corresponding pyro- and meta-salts.131 Therefore, the obtained scale contains a number of errors. 9.2.3.3 Molten sulfates Sulfate melts are referred to melts with their own acid-base dissociation equilibrium: [9.2.93] There are rather few contributions devoted to the Lux acidity studies in similar melts. This may be explained by relatively high melting points of both single sulfates and their eutectic mixtures. Low stability of acidic solutions in sulfate melts can also be considered as a reason why these melts are studied insufficiently. Indeed, reaction [9.2.93] should result in SO3 formation in the melt. Reference data, however, show that decomposition 2temperatures of pyrosulfates (i.e., SO 3 • SO 4 complexes do not exceed 460°C90,130 in a dissolved state of solvated SO3; their stability is expected to be even lower). The absence of SO3 partial pressure over the melt gives rise to removing SO3 from the melt and, since the equilibrium state of [9.2.93] is not attained, SO3 is removed completely. Among sulfate melts the ternary eutectic mixture K2SO4−Li2SO4−Na2SO4 (0.135:0.78:0.085) with the lowest melting point 512°C132 may be the most promising for the acidity studies since it is possible to perform studies at the temperatures significantly lower than in the classical works by Lux.16 Under these conditions, the stability of acidic and basic solutions increases.

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Lux16 reported the oxygen electrode reversibility investigation and construction of empirical acidity scale for the molten eutectic mixture K2SO4−Na2SO4 at 800°C. The thermal stability of pyrosulfates has been shown by Flood et al.17-19 to decrease with the strengthening of the melt cation acidity. Kaneko and Kojima133,134 investigated acid−base properties of different solutions in the molten K2SO4-Li2SO4-Na2SO4 at 550°C; the empirical acidity scale length was approximately 10 pO units for 0.01 mole kg-1 solutions of 22S 2 O 7 and O 2 ions. The acid−base range of this solvent can be easily estimated as the length of acidity scale between standard solutions of strong acid and base, it is ca. 14 pO units. The pO range of VO2+ stability was 8.5 to 10.6. Other studies135 include potentio24metric studies of the acidic properties of MoO3, Cr 2 O 7 , PO 3, P 2 O 7 , and V2O5 in molten K2SO4−Li2SO4−Na2SO4 at 625°C. These acids were neutralized by sequential addition of sodium carbonate. The potential (pO) drop at equivalence point was observed at “acid− base” ratio 1:3 for vanadium oxide and 1:1 for all other studied Lux-Flood acids. Values of equilibrium constants were not presented. 9.2.3.4 Silicate melts The studies performed in the molten silicates are of importance for applied purposes, since systems under consideration are widely used in various industries (slugs, glasses, etc.). Flood et al.136,137 studied the acidity dependence of silicate melts upon their composition. A system PbO−SiO2 have been studied in the range of SiO2 molar fractions from 0 to 0.6 63at 1100-1200°C. The coexistence of ( SiO 3 ) 3 and other ( SiO 2.5 ) 3 polyanions together 4with the ordinary orthosilicate ions, SiO 4 has been confirmed. The basicities of molten glasses vs. Na2O/SiO3 ratio were studied138 by the potentiometric method with the use of the gas oxygen electrode Ag(O2) in concentration cells. The decrease of ratio caused reduction of basicity, while magnesium oxide was found to have no effect on the melt basicity. The gas oxygen electrode reversibility in molten PbO−SiO2, Na2O−CaO−SiO2, MeO−PbO−SiO2 (where Me the alkaline earth metal cation) was investigated. The electrode Pt(O2) possessed reversibility to O2−. The use of a membrane oxygen electrode Pt(O2)|ZrO2 for control of molten silicate acidity during glass making has been discussed.139 Studies of basicities in molten Na2O− Al2O3−SiO2 using a potentiometric method show that the acidic properties of A12O3 are weaker, than those of SiO2.141 Processes of glass corrosion in the molten alkaline earth nitrates have been studied for glass compositions Na2O−xAl2O3−2SiO2, where x was varied in the range from 0 to 0.4.141 The degree of interaction between the melt and immersed glass increased with decrease of the alkaline earth cation radius. The effect of the cation charge and the radius on the basicity of lead metasilicate melt at 800, 850, 900°C by additions of T12O, PbO, CdO, ZnO and Bi2O3 was studied by potentiometry.142 9.2.3.5 Molten alkali metal halides 9.2.3.5.1 The equimolar mixture KCl-NaCl This melt is the most investigated among chloride-based melts. The oxoacidity studies were performed by Shapoval et al. The main purpose of these works is to investigate oxygen electrode reversibility and to obtain equilibria constants for acid−base reactions including oxo-compounds of CrVI, MoVI, and WVI at 700°C. Equilibrium constants of

560

9.2 Acids and bases in molten salts, oxoacidity

acid−base interactions for CrO3 and PO3− were determined.62,143,144 The titration of the former substance proceeds in two stages: , K=2.88×103 (mole fractions, m.f.)

[9.2.94]

and , K=1.4×101 (m.f.)

[9.2.95]

According to the potentiometric data, sodium metaphosphate NaPO3 is a two-basic acid too: , K=(2.88±1.2)×103 (m.f.)

[9.2.96]

, K=(2.5±1.4)×101 (m.f.)

[9.2.97]

2−

The excess of titrant, O , was found to cause the formation of basic phosphates with 23the assumed composition of PO 4 • O . In the case of a weaker base (Na2CO3) for the titration, there was no formation of the basic products. Ba2+ and Li+ cations possess appreciable acidic properties and the corresponding constant values were estimated as 8.1×101 and 3.53×102. The same authors studied oxoacidic properties of MoO3 and found that its neutralization presented two-staged process similar to that in the case of CrO3 titration:145 , K=(1.46±0.39)×104 (m.f.)

[9.2.98]

, K=(8.8±8.8)×102 (m.f.)

[9.2.99]

and

Since the latter equilibrium is described by a constant which presents the statistical zero, therefore, these data cannot be considered as reliable. Acidic properties of oxo-compounds of WVI have been studied.146,147 The titration of WO3 in molten chlorides was a two-stage process: , K=5×104 (m.f.)

[9.2.100]

and , K=(8.8±8.8)×102 (m.f.)

[9.2.101]

It is interesting that the constant of the latter equilibrium coincides with a similar parameter of the titration of MoO3 and also it is the statistical zero. The obtained results formed the basis for the following electrochemical studies of electroreduction processes of Group VI metals.148-150 These studies developed theoretical base and principles to control electrochemical processes of metals and their compounds (carbides, borides, silicides) deposition from ionic melts, the so-called high-temperature electrochemical synthesis.151

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The acid−base equilibria in the scheelite (CaWO4) solutions in the chloride mixture at 1000K were studied by Combes and Tremillon.152 CaO solubility in molten KCl−NaCl is about of 0.084 mol%. The similar parameter for scheelite equals to 10-3.5 mol kg-1. Equilibrium constants for acid−base reactions with WO3 participation are also determined. The data152 show that the neutralization of WO3 is the one-stage process: , K~1010 (molality)

[9.2.102]

However, the reverse titration was assumed by these authors to result in the forma2tion of polyanion W 3 O 10 , pK = 12.7. The titration curve of wolfram (VI) oxide is irreversible. This result can be easily explained taking into account that WO3 is unstable in strong acidic chloride melts and evaporated from them as volatile oxochloride WO2C12. Therefore, additions of WO3 to the acidic melt should lead to uncontrolled titrant loss affecting experimental results. It is referred to all results obtained by the reverse titration by MoO3 and CrO3 after the equivalence point. Acidic properties of phosphorus (V) oxocompounds in the chloride melt at 700°C were investigated using a membrane oxygen electrode Ni,NiO|ZrO2.153 Polyphosphates of compositions with Na2O−P2O5 ratio from 1.67 to 3 are formed in the acidic region: [9.2.103] The corresponding equilibrium constants are estimated. Polyphosphate solubilities were determined by a cryoscopic method. The titration of V2O5 according to data154 proceeds in two stages: , pK=-9.3±0.3 (molality)

[9.2.104]

, pK=-8.3±0.3 (molality)

[9.2.105] 155-159

Our results of oxoacidity studies in molten KCl−NaCl 9.2.4.

are presented in Table

Table 9.2.4. The Lux-Flood acid−base equilibrium constants in molten KCl−NaCl equimolar mixture and NaI (at the confidence level of 0.95)154-159 Equilibrium

-pK m (molality)

x (m.f.)

mol%

8.01 ± 0.1

10.67

6.67

5.93 ± 0.1

7.26

5.26

7.24 ± 0.1

-

-

8.41 ± 0.1

9.77

7.77

7.18 ± 0.1

7.18

7.18

1.60 ± 0.2

4.26

0.26

KCl−NaCl -

2PO 3 + O PO 3 PO 3

2-

2-

4-

= P2 O7

3+ O = PO 4 223+ 2O = PO 4 • O 22CrO 3 + O = CrO 4 222Cr 2 O 7 + O = 2CrO 4 2262CrO 4 + O = Cr 2 O 9

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9.2 Acids and bases in molten salts, oxoacidity

Table 9.2.4. The Lux-Flood acid−base equilibrium constants in molten KCl−NaCl equimolar mixture and NaI (at the confidence level of 0.95)154-159 Equilibrium 2MoO 3 + O = MoO 4 24MoO 3 + 2O = MoO 5 22WO 3 + O = WO 4 24WO 3 + 2O = WO 5 22B 4 O 7 + O = 4BO 2 23BO 2 + O = BO 3 2V 2 O 5 + O = 2VO 3 24V 2 O 5 + 2O = V 2 O 7 23V 2 O 5 + 3O = 2VO 4 210V 2 O 5 + 5O = 2V 2 O 10 222GeO 2 + O = Ge 2 O 5 2-

-pK m (molality)

x (m.f.)

mol%

8.32 ± 0.2

9.65

7.65

9.71 ± 0.3

11.37

7.37

9.31 ± 0.2

10.64

8.64

10.67 ± 0.5

13.33

9.33

4.82 ± 0.1

2.16

4.16

2.37 ± 0.2

3.17

1.70

6.95 ± 0.2

6.95

6.95

12.23 ± 0.1

14.89

10.89

12.30 ± 0.1

14.96

10.96

13.88 ± 0.5

19.2

11.20

4.18 ± 0.4

6.84

2.84

NaI V 2 O 5 + 2O

2-

42V2 O7 + O 22B4 O7 + O

= V2 O7

4-

5.40 ± 0.3

7.10

4.10

32VO 4 4BO 2

1.68 ± 0.3

1.68

1.68

5.02 ± 0.8

3.37

5.37

= =

The results included in Table 9.2.4 are in good agreement with similar studies performed using a membrane oxygen electrode Ni,NiO|ZrO2. The use of the gas platinumoxygen electrode resulted in significant underrating of constant values (in order of 3-4 pK units). 9.2.3.5.2 Other alkali metal halide melts Some studies of oxoacidity in molten alkali metal halides were performed by Rybkin et al. The empirical acidity scales were constructed on the base of potentiometric studies in molten KCl and CsI.49,50 The acidity scale in molten KCl was constructed on the basis of pO values of the buffer solutions having 0.01 mol kg-1 concentration. The pO value of the equimolar mixture of NaPO3 and Na3PO4 was chosen as the reference point (the conditional pO equal to 0 was attributed to this mixture). This mixture is nothing other than a relatively strong Lux acid, Na4P2O7. The progression of acidity can be presented by the sequence of the buffer solutions: KPO3(0.54) → Na3PO4 + Na4P2O7(0.12) → Na3PO4 + NaPO3(0) → Na2W2O7 + Na2WO4(−0.10) → Na2WO4(−0.32) → Na2B4O7(−0.72) → K2SO4 + K2S2O7(−0.84) → Na2SO4 + Na2S2O8(−1.56) → KNO3 + KNO2(−3.16) → K2CO3 + Na2O(−3.74). Another investigation by these authors50 concerns construction of the acidity scale in the molten CsI at 650oC on the basis of similar experimental technique. The acidity scale is presented by the sequence: KPO3(4.12) → CsI(0.63) → Na3PO4 + NaPO3(0)

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→ Na2SO4(−0.07) → K2CO3(−0.32) → KOH(−0.71) → Na2WO4(−1.51) → Cs2CO3(−2.12). The practical significance of the investigations is in the proposition to use some buf222234fer solutions, such as, SO 4 ⁄ S 2 O 8 , WO 4 ⁄ W 2 O 7 , PO 4 ⁄ P 2 O 7 as reference standards for the indicator electrode calibration and determination of pO in molten alkali metal halides. Rybkin and Banik obtained the empirical acidity scale in molten Nal at 700°C.51 The acidity sequence in NaI at 700oC called “acidity scale” by investigators was constructed51 for the solutions of 0.01 mol kg-1. It is presented by the following sequence (the differences in pO indices in the pure NaI solvent and in the studied solution are presented in parentheses): HPO42−(3.0) → P2O74−(2.52) → PO3−(1.60) → H2PO4−(1.50) → B4O72−(1.05) → VO3−(0.98) → SO32−(0.15) → pure NaI(0) melt → SO42−(−0.16) → WO42−(−0.20) → PO43−(−0.88) → IO3−(−1.54) → OH−(− 2.28) → CO32−(−2.39). The basicities of CO32− and OH− are close, which is incorrect since 0.01 mole kg-1 solutions are used for the scale constructing, while equations: [9.2.106] [9.2.107] show that basicities of these ions are not equivalent. Carbonate concentration recalculated to oxide ion was twice as high as that of hydroxide ion. Indeed, when conducting experiments on determination of the comparative strength of bases (SO42-, CO32- and OH-) by their potentiometric titration with sodium pyrophosphate, these authors found hydroxide ion to be stronger base than carbonate.160 We have performed a study of acidic properties of boron (III) and vanadium (V) oxo-compounds in molten NaI at 700°C (see Table 9.2.4). 22A comparative study of the strength of Lux bases OH−, CO 3 , and SO 4 was performed by potentiometric titration using sodium pyrophosphate as acid.160,161 Two moles 4of the first base may be neutralized by 1 mole of P 2 O 7 , while two other moles react with the acid in ratio 1:1. On the base of emf drop magnitude at the equivalence point, the bases 22were arranged in sequence OH > CO 3 > SO 4 with oxobasicity decreasing. The equilibrium constants were not estimated. There is no correlation between substances entered into the melt and those really existing in it.49,51 For example, potassium nitrate and nitrite are decomposed to K2O at temperatures considerably lower than the temperature of the experiment (ca. 700°C). The same regards K2S2O7 and Na2S2O8 and the studied acidic phosphates.51 In the latter work, it was found that pyrophosphate acidity was larger than that for metaphosphate. However, titration of phosphorus (V) oxo-compounds in melts runs according to the scheme: 3-

4-

3-

PO → P 2 O 7 → PO 4

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In this sequence, acidic properties decrease and, hence, pyrophosphate acidity should be lower, since in pair “metaphosphate-pyrophosphate” the latter is the conjugated base of considerably lower acidic properties. The absence of correlation between pH in aqueous solutions and pO in melts for the same substance is often noted, this conclusion is made mainly from data for oxocompounds of phosphorus (V). This fact is caused by the following reason. The stages of phosphoric acid neutralization in aqueous solutions are: [9.2.108] and in molten salts, the similar sequence can be presented as [9.2.109] Therefore, actual correlations should be found between the anion in aqueous solution and corresponding anhydroacids in molten salts. NaPO3 and Na4P2O7 may be easily obtained by calcination of the corresponding acidic salts, but reverse processes do not take place in aqueous media and pyro- and metaphosphate exist in water as salts of stable acids. For arsenates which are more prone to hydrolysis, similar correlation should take place. The absence of the correlation is caused mainly by kinetic limitations of the hydrolysis of meta- and pyrophosphate in aqueous solutions. Investigation of the oxoacidic properties of Na4P2O7 in molten NaCl was reported.162 The pO drop at the equivalence point corresponds to Na4P2O7/2KOH ratio equal to 1, that confirms suitability of equation [9.2.97] for a description of the neutralization reaction. The points belonging to the acidic section can be used for the averaging pK estimated as – 5.74 ± 0.15 , i.e., by 2 units lower than the value obtained in the KCl−NaCl equimolar mixture at 700oC (−3.75 ± 0.15 ).155 The acidity of pyrophosphate ion strengthens considerably together with an increase in the chloride melt temperature. Authors71,73,74 studied interactions of oxide ions with Li+ in CsCl+LiCl system containing 10-4 mol kg-1 of O2- and Y3+ in CsCl−LiCl+YCl3 system containing 10-4 mol kg-1 of O2- at 700°C by potentiometric method with the use of Pt(O2)|YSZ oxygen electrode. The addition of an appreciable excess of Li+ to CsCl melt as compared with the initial O2molality leads to the fixation of O2- in Li2O and the stability constant of the latter is (2.11 ± 0.04 )·103 (molality). The decimal logarithm of the constant of process inverse to [9.2.61] agrees with the oxobasicity index of melts containing Li+ as the most acidic cation. The solubility product of Li2O in 2CsCl−LiCl melt is estimated as 0.22 mol3 kg-3. Addition of a considerable excess of Y3+ to 2CsCl−LiCl causes the formation of YO+ complexes with the stability constant equal to (3.11 ± 0.05 )x102 that confirms higher acidity of Y3+ cations comparing with that of Li+. The formation of YO+ is the main reason for considerable slowdown of purification of CsCl−LiCl−YCl3 melt system from oxide impurities.

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9.2.4 REACTIONS OF MELTS WITH GASES OF ACIDIC AND BASIC CHARACTER Aggressive oxygen-containing gases existing in the atmosphere over molten salts (O2, H2O, CO2) can react both with their constituent components and with impurities (oxygencontaining admixtures) in the melt. The reactions with oxygen-containing gases (e.g., melt hydrolysis) occur in the presence of an active gaseous component (water vapor). Water is a Lux-Flood base and it is the source of formation of oxide ions. On the contrary, impurities form acidic environment by fixation (in some cases, with subsequent removal from the melt) or decomposition of various oxygen impurities present in melts due to different factors. These reactions also occur in the process of purification of molten alkali metal halides by halogenating agents. Let us begin a consideration of processes taking place in reactive gas atmosphere from pyrohydrolysis. 9.2.4.1 Pyrohydrolysis These reactions were investigated for alkaline halides and their mixtures. Hanf and Sole163 studied pyrohydrolysis of solid and molten NaCl in the temperature range 600-950°C by the so-called “dynamic method” which consisted of passing inert gas (N2) containing water vapor through a layer of solid or molten sodium chloride. The developed routine determined the equilibrium constant of the following reaction: [9.2.110] The values of the obtained equilibrium constants (log K) of reaction [9.2.110] for solid and liquid sodium chloride were changed from −8 to −6 at 650-800°C temperature range and from −6 to −5 at 800-900°C range. The pyrohydrolysis of molten or solid NaCl occurs to some extent, therefore the authors added SiO2 to increase the oxoacidic properties of the solid sample or melt. Silicon dioxide takes part in the decomposition of NaOH according to the following reaction: [9.2.111] This reaction caused a shift of the equilibrium of reaction [9.2.110] to the right. The rate of HCl evolution exceeded the expected value because of dissolution of NaOH in solid or liquid NaCl. An evident disadvantage of the above method162 is an assumption that the partial pressure of HC1 in the gas phase is equal to the equilibrium pressure. Rybkin and Nesterenko used the same experimental routine to investigate the processes of high-temperature hydrolysis and oxidation of solid and fused sodium iodide.164,165 According to the authors' estimation, the enthalpies of the following reactions [9.2.112] [9.2.113] are 32.8±2 and 13.9±1 kJ mol-1 for solid NaI and 30.6±2 and 9.3±2 kJ mol-1 for liquid sodium iodide. These values suggest that NaI has a greater tendency to oxidation than

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hydrolysis. These conclusions cannot be adopted without supposition because they are based on values of ΔH but not ΔG, although only the sign of the latter parameter determines the direction of reversible reactions at the constant pressure and temperature. A simple but unquestionable method has been used in54 to investigate high-temperature hydrolysis of molten KCl−NaCl. A mixture of HCl and H2O obtained by passing an inert gas through aqueous solutions at a definite concentration was passed into the melt. The measurements of the equilibrium O2− concentration by potentiometric method permits calculation of the equilibrium constant of [9.2.57] as pK = 55.3×103 T-1 − 40.2. At 1000K, pK value equals 15.1. It means that equilibrium [9.2.57] in molten KCl−NaCl equimolar mixture is shifted to the left. Such a routine was used to study the processes taking place at the pyrohydrolysis of the KCl−LiCl eutectic at 500oC. The equilibrium constant of reaction [9.2.57] was found to be pK = 9.77±0.4. The hydrolysis of the chloride melt is thermodynamically unfavorable and it is completely suppressed in the presence of bases (even at a concentration of ~10-3 mole kg-1). Smirnov, Korzun, and Oleynikova investigated the pyrohydrolysis of individual alkali metal halide melts excluding the lithium and rubidium salts in the wide temperature range.166 The potentiometric cell of the following principal scheme: [9.2.114] was used to investigate the hydrolysis of individual alkaline halide melts. The emf of cell [9.2.114] is related to the concentration of the reactants by the expression: [9.2.115] where: p H and p X 2

2

the partial pressures of hydrogen and halogen over the melt, respectively.

The logarithms of the equilibrium constants [9.2.116) are negative for all melts studied, which indicates that the hydrolysis of alkali metal halide melts is thermodynamically unfavorable. The trend towards hydrolysis of melts of individual alkaline halides diminishes with increase of radii of both cation and anion. According to the results obtained by Smirnov et al.166 solutions of alkali metal hydroxides in the corresponding individual halides are close to ideality. 9.2.4.2 Processes of removal of oxide-containing admixtures from halide melts The studies of elimination of oxygen-containing impurities from ionic melts are, mainly, of applied character and are performed in melts having industrial applications. Various halogenating agents, usually hydrogen halides or pure gaseous halogens are used to eliminate the impurities:167-175

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[9.2.117] [9.2.118] However, water formed in reaction [9.2.117] exhibits oxoacidic properties owing to process opposite to [9.2.117] and this retards the purification process. Cessation of the HX effect may lead to partial hydrolysis because reactions of [9.2.117] type are reversible. The shift of [9.2.117] to the left is also promoted by the relatively low thermal stability of HBr and HI. The efficiency of the molten lithium halides purification by hydrogen halides is appreciably lower. This is because molten lithium halides keep water, which is able to dissolve in these melts in considerable quantities. Even mixed halide mixtures retain this property, e.g., the molten KCl−LiCl eutectic strongly keeps the dissolved water at temperatures of the order of 400oC69,176 and bubbling of dry HCl during an hour does not result in complete removal of H2O. The effectiveness of purification by halogens depends on their oxidation-reduction potentials and decreases from chlorine to iodine. In addition, the latter can disproportionate: [9.2.119] The information about high purifying ability of the free iodine in molten alkali metal iodides cannot be considered as reliable.177 The addition of NH4X can be recommended only for drying and heat treatment of the raw initial components,178,179 and its use for industrial purification of fused salts is undesirable because it is much easier to ensure the continuous supply of the corresponding hydrogen halide in the melt being purified. An additional lack of this purifying agent results in the evolution of gaseous ammonia as one of the finishing products. Many investigators consider different variations of carbohalogenation as the most convenient way for removal of oxygen-containing impurities from molten ionic halides.180-187 The reduction of O2− concentration under the action of CC14, Cl2, C (C is acetylene carbon black or graphite) + Cl2, and COCl2 may be explained by the following reactions: [9.2.120)] [9.2.121] [9.2.122] Thermodynamic analysis of processes [9.2.120-9.2.122] shows that the effectiveness of purification in all cases is approximately the same,181 but reaction [9.2.120] has the advantage that highly toxic reagents (Cl2, COCl2) are not used in it. For this reason, CC14 is exclusively used in virtually all subsequent studies involving the carbochlorination of chloride melts.182-186

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Authors187 proposed to use CHBr3, CBr4, C2H5Br, and CHI3 for removal of oxygencontaining impurities from bromide and iodide melts. A significant advantage of carbohalogenation is that it leads to an appreciable decrease in the concentration of transition metal cations in the melt being purified. However, in the purification of melts by halogensubstituted compounds with a relatively low halogen content, carbon (carbon black) accumulates in the melt and is displaced by the crystallization front when single crystals are grown.180 However, the presence of a suspension of carbon in alkali metal halide melts is not always desirable and this method cannot, therefore, be recognized as universal. The carbohalogenation of melts results in the formation of CO2 as one of the products of [9.2.120], [9.2.122] processes. Carbon dioxide reacts with remaining oxide ions and induces the accumulation of fairly stable carbonate ions. The latter is the main form in which oxygen-containing impurities exist in melts purified in this way. The purification threshold of carbohalogenation is estimated as (1÷2)10-4 mol kg-1 of O2−.75 Thermodynamic analysis of carbohalogenation processes using “C + X2” pairs was conducted.188-190 The purification threshold values of Ω of Na+-based halide melts by pure halogens according to reaction [9.2.118] are as follows: 9.5 for chlorides, 5.5 for bromides, and 0.5 for iodides. From these data, it follows that halogenation of melts by pure gaseous halogens can be effective only for chloride melts. Addition of carbon increases these values to ca. 20, 16, and 11, respectively. Practically these thresholds are considerably lower and they corresponds to Ω values near 9-10 for chloride and bromide melts.191 For melts containing acidic cations, the thresholds decreases by values of corresponding pIL indices. Eckstein, Gross and Rubinova reported the use of halide derivatives of silicon for purification of alkali metal halide melts from oxygen impurities by means of the interaction of SiX4 with admixtures according to reaction:192 [9.2.123] The product of [9.2.123] is silicon dioxide, which can be separated from melt because of the difference in densities of melt and SiO2. Thermodynamic analysis shows that the effectiveness of purification of iodide melts diminishes in order of SiI4 > HI > I2.193 The use of silicon halides for purification of melts used to grow single crystals does not lead to the formation of additional impurities because the processes are carried out in quartz (i.e., SiO2) containers. Although the methods of purification described are fairly effective, oxygen-containing and cationic impurities, characteristic of each method, always remain in the melt. Therefore, the method of purification must be selected depending on aims of subsequent application of melt.

9.2.5 REACTIONS OF METAL OXIDE PRECIPITATION The ability of high-temperature ionic melts to dissolve various substances (e.g., metals, their oxides, etc.) is considered as one of their most important properties. In the case of scintillation single crystals based on alkali metal halides, definite halides-dopants (TlI, cerium halides, etc.) are referred to as “desirable” admixtures, since they create levels in the forbidden zone of the dielectric matrix which are responsible for the luminescence. On

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the contrary, oxygen-containing admixtures are harmful, since their incorporation in the scintillation crystals causes a considerable decrease of their low yield, radiation resistance, etc. Therefore, investigation of oxide solubility in molten salts are of great interest due to the following reasons. For some practical purposes (fluxes, etching, the growth of oxide crystals, and composites from ionic melts), it is required to choose a melt where the solubility of oxide materials should be as high as possible. If an ionic melt is used as a material for optical single crystal (alkali and alkaline earth metal halides) growth then the requirements should be quite opposite: the solubility of the oxygen-containing admixtures should be very low to provide a low quantity of additional absorption bands and disseminating centers in the crystals. Investigations of oxide solubilities in high-temperature ionic melts, especially based on alkali and alkali earth metal halides, presents an important branch of oxoacidity studies, which did not develop considerably during past few decades. One of the most serious causes of the absence of essential progress in the studies of oxide solubility is bad reproducibility of data on the solubility product values of oxides obtained by different investigators. Their scatter is some orders of pKs,MeO depending on experimental routine used. Other reasons include synthesis of initial metal halides, thorough purification of ionic solvents from oxide ion traces, apparatus design for experiments, and complicated determination of solubility characteristics in high-temperature ionic melts. 9.2.5.1 Methods used for solubility estimations of ionic melts Processes of dissolution of metal oxides in ionic melts are accompanied by interactions between ions of dissolved substance with ions of the melt (solvation). The superimposition of the mentioned processes results in the formation of metal complexes with the melt anions and cation complexes with oxide-ions. A part of oxides is transferred into solution without dissociation. In the saturated solution of oxide, the following equilibria take place: [9.2.124] [9.2.125] [9.2.126] [9.2.127] where: s and l Me Ktm+ Xk−

subscripts denoting solid and dissolved oxide, respectively the designation of metal forming double-charged cation the constituent cation of the melt (such as Cs+, K+, Na+, Ba2+, Ca2+, etc.) the melt anion (Cl−, Br−, I−, SO42−, PO43−, etc.)

Since at the dissolution of an oxide in the melt of a constant composition, a degree of Ktm+ − O2− interaction should be considered as the same and complexation with melt anions to cations of oxide may be assumed as approximately the same,194 therefore, it can be supposed that oxide solubilities depend mainly on the degree of interactions [9.2.124]

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and [9.2.125], where the latter may be considered as an acid−base interactions as proposed by Lux and Flood. The constant of Eq. [9.2.125]: [9.2.128] where: a and m

activities and molalities of the components noted in the subscripts

may be considered as a measure of acidic properties of cation if reaction [9.2.125] is homogeneous. However, the majority of oxides has limited solubility in molten salts and excess of oxide should precipitate. In this case the fixation and removal of oxide ions from melt takes place not only because of the cation acidity but also due to formation of new phase − the precipitated oxide. Therefore, works, in which the estimations of cation acidities are based on measurements of changes in oxide concentration before and after cation addition52 or by interactions between, e.g., carbonates with Lux-Flood acids,114,115 contain distorted results. The results of these studies114,115 contain an additional error − insoluble metal carbonates MeCO3 after interaction with acid K2Cr2O7114 or NaPO3115 are transformed into insoluble chromates or phosphates − all reactions are heterogeneous. The above-said may also be applied to works of Slama104,105 where cation acidities were estimated on the base of reactions [9.2.45] and [9.2.84]; there was no confirmation of the homogeneity of the former stage of interaction. Therefore, the mentioned method seems to have no wide use for studying behavior of oxides in molten salts, solubility studies by isothermal saturation, and potentiometric titration methods are more precise and informative. From the listed above scheme of equilibria [9.2.124-9.2.127], it follows that the fixation of oxide ions by metal cations is a common case of a heterogeneous process resulting in the formation of a new phase. The cation acidity may have no influence on completeness of Me2+ − O2− interaction in molten salts. From Eq. [9.2.124] it is clear that the concentration of non-dissociated oxide in the saturated solution does not depend on the concentration of constituent ion but it depends on precipitate properties, mainly on the molar surface of the deposit, s. Since the concentration of the non-dissociated oxide in the saturated solution is rarely determined, the magnitudes of Ks, MeO (used below pKs, MeO is −logKs, MeO), are usually employed for a description of the saturated solutions. The known values of Ks, MeO and KMeO permit to estimate the concentration of non-dissociated oxide, sMeQ, in the saturated solution: [9.2.129] It should be noted, however, that there was no reliable method for determining dissociation constants and sMeO. Below, two generally accepted methods: isothermal saturation and potentiometric titration of the corresponding cation solution are discussed. 9.2.5.1.1 Isothermal saturation method This method is simple and it includes some modifications: 1. placing a baked sample of oxide in the melt-solvent and testing the metal concentration in the melt up to saturation. Known test routines are either radiochemical195 or complexometric196,197 analysis of cooled samples of saturated solutions;

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2.

the addition of known weights of oxide to melt up to the saturation detected by potentiometric technique.58,198 The sum of concentrations of the molecular and ionic forms in the saturated solution, ΣsMeO, obtained as a result of such investigations can be expressed by the following equation: [9.2.130] Since the value of ΣsMeO is the main result of this method, the dissociation constant could be determined using the second method, if the oxygen electrode was preliminary calibrated by known additions of a strong Lux-Flood base. But there is no information about such studies. Studies of cooled samples permit to obtain thermal dependencies of oxide solubilities by analysis of the saturated melt heated to a defined temperature. The following disadvantages of the method should be noted: • the possibility of inclusion of suspended oxide components in sample for analysis, followed by overvaluing the solubility results; • the determined value is determined as concentration (not its logarithm). This method is not suitable for studies of practically insoluble substances. The presence of oxygen-containing impurities in the melt lowers calculated solubilities, especially, if oxide solubility is of the same order as the initial oxide concentration (oxide admixtures suppress the oxide dissolution). As for the existence of the suspended particles of oxide in the bulk of the melt, it should be noted that this effect was observed in some studies. Essin and Lumkis194 visually observed the formation of two layers of stable suspensions in the saturated solutions of colored oxides (CoO, NiO, CuO and FeO) in molten chlorides: more dense (probably lower layer containing large-sized oxide particles) and less dense (upper layer containing oxide particles of smaller size). Naturally, for colorless oxides the formation of the suspension cannot be observed visually and direct sampling without filtration the melt should result in the overestimation. Another confirmation of capturing of suspended particles at sampling without filtration performed by authors199 at investigation of CaO solubility in some chloride melts was obtained in our work.200 The sampling in199 was performed by usual spoon and the samples were obtained from the upper layer of the saturated melt. It was proven that at the ratio of densities of the melt-solvent and the dissolved solid substance ca. 0.6 (CaCl2-containing melts) the overestimation degree achieved 20% and this error increased at closer densities of the components of the systems studied (SrCl2- or BaCl2-containing melts). To avoid crude experimental errors, oxide powders should be annealed at temperatures higher than the experimental ones, or pressed tablets by pressing the powder with the following calcination that permits to obtain the correct results.196 Enough separation effect was achieved by Barbin et al.201 Here the authors used pre-annealed powder of alkaline earth oxides and applied special sampling routine: the saturated solution samples were taken using special sampling tube with input hole of 0.2-0.5 mm diameter.

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9.2.5.1.2 Potentiometric titration method This method is more frequently used than the previously discussed method. It may be employed for oxide solubility studies in a wide range of concentrations of saturated solutions. The method permits determination of solubility products of oxides and in some cases (the existence of the appreciable non-saturated solution region) the dissociation constants of oxide may be calculated. As compared with isothermal saturation, a potentiometric method has the following advantages: • emf values are linearly dependent on the logarithm of O2− concentration; it is possible to measure the latter even in solutions with extremely low potential-determining ion concentration; • the relative simplicity of emf measurements and good reproducibility of the experimental values and derived parameters; • possibility to conduct studies in situ, i.e., without any effect on the process studied. The principal limitation of the potentiometric titration is the potential of the liquid junction, which is often negligible in molten salts,70 as well as the absence of a reliable and generally accepted method of calculation of the activity coefficients of oxide ions, cations and non-dissociated oxide in melts. As for determination of solubility and dissociation parameters, it should be noted that this method determines KMeO only if the corresponding potentiometric titration curve contains the non-saturated solution region. Studies in the wide temperature range are impeded as compared with the isothermal saturation method. 9.2.5.2 Oxide solubilities in oxygen-containing melts Frederics and Temple studied CuO, MgO, PbO and ZnO solubilities in the molten equimolar KNO3−NaNO3 mixture in 290-320°C temperature range.202,203 The solubilities were determined by isothermal saturation method with potentiometric control of solubility. The following solubility values (molalities) were determined at 290°C: 2.24×1013 for CuO, 2.2×10-13 for ZnO, 2.16×10-14 for MgO, and 4.34×10-12 for PbO. The increase in the melt temperature to 320°C led to the increase of solubilities by factor of 6-10.203 Lux-Flood acids derived from B2O3 (borax) and P2O5 (sodium metaphosphate) are often used as acidic components of different fluxes. Delimarsky and Andreeva determined PbO solubility in molten NaPO3 at 720°C by isothermal saturation method using potentiometric control of saturation.198 The concentration cell with gas oxygen electrode Pt(O2) was used. PbO solubility was estimated to be 31.6 mol%. Shen Tsin Nan and Delimarsky investigated solubilities of acidic metal oxides (MoO3, WO3, TiO2) in molten borax at 900°C by a similar method.204 The control of saturation was performed by a gravimetric analysis. Solubilities of oxides deviate from those predicted by Shreder’s equation, because of chemical interactions between the dissolved substances and the solvent. Oxide solubilities increase with the reduction of oxide melting point. Solubilities were 66.1 mol% for MoO3, 63.2 mol% for WO3, and 21.2 mol% for TiO2.

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9.2.5.3 Oxide solubilities in halide melts 9.2.5.3.1 The eutectic mixture KCl−LiCl (0.41:0.59) Delarue conducted semi-quantitative studies of oxide solubilities at ~500°C by a visual method.205,206 Potassium hydroxide, KOH, was added to the metal chloride solution in KCl−LiCl. If there was no formation of the oxide deposit then the oxide was considered as soluble, in other case oxide was referred to as slightly soluble or insoluble depending on the amount of the deposited oxide. According to this investigation, CdO, PbO, BaO, CaO, and Ag2O belong to the group of soluble oxides, CoO, NiO, ZnO are examples of slightly soluble oxides, and MgO, BeO and A12O3 have extremely low solubility (insoluble). Copper (II) oxide is found205,206 to be unstable in molten chlorides since its dissolution is accompanied by the reduction of CuII to CuI. This transformation was substantial even under the partial pressure of chlorine equal to 1 atm.207 Similar behavior is typical to other transition cations at the highest degree of oxidation, e.g., TlIII, FeIII, and AuIII. The addition of corresponding chlorides to the saturated solutions of oxides formed by non-oxidizing cations resulted in the dissolution of these oxides due to reactions similar to: [9.2.131] The essential difference of solubility values of “powdered” (added as powder of the commercial oxide) and prepared in situ (by addition of KOH to the solution of the corresponding chloride) oxide solubilities is an important feature of oxide solubilities.205,206 Solubilities of the in situ samples have been found to be considerably greater (CaO, CdO), although there was no explanation to this observation. Quantitative characteristics of oxide solubilities in KCl−LiCl eutectic were not presented in these studies. Laitinen and Bhatia studied the behavior of several metal-oxide electrodes in the KCl−LiCl eutectic melt at 450oC.208 They determined the solubilities and solubility products of certain oxides in order to use corresponding metal-oxide electrodes for oxoacidity measurements in molten salts. Oxide solubilities were as follows (mole kg-1): 3.3×10-4 for NiO, 6.8×10-4 for BiOCl, 9.4×10-3 for PdO, 3.32×10-2 for PtO and 3.8×10-2 for Cu2O. The relatively high PtO solubility was unexpected. It follows that platinum gas oxygen electrode, sometimes considered as a metal-oxide electrode, cannot be used for measurement of pO in strongly acidic media because of dissolution of the oxide film on its surface. This was confirmed209 when Pt|PtO electrode was used for pO index measurements in Ni2+/NiO buffer solutions. Shapoval et al. studied saturated solutions of different oxides by polarographic techniques.66,67,210 A degree of interaction between the dissolved oxide and the melt was estimated taking into account potential and polarogram shifts and their deviations from theoretical ones. The rate of cation reduction was limited by the acid−base dissociation stage. The stability constants of oxides are (in mol%): CoO − (9.9±1.9)x10, NiO − (6.8±0.8)x103, PbO − (3.4±1.3)×103, Bi2O3 − (8.7±3.5)×103. Cadmium, copper (I) and silver oxides have been shown66,67,210 to completely dissociate under the experimental conditions (400-600°C) and this was in a good agreement with the results of Delarue.205,206 Stabilities of iron (II) and (III) oxides in KCl−LiCl eutectic melt at 470°C were also 22investigated.211,212 Oxide precipitation by carbonate CO 3 ≡ O was shown by potentio-

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metric and diffractometric data to yield FeO from FeII solutions. The precipitation of oxides from FeIII solution led to the formation of solid solutions having LiFeO2−LiyFe1-yO composition. The solubilities of products in molality scale were as follows: FeO − 10-5.4, Fe3O4 − 10-36.3, Fe2O3 − 10-29.6. Fe3+ cations oxidize chloride melt with the evolution of gaseous chlorine that was in a good agreement with results of other studies.205,206 Dissociation of carbonate ion as oxide donor was essentially incomplete and, therefore, obtained solubility products gave a systematic error.66,67,210 Potentiometric studies of the solubility of some metal oxides (MgO, CoO, and NiO) at 700oC and magnesium oxide at 600, 700 and 800oC are reported in our works.83,213 Solubilities of such products as CoO (pKs, CoO = 4.43±0.11) NiO (pKs, NiO = 5.34±0.2) and MgO (pKs, MgO = 5.87±0.05) were higher than those in molten eutectic KCI−NaCl. The shift of the solubilities in molar fraction scale were ~3.36 log units and permitted to estimate solubilities of other MeO oxides on the base of the known values in KCl−NaCl. It has been shown that acidic properties of Pb2+ and Cd2+ cations were suppressed by those of Li+, therefore, these cations and weaker Pearson acids (Ba2+ and Sr2+) did not change oxoacidic properties of the molten KCl−LiCl. The existence of the non-saturated solution section permitted to calculate the dissociation constant of CoO in the molten KCl−LiCl eutectic at 700oC as pKCoO = 2.03±0.50. The solubility products of MgO (molality) were 6.99±0.08 at 600oC and 5.41±0.04 at 800oC. Temperature increase does not result in unsaturated solution section in the potentiometric titration curve. This means that MgO remains practically insoluble in the molten KCl−LiCl eutectic at all temperatures, even enhanced acidity of the molten background does not provide a sufficient solubility rise. The molten KCl−LiCl eutectic, due to its enhanced oxoacidic properties, can dissolve sufficiently larger quantities of various oxide materials as compared with chloride melts containing cations of lower acidity such as Na+, K+, Cs+. The data on the solubility products of oxides in this melt point to a relatively low probability of formation of precipitates owing to the interactions of cations of alkaline earth and transition metals with the traces of oxide ion impurities in the melt. The conclusion is correct only for the solubility product values. However, in addition to ionized form, some quantity of oxide is dissolved without dissociation (the Shreder's component of solubility) which is not subjected to the action of the acidic cations of the melt. Castrillejo et al.214 determined solubility products of rare earth oxochlorides in KCl− LiCl at 450°C, as follows: [9.2.132] The pKs, MeOCl values (in molality) were: 7.00±0.09 for LaOCl, 7.45±0.05 for CeOCl, 7.67±0.24 for NdOCl, and 7.45±0.25 for PrOCl.214 It was found that Y3+ cation did not form oxochloride and solubility product index of Y2O3 was estimated as 19.90±0.22. Later the formation of oxochlorides by La and Nd was confirmed by Hayashi and Minato,215 whereas Gd3+, having ionic radius close to that of Y3+, did not form oxochloride. De Cordoba and Caravaca studied electrochemical behavior of Sm3+ in KCl− LiCl melt.216 They found that there was the formation of oxochloride and its solubility product index was estimated as 7.54±0.17.

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The solubility product index of Pu2O3 in KCl−LiCl eutectic at 450°C determined for217 [9.2.133] was pK s, Pu O = 22.8±1.1. 2 3 9.2.5.3.2 Molten KCl−NaCl equimolar mixture One of the first works devoted to oxide solubility determination was published by Naumann and Reinhardt.195 CaO, SrO, and BaO solubilities have been determined by isothermal saturation technique with isotopic control of the saturation in the temperature range from the melting point to 900°C. KCl−NaCl and individual molten chlorides, KCl and NaCl, were used as solvents. Oxide solubilities increased in the sequence CaO < SrO < BaO and solubility product values in KCl−NaCl and KCl melts were close, whereas the values for NaCl were somewhat higher.195 A comparison of the experimental and thermodynamic data for MeO and Me2+ + O2+ solutions shows that the solubility values are intermediate between values calculated for solutions of dissociated and molecular oxide. It means that these constituents were present in the saturated melts simultaneously. Similar investigations were done in the temperature range of 700-800°C by Volkovich.197 The saturated solutions of oxides were prepared by placing pressed oxide tablets in melt and holding them for 2-3 h. The analysis of the saturated solution samples was performed by complexometric titration method. Potentiometric studies of cations Ca2+, Li+ and Ba2+ were conducted to determine their acidic properties at 700°C.62,218 The calculated dissociation constants (in mol%) were 2.8x10-3 for Li2O, and 1.2x10-2 for BaO. These values showed that all studied cations had considerable acidic properties in KCl−NaCl melt. Ovsyannikova and Rybkin developed the cation acidity scale in molten KCl−NaCl at 700°C on the basis of emf shifts between “pure” solvent and solution formed after addition of metal sulfates.52 Acidic properties of the main subgroup elements decreased with the increase of their atomic numbers and there was no similar relationship for side groups or transition metals. Quantitative data explanation according to acid−base equilibrium [9.2.125] is affected by additional reaction [9.2.48] caused by the addition of sulfates to the studied chloride melt. The use of sulfates may cause SO3 formation from highly acidic cation solutions. In particular, Na+ is the most acidic cation of KCl−NaCl system, therefore, additions of more basic oxides than Na2O should result in oxide ion exchange: [9.2.134] where:

MeI

Cs, Rb, K

which is shifted to the right. Similar considerations can be made for K+ − Na+ − O2− system in molten KCl−NaCl.219 From [9.2.134] it follows that any solution of cations in Na+based melts cannot create oxide ion concentration exceeding that of the equimolar addition of the corresponding salt of the most acidic cation of the melt (Na+). However, the oxide ion concentration in BaSO4 solution has been shown52 to be 10 times higher than

576

9.2 Acids and bases in molten salts, oxoacidity

that in K2SO4 and Na2SO4 (ΔE = 0.11 V). Similar deviations for other cations are smaller, e.g., Cs+ − 0.49 V, Sr2+ − 0.30 V, Rb+ − 0.1 V. Delimarsky, Shapoval, and Ovsyannikova reported studies of solubilities of ZnO, MgO, NiO, and SrO in the molten KCl−NaCl equimolar mixture at 700oC.220 The solubility was studied by potentiometric titration of solutions containing 0.01 mol kg-1 of the corresponding chloride with KOH and KOH solutions the studied chloride (the reverse titration). On the basis of the obtained experimental data, the equilibrium parameters corresponding to the solubility product and the dissociation constant were calculated. Unfortunately, there was no statistical treatment of the calculated values. The paper220 did not contain the average values of the equilibrium parameters, this averaging was made by Combes et al.221 The values of KMeO and Ks, MeO calculated for the same oxide at the direct and reverse titration were demonstrated221 to measurably differ. This discrepancy of the data shows that systematic investigation of oxide solubilities aimed at finding common regularities and correlations should be performed using the same investigation technique. Among all methods discussed, the direct potentiometric titration is the most convenient way of obtaining good results. Returning to the paper,220 it should be noted that the authors concluded it by the following main result: the solubility of the studied oxides increased in the following sequence MgO → NiO → ZnO → SrO. Oxide solubilities in KCl−NaCl equimolar mixture at 1000K were studied.54,58,152,219,222 According to these data MgO is neutralized in two stages: the first stage product is Mg2O2+ and the final product is MgO.221 It should be noted, however, that although MgO solubilities were investigated in a similar manner and in different melts (KCl−NaCl,64,223 CsCl−KCl−NaCl,224 and BaCl2−CaCl2−NaCl86) there was no pronounced first stage of Mg2O2+ formation. Thermal dependence of CaO solubility has been determined by isothermal saturation method219,222 to be approximated by the following plot pKs, CaO = 10800T-1 − 5.8. We studied solubilities of 11 oxides in this melt at 700°C and developed the methods of saturation detection gives us the possibility to determine in some cases dissociation constants.64,223,224 The dependence of pKs index in molar fractions (pKsx, MeO) vs. polarizing action of a cation by Goldschmidt ( ) for all cations (excluding Pb2+ and 2+ Cu2 ) can be expressed by the following equation: [9.2.135] The thermal dependence of ZrO2 solubility (molar fractions) in molten KCl−NaCl was evaluated in the temperature range of 973-1174K x = (−5.7±3.1)10-6 + (7±3)10-9T.225 The calculations made on the basis of this dependence show that ZrO2 solubility in KCl− NaCl melt at T ~ 973K is negligible. Barbin et al.225-228 determined the thermal dependence of Li2O solubility in KCl− NaCl equimolar mixture by isothermal saturation technique in the temperature range of 973-1073K; the corresponding dependence was x = 0.107 − 5.221T-1. In this range, the solubility varied from 0.52 to 0.86 mol%. Kaneko and Kojima found that the solubility of this oxide in KCl−NaCl melt at 973K was lower (0.31 mol%).229 The solubility of lithium oxide turned out to be close to that for BaO.

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

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Figure 9.2.9. The dependences of pKs, MeO vs. polarizing action of the corresponding cation by Goldschmidt ) on the data obtained by different investigators: 1 − Tremillon et al.,54,58,152,219,222, 2 − Delimarsky et

( 220

, 3 − Naumann and Reinhardt,195, 4 − Volkovich,197, 5 − our data,64,223, 6 − Barbin et al.,226-228, 7 − Kaneko

al.,

and Kojima229.

Solubility products of some oxides in molten KCl−NaCl equimolar mixture in molality scale are presented in Table 9.2.5 and plotted in Figure 9.2.9 (data obtained by same author team are connected by lines). Table 9.2.5. The solubility products of several oxides in molten KCl−NaCl equimolar mixture at T~1000 K, pKs, MeO, molality scale. Oxide

pKs, MeO, literature sources 54,58,152,219,222

220

MgO

9.00 ± 0.15

8.46

CaO

6.29

SrO

3.00

BaO

2.31 ± 0.05

NiO

11.2

ZnO Cu2O

8.32 6.18

5.4

195

197

64,223 9.27 ± 0.06

8.36

6.62

4.36 ± 0.06

7.60

5.84

3.08 ± 0.40

7.05

4.22

2.30 ± 0.15 9.03 ± 0.06 6.93 ± 0.20 4.17 ± 0.30

578

9.2 Acids and bases in molten salts, oxoacidity

Table 9.2.5. The solubility products of several oxides in molten KCl−NaCl equimolar mixture at T~1000 K, pKs, MeO, molality scale. pKs, MeO, literature sources

Oxide

54,58,152,219,222

220

195

197

64,223

MnO

6.78 ± 0.05

CoO

7.89 ± 0.03

CdO

5.00 ± 0.03

PbO

5.12 ± 0.05

All results can be conditionally divided into two groups: obtained by isothermal saturation and potentiometric titration methods. The precision of results from isothermal saturation is worse. The potentiometric results should give lower values than isothermal saturation because they include molecular oxide concentration. Figure 9.2.9 shows that results have opposite trend to [9.2.130]. The following explanation of the above discrepancy is proposed in our works.230-232 Let us consider the expression for the chemical potential, μs, MeO, of the metal oxide in its saturated solution: [9.2.136] where:

0

μ MeO sMeO

the standard chemical potential of the metal oxide the concentration of MeO in its saturated solution

From this equation, it follows that the oxide solubility should be constant. But every precipitate possesses a definite area, hence, its effect should be taken into account too: [9.2.137] where:

σ S

the surface energy the molar surface square of the precipitate

Since for the same oxide σ is constant, the increase of the precipitate square should result in the increase of precipitate solubility. Similar considerations were included in the well-known Ostvald-Freundlich equation.233 For substances having 1:1 dissociation stoichiometry, the similar equation can be rewritten in the following form:

[9.2.138] where: MMeO s1, MeO, s2, MeO dMeO

the molecular mass of the oxide the solubilities of the oxide crystals with radii r1, MeO and r2, MeO, respectively the density of the oxide

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

579

From this equation, it follows that the increase of crystal size reduces its solubility. Oxide components, deposited from more concentrated cation solution, should possess larger sizes due to the so-called “deposit aging”, than those obtained from more diluted solutions. Therefore, results of Delimarsky et al.220 obtained from 0.01 mol kg-1 solutions should be higher than those obtained in other works54,58,64,223 using 0.05 mol kg-1 solutions. In the first case, solubility was greater approximately by half-order of the magnitude than in the second one. The oxide formed from more concentrated solution should have less surface square, and, hence, lower solubility. Data obtained in papers54,58,64,223 are practically coincident although we used NaOH as titrant similarly to other study reported.220 The precipitating titration results in the formation of finely dispersed oxide which immediately begins to age because of the recrystallization, i.e., the growth of larger crystals and disappearance of smaller ones, this process leads to the decrease of the surface energy, σS. Continuous holding at high temperatures and relatively high solution concentration favors this process. In particular, samples used for isothermal saturation technique studies exposed to high temperatures for a long time, and tablets obtained are held in the contact with the melt for some hours. High concentration of solutions favors transfer of a substance from small to large crystals (diffusion). The differences between data in references194,196 may be explained by different conditions of the oxide powder calcination. During the annealing of the oxide sample, the recrystallization processes occur that leads to the reduction of the surface square of the powder and the decrease of its solubility in the melt. The differences in data for KCl−NaCl are caused by the differences in crystal sizes of solid oxide being in an equilibrium state with the saturated solution. Our papers234,235 report investigation of the effect of the grain sizes of lead, cadmium, calcium, and zinc oxides on their solubilities in the molten KCl−NaCl equimolar mixture at 700oC. The data gave possibility to estimate the dissociation constants of several oxides: pKZnO = 6.37±0.08, pKCdO = 5.37±0.07, pKCaO = 3.38±0.3 and pKPbO = 3.50±0.07 for the oxides possessing different grain sizes. It should be noted that the latter value is in a good agreement with the dissociation constant value obtained by potentiometric titration, which gave pKPbO = 3.29±0.04.64 The obtained data confirm an assumption that the grain sizes have no effect on the dissociation constants, since this kind of the Lux-Flood acid−base equilibria runs without the phase boundaries and they are not affected by the interface energy. The results permitted to construct the dependences of oxide solubilities −logsMeO Figure 9.2.10. Dependences of −logsMeO of CaO (1), and the molar surface area of the studied PbO (2) and ZnO (3) against the molar surface area (SMeO) of solid oxide components contacting with mol- oxide. These dependencies for some of the ten KCl−NaCl equimolar mixture at 700oC. studied oxides are presented in Fig. 9.2.10.

580

9.2 Acids and bases in molten salts, oxoacidity

All dependencies are close to linear plots. Their slopes permit to estimate the surface energy values at the metal oxide−alkali metal halide melt interface boundary. The calculated values of the surface energy at the oxide−chloride melt interface boundary were calculated235 to be within 30-40 J m-2 range. These values considerably exceed the corresponding parameters estimated for aqueous solutions of electrolytes thus giving rise to essential changes in the solubility with the component sizes. In addition to the oxide solubility data, there are also data on solubility products of alkaline earth carbonates in KCl−NaCl melt.236 The dissolution process can be described as follows: [9.2.139] The experimental data are presented in Table 9.2.6. Table 9.2.6. Data on oxide and carbonate solubilities (in molalities) in molten KCl−NaCl equimolar mixture at 700oC. Compound BaCO3

– log m

2-

CO 3

, saturation

pK s, MeCO3 , molality

0.18

0.36

SrCO3

0.67

1.34

CaCO3

1.02

2.04

It was shown that CO2 bubbling through the melt containing oxide precipitate leads to dissolution of oxide. The observation can be used for the crystals growth of mixed metal oxides, which is especially convenient for metal oxides which form carbonates unstable at high temperatures. To explain the essence of the synthesis routine, let us consider the following scheme of the assumed technological process: • addition of the oxide mixture to low-acidic chloride melt, • passing CO2 through the melt, • removal of CO2 from the melt, • separation of the obtained material from the melt. At the first stage the mixture of oxides is placed into chloride melts, and the system is heterogeneous since all oxides are slightly soluble in the ionic liquid. Passing carbon dioxide through the melt results in a considerable increase of pO (acidity), which causes an increase of the metal oxide solubility. At this stage the oxides intensely dissolve in the melt, and, at a certain “metal oxide/melt” mass ratio, the mixture can be completely dissolved in melt. The third stage can be realized in two manners. One of them consists in a slow decrease of the partial pressure of CO2 over the melt that causes a gradual decrease in the melt acidity and results in small oversaturation values. Hence, the rate of the oxide crystal growth from the melt is low and the crystals are of relatively larger size. This routine may be very promising for obtaining oxide single crystals from the halide melts. Another way is the fast removal of carbon dioxide, e.g., by bubbling an inert gas through the melt, this favors high oversaturation providing faster crystallization processes

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

581

as compared with the first case. The obtained oxide crystals will possess smaller sizes that result in the formation of fine size mixtures, which can be used for subsequent thermal treatment. And the fourth stage consists of separation of the oxide crystals from melts, which can be done using different ways, which in essence are not so difficult to be specially discussed here. Treatment of metal oxide solutions in molten salts by carbon dioxide is a promising method to monitor the crystal size and composition of complex oxide materials. 9.2.5.3.3 CsCl-KCl-NaCl (0.455:0.245:0.30) eutectic As mentioned above, the oxoacidic properties of melt are close to those of the KCl−NaCl equimolar mixture. An essential advantage of the ternary mixture is a considerably lower melting point (near 480oC). This creates a possibility to perform investigations of the metal oxide solubilities at relatively low and relatively high temperatures and to elucidate the effect of the melt temperature on the oxide solubilities in molten alkali metal chlorides. Apart from the thermal dependence, such studies allow obtaining the solubility data, which serve as an initial point for estimation of relative acidic properties in other halide melts at the corresponding temperatures. It should be noted again that the molten KCl− NaCl equimolar mixture cannot be used for this purpose at temperatures below 658oC. The data presented below were obtained in our investigations and no similar data were reported. The potentiometric titration of cations was performed at 600 and 700oC using NaOH as a base-titrant.224,237,238 The results of these studies are included in Table 9.2.7. Table 9.2.7. Metal oxide solubilities in the molten CsCl−KCl−NaCl eutectic at 600 and 700°C, molality. Oxide BaO SrO

600oC

700oC

pKs, MeO

pKMeO

sMeO

2.85 ± 0.10

−

−

3.95 ± 0.40

1.76 ± 0.3

-3

7.07x10

-4

ΣsMeO

pKs, MeO

pKMeO

sMeO

−

~2.59

−

−

1.8x10

-2 -3

CaO

5.83 ± 0.05

2.76 ± 0.2

8.51x10

2.1x10

MgO

10.78 ± 0.11

−

−

MnO

7.83 ± 0.15

−

−

3.64 ± 0.13

1.19 ± 0.22

ΣsMeO −

3.54x10

-3

1.9x10-2

-3

4.9x10-3

4.90 ± 0.13

2.04 ± 0.25

1.38x10

−

9.78 ± 0.04

−

−

−

−

7.59 ± 0.14

−

−

−

CoO

9.02 ± 0.06

−

−

−

8.60 ± 0.03

−

−

−

NiO

10.70 ± 0.08

−

−

−

9.52 ± 0.06

−

−

−

Cu2O

5.05 ± 0.10

2.35 ± 0.3

4.45 ± 0.05

1.64 ± 0.22

1.55x10-3

7.5x10-3

-4

1.5x10-3

1.95x10-3 4.9x10-3

ZnO

6.90 ± 0.07

−

−

−

6.25 ± 0.03

3.12 ± 0.20

7.40x10

CdO

5.64 ± 0.48

−

−

−

5.19 ± 0.05

−

−

SnO

9.38 ± 0.02

−

−

−

−

−

−

PbO

6.31 ± 0.05

4.13 ± 0.1

-3

6.61x10

6.7x10

-2

5.14 ± 0.02

3.08 ± 0.20

8.70x10

− − -3

1.1x10-2

582

9.2 Acids and bases in molten salts, oxoacidity

The obtained results demonstrate that increase in the melt temperature causes the increase of the oxide solubility (pKs, MeO) by 0.3-0.4. These data show the metal oxide solubilities in chloride melts of different cation compositions. Practically the same oxoacidic properties at the same temperature are approximately the same if the solubilities are expressed in molar fractions. Although oxide solubilities in the studied melt are lower than those predicted by the Shreder equation:

[9.2.140] where:

ΔHm, MeO and Tm, MeO

the heat of melting and the melting point of the oxide, respectively

their changes with the temperature are in a good agreement with equation [9.2.140]. The dependence of pKsx, MeO vs. polarizing action of cation by Goldschmidt for all cations (excluding Pb2+, Sn2+, and Cu22+) can be expressed by the equations:239 , 600 °C

[9.2.141]

, 700 °C

[9.2.142]

In the ternary CsCl−KCl−NaCl eutectic, the plots similar to [9.2.135] remain correct and they can be used for prediction of oxide solubilities based on their physicochemical parameters. We investigated reactions of Be2+ and Mg2+ cations with O2− in the molten eutectic mixture of CsCl−KCl−NaCl at 783oC by a potentiometric method using Pt(O2)|YSZ indicator electrode.240 Addition of O2− ions to the melt containing Mg2+ results in precipitation of MgO (pKs, MgO = 11.89±0.3, molality) whereas interaction of Be2+ with O2− is accompanied by sequential formation of Be2O2+ (pK = 15.68±0.5, molality) and precipitation of BeO (pKs, BeO = 9.62±0.3, molality). On the basis of the obtained and known data pKs, MgO − T-1 dependence in CsCl−KCl−NaCl eutectic is constructed. The slope of this dependence is in a good agreement with the value predicted by the Shreder's equation that extends the range of use of the Shreder's equation for predictions of metal oxide solubilities in the molten halides at temperatures of the order of 500°C. 9.2.5.3.4. Molten bromides. As it was shown in our papers241,242 the metal oxide solubilities in molten bromide melt of 2CsBr−KBr composition were considerably lower than in 'standard' KCl−NaCl equimolar mixture. For example, strontium oxide, which is referred to as moderately soluble in lowacidic chloride melts, becomes slightly soluble in the bromide melt. Calcium and cadmium oxides which are slightly soluble in Na+-based chloride melts become practically insoluble in molten CsBr−KBr mixture. The basic properties of BaO in the bromide melt essentially weaken, and the degree of its dissociation in the saturated solution considerably diminishes. It should be added that the bromide melt is a very capricious ionic solvent. An obvious cause of this consists in stronger reductive properties of bromide ion as compared with

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

583

chloride ion. Some progress in the studies of strongly acidic cations was achieved by passing the initial argon through the titanium sponge. Owing to fixation of gaseous oxygen by the sponge its concentration reduces to approximately 10-8 vol%. This purification of argon makes it possible to determine the solubility product values even of such oxides as MgO, NiO, CoO, MnO and ZnO. The oxide solubility parameters obtained in the bromide melt by the method of potentiometric titration are included in Table 9.2.8. It should be noted that the reproducibility of the obtained solubility parameters is appreciably worse (the confidence ranges are wider) than that in the molten alkali metal chlorides. Lower values of oxide solubilities together with an enhanced sensitivity of the bromide melt to oxidants (traces of free oxygen) provides additional sources of experimental errors. Table 9.2.8. Parameters of metal oxide solubilities in the molten CsBr−KBr (2:1) mixture at 700oC, molality. Oxide BaO

pKs, MeO 3.67 ± 0.30

pKMeO 1.70 ± 0.43

Σs

sMeO 1.07x10

-2

2.53x10-2

-3

6.95x10-3

5.33 ± 0.12

3.01 ± 0.50

4.79x10

CaO

8.44 ± 0.06

−

−

−

MgO

11.27 ± 0.06

−

−

−

MnO

9.21 ± 0.04

−

−

−

CoO

9.84 ± 0.20

−

−

−

NiO

11.22 ± 0.30

−

−

−

ZnO

9.54 ± 0.16

−

−

−

CdO

7.86 ± 0.16

−

−

−

PbO

7.03 ± 0.07

5.06 ± 0.36

1.07x10-2

1.10x10-2

SrO

As it was demonstrated,241,242 all correlations of metal oxide solubilities with the physico-chemical characteristics of oxides and cations found in the chloride melts remain correct for the molten CsBr−KBr mixture. The dependence of pKsx, MeO on the polarizing action of a cation by Goldschmidt is as follows: , 700°C

[9.2.143]

The slopes of these plots in different melts remain the same although the absolute terms change, therefore, the latter can be considered as the main characteristic, defining dissolution ability of a given melt. The addition of more acidic cations (such as Na+, Ba2+, or Li+) to the melt, results in strengthening their affinity to oxide ions and the shift of equilibrium [9.2.125] to the

584

9.2 Acids and bases in molten salts, oxoacidity

right.243-246 The mentioned papers contain information on solubility of several oxides and the corresponding solubility product values at 700 °C are presented in Table 9.2.9. Table 9.2.9. Solubility products of some oxides (pKs,MeO) in molality (m) and mole fraction (x) scales in melts based on alkali metal bromides and chlorides at 700°C.

Oxide

KCl-NaCl CsBr-KBr (0.67:0.33) (0.5:0.5) Ref. 64,223 Ref. 241,242 x x

KBr-NaBr (0.5:0.5) Ref. 243,244

BaBr2-KBr (0.5:0.5) Ref. 245

m

x

m

x

m

x

5.0

6.9

3.81

5.72

6.31

767

4.36

6.33

5.19

7.16

6.25

8.22

MgO

11.62

CaO

6.72

SrO

5.44

6.82

BaO

4.66

5.16

MnO

9.13

10.69

7.85

976

CoO

10.24

11.32

8.80

10.71

NiO

11.38

12.70

9.72

11.63

8.05

9.41

PbO

7.47

8.52

5.20

7.10

3.92

5.28

KBr-LiBr (0.4:0.6) Ref.246

12.76

For molten KBr−NaBr equimolar mixture as the most studied from the considered here melts we found the correlation between the oxide solubility product index and the polarizing action of the corresponded cation by Goldschmidt. This correlation can be presented as follows: , 700 °C

[9.2.144]

As is seen, for the said melts with the same cation composition (KCl−NaCl and KBr−NaBr) the absolute terms and the slopes are very close. Comparison of the data presented in Table 9.2.9 shows that the average difference of pKs,MeO in the chloride and bromide melts is equal to 0.24±0.4, which is statistically insufficient. It means that the oxide solubilities in 1 mole of the KBr−NaBr melt are practically equal to the corresponding values in 1 mole of KCl−NaCl. Therefore, similarly to KCl−NaCl equimolar mixture, which is the reference chloride melt for a number of investigations, molten KBr−NaBr equimolar mixture can be chosen as a reference point while studying bromide melts. The change of anion in Cl→Br sequence does not result in appreciable solubility changes. Comparing the oxide solubilities in KBr−NaBr and 2CsBr−KBr melts, we can establish that in the latter melt the average increase of pKs,MeO is 1.15±0.2. This takes place since the equilibrium [9.2.145]

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

585

occurring in the Na+-based melt is shifted to the right to a larger extent than the equilibrium [9.2.146] +

in molten 2CsBr−KBr mixture where the most acidic constituent cation is K . These data show that the discussed melts of KX−NaX compositions (where X=Cl, Br) dissolve oxides practically in the same degree, ditto is true for molten KX−LiX eutectic mixture. So, the change of melt anion in Cl Br sequence does not result in appreciable changes of oxoacidic properties of these melts. 9.2.5.3.5 Molten iodides The range of oxides suitable for investigations in this melt is appreciably narrower as compared with the molten CsBr−KBr mixture. The solubility products of alkaline earth oxides (excluding MgO) cadmium and lead oxides were determined.239-243 The values of solubility products and the derived oxide solubilities in molten CsI at 700oC are presented in Table 9.2.10. Table 9.2.10. Solubility products of some oxides in molten CsI at 700°C, molality. Oxide

s

pKs, MeO

Me

2+

BaO

3.80±0.15

1.26×10-2

SrO

5.10±0.30

2.82×10-3

CaO

6.32±0.14

6.29×10-4

CdO

6.82±0.06

3.89×10-4

PbO

6.52±0.10

5.50×10-4

The dependence of pKsx, MeO on the polarizing action of a cation by Goldschmidt is as follows: , 700°C

[9.2.147]

The oxide solubility in CsI melt is intermediate between that in chloride melts and CsBr−KBr melts.252 There are several papers devoted to the use of metal cations forming most refractory oxides as scavengers for purification of CsI melt for growing scintillation single crystals belonging to high-performance scintillators. They are widely used for detection and investigation of powerful ionizing irradiation fluxes in high-energy physics.253 The functional parameters of these crystals are considerably dependent on the admixture composition of the initial salt and the growth melt. From Eqs. [9.2.124] and [9.2.125], it follows that after the purification by the metal cation oxygen-containing admixtures may remain in melts as O2− and undissociated MeO. The addition of a considerable excess of cation permits to decrease the concentration of O2− practically to any desirable low value in the case of very low solubility products. However, such a treatment does not decrease the concentration of MeO. The latter

586

9.2 Acids and bases in molten salts, oxoacidity

depends only on the melting point of oxide: most refractory oxides have the lowest solubilities in molten salts in non-dissociated form. Papers254,255 are devoted to the scavenging CsI melt by Mg2+ cations forming oxides having melting point ca. 2830°C.90 Such purification of the growth melt gives the possibility to enhance performance of the scintillator due to suppression of slow microsecond luminescence components. This method can be proposed for different halide melts which need deep purification from oxygen-containing admixtures. The effect of Y3+ is not so pronounced,256,257 since the melting point of Y2O3 is ca. 2430°C90 and according to the Shreder equation residual concentration of oxide admixtures is limited by the solubility of this oxide which is higher than MgO. The use of Eu2+ (melting point ca. 1980°C258) is not appropriate at all.259Although the solubility product of EuO in molten CsI is low enough (Ks, EuO=7.9×10-14 mol2 kg-2)251 its total solubility determined by the sequential addition method is ca. 4·10-4 mol·kg-1 that is enough to distort the luminescence properties of undoped CsI single crystals. We performed investigations of EuO solubilities in melts of NaI−NaBr system since recently Shiran et al.260 showed that NaI single crystal doped with Eu2+ was a good scintillation material which light yield achieved 30000 photons per MeV. Naturally, the effect of oxygen-containing admixtures on the behavior of Eu2+ ion in NaI melt should be clarified. Since modern trends in material science of scintillators are connected with the use of complex matrixes based on solid solutions the system NaI−NaBr also deserves attentive studying. We performed investigations of several solvents: NaBr−NaI (0.77:0.23)261-263 and NaBr−NaI (0.31:0.69),264 the generalized results could be found in our paper.265 The obtained data concerning EuO solubility and dissociation are presented in Table 9.2.11. Table 9.2.11. Parameters describing solubility and dissociation of EuO in melts of NaBr−NaI system at 700°C expresses via molality (m) and mole fraction (x) (xNaI the mole fraction of NaI in the melts). xNaI

pKs,EuO

Ks,EuO

m

m -2

pKsx,EuO

pKEuO

KEuO

x

m

m

pKx,EuO x -3

0.23

7.81±0.07

1.55×10

9.70±0.07

4.96±0.03

1.1×10

5.90±0.03

0.69

8.44±0.16

3.63×10-9

10.18±0.16

5.56±0.06

2.8×10-6

6.43±0.06

5.70±0.20

-6

6.52±0.20

1

8.65±0.13

2.2×10

-9

10.30±0.13

2.0×10

Data reflecting relation between ionic (Eu2+, O2-) and non-dissociated (EuO) forms of europium monoxide in melts of NaBr−NaI system are listed in Table 9.2.12. To facilitate the comparison of data obtained in different melts, the latter are presented in mole fraction scale.

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Table 9.2.12. Data on concentrations of Eu2+ and EuO in saturated solutions of EuO in melts of NaBr−NaI system at 700°C, mole fractions. xNaI

Concentration in saturated solution EuO

Eu

Dissociation degree

2+

α

Total solubility

0.23

1.6×10-4

1.42×10-5

0.081±0.010

1.75×10-4

0.69

1.79×10-4

8.2×10-6

0.044±0.015

1.87×10-4

-6

0.400±0.015

1.77×10-4

1

-4

1.7×10

7.1×10

These data show that non-dissociated EuO is the prevailing form in all the saturated solutions of europium monoxide in the molten bromide-iodide mixtures. Its concentration decreases going from NaI to the studied melt with the maximal content of bromide-ion that can be explained by the fact that dissolution of oxide without dissociation proceeds according to the so-called physical mechanism. That is, the oxide particles become embedded in the hollow spaces in solvents which sizes are close to those of particles of non-dissociated oxide. Since the crystal radius of bromide ion is smaller than that of iodide ion in the common case we can expect a sequential decrease of a number and sizes of the available hollow spaces with the rise of bromide ion concentration. In its turn this causes the decrease of EuO concentration in the saturated solutions and, hence, a reduction of the total solubility. As to the parameters concerning the ionization of EuO, it should be noted that the dissociation degree decreases with the rise of the iodide ion concentration in the melt, although for two the most iodide-rich melts the difference is statistically insignificant. The similar conclusion can be made on the basis of the concentrations of Eu2+ in the discussed saturated solutions. The observed effect can be explained using the Pearson's concept of hard and soft acids and bases (see subsection 9.2.1.1). The process of europium oxide dissociation in halide melts is accompanied with the formation of halide complexes of europium and oxo-complexes of sodium that can be expressed by the following simplified scheme: , 700°C

[9.2.148]

Taking into account the fact that all the above-discussed melts contain only Na+ cations, one can assume that the formation of the oxo-complexes occurs in approximately the same extent. EuO consists of hard acid (Eu2+) and hard base (O2-), bromide ion is an intermediate base and iodide belongs to soft bases. Going from this classification, 'hard-hard' Eu2+−O2- complex is the most stable form in saturated solutions of EuO. The formation of Eu2+−Br- complexes is not so advantageous and Eu2+−I- stability is the lowest in this sequence. Therefore, the addition of bromide ion to iodide melts should result in the increase of dissociation of the products formed by strong and intermediate Pearson's acids.

588

9.2 Acids and bases in molten salts, oxoacidity

9.2.5.3.6 Molten potassium halides There are a few papers devoted to the studies of metal oxide solubilities in molten potassium halides. In particular, Guyseva and Khokhlov reported the determination of the solubility product of MgO in molten KCl in the temperature range of 1067-1195K,266 the thermal dependence of the oxide solubility can be described by the following equation: [9.2.149] 2+

2−

The equilibrium concentration of Mg and O in the melt at 800°C equals to 2.1x10-6 mol kg-1. Similar investigation performed by the isothermal saturation method gave the total solubility of MgO at 800oC.267 Taking into account that the concentration of the non-dissociated oxide is 4.9x10-2 mol kg-1.267 The data gave the evidence of incomplete dissociation of magnesium oxide in molten KCl at 800oC.266 Recently, we have studied the oxide solubilities in molten KCl at 800oC.268 The results are presented in Table 9.2.13.. Table 9.2.13. Oxide solubility parameters in molten KCl at 800oC Oxide MgO

pKs, MeO, molalities

pKsx, MeO, m.fr.

9.32 ± 0.1

11.74

CaO

4.58 ± 0.2

6.84

SrO

3.04 ± 0.3

5.30

CoO

7.78 ± 0.2

10.04

NiO

8.59 ± 0.1

10.85

CdO

4.68 ± 0.1

6.94

CdO (pK)

2.23 ± 0.1

3.36

PbO

4.66 ± 0.2

6.92

PbO (pK)

2.44 ± 0.1

3.57

The data collected in this table show that the order of arrangement of oxides according to increase of their solubility corresponds to the similar dependences in the KCl−NaCl and CsCl−KCl−NaCl melts at 600 and 700oC. The performed study makes it possible to estimate the dissociation constants of PbO and CdO, which are close, therefore, it can assumed that the dissociation constants of oxides, having close solubility product values, are practically the same. The solubility parameters are close to those in the KCl−NaCl melt at 700°C. The dependences of the oxide solubility on the polarizing action of a cation by Goldschmidt can be approximated by the following equation: pK sx, MeO = 1.81 ( ± 1.2 ) + 0.161 ( ± 0.03 ) Z • e • r

-2 Me

o

2+

, 700 C

[9.2.150]

Both coefficients coincide with those for the KCl−NaCl melt (1.8±0.9 and 0.162±0.02, respectively), this means that the character of interaction between the metal

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

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cations and chloride ions remains unchanged within, at least, 100-200oC temperature range. We investigated solubilities of MgO and CaO in molten potassium halides at 800oC to elucidate the effect of anion composition of halide melt on metal oxide solubility.269 As for MgO, this oxide was found269 to be practically insoluble in chloride and bromide melts. The iodide melt was unavailable for investigation owing to the intense iodine evolution from strongly acidic solutions. On the contrary, CaO solubility products were successfully determined in all potassium halide melts at 800oC by the potentiometric titration method. The solubility parameter of CaO and MgO in molten potassium halides are presented in Table 9.2.14. The oxide solubility changes in molten potassium halides can be successfully explained in the framework of the HSAB concept. Indeed, Ca2+ ion belongs to hard acids, whereas chloride ion is a hard base, bromide ion is an intermediate base and iodide ion is a soft base. Therefore, the stability of calcium halide complexes should be reduced in the “chloride → bromide → iodide” sequence. Since increase of the halide complex stability results in elevation of the oxide solubility in melts, one should expect a decrease of solubility of CaO and other oxides in the “chloride → bromide → iodide” sequence that actually takes place. Table 9.2.14. Solubilities of CaO and MgO in molten potassium halides at 800oC (m.fr.) Parameter

KCl

KBr

KI

pKsx, CaO

7.09 ± 0.07

7.83 ± 0.04

12.35 ± 0.18

pKsx, MgO

11.74 ± 0.09

12.49 ± 0.09

−

9.2.5.3.7 Other solvents based on alkali metal halides Inyushkina et al.270 investigated MgO solubility in molten alkali metal chlorides: CsCl (700-850oC), KCl (820-1000oC), NaCl (850-1100oC) and RbCl (750-900oC). The study was conducted by the method of isothermal saturation. MgO was added to the melt in both forms of the ordinary commercial powder and pills pressed at p = 80 MPa and annealed at 1250oC. Saturation of the solution with respect to MgO solubility was achieved after 4 hours of keeping the oxide in contact with the melt.270 The solubility of the powdered MgO in molten KCl was 140-420 times larger than that of oxide subjected to pressing and preliminary thermal treatment. This was explained by the formation of suspensions in the solution in contact with the powdered oxide. The slope of the dependence of the solubility of MgO pressed in pills against the inverse temperatures is 3 times as large as that for the dependence of the solubility of the powdered oxide in molten KCl. In order to estimate the effect of cation composition of melts based on alkali metal halides on the metal oxide solubilities, we investigated the solubility of MgO in the following melts: KCl and CsCl at 800oC, NaCl (830oC) and molten CsCl−KCl−NaCl and KCl−LiCl eutectic mixtures at 800oC. The obtained solubility parameters are included in

590

9.2 Acids and bases in molten salts, oxoacidity

Table 9.2.15, where the oxoacidic properties of the chloride melts increase from the top to the bottom. Table 9.2.15. The solubility of MgO (pPMgO) in the molten alkali metal chlorides at ~800oC (m.fr.) Melt

pKsx, MgO

KCl

11.74 ± 0.09

CsCl

11.40 ± 0.12

CsCl−KCl−NaCl

11.44 ± 0.10

NaCl

11.22 ± 0.03

KCl−LiCl

7.87 ± 0.04

From the data in this table, it follows that the solubility products of MgO increase with the substitution of the low-acidic constituent cation by that possessing enhanced acidic properties. The increase in the concentration of constituent acidic cation in the melt causes an increase of MgO solubility in the KCl−CsCl−KCl−NaCl (CsCl)−NaCl sequence, where the concentration of Na+ and, hence, the melt acidity, increases. The solubility product index of MgO in the molten KCl−LiCl exceeds the corresponding values in the low-acidic chloride melts by approximately 3.5 pKsx, MgO units. This is in a good agreement with the data obtained at 600 and 700oC. Moreover, this difference shows that the relative acidic properties of ionic melts do not undergo a sharp change with the melt temperature elevation. Now let us review several investigations, which are not systematic, but they give an idea on metal oxide solubilities in several ionic melts. Smolenski et al.271 studied solubility of Cr2O3 in 2CsCl−NaCl melt at 843-1008K temperature range. They found that reaction of Cr3+ and O2− in the whole temperature range led to the formation of CrOCl and calculated the solubility product indices: 13.36±0.2 at 843K, 13.36±0.2 at 923K, and 10.32 ± 0.3 at 1008K. Woskressenskaja and Kaschtschejev performed one of the first studies of oxide solubilities in molten salts.196 The solubilities of oxides of calcium, magnesium, zinc, chromium(III) and copper(II) in molten sodium and lithium as well as potassium sulfates and chlorides were determined in the 700-1200oC temperature range. The solubilities of all studied oxides determined by the isothermal saturation method increased with the melt temperature increase. In the case of magnesium oxides, this was not reliably confirmed. The solubilities of the metal oxides decrease in the following order: CaO ≈ Cu(2)O > ZnO > MgO > Cr2O3. Dissolution of copper (II) oxide in the chloride melt is accompanied by its simultaneous oxidation with reduction of Cu (II) to Cu+. However, the total copper concentration in melts did not depend on the initial oxidation degree of copper in the oxide, i.e., the addition of CuO or Cu2O to the melt led to the same final distribution of copper at both oxidation stages. The eutonic CuO−Cu2O mixtures were formed. The data on solubility of CaO and ZnO in the chloride melts permit to follow the effect of the acidic properties of the melt constituent cation on the metal oxide solubilities.

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The ratio of solubilities in K+, Na+, and Li+-based melts is as follows: 1 : 1.5 : 15. The total solubilities are discussed and the obtained data are distorted by the contribution of appreciable concentrations of non-dissociated oxide, which is not sensitive to the melt acidity changes. It should be emphasized that, since we do not know the ratios of the ionized fraction to the non-dissociated fraction in the melts studied, we cannot quantitatively estimate the oxoacidic properties of these melts. The metal oxide dissociation was neglected because studies were conducted in 1923, whereas the Lux-Flood definition was formulated only in 1939. Therefore, the authors196 did not take into account the dissociation of the studied oxides in the molten salts, which decreased the significance of this investigation. Woskressenskaja and Kaschtschejev196 found some correlations of the metal oxide solubilities in the studied melts and the generalized ionic moments of oxide. The dependencies are non-linear and they are characterized by a considerable scattering of points. Grigorenko et al.272 investigated ZrO2 solubility in the molten KCl, KPO3, and KCl+KPO3 mixtures at 800oC. ZrO2 solubility has been shown in this work to be 1.34 wt% in pure KPO3, and in the equimolar KCl−KPO3 mixture it was 3.25 wt%. The main cause of the increase of ZrO2 solubility at decreasing KPO3 concentration in the mixed melt was explained by depolimerization of potassium metaphosphate that resulted in the strengthening of oxoacidic properties of the melt.272 If the concentration of KCl in the mixed melt exceeds 60 mol%, then the solubility of ZrO2 decreases sharply since the strengthening of potassium metaphosphate dissociation under such conditions cannot compensate the decrease of the total concentration of the Lux-Flood acid. The solubilities of nickel and thorium (IV) oxides in molten KF−LiF mixture at 550oC were investigated by the potentiometric titration method using a membrane oxygen electrode.273,274 The solubility product of NiO in the fluoride melt is equal to 1.3x10-6 (molality) that considerably exceeds the corresponding values in the chloride melts. The solubility of NiO seemingly increases owing to the fixation of Ni2+ cations in strong fluoride complexes. Gorbunov and Novoselov reported an investigation of the interaction of LaF3 and CeF3 with CaO and La2O3 in molten LiF−NaF (0.6:0.4) eutectic mixture.275 The solubilities of CaO and La2O3 at 800oC were 0.1 and 0.05 wt%, respectively. After determining these solubilities the authors added CaO and La2O3 to the solutions of the rare earth fluorides in the melt. The stoichiometry of these interactions was found by the analysis of the lanthanide (Ln) concentration after each CaO addition, as follows: [9.2.151] The solubility of LaOF in the melt equals to 0.8 wt% and that of CeOF is 1 wt%. The addition of CaO over the stoichiometry predicted by equation [9.2.147] leads to the following interaction: [9.2.152] Dissolution of La2O3 in the fluoride melt containing LnF3 results in the formation of LaOF and La2O3−LaOF solid solutions in the case of LaF3, and the mixture of

592

9.2 Acids and bases in molten salts, oxoacidity

2LaOF+CeOF composition in the case of CeF3. In this case, the phase composition of the precipitate was not examined. Deanhardt and Stern reported investigations on solubilities of CoO, NiO, and Y2O3 in molten NaCl and Na2SO4 at 1100K.276,277 The solubility products of oxides were found by the method of potentiometric titration to be (0.99±3.3)10-11 (Co3O4), (1.9±4.9)10-12 (NiO) and (1.4±2.2)10-36 (Y2O3) in the chloride melt (m.fr.). The corresponding values in the sulfate melt were as follows: (0.8±2.2)10-10, (1.6±8)10-11 and (4.5±6.4)10-31. With the excess of titrant, all oxides showed appreciable oxoacidic properties and fixed the oxide ions into oxo-complexes such as NiO2−, CoO2−, YO2−. A considerable increase of the calculated solubility products of the metal oxides in the sulfate melt as compared with chloride one confirms the assumption that the acidic properties of the studied cations are leveled to the acidity of SO3. Combes and Koeller studied solubility of CaO in molten NaCl at 1100, 1150 and 1200K by the sequential addition method.278 Temperature increase in the studied temperature range leads to a small increase in the CaO solubility from pKs, CaO = 4.3±0.3 at 1100K to 4.1±0.3 at 1150K, and to 3.9±0.3 at 1200K. The first value is in a good agreement with the data obtained in our works for CaO solubility in molten KCl at 800oC − 4.8±0.1, taking into account that the oxobasicity index of NaCl as compared with KCl is close to 0.5. The dependences of emf and the initial concentration of CaO had an inclined section corresponding to the unsaturated solution and a plateau (formation of the saturated solution of CaO). In addition to CaO solubility, the dissociation constants of hydroxide ion and the hydrolysis constant of NaCl, at the temperatures of the experiment, were determined. Their values at 1100K were 11.0±0.3 and 1.6±0.3, respectively. This shows that the strength of OH− as a strong Lux base increases with the temperature and with an increase of the melt acidity. A similar study of CaO solubility discussed in our papers162,279 helps to refine 278 data. Value of CaO solubility was obtained without additional calibration of the potentiometric cell with strong Lux bases,278 therefore, the solubility product of CaO was calculated using the initial molality of CaO corresponding to the onset of the plateau. The value of pKCaO at 830oC equals to 2.59±0.2. The solubility product of CaO in the chloride melt is estimated as pKs, CaO = 3.77±0.05, i.e., the solubility of CaO is somewhat higher than that obtained.278 The total solubility of CaO in molten NaCl at 830oC is 0.079 mol kg-1, whereas Ca2+ molality is 0.013 mol kg-1, and CaO molality is 0.066 mol kg-1. The degree of CaO dissociation in the saturated solutions equals to 16%. The total molality of CaO in the saturated solution is 0.079. The authors60 determined the solubility products of ZnO and K2ZnO2 in molten KCl at 800oC. They were 2.3x10-8 (ZnO) and 3.2x10-12 (K2ZnO2). 9.2.5.3.8 Oxide solubilities in melts based on alkali and alkaline earth metal halides The latest promising developments in material science of scintillators are connected with the creation of new Eu2+-doped halide materials possessing high light yield and excellent energy resolutions. The latter property makes them suitable for a series of high-precision experiments.

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Alkaline earth metal halides present the best matrixes for the europium doping since alkaline earth metal cations are isomorphic to Eu2+. An obvious disadvantage of individual alkaline earth halides lies in their high hygroscopicity which causes essential difficulties during the preparation of the raw materials, the process of crystals growth and shortens the term of use of the corresponding scintillators. Therefore, the mixed halides based on alkali and alkaline earth metal halides deserves intent attention since they are characterized by relatively low hygroscopicity. Such matrixes are available for Eu2+-doping since this cation substitutes alkali earth metal cations in the crystal lattice. The examples of new materials can be found in several recent publications.280-282 Oxygen-containing admixtures are very harmful for the mentioned scintillation materials since their existence leads to the fixation of Eu2+ ions in europium oxide which worsens the functional properties of the scintillators. The effect of these admixtures is dependent on the melts' acidities, which can be estimated on the solubility data. This forces investigators to perform studies of metal oxide solubility in mixed melts based on alkali and alkaline earth metal halides. These halide systems as solvents for oxides were practically never studied, although they are of great interest for practical purposes as media for electrochemical production of sodium and magnesium. Bocage et al. reported a study of MgO solubility in BaCl2− CaCl2−NaCl (0.235:0.245:0.52) melt at 600oC.80 According to their data, the solubility product index of MgO is pKs, MgO = 6.2±0.1. The initial section of the potentiometric titration curve includes a sharp pO decrease at small quantities of the base−titrant. This points to the fact that under these conditions the MgO solution is unsaturated. The treatment of data,80 accounting for the formation of the unsaturated solution, permits to estimate the dissociation constant of MgO in melts as pKMgO ≈ 4.6. This melt possesses the upper limit of basicity because of precipitation of CaO from the saturated solution. The solubility of CaO in the molten BaCl2−CaCl2−NaCl mixture is estimated to be 0.12±0.07 mol/kg. Authors283 investigated solubility of calcium oxide in the molten CaCl2−KCl−NaCl mixture at 650-750oC and found that the solubility of CaO (wt%) grew with a CaCl2 concentration in the studied melt. At a temperature of 700oC and within the range of 10-50 wt% of CaCl2, the solubility increases in the following sequence: 0.26 wt% (at 10% of CaCl2) 0.68 wt% (30% of CaCl2) 1.45 wt% (50% of CaCl2). The obtained solubility values are considerably lower than those in the CaCl2−CaO system, where the temperature elevation from 970 to 1030K causes the increase of CaO solubility from 2 to 10 wt%.284 Threadill reported on the solubility of CaO in molten calcium chloride, and examination of the process of electrochemical deposition of metallic Ca from the melt.285 The increase in concentration of oxygen-containing admixtures in melt retarded the process of formation of Ca powder by electrolysis. Castrillejo et al. studied solubility of several oxides in CaCl2−NaCl equimolar mixture. The solubility product of MgO in the molten CaCl2−NaCl equimolar mixture at 575oC was found68 to be pKs, MgO = 5.3±0.1 (molality). Investigations of the electrochemical behavior of Ti in the same melt at 500°C permitted to estimate of the solubility products of titanium oxides at lower oxidation degrees of Ti. They were (molality): pKs,TiO=9.01 and pK s, Ti O = 25.7.286 These data confirm that the dissociation of the tita2 3

594

9.2 Acids and bases in molten salts, oxoacidity

nium oxides in this melt is negligible, however, the non-dissociated oxides, owing to their low melting points, can dissolve in molten salts in appreciable amounts that was previously shown.287 Solubility products of several oxochlorides of rare-earth metals (LnOCl) at 550°C have been estimated.214 Their dissolution occurs according to Eq. [9.2.132]. The pKs, LnOCl values were (molality): 5.19±0.05 for LaOCl, 5.62±0.07 for CeOCl, 5.80±0.31 for NdOCl and 5.46±0.08 for PrOCl. The pKs values are lower than in KCl−LiCl eutectic that shows essentially higher acidity of Ca2+-containing chloride melt. Strelets and Bondarenko studied interaction between MgCl2 and CaO in carnallite (KMgCl3 having melting point of 488oC) melt:288 [9.2.153] 45

using the radiochemical method, which consisted in the addition of Ca isotope to the ordinary CaO. The investigation of different layers of the carnallite melt after the interaction showed that the distribution of 45Ca and, consequently, Ca2+ was uniform in all layers, whereas Mg concentration was equal zero in the upper layers and was found only on the precipitate, which was pure MgO. As it can be estimated from the thermodynamic calculations, the equilibrium constant of [9.2.153] varies within 106-107 range at 700-800oC, the complete transformation of MgCl2 in MgO was achieved under the experimental conditions (action of the stronger Lux base). Equilibrium [9.2.149] was studied in the so-called calcium electrolyte consisting of 10 wt% of MgCl2 + 34 wt% of CaCl2 + 50 wt% of NaCl + 6 wt% of KCl used for the deposition of metallic calcium by electrolysis of melt. The addition of 1-3 wt% CaO to melt leads to its complete transformation into CaCl2 with precipitation of equivalent quantity of MgO. This means that MgCl2 suppresses formation of CaO due to pyrohydrolysis. The rate of interaction of MgCl2 with oxygen-containing admixtures considerably affects the sizes of the formed MgO crystals. In the case of the interaction of melts with moisture, or because of addition of CaO (slow interaction), finedispersed particles of MgO are formed (their sizes are of the order of 1 μm), whereas pyrohydrolysis of MgCl2 containing melts without calcium results in the formation of relatively large (~20-30 μm) MgO crystals. In authors' opinion, this means that fine-dispersed crystals are formed owing to the intermediate formation of CaO in the process of pyrohydrolysis. There is also another explanation of this effect: the presence of acidic cations of calcium in melt slows down the formation of the solid oxide phase that results in the formation of crystals of smaller sizes. We studied solubility of some metal oxides in the chloride melts based on alkali metal salts with the addition of approximately 25 mol% of alkaline earth metal chlorides (CaCl2, SrCl2 or BaCl2). The solubility of MgO and NiO in the molten CaCl2−KCl (0.235:0.765) mixture at 700oC was determined.84 The range of oxides available for the potentiometric investigations in this melt was very narrow owing to the leveling of the acidic properties of the metal cations: the acidic properties of Cd2+, Sr2+, Ba2+, Pb2+ were leveled undoubtedly, the solubilities of ZnO, MnO should be very high. Both studied oxides are practically insoluble in the chloride melts even of relatively high acidity. Their solubility product indices (molality) are as follows: pKs,MgO = 5.34±0.2 and pKs,NiO=5.24±0.2. The value of pKs,CaO equals 0.72±0.2.

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

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The solubilities of metal oxides in the molten SrCl2−KCl−NaCl (0.22:0.42:0.36) mixture at 700oC were determined by the potentiometric titration method.85 The increase of the solubility products of the studied oxides as compared with the molten KCl−NaCl equimolar mixture were caused, mainly, by the strengthening of the Sr2+-containing melt acidity. As seen from the data of Table 9.2.16, they are practically the same. All solubility products undergo small fluctuations about the average value of +1.95 logarithmic units. The latter was the oxobasicity index of the SrCl2−KCl−NaCl melt at 700oC. The titration of Pb2+ cations with quantities of a strong Lux base did not result in precipitation of PbO from the melt and determination of the solubility product of PbO failed. Hence, PbO solubility is high enough and the solutions remain unsaturated at all titrant weights. However, it is possible to estimate the dissociation constant value of PbO as pKPbO = 2.58±0.05. The oxobasicity index of the Sr2+-containing chloride melt is in a good agreement with the values of the dissociation constant indices of SrO in the molten KCl and CsCl−KCl−NaCl mixtures at 700oC, which are equal to 2.30 and 2.14, respectively. Table 9.2.16. Solubility products of some oxides in molten SrCl2−KCl−NaCl at 700oC. Oxide MgO

pKs,MeO, molality

pKsx, MeO, m.fr.

7.61 ± 0.06

9.63

NiO

7.44 ± 0.09

9.56

CoO

6.25 ± 0.12

8.37

MnO

5.20 ± 0.17

7.32

ZnO

4.97 ± 0.07

7.09

CdO

3.21 ± 0.07

5.33

The dependence of the solubility product values on the polarizing action of a cation by Goldschmidt in SrCl2-KCl−NaCl− melt is approximated by the equation: , 700 °C

[9.2.154]

The slope of this dependence is close to that for the KCl−NaCl equimolar mixture (0.162), and this confirms again an assumption that the interaction of “multivalent metal cation−chloride ion” is subjected to small changes following the change of cation in melt. Cherginets et al. determined MgO solubility in melts based on potassium and strontium chlorides of the following compositions K2SrCl4289 and KSr2Cl5290 which correspond to congruent or quasi-congruent compounds prospective as matrixes for the growth of single crystal of Eu2+-activated luminescent materials. The values of the solubilities in mole fraction scale 9.29±0.13 and 8.37±0.02, respectively. The solubilities of metal oxides in molten chloride mixtures with the addition of Ba2+ cations were determined by the potentiometric titration technique.86,87 The solubility products of MgO, NiO, CoO, MnO, ZnO, CdO in the BaCl2−KCl−NaCl (0.43:0.29:0.28) melt were found to be considerably higher than those in the molten KCl−NaCl equimolar mixture. The titration of Ca2+ cations with KOH in the melt does not result in CaO precipita-

596

9.2 Acids and bases in molten salts, oxoacidity

tion, although, according to the titration data, Ca2+ cations have appreciable oxoacidic properties. The data on the oxide solubility in the molten BaCl2−KCl−NaCl mixture is included in Table 9.2.17. Table 9.2.17. Solubility products of some oxides in molten BaCl2-KCl-NaCl at 700oC. pKs, MeO, molality

pKsx, MeO, m.fr.

MgO

7.97 ± 0.12

9.76 ± 0.12

NiO

7.47 ± 0.11

9.26 ± 0.11

CoO

6.33 ± 0.12

8.12 ± 0.12

MnO

5.59 ± 0.06

7.38 ± 0.06

ZnO

5.18 ± 0.06

6.97 ± 0.06

CdO

3.64 ± 0.13

Oxide

CaO

5.43 ± 0.13 pK = 2.65 ± 0.12

Similar to melts based on alkali metal chlorides, a tendency to the increase the oxide solubility along with the increase of the radius of the oxide cation is also observed in the Ba2+-based melts: pK sx, MeO = 1.14 ( ± 2.5 ) + 0.140 ( ± 0.08 ) Z • e • r

-2 Me

2+

[9.2.155]

The slope of this dependence is close to that of a similar plot obtained in the molten KCl−NaCl equimolar mixture. The increase of the metal oxide solubilities in the Ba2+based melt as compared with the KCl−NaCl melt (see Table 9.2.14) demonstrates that the oxoacidic properties of the Ba2+ cation are considerably stronger than those of K+ or Na+ cations. It should be added that the value of the dissociation constant of BaO in the molten KCl−NaCl was determined218 to be 81. The logarithm of the latter magnitude equals to 1.91 that is very close to 1.84 and to the oxobasicity index of the BaCl2−KCl−NaCl eutectic, which is 2.01 as it has been previously pointed out. Comparison of this data with the results for Sr2+-based melts shows that the oxobasicity indices of SrCl2−KCl−NaCl and BaCl2−KCl−NaCl melts are practically the same: 1.95±0.3 and 2.01±0.3, respectively, although in the latter case the concentration of alkaline earth metal cation is approximately two times as high as in the former case. Following conclusion can thus be made: the acidic properties of the Ba2+ cation are weaker than those of Sr2+. To confirm this without any doubts let us study the Ba2+-based melt in more detail. We reported the investigation of the solubility of ZnO and CdO in the molten BaCl2− KCl (0.26:0.74) eutectic.87 The former oxide was studied by the potentiometric titration method, and it was practically insoluble in the melt, whereas the latter oxide was not only found to be soluble. It did not have acidic properties in unsaturated solutions in Ba2+based melt. The oxoacidic properties of Cd2+ are comparable with those of Ba2+ oxide. The results of the oxide solubility determinations, which are presented in Table 9.2.18, permit to estimate the relative oxoacidic properties of both Ba2+-containing melts:

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

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the corresponding oxobasicity indices are equal to 2.01 for the molten BaCl2−KCl−NaCl eutectic and 1.83 for the BaCl2−KCl (0.26:0.74) melt. This shows that increasing concentration of the acidic cation in melt gives rise to the strengthening of the melt acidity, which leads to the increase of metal oxide solubility. Table 9.2.18. Solubility products of ZnO and CdO in some BaCl2-based melts at 700oC. Oxide

pKs, MeO (molality) BaCl2−KCl

pKsx, MeO (m.fr.) BaCl2−KCl

BaCl2−KCl−NaCl

ZnO

5.14 ± 0.1

7.14

6.97

CdO

3.62 ± 0.1

5.62

5.43

Concluding the consideration of oxide solubility studies in the molten BaCl2-based chloride mixtures, the results of Ivenko et al., who studied the solubilities of BaO, CuO and Y2O3 in this melt in the temperature range of 920-1200K, should be mentioned.291,292 The choice of the objects of the investigation was related to the development of superconductive materials which was one of the most fashionable directions at that time. YBa2Cu3O7-δ is considered among the most promising superconductor compounds293,294 and the methods of its synthesis (and co-precipitation from melts) were extensively studied. The solubilities of oxides in the Ba2+-based melt were appreciably higher than those in the molten KCl−NaCl eutectic, e.g., CuO solubility was 1.3 mol% at 1073K and 1.6 mol% at 1123K. BaO is more soluble in the melt and its solubility increases with the temperature as follows: 13-19 mol% at 973K, 16-20 mol% at 1073K and 20-22 mol% at 1173K. Y2O3 has the smallest solubility among the mentioned oxides, it is only of the order of 0.01 mol%. It should be added that investigations of CuO have no relation to the equilibrium [9.2.156] since Cu2+ ions dissolved in the melt are subjected to reduction by chloride ions, resulting in the formation of Cu22+ ions (or Cu+) and chlorine evolution. It means that the system of composition (Cu2O + CuO)−(CuI + CuII) ions was studied. As for the solubility of BaO in the molten BaCl2−KCl−NaCl eutectic, it permits to determine the upper limit of oxobasicity in this melt, which equals to pO = −0.3. If we recalculate this value with respect to the common oxoacidity function Ω then it will be near Ω = 2. After the onset of the solid phase precipitation, there is a small change of oxide ion concentration in the melt that is explained by the formation of barium oxochloride according to the following reaction: [9.2.157] Going from the data on oxide solubility in melts based on alkaline earth metal chlorides we estimated the relative oxoacidic properties of all the above-mentioned chloride melts. The melt acidity was estimated as the oxobasicity index pIL according to the following equation:

598

9.2 Acids and bases in molten salts, oxoacidity

[9.2.158] where: '*' and 'L' 11.62

are referred to KCl-NaCl and the studied melt, respectively pKsx,MgO in KCl-NaCl reference melt

The dependences of the oxobasicity indices of the chloride melts containing alkaline earth metal chlorides vs. logarithm of mole fraction of the alkaline earth metal chloride are presented in Fig. 9.2.11. It can be seen from this Figure that the increase of the concentration of alkaline metal cation in the chloride melts causes monotonous strengthening of their oxoacidic properties. However, the slopes of dependences for Ca2+, Sr2+ and Figure 9.2.11. The dependence of the oxobasicity index pIL vs. Ba2+ cations are essentially differlogarithm of mole fraction of the alkaline earth metal chloride in mixed melts of alkali and alkaline earth metal chlo- ent. The explanation of the coorrides: 1 − SrCl2-based melts, 2 − BaCl2-based melts, 3 − CaCl2based melts. dinate choice for Fig. 9.2.11 and the obtained slopes is following. Let us consider the process of oxide ions solvation in a melt of KCl(or NaCl)−MeCl2 (Me=Ca, Sr, Ba): [9.2.159] (all the concentrations are equilibrium ones). The equilibrium constant for this reaction is presented as follows: [9.2.160] Then let us perform some transformations taking into account that practically all oxide ions are fixed in the complexes, i.e., mc is the constant: [9.2.161] [9.2.162]

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

599

Since the initial molality of oxide ion is constant the changes of to changes of pIL, so:  ∂ ( – log m O 2- )  ∂ pI L  =  -------------------------- = n  ------------------------------- 0  ∂ log m Me2+  p, T, mc, mO2 ∂ log m Me2+ p, T, mc, m0 2-

is equal

[9.2.163]

O

So, the slope of should be equal to the average amount of Me2+ 2in the complexes with O . It means that in Ba2+-based chloride melts the formation of BaO occurs due to the solvation of O2- ions (tgα = 1) and in Sr2+-based ones the solvation leads to the formation of 2SrCl2·SrO (tgα = 3). As to CaCl2-based melts it should be noted that the phase diagram of CaCl2−CaO system is well-studied. According to the data of Perry and Macdonald295 congruent compound of 4CaCl2·CaO composition is formed that should correspond to tgα =5. Wenz et al.296 detected that only incongruent 2CaCl2·CaO is formed in this system and in this case tgα should be equal to 3. Using these data to explain the fact that the value of tg being intermediate between 3 and 5 one can conclude that in CaCl2-based melts the solvation of oxide ion leads to the formation of both complexes: 4CaCl2·CaO and 2CaCl2·CaO. Concluding discussion of metal oxide solubility in molten ionic halides, it should be mentioned that investigation of cerium (III) oxide solubility in melts of KCl−NaCl−CeCl3 mixtures studied by Combes et al.57,297 is of interest for preliminary purification of growth melts for new scintillation materials LnX3:Ce (La, Gd, Lu) and MenLnX3+n (La,Gd, Lu) discovered by Van Eijk et al.298 The raw materials used for the synthesis and growth of scintillators from the melt are exposed to pyrohydrolysis with formation of the corresponding oxide deposits or inclusions (Ln2O3, or CeO2 in the case of cerium in the presence of oxygen traces in the atmosphere over the growth melt). These contaminants can exist both in liquid and in solid state that worsens optical and scintillation properties of lanthanide halide-based materials. The increase in LnX3 concentration results in the rise of the solubility of the corresponding oxide in melts. The solubility values exceed 0.5 wt% at the concentration of CeCl3 of the order of 30 mol%. It shows that the homogeneous melt used for the growth of the scintillation crystals may contain an appreciable concentration of oxides of lanthanides (near 1 wt%). Cooling this melt may result in precipitation of oxide or oxochloride from a melt that creates a number of crystallization centers,

9.2.6 ON SOME PRACTICAL APPLICATIONS OF OXOACIDITY IN MOLTEN HALIDES Finishing the consideration of features of Lux-Flood acid-base interactions in molten salts let move on to the peculiarities of application of the said theoretical data for resolving different basic and technological problems. Most of all it will concern deep purification of molten halides from traces of oxygen-containing admixtures - so-called 'deoxidization' process. The deoxidization is used in the cases if oxygen-containing admixtures effect negatively processes running in the melts (mainly, the electrochemical ones) or worsen the

600

9.2 Acids and bases in molten salts, oxoacidity

quality of the final product obtained from halide melt (optical or acoustical single crystals). Although we had recently published a monograph devoted to some aspects of the deoxidization299 this direction obtained essential development during last years and it makes sense to perform the generalization of its most urgent aspects. Deoxidization process consists in the removal of oxygen-containing admixtures from the melt into gaseous (treatment in reactive gas atmosphere) or solid (precipitation deoxidization) phase. As for the treatment in reactive gaseous media, this variant is more drastic comparing with the precipitating deoxidization since oxygen-containing admixtures are removed into gas phase and further pass away from reaction zone by the flow of inert gas. The precipitation deoxidization results in the formation of oxide precipitate which remains in contact with the melt, therefore, under a definite conditions the solid phase can dissolve in the purified melt. Let us consider these variants in more detail. 9.2.6.1 Deoxidization of halide melts under the action of reactive gas atmosphere The treatment of molten halides by gaseous halogenating agent can be performed with the use of the following halogen-containing substances: free halogens (this way of the deoxidization will be more effective in the case of addition of carbon, formation of carbon suspension in the melt, see Eq. [9.2.121]), halogen halide (Eq. [9.2.117]) or halogenated derivatives of alkanes (HDA). Further let us stay of some features of the running of these processes in time. 9.2.6.1.1 The use of hydrogen halides. It should be mentioned again that there are some disadvantages of the practical use of HX for the purification. First of all, the main purpose of the deoxidization is to remove oxide ions formed due to pyrohydrolysis of halide melts consisting of salts that are hygroscopic at room temperature. However, HX application for the deoxidization process [9.2.117] results in the formation of water which can be captured by the melt and cause the reverse process (hydrolysis) after the finishing of the process. Furthermore, hydrogen halides are referred to very strong corrosive gases causing damaging of metallic parts of the experimental equipment. Nevertheless, the treatment with HX remains the only possible method of iodide melts' purification since both iodine and iodine-derivatives of alkanes with high content of iodine are slightly volatile that leads to considerable difficulties in experiment design and slows down the purification process due to the low pressure of the halogenizing agent. We used HI for the purification of molten CsI with the content of O2- impurities ca.10-4 mol kg-1 at 700°C and found that under such conditions the rate of purification was so high that the corresponding kinetic parameters could not be detected by a potentiometric method (the pO value increased from 4 to 9 was during 30-40 sec). Some data concerning the running of the halogenation process can be obtained from paper300 which authors studied the process of CeOCl dissolution in molten KCl−LiCl eutectic at 450°C and molten CaCl2−NaCl equimolar mixture at 550 °C. The data presented in Figure 9 in the paper300 can give us illustration of some kinetic aspects of the

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

601

deoxidization process [9.2.117] in melts containing merely acidic constituent cations (Li+ and Ca2+). To obtain the necessary information the mentioned graphs were digitized. It is obvious that the process of CeOCl solubilization (solid+dissolved) using HCl (gas) is heterogeneous process and, hence, it can be referred to the complex processes from viewpoint of chemical kinetics. So, a problem arises: how to divide the separate stages of this process and analyze them. Therefore, before the discussion of the results300 we Figure 9.2.12. The illustration of the use of Lagrange mean value theorem for calculation of the chemical process order: c1, c2, and c3 would like to mention the solution the reagent concentration at times t1, t2, and t3, respectively. proposed in our work just for treatment of melt by gaseous halogenating agent. It consists in the building of van't Hoff diagrams to divide a kinetic plot into sections which are characterized by different kinetic orders. As is known the kinetic order for any reactions can be determined from the van't Hoff equation: [9.2.164] where: w1 and w2, c1 and c2 reaction rates and reagent concentrations at times t1 and t2, respectively.

This equation gives the possibility to calculate the reaction order for two points. For arbitrary section linear in log w − log c coordinates the reaction order is equal to the slope of this dependence: [9.2.165] which can be estimated using the least squares method. The definite complication of this routine consists in the fact that the reaction rate is the derivative which value can be preliminary found. For the reaction order estimation we proposed the use of the Lagrange mean value theorem which essence is shown in Figure 9.2.12. In respect to our case it may be formulated by such a manner. Since the concentration of oxide ion c is continuous function defined in [t1, t3] time interval there exist the point c2 corresponding to time t2 in this interval such that:

602

9.2 Acids and bases in molten salts, oxoacidity

[9.2.166] We ascribed the value w to the concentration c2 which is equal to [9.2.167] since the curves c=f(t) are smooth; the differences between neighboring emf (and, log c) values and the corresponding time intervals are small. An example of such a dependence for the process of CeOCl dissolution (solubilization) in molten KCl−LiCl eutectic under the action of gaseous HCl at 450°C is presented in Fig. 9.2.13. It can be seen from Figure 9.2.13 that the process of CeOCl solubilization in molten KCl−LiCl eutectic can be conditionally divided into 3 sections. The 1st section is referred to the reaction of HCl with oxide ion in melt, here the dissolution of CeOCl does not effect the running of the process. Figure 9.2.13. The dependence log w = f(log c, oxide-ion) for the Since there are data only for O2process of CeOCl dissolution (solubilization) in molten KCl−LiCl concentration, one can speak only eutectic under the action of gaseous HCl at 450°C, the limiting stages: 1 − initial, the process [9.2.117], 2 − process of CeOCl dis- about pseudo-order of reaction solution, 3 −- reaction [9.2.117] in KCl−LiCl−CeCl3 melt. [9.2.117] with respect to oxide ion. It is equal to 1 (1.03±0,11) that correspond to the reaction stoichiometry. The rate constant of reaction [9.2.117] can be estimated from ln c = f(t) slope as 0.26±0.01 min-1. This value means that the treatment with HCl provides the reduction of O2− concentration in the said melt by a factor of 10 during 9-10 min. This value can serve as the starting point for estimation of kinetics of deoxidization of mere acidic melts by action of HCl. As for the stages 2 and 3 it should be noted that the former concerns dissolution of CeOCl in the melt during the permanent decrease of oxide ion concentration. The transition of the oxochlorides from the solid phase into liquid one is the rate-determined process. In the case of unchanged surface area of CeOCl this reaction should possess zero order, however the dissolution reduces the square and reaction has the non-integral order between 0 and 1. The stage 3 is referred to the reaction of oxide ion KCl−LiCl−CeCl3 melt with HCl, here the rates of purification of the melt and its contamination with O2− from the container material and atmosphere equalize. This results in the non-integral order between 1 and 2.

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

603

9.2.6.1.2 The action of 'C+X2' red-ox couple, carbohalogenation. The action of 'C+X2' couple is following. The halogen passing provides the oxidation of oxide ions to oxygen according to reaction [9.2.168] and O2 reacts with carbon forming CO or CO2: , n=1, 2

[9.2.168]

Since the equilibrium of the above reaction is shifted to the right side as it is usual for the carbohalogenation temperatures (1000 K, for n=1, ΔG = −4.23 kJ mol-1) this causes additional shift of the equilibrium [9.2.168] to the right. The practical implementation of the carbohalogenation consists in either halogen passing through the melt containing suspension of carbon or bubbling a gaseous substance which is theoretically able for the decomposition with the formation of C and free halogen. HDA can serve as precursor for formation of 'C+X2' couple and, in contract to HX they are not corrosive. Since the HDA can contain hydrogen the increase of H content favors the volatility of these halogenating agent. However, hydrogen-rich HDA are disposed to coalification at high-temperatures and a part of halogen forms the corresponding hydrogen halide. For preliminary estimation of mechanism of HDA action it will be useful to consider the decomposition schemes of arbitrary halogen derivative of CkHmXn composition. There are three cases of m and n ratio, as it is presented below:

[9.2.169] The first case takes place if a number of hydrogen atoms in HDA molecule is more than number of halogen atoms (m>n). In this case the decomposition leads to the formation of carbon and hydrogen halide together with hydrocarbons (prone for the following coalification) and the purification occurs according to the acid-base mechanism described in the previous subsection and its efficiency is not high. The main disadvantage of such a purification consists in the considerable contamination of the purified melts with carbon which forms suspensions in the melt. The use of HDA of this kind seems to be worse than simple treatment by HX. The similar situation arises in the case of m=n and carbon and hydrogen halide are only products of the decomposition. Such a halogen-derivative also acts as acid-base purifying agent. As for the usability of CkHmXn substances with m≥n for the purification, it should be concluded that they are appropriate for the treatment of melts based on alkali and alkaline earth metal halides and their mixtures. Rare earth halides are practically out of range of melts which can be efficiently purified from oxide ion traces by these halogenderivatives. And, finally, one can expect that a halogen-derivative compound will react according to red-ox mechanism only in the case of m723

-361.5

-361.5

-189.7

+

Cs

Cs2O

763

-317.0

-317.0

-233.2

Ca2+

CaO

2900

-635

-635

84.8

2+

Sr

SrO

2933

-590.5

-590.5

40.3

Ba2+

BaO

2290

-548

-548

2.2

Ti

Ti2O3

2115

-1518

-506

-44.2

TiO2

2143

-944

-472

-78.2

Ta

Ta2O5

2161

-2047

-409

-141.2

Zr

ZrO2

2983

-1100.3

-550.2

0

Hf

HfO2

3053

-1117

-557.5

7.3

Th

ThO2

3623

-1226.4

-613.2

63.0

As for the getters, their efficiency will increase in the following sequence: Ta−Ti− Zr(≈Hf)−Th from the viewpoint of both the enthalpy of the oxide formation and the melting points of the corresponding oxide. The estimations of Δ(ΔH) show that the use of getters will be the most effective in the case of cesium, rubidium or potassium halides, their efficiency for the purification of sodium halides is considerably lower. This gives the possibility to state that for the effective purification Δ(ΔH) values should be ca. 200 kJ mol-1. Molten halides of alkaline earth metals cannot be purified from oxide ion traces with the application of the getters. These predictions were confirmed by the corresponding investigations performed in CsI and NaI melts. The purity degree was determined by both potentiometric method (melt) and spectral methods (optical crystals). It was found later that the use of 'Zr−Pt' galvanic couple essentially increased the efficiency of the purification in comparison with the single getter. The residual concentration of oxide ions was ca. 10-8 mol kg-1 (vs. 10-4 mol

Victor Cherginets, Tatyana Rebrova, and Alexander Rebrov

611

kg-1 for the single metallic getter) and the surface capacity of the getter with Pt was considerably higher.320,321 From the Table 9.2.21 it follows that thorium is the best possible getter. However, it cannot be used for the purification of the growth melts for scintillation crystals since one of the products of its decay is mesothorium (228Ra) which gives 4 decays in 1 mg of Th per second. Since 228Ra is typical alkaline earth metal its following separation from the melt seems more difficult. The use of metals-getters should be recommended for various purposes since the excess of the metal-getter is not soluble in the treated halide melt. It should be especially emphasized, however, that all the conclusions made for the case of the metals-getters are not true in molten fluorides since the interaction of the latter with the entered metal leading to the formation of extremely stable fluoride complexes can be very intensive.

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USSR, No 27, 61 (1978). 226 N.M. Barbin, V.N. Nekrasov, L.E. Ivanovskii, P.N. Vinogradov and V.E.Petukhov, Rasplavy, No 4, 117 (1990). 227 N.M. Barbin, V.N. Nekrasov, L.E. Ivanovskii, 5th Int. Symp. Solubility Phenomena, Moscow, Russia, 1992, p. 64-65. 228 N.M. Barbin and V.N. Nekrasov, Electrochim. Acta, 44, 4479 (1999). 229 Y. Kaneko and H. Kojima, Denki Kagaku, 42, 304 (1974). 230 V.L. Cherginets, Functional Materials, 4, 109 (1997). 231 V.L. Cherginets, Electrochim. Acta, 42, 3619 (1997). 232 V.L. Cherginets, Uspekhi Khimii, 66, 661 (1997). 233 H.A. Laitinen and W.E. Harris, Chemical analysis, 2nd edition, McGraw-Hill Company, London, 1975. 234 V.L. Cherginets, T.G. Deineka, O.V. Demirskaya and T.P. Rebrova, Estimation of interface energy of 'metal oxide/ionic melt' system from data on lead oxide solubility in molten KCl-NaCl eutectic, Prepr., Chemistry Preprint Server, http://preprint.chemweb.com/physchem/0103006 Uploaded 2 March 2001, 3p. 235 V.L. Cherginets, T.G. Deineka, O.V. Demirskaya and T.P. Rebrova, J. Electroanal. Chem., 593, 171 (2002). 236 V.L.Cherginets,O.V. Demirskaya,T.P. Rebrova. On solubility of alkaline earth carbonates in molten KCl-NaCl at 700 °C, Prepr., Chemistry Preprint Server, http://preprint.chemweb.com/physchem/0111003, Uploaded 5 November 2001, 2p. 237 T.P. Boyarchuk, E.G. Khailova and V.L. Cherginets, Electrochim. Acta, 38, 1481 (1993). 238 V.L. Cherginets and E.G. Khailova, Zhurn. Fiz. Khim., 66, 1654 (1992). 239 V.L.Cherginets and E.G.Khailova, Zhurn. Neorg. Khim., 38, 1281 (1993). 240 V.L. Cherginets, T.P. Rebrova, J. Chem. Thermodynam., 54, 429 (2012). 241 O.V. Demirskaya, E.G. Khailova and V.L. Cherginets, Zhurn. Fiz. Khim., 69, 1658 (1995). 242 V.L. Cherginets and E.G. Khailova, Ukr. Khim. Zhurn., 62, 90 (1996). 243 V.L. Cherginets, V.A. Naumenko and T.P. Rebrova, Problems of Chemistry and Chemical Technology, No 2, 41 (2014). 244 V.L. Cherginets, T.P. Rebrova and V.A. Naumenko, Zhurn.Fiz.Khim., 88,1345 (2014). 245 T.P. Rebrova, V.L. Cherginets and V.A. Naumenko, Zhurn. Neorg. Khim., 59, 534 (2014). 246 V.L. Cherginets, T.P. Rebrova and V.A. Naumenko, J. Chem.Thermodynam., 74, 216 (2014). 247 V.L. Cherginets, E.G. Khailova and O.V. Demirskaya, Zhurn. Fiz. Khim., 71, 371 (1997). 248 T.P. Rebrova, V.L. Cherginets, N.V. Rebrova and Yu.N. Datsko, Zhurn. Neorg. Khim., 55, 1224 (2010). 249 V.L. Cherginets, K.N. Belikov, Yu.N. Datsko, Yu.I. Dolzhenko, E.N. Kisil, N.N. Kosinov, T.P.Rebrova and E.E. Voronkina, Functional Materials, 17, 334 (2010). 250 V.L. Cherginets, T.P.Rebrova, Yu.N. Datsko, K.N. Belikov and E.Yu Bryleva, Ukr. Khim. Zhurn., 76, 99 (2010). 251 V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, T.G. Deineka, E.N. Kisil, N.N. Kosinov and E.E. Voronkina, J. Chem. Eng. Data, 55, 5696 (2010). 252 V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, V.A. Shtitelman and E.Yu. Bryleva, J. Chem. Thermodynam., 43, 1252 (2011). 253 S. Kubota, S. Sakuragi, S. Hashimoto and J. Ruan. Nucl. Instrum. Methods Phys. Res., Sect. A, 268, 275 (1988). 254 V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, V.F. Goncharenko, N.N.Kosinov and V.Yu. Pedash, Mater. Lett., 65, 2416 (2011). 255 V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, V.Yu. Pedash and N.N.Kosinov, Visn. Hark. Nac. univ., Ser. Him., 20(43), 121 (2011). (http://chembull.univer.kharkov.ua/archiv/2011/13.pdf). 256 V.L. Cherginets, Yu.N. Datsko, T.P. Rebrova, V.Yu. Pedash, R.P. Yavetrky and S.V. Parkhomenko, Visn. Hark. Nac. univ., Ser. Him., 21(44), 308 (2012). (http://chembull.univer.kharkov.ua/archiv/2012/35.pdf). 257 V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, T.V. Ponomarenko, R.P. Yavetsky, V.Yu. Pedash, Cryst. Res. Technol., 48, 16 (2013). 258 Chemical Encyclopedia, in 5 vol, A.I.Knunyantz, Ed., V.3, Sovietskaya Entsyklopediya, Moscow, 1990. 259 V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, V.F. Goncharenko, N.N. Kosinov, R.P. Yavetsky, V.Yu. Pedash, Cryst. Res. Technol., 684 (2012). 260 N. Shiran, A. Gektin, Y. Boyarintseva, S. Vasyukov, A. Boyarintsev, V. Pedash, S. Tkachenko, O. Zelenskaya and D. Zosim, Optical Materials, 32, 1345 (2010). 261 T.P. Rebrova and V.L. Cherginets, Problems of Chemistry and Chemical Technology, No 3, 45 (2015). 262 V.L. Cherginets, T.P. Rebrova and Yu.N. Datsko, In Modern Problems of Electrochemistry: Education, Science, Industry, NTU KhPI, Kharkov, 2015, pp.228-229.

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V.L. Cherginets, T.P. Rebrova, A.L.Rebrov and O.I. Yurchenko, Phys. Chem. Liq., 55, 248 (2017). T.P. Rebrova and V.L. Cherginets, Rasplavy, No 5, 66 (2015). V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko and A.L. Rebrov, J.Chem.Thermodynam., 91, 136 (2015). L.T. Guyseva and V.A. Khokhlov, Abstr. 5th Int. Symp. Solubility Phenomena, Moscow, Russia, 1992, p. 69. S.F. Belov and G.D. Seredina, Izv. vuzov. Tsvet. Metall., No 4, 19 (1990). V.L. Cherginets, T.P. Rebrova and M.A. Sorotchan, Zhurn. Neorg. Khim., 50, 1717 (2005). V.L. Cherginets, O.V. Demirskaya and T.P. Rebrova, Electrochem. Commun., 2, 762 (2000). T.L. Inyushkina, L.I. Petukhova and V.T.Kornilova, Zhurn. Neorg. Khim., 20, 1058 (1975). V.V. Smolenski, A.V. Novoselova, Ya.M. Luk'yanova, A.A. Mayorshin, A.G. Osipenko, M.V. Kormilitsyn, Electrochim. Acta, 55, 4960 (2010). F.F. Grigorenko, A.V. Molodkina, V.M. Solomakha and M.S. Slobodyanik, Visnyk Kyivskogo Universitetu, Ser. Khim., No 14 38, 81 (1973). Y. Ito, H. Hayashi, Y. Itoh and S. Yoshizawa, Bull. Chem. Soc. Jpn., 58, 3172 (1985). Y. Ito, Proc. Electrochem. Soc., 86, 445 (1986). V.F. Gorbunov and G.P. Novoselov, Zhurn.Neorg.Khim., 19, 1734 (1974). M.L. Deanhardt and K.H. Stern, J. Electrochem. Soc., 128, 2577 (1981). M.L. Deanhardt and K.H. Stern, J. Electrochem. Soc., 129, 2228 (1982). R.L. Combes and S.L. Koeller, Quimica Nova, 25, 226 (2002). V.L. Cherginets and T.P. Rebrova, Zhurn. Fiz. Khim., 71, 1886 (2004). M. Zhuravleva, B. Blalock and K. Yang, J.Cryst. Growth, 352, 115 (2012). V.L. Cherginets, N.V. Rebrova, A.Yu. Grippa, Yu.N. Datsko, T.V.Ponomarenko, V.Yu.Pedash, N.N.Kosinov, V.A. Tarasov, O.V. Zelenskaya, I.M. Zenya and A.V. Lopin, Mater.Chem.Phys., 143, 1296 (2014). L. Stand, M. Zhuravleva, B. Chakoumakos, J.Johnson, A. Lindsey and C.L.Melcher, J. Lumin., 169, 301 (2016). G.T. Kosnyrev, V.N. Desyatnik, N.A. Kern and E.N. Nosonova, Rasplavy, No 2, 121 (1990). B. Neumann, C. Kröger and H. Yuttner, Z. Elektrochem., 41, 725 (1935). W.D. Threadill, J. Electrochem. Soc., 112, 632 (1965). A.M. Martinez, Y. Castrillejo, E. Barrado, G.M. Haarberg, G. Picard, J. Electroanal. Chem., 449, 67 (1998). V.L. Cherginets, T.P. Rebrova, Yu.N. Datsko, N.N. Kosinov, E.E.Shevchenko and V.Yu. Pedash, J. Cryst. Growth, 371, 143 (2013). K.L. Strelets and N.V. Bondarenko, Zhurn. Neorg. Khim., 8, 1706 (1963). V.L. Cherginets, T.P. Rebrova, A.L. Rebrov, T.V. Ponomarenko and O.I. Yurchenko, J. Chem. Thermodynam., 102, 248 (2016). V.L. Cherginets, T.P. Rebrova, A.L. Rebrov, T.V. Ponomarenko and O.I. Yurchenko, J.Chem. Thermodynam., 113, 1 (2017). V. Ivenko, A. Shurygin, O. Tkacheva and S. Dokashenko, Abstr. 5th Int. Symp. Solubility Phenomena, Moscow, Russia, 1992, p. 71. V.M. Ivenko, Abstr. X All-Union Conference on physics, chemistry and electrochemistry of ionic melts and solid electrolytes, Ekaterinbourg, 1992, V. 1, p.74. Chemistry of high-temperature superconductors, D.L.Nelson, M.S. Whittinghan and T.F.George, Eds., Mir, Moscow, 1988. G.K. Strukova, I.I. Zverkova, V.S. Chekhtman and V.P. Korzhov, Superconductivity: Physics, Chemistry, Technology, 4, 2225 (1991). R. Combes, M.-N. Levelut and B. Tremillon, J. Electroanal. Chem., 91, 125 (1978). G.S. Perry and L.G. Macdonald, J. Nucl. Mater., 130, 234 (1985). D.A. Wenz, I. Johnson and R.D. Wolson, J. Chem. Eng. Data, 14, 250 (1969). E.V.D. van Loef, P. Dorenbos, C.W.E. van Ejik, K. Kramer, and H.U. Gudel, Appl. Phys. Lett., 79, 1573 (2001). V.L. Cherginets and T.P. Rebrova, Chemistry of deoxidization processes in molten ionic halides, Lambert Academic Publishing, Saarbrüken, 2014. Y. Castrillejo, M.R. Bermejo, R. Pardo and A.M. Martinez, J. Electroanal. Chem., 522, 124 (2002). Chemical Encyclopedia (in 5 v.). V.4, Ed. N.S. Zefirov et al., Bolshaya Rossiykaya Entsyklopediya, Moscow, 1995. A.F. Kuznetsov and G.F. Pekhov, Patent USSR 201,386. V.L. Cherginets, V.A. Naumenko, T.V. Ponomarenko and T.P. Rebrova, Probl. Chem. Chem. Technol.,

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No 2, 138 (2013). 304 V.L. Cherginets, T.P. Rebrova, T.V. Ponomarenko, V.A.Naumenko and E.Yu.Bryleva, React. Kinet. Mech. Catal., 116, 327 (2015). 305 V.L. Cherginets, T.P. Rebrova, V.A. Naumenko and T.V. Ponomarenko, Phys.Chem.Liq., 33, 193 (2015). 306 V.L. Cherginets, T.P. Rebrova, V.A. Naumenko, A.L. Rebrov and O.I. Yurchenko, RSC Adv., 6, 58780 (2016). 307 V.L. Cherginets, T.P. Rebrova, T.V. Ponomarenko, A.L. Rebrov, O.I. Yurchenko and Y.I. Dolzhenko, Reaction Kinetics, Mechanisms and Catalysis, 120, 31 (2017). 308 A.L. Rebrov, V.L. Cherginets, O.I. Yurchenko and T.V. Ponomarenko, Abstr. I Int. Sci. Conf. 'Today Chemical Problems', Vinnitsa, 2018, p.209. 309 V.L. Cherginets, T.P. Rebrova, V.A. Naumenko, T.V. Ponomarenko and Yu.I. Dolzhenko, Scientific Notes of Tavrida V. Vernadsky National University, Series: biology, chemistry, 26, No 4, 407 (2013). 310 V.L. Cherginets, T.P. Rebrova, V.A. Naumenko and T.V. Ponomarenko, Rasplavy, No 5, 30 (2014). 311 V.L. Cherginets, T.P. Rebrova, V.A. Naumenko and T.V. Ponomarenko, Russ. Metall., 2015, 110 (2015). 312 V.L. Cherginets, T.P. Rebrova, V.A. Naumenko and T.V. Ponomarenko, Visn. Hark. Nac. univ., Ser. Him., issue 23 (46), 32 (2014). (http://chembull.univer.kharkov.ua/archiv/2014/04.pdf) 313 V.L. Cherginets, T.P. Rebrova, T.V. Ponomarenko, V.A. Naumenko and Yu.N. Datsko, RSC Adv., 4(95), 52915 (2014). 314 Chemical Encyclopedia (in 5 v.). V.1, Ed. L.I. Knunyants et al., Sovetskaya Entsyklopediya, Moscow, 1988. 315 Short handbook of physicochemical magnitudes, Ed. A.A. Ravdel and A.M. Ponomaryova, Khimiya, Leningrad, 1983. 316 N.V. Rebrova, V.L. Cherginets, T.P. Rebrova, A. Yu. Grippa, V.A. Tarasov and V.V. Ponomarenko, Patent on utility model Ukraine 114,453. 317 A.L. Rebrov, O.I. Yurchenko, T.P. Rebrova, V.L. Cherginets and T.P. Ponomarenko, Abstr. X All-Ukraine Conf. 'Chemical Karazin Readings', Kharkov, 2018, p.45. 318 D.N. Finkelstein, Purity of substances, Atomizdat, Moscow, 1975. 319 V.L. Balkevich, Technical ceramics, Stroyizdat, Moscow, 1984. 320 Yu.N. Datsko, T.P. Rebrova, V.L. Cherginets, V.A.Naumenko, A.L. Rebrov, P.V. Mateychenko and I.N. Vjunnik, Functional Materials, 21, 312 (2016). 321 V.L. Cherginets, T.P. Rebrova, Y.N. Datsko, A.L. Rebrov and P.V. Mateychenko, Functional Materials, 23, 644 (2016).

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9.3 SOLVENT EFFECTS BASED ON PURE SOLVENT SCALES Javier Catalan Departamento de Quimica Fisica Aplicada Universidad Autonoma de Madrid, Madrid, Spain

INTRODUCTION The solvent where a physico-chemical process takes place is a non-inert medium that plays prominent roles in chemistry. It is well-known1 that, for example, a small change in the nature of the solvent ca n alter the rate of a reaction, shift the position of a chemical equilibrium, modify the energy and intensity of transitions induced by electromagnetic radiation, or cause protein denaturation. As a result, the possibility of describing the properties of solvents in terms of accurate models has aroused the interest of chemists for a long time. The interest of chemists in this topic originated in two findings reported more than a century ago that exposed the influence of solvents on the rate of esterification of acetic acid by ethanol, established in 1862 by Berthelot and Saint-Gilles,2 and on the rate of quaternization of tertiary amines by alkyl halides, discovered in 1890 by Menschutkin.3 In his study, Menschutkin found that even so-called “inert solvents” had strong effects on the reaction rate and that the rate increased by a factor about 700 from hexane to acetophenone. Subsequent kinetic studies have revealed even higher sensitivity of the reaction rate to the solvent. Thus, the solvolysis rate of tert-butyl chloride increases 340,000 times from pure ethanol to a 50:50 v/v mixture of this alcohol and water,4,5 and by a factor of 2.88x1014 from pentane to water.6 Also, the decarboxylation rate of 6-nitrobenzisoxazol 3carboxylate increases by a factor of 9.5x107 from water to HMPT.7 9.3.1 THE SOLVENT EFFECT AND ITS DISSECTION INTO GENERAL AND SPECIFIC CONTRIBUTIONS Rationalizing the behavior of a solvent in a global manner, i.e., in terms of a single empirical parameter derived from a single environmental probe, appears to be inappropriate because the magnitude of such a parameter would be so sensitive to the nature of the probe that the parameter would lack predictive ability. One must therefore avoid any descriptions based on a single term encompassing every potential interaction of the solvent, often concealed under a global concept called “solvent polarity”. One immediate way of dissecting the solvent effect is by splitting it into general (non-specific) interactions and specific interactions. In relation to general interactions, the solvent is assumed to be a dielectric continuum. The earliest models for this type of interaction were developed by Kirkwood8 and Onsager,9 and were later modified with corrections for the effect of electrostatic saturation.10,11 The intrinsic difficulty of these models in accurately determining the dimensions of the cybotactic region (viz. the solvent region where solvent molecules are directly perturbed by the presence of solute molecule) that surrounds each solute molecule in the solvent bulk, have usually raised a need for empirical approximations to the determination of a parameter encompassing solvent polarity and polarizability. An alternative approach to

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the general effect was recently reported that was derived from liquid-state theories. One case in point is the recent paper by Matyushov et al.,12 who performed a theoretical thermodynamic analysis of the solvent-induced shifts in the UV-Vis spectra for chromophores; specifically, they studied p-nitroanisole and the pyridinium-N-phenoxide betaine dye using molecular theories based on long-range solute-solvent interactions due to inductive, dispersive and dipole-dipole forces. A number of general empirical solvent scales have been reported;1,13-15 according to Drago,14 their marked mutual divergences are good proof that they do not reflect general effects alone but also specific effects of variable nature depending on the particular probe used to construct each scale. In any case, there have been two attempts at establishing a pure solvent general scale over the last decade. Thus, in 1992, Drago14 developed the “unified solvent polarity scale”, also called the “S’ scale” by using a least-squares minimization program16 to fit a series of physico-chemical properties (χ) for systems where specific interactions with the solvents were excluded to the equation Δχ =PS’ + W. In 1995, our group reported the solvent polarity-polarizability (SPP) scale, based on UV-Vis measurements of the 2-N,N-dimethyl-7-nitrofluorene/2-fluoro-7-nitrofluorene probe/homomorph pair.15 According to Drago,17 specific interactions can be described as localized donoracceptor interactions involving specific orbitals in terms of two parameters, viz. E for electrostatic interactions and C for covalent interactions; according to Kamlet and Taft,18a such interactions can be described in terms of hydrogen-bonding acid-base interactions. In fact, ever since Lewis unified the acidity and basicity concepts in 1923,19 it has been a constant challenge for chemists to find a single quantifiable property of solvents that could serve as a general basicity indicator. Specially significant among the attempts at finding one are the donor number (DN) of Gutmann et al.,20 the B(MeOD) parameter of Koppel and Palm,21 the pure base calorimetric data of Arnet et al.22 and parameter β of Kamlet and Taft.18b

9.3.2 CHARACTERIZATION OF A MOLECULAR ENVIRONMENT WITH THE AID OF THE PROBE/HOMOMORPH MODEL As a rule, a good solvent probe must possess two energy states such that the energy or intensity of the transition between them will be highly sensitive to the nature of the environment. The transition concerned must thus take place between two states affected in a different manner by the molecular environment within the measurement time scale so that the transition will be strongly modified by a change in the nature of the solvent. For easier quantification, the transition should not overlap with any others of the probe, nor should its spectral profile change over the solvent range of interest. Special care should also be exercised so that the probe chosen will be subject to no structural changes dependent on the nature of the solvent; otherwise, the transition will include this perturbation, which is external to the pure solvent effect to be quantified. All probes that meet the previous requirements are not necessarily good solvent probes, however; in fact, the sensitivity of the probe may be the result of various types of interaction with the solvent and the results difficult to generalize as a consequence. A probe suitable for determining a solvent effect such as polarity, acidity or basicity should

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be highly sensitive to the interaction concerned but scarcely responsive to other interactions so that any unwanted contributions will be negligible. However, constructing a pure solvent scale also entails offsetting these side effects, which, as shown later on, raises the need to use a homomorph of the probe. The use of a spectroscopic technique (specifically, UV-Vis absorption spectrophotometry) to quantify the solvent effect provides doubtless advantages. Thus, the solute is in its electronic ground state, in thermodynamic equilibrium with its environment, so the transition is vertical and the solvation sphere remains unchanged throughout. These advantages make designing a good environmental probe for any of the previous three effects quite easy. A suitable probe for the general solvent effect must therefore be a polar compound. Around its dipole moment, the solvent molecules will arrange themselves as effectively as possible − in thermal equilibrium − and the interaction between the probe dipole and the solvent molecules that form the cybotactic region must be strongly altered by electronic excitation, which will result in an appropriate shift in charge; the charge will then create a new dipole moment enclosed by the same cybotactic cavity as in the initial state of the transition. The change in the dipole moment of the probe will cause a shift in the electronic transition and reflect the sensitivity of the probe to the solvent polarity and polarizability. A high sensitivity in the solvent is thus usually associated with a large change in the Scheme I. dipole moment by effect of the electronic transition. However, the magnitude of the spectral shift depends not only on the modulus of the dipole moment but also on the potential orientation change. In fact, inappropriate orientation changes are among the sources of contamination of polarity probes with specific effects. For simplicity, orientation changes can be reduced to the following: (a) the dipole moment for the excited state is at a small angle to that for the ground state of the probe, so the orientation change induced by the electronic excitation can the angle, which hinders its use in practice (see Scheme Ia). This difficulty vanishes at 0 and 180o, which are thus the preferred choices. A transition giving rise to an orientation change at 180o is usually one involving a molecule where charge is strongly localized at a given site and is discharged by delocalization upon electronic excitation; as a result, specific solvating effects in the initial state are strongly altered in the final state, so the transition concerned is strongly contaminated with specific interactions (see Scheme Ib). This situation is also inadvisable with a view to constructing a scale for the general solvent effect. The third possibility, where the transition causes no orientation change in the dipole moment, is the most suitable with a view to establishing the general effect of a solvent; the solvent box, which was the most suitable for solvating the probe, will continue to be so now with

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an increased dipole moment (see Scheme Ic). In summary, a suitable probe for estimating the general solvent effect must not only meet the above-described requirements but also be able to undergo a transition of the dipole moment which will increase markedly as a result of preserving its orientation. A suitable basicity probe will be one possessing an acid group, the acidity of which changes markedly with the electronic transition, so that the transition is affected mostly by solvent basicity. For its acidity to change to an appropriate extent upon excitation, the group concerned should resound with an appropriate electron acceptor and the resonance should increase during the transition by which the effect is probed. Obviously, the presence of this type of group endows the probe with a polar character; in addition, the charge transfer induced by the excitation also produces side effects that must be subtracted in order to obtain measurements contaminated with no extraneous effects such as those due to polarity changes or the acidity of the medium described above. Finding a non-polar probe with a site capable of inducing a specific orientation in the solvent appears to be a difficult task. The best choice in order to be able to subtract the above-mentioned effects appears to be an identical molecular structure exhibiting the same transition but having the acid group blocked. One interesting alternative in this context is the use of a pyrrole N−H group as probe and the corresponding N−Me derivative as homomorph.23 The same approach can be used to design a suitable acidity probe. The previous comments on the basicity probe also apply here; however, there is the added difficulty that the basic site used to probe solvent basicity cannot be blocked so easily. The situation is made much more complex by the fact that, for example, if the basic site used is a ketone group or a pyridine-like nitrogen, then no homomorph can be obtained by blocking the site. The solution, as shown below, involves sterical hindering the solvent approach by protecting the basic site of the probe with bulky alkyl (e.g., tert-butyl) groups at adjacent positions.24 One can therefore conclude that constructing an appropriate general or specific solvent scale entails finding a suitable molecular probe to preferentially assess the effect considered and a suitable homomorph to subtract any side effects extraneous to the interaction of interest. Any other type of semi-empirical evaluation will inevitably lead to scales contaminated with other solvent effects, as shown later on. Accordingly, one will hardly be able to provide a global description of solvent effects on the basis of a single-parameter scale.

9.3.3 SINGLE-PARAMETER SOLVENT SCALES: THE Y, G, ET(30), PY, Z, χ R , Φ, AND S’ SCALES Below, the most widely used single-parameter solvent scales are briefly described, with special emphasis on their foundation and use. 9.3.3.1 The solvent ionizing power scale or Y scale In 1948, Grunwald and Winstein25 introduced the concept of “ionizing power of the solvent”, Y, based on the strong influence of the solvent on the solvolysis rate of Scheme II alkyl halides in general and tert-butyl chloride in particular (see Scheme II). Y is calculated from the following equation:

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Y = log k

623 tBuCl

tBuCl

– log k 0

[9.3.1]

where ktBuCl and k0tBuCl are the solvolysis rate constants at 25oC for tert-butyl chloride in the solvent concerned and in an 80% v/v ethanol/water mixture − the latter constant is used as reference for the process. The strong solvent dependence of the solvolysis rate of tert-butyl chloride was examined by Grunwald and Winstein25,26 in the light of the Brönsted equation. They found the logarithmic coefficient of activity for the reactant and transition state to vary linearly in a series of mixtures and the variation to be largely the result of changes in coefficient of activity for the reactant. By contrast, in the more poorly ionizing solvents, changes in k were found to be primarily due to changes in coefficient of activity for the transition state. In a series of papers,25-32 Grunwald and Winstein showed that the solvolysis rate constants for organic halides which exhibit values differing by more than 6 orders of magnitude in this parameter can generally be accurately described by the following equation: log k = mY + log k 0

[9.3.2]

where k and k0 are the rate constants in the solvent concerned and in the 80:20 v/v ethanol/ water mixture, and coefficient m denotes the ease of solvolysis of the halide concerned relative to tert-butyl chloride. By grouping logarithms in eq. [9.3.2], one obtains log ( k ⁄ k 0 ) = mY

[9.3.3]

which is analogous to the Hammett equation:33 log ( k ⁄ k 0 ) = ρσ

[9.3.4]

There is thus correspondence between coefficient m and the Hammett reaction constant, ρ, and also between the ionizing power of the solvent, Y, and the Hammett substituent constant, σ. In fact, the solvolysis of tert-butyl chloride is one of the cornerstones of physical organic chemistry.34-36 Thus, some quantitative approaches to the kinetics of spontaneous reactions in various solvents − and, more interesting, solvent mixtures − are based on linear free-energy relations such as that of Grunwald and Winstein25 or its extensions.34,37-41 These equations allow one to interpolate or extrapolate rate constants that cannot be readily measured, and also to derive mechanistically significant information in the process. 9.3.3.2 The G values of Allerhand and Schleyer Allerhand and Schleyer42 found that a proportionality exists between the stretching frequencies of vibrators of the type X=O (with X=C, N, P or S) and the corresponding stretching frequencies in situations involving hydrogen bonds of the X−H...B type in a variety of solvents. They thought these results to be indicative that the solvents studied interacted in a non-specific manner with both types of vibrator, in contradiction to the specific interaction-only approach advocated by Bellamy et al.43-45 They used this information to construct a solvent polarity scale that they called “the G scale”. Allerhand and Schleyer42 used an empirical linear free-energy equation to define G:

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9.3 Solvent effects based on pure solvent scales 0

s

G = ( v – v ) ⁄ av

0

[9.3.5]

where v0 and vs are the corresponding stretching frequencies for one such vibrator in the gas phase and in solution, respectively; a is a function of the particular vibrator in a given probe and also a measure of its sensitivity to the solvent; and G is a function of the solvent alone. The scale was initially constructed from 21 solvents; zero was assigned to the gas phase and 100 to dichloromethane. Subsequently, other authors established the G values for additional solvents.46,47 9.3.3.3 The ET(30) scale of Dimroth and Reichardt The ET(30) scale48 is based on the extremely solvatochromic character of 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyrido)phenoxide (1) and is defined by the position (in kcal mol-1) of the maximum of the first absorption band for this dye, which has marked intramolecular charge-transfer connotations and gives rise to an excited electronic state that is much less dipolar than the ground state (see scheme III). This results in strong hypsochromism when increasing solvent polarity.

Scheme III.

On this ET(30) scale, pure solvents take values from 30.7 kcal mol-1 for tetramethylsilane (TMS) to 63.1 kcal mol-1 for water. These data allow one to easily normalize the scale by assigning a zero value to tetramethylsilane and a unity value to water, using the following expression:

Javier Catalan

625

N

E T = ( E T ( solvent ) – E T ( TMS ) ⁄ E T ( water ) – E T ( TMS ) ) = = ( E T ( solvent ) – 30.7 ⁄ 32.4 )

[9.3.6]

N ET

The corresponding values (between 0 and 1) allow one to rank all solvents studied. This is no doubt the most comprehensive solvent scale (it encompasses more than 300 solvents) and also the most widely used at present.1,13 The probe (1) exhibits solubility problems in non-polar solvents that the authors have overcome by using a tert-butyl derivative (2). One serious hindrance to the use of this type of probe is its high basicity (pKa = 8.6449), which raises problems with acid solvents. 9.3.3.4 The Py scale of Dong and Winnick The Py scale50 is based on the ratio between the intensity of components (0,0) I1 and (0,2) I3 of the fluorescence of monomeric pyrene (3) in various solvents. It was initially established for 95 solvents50 and spans values from 0.41 for the gas phase to 1.95 for DMSO. This scale is primarily used in biochemical studies, which usually involve fluorescent probes. However, it poses problems arising largely from the difficulty of obtaining precise values of the above-mentioned intensity ratio; this has resulted in divergences among Py values determined by different laboratories.51 One further hindrance is that the mechanism via which low-polar solvents enhance the intensity of symmetry-forbidden vibronic transitions through a reduction in local symmetry is poorly understood.52 9.3.3.5 The Z scale of Kosower The Z scale53,54 is based on the strong solvatochromism of the 1ethyl-4-(methoxycarbonyl)pyridinium iodide ion-pair (4) and defined by the position (in kcal mol-1) of the maximum of its first absorption band, which has marked intermolecular chargetransfer connotations according to Scheme IV (the excited state of Scheme IV. the chromophore is much less dipolar). This transition undergoes a strong hypsochromic shift as solvent polarity increases, so much so that it occasionally overlaps with strong π → π * bands and results in imprecise localization of the maximum of the charge-transfer band. The Z values for the 20 solvents originally examined by Kosower53 spanned the range from 64.2 for dichloromethane to 94.6 for water. The scale was subsequently expanded to an overall 61 solvents by Marcus56 and the original range extended to 55.3 kcal mol-1 (for 2-methyltetrahydrofuran). Further expansion of this scale was precluded by the fact that high-polar solvents shift the charge-transfer band at the shortest wavelength to

626

9.3 Solvent effects based on pure solvent scales

such an extent that it appears above the strong first π → π * transition of the compound, thus hindering measurement; in addition, the probe (4) is scarcely soluble in non-polar solvents. One should also bear in mind that many solvents require using a high concentration of the probe in order to obtain a measurable charge-transfer band; as a result, the position of the band often depends on the probe concentration. One other fact to be considered is that the interest initially aroused by this scale promoted attempts at overcoming the above-mentioned measurement problems by using correlations with other solvent-sensitive processes; as a result, many of the Z values currently in use are not actually measured values but extrapolated values derived from previously established ratios. 9.3.3.6 The χR scale of Brooker In 1951, Brooker57 suggested for the first time that solvatochromic dyes could be used to obtain measures of solvent polarity. This author58 constructed the χR scale on the basis of the solvatochromism of the merocyanine dye (5), the electronic transition of which gives rise to a charge-transfer from the amine nitrogen to a carboxamide group at the other end of the molecule. Hence, the excited status is more dipolar than the ground state, and the resulting band is shifted bathochromically as solvent polarity increases. χR values reflect the position of the maximum of the first band for the chromophore in kcal mol-1. The original scale encompassed 58 solvents spanning χR values from 33.6 kcal mol-1 for m-cresol to 50.9 kcal mol-1 for n-heptane. 9.3.3.7 The Φ scale of Dubois and Bienvenüe Dubois and Bienvenüe59 developed the F polarity solvent scale on the basis of the position of the n → π * transition for eight selected aliphatic ketones that were studied in 23 solvents, using n-hexane as reference and the following equation for calculation: S

S

ΔvH = v – v

H

H

= Φ ( v – 32637 ) – 174

[9.3.7]

where vS is the absorption wavenumber in solvent S and vH in n-hexane (the reference solvent). The absorption maxima of these ketones depend both on the solvent and on its own structure. The Φ values spanned by the 23 solvents ranging from −0.01 for carbon tetrachloride to 0.65 for formic acid. The values for DMSO and water are 0.115 and 0.545, respectively. 9.3.3.8 The S’ scale of Drago Drago60 developed a “universal polarity scale” (the S’ scale) from more than three hundred spectral data (electronic transitions, 19F and 15N chemical shifts and RSE coupling constants) for 30 solutes in 31 non-protic solvents from cyclohexane to propylene carbonate. He used the equation

Δχ = S'P + W

[9.3.8]

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where Δχ is the measured physico-chemical property, S’ the solvent polarity, P the solvating susceptibility of the solute, and W, the value of Δχ at S’ = 0. Drago assigned an arbitrary value of 3.00 to DMSO in order to anchor the scale. The S’ scale was constructed from carefully selected data. Thus, it excluded data for (a) all systems involving any contribution from donor-acceptor specific interactions (donor molecules where only measured in donor solvents and data for π solutes were excluded); (b) concentrated solutions of polar molecules in non-polar solvents (which might result in clustering); and (c) polar solvents occurring as rotamers (each rotamer would be solvated in a different way). In order to extend the S’ scale to acid solvents, Drago61 devised an experiment involving separating general interactions from specific interactions using the ET(30) scale. First, the probe [ET(30)] was dissolved in a non-coordinating solvent of weakly basic character (so that it would not compete with the solute for the specific interaction) and slightly polar nature (so that the probe would not cluster at low concentrations of the acceptor solvent); then, the acceptor solvent was added and the variation of the maximum on the absorption band for the ET(30) probe was plotted as a function of the solvent concentration. By extrapolation to dilute solutions, the non-specific solvation component for the solvent was estimated. An interesting discussion of the solvent scales developed by Drago can be found in his book.62

9.3.4 SOLVENT POLARITY: THE SPP SCALE15 As noted earlier, a suitable probe for assessing solvent polarity should meet various requirements including the following: (a) the modulus of its dipole moment should increase markedly but its orientation remain unaltered in response to electronic excitation: (b) it should undergo no structural changes by effect of electronic excitation or the nature of the solvent; (c) its basicity or acidity should change as little as possible upon electronic excitation so that any changes will be negligible compared to those caused by polarity; (d) the spectral envelope of the electronic transition band used should not change with the nature of the solvent; and (e) its molecular structure should facilitate the construction of a homomorph allowing one to offset spurious contributions to the measurements arising from the causes cited in (b) to (d) above. A comprehensive analysis of the literature on the choice of probes for constructing polarity scales led our group to consider the molecular structure of 2-amino-7-nitrofluorene (ANF) (6) for this purpose. This compound had previously been used by Lippert63 to define his well-known equation, which relates the Stokes shift of the chromophore with the change in its dipole moment on passing from the ground state to the excited state. He concluded that, in the first excited state, the dipole moment increased by 18 D on the

628

9.3 Solvent effects based on pure solvent scales

5.8 D value in the ground state. This data, together with the dipole moment for the first excited electronic state (23 D), which was obtained by Czekalla et al.64 from electric dichroism measurements, allow one to conclude that the direction of the dipole moment changes very little upon electronic excitation of this chromophore. Baliah and Pillay65 analyzed the dipole moments of a series of fluorene derivatives at positions 2 and 7, and concluded that both positions were strongly resonant and hence an electron-releasing substituent at one and an electron-withdrawing substituent at the other would adopt coplanar positions relative to the fluorene skeleton. In summary, a change by 18 D in dipole moment of a system of these structural features reflects a substantial charge transfer from the donor group at position 2 to the acceptor group at 7 upon electronic excitation. Although ANF seemingly fulfills requirements (a) and (b) above, it appears not to meet requirement (c) (i.e., that its acidity and basicity should not change upon electronic excitation). In fact, electronic excitation will induce a charge transfer from the amino group, so the protons in it will increase in acidity and the transition will be contaminated with specific contributions arising from solvent basicity. In order to avoid this contribution, one may in principle replace the amino group with a dimethylamino group (DMANF, 7), which will exhibit appropriate charge transfer with no significant change in its negligible acidity. The increase in basicity of the nitro group upon electronic excitation (a result of charge transfer from the N,N-dimethyl group), should result in little contamination as this group is scarcely basic and its basicity is bound to hardly change with the amount of charge transferred from the N,N-dimethylamino group at position 2 to the fluorene structure. The analysis of the absorption spectra for DMANF in a broad range of solvents suggests that this probe possesses several interesting spectroscopic properties as regards its first absorption band, which is used to assess the polar properties of solvents. Thus,15 (a) its first absorption band is well resolved from the other electronic bands (an increase in solvent polarity results in no overlap with the other electronic bands in the UV-Vis spectrum for this probe); (b) the position of this band is highly sensitive to solvent polarity and is bathochromically shifted with increase in it (the bathochromic shift in the absorption maximum between perfluorohexane and DMSO is 4130 cm-1); (c) in less polar solvents, where the band appears at lower wavelengths, it is observed at ca. 376 nm (i.e., shifted to the visible region to an extent ensuring that no problems derived from the cut-off of the solvent concerned will be encountered); and (d) its first band becomes structured in nonpolar solvents (see Figure 1 in ref. 15). In summary, DMANF is a firm candidate for use as a solvent dipolarity/polarizability probe since its absorption is extremely sensitive to changes in the nature of the solvent, largely as a result of the marked increase in its dipole moment on passing from the electronic ground state to the first excited state. In addition, the change does not affect the dipole moment direction, which is of great interest if the compound is to be used as a probe. Because it possesses a large, rigid aromatic structure, DMANF is highly polarizable; consequently, its first electronic transition occurs at energies where no appreciable interferences with the cut-offs of ordinary solvents are to be expected.

Javier Catalan

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However, the change in structure of the first absorption band for DMANF in passing from non-polar solvents to polar solvents and the potential contaminating effect of solvent acidity on the position of this band entails introducing a homomorph for the probe in order to offset the detrimental effects of these factors on the estimation of solvent polarities. The homomorph to be used should essentially possess the same structure as the probe, viz. a nitro group at position 7 ensuring the occurrence of the same type of interaction with the solvents and an electron-releasing group at position 2 ensuring similar, through weaker, interactions with the nitro function at 7 in order to obtain a lower dipole moment relative to DMANF). The most suitable replacement for the −NMe2 function in this context is a fluorine atom, which poses no structural problems and is inert to solvents. The homomorph chosen was thus 2fluoro-7-nitrofluorene (FNF) (9). The analysis of the absorption spectra for FNF in a broad range of solvents clearly revealed that its first absorption band behaves identically with that for DMANF (its structure changes in passing from non-polar solvents to polar ones). However, the bathochromic shift in this band with increase in solvent polarity is much smaller than that in DMANF (see Figure 1 in ref. 15). Obviously, the difference between the solvatochromism of DMANF and FNF will cancel many of the spurious effects involved in measurements of solvent polarity. Because the envelopes of the first absorption bands for FNF and DMANF are identical (see Figure 1 in ref. 15), one of the most common source of error in polarity scales is thus avoided. The polarity of a solvent on the SPP scale is given by the difference between the solvatochromism of the probe DMANF and its homomorph FNF [Δv(solvent) = vFNF − vDMANF] and can be evaluated on a fixed scale from 0 for the gas phase (i.e., the absence of solvent) to 1 for DMSO, using the following equation: SPP(solvent) = [Δv(solvent) − Δv(gas)]/[Δv(DMSO) − Δv(gas)]

[9.3.9]

Table 9.3.1 gives the SPP values for a broad range of solvents, ranked in increasing order of polarity. Data were all obtained from measurements made in our laboratory and have largely been reported elsewhere,15,66-70 some, however, are published here for the first time. Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents

SPP

SB

SA

0

0

0a

perfluoro-n-hexane

0.214

0.057

0a

2-methylbutane

0.479

0.053

0a

gas phase

630

9.3 Solvent effects based on pure solvent scales

Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents

SPP

SB

SA

petroleum ether

0.493

0.043

0a

n-pentane

0.507

0.073

0a

n-hexane

0.519

0.056

0a

n-heptane

0.526

0.083

0a

isooctane

0.533

0.044

0a

cyclopentane

0.535

0.063

0a

n-octane

0.542

0.079

0a

ethylcyclohexane

0.548

0.074

0a

n-nonane

0.552

0.053

0a

cyclohexane

0.557

0.073

0a

n-decane

0.562

0.066

0a

n-undecane

0.563

0.080

0a

methylcyclohexane

0.563

0.078

0a

butylcyclohexane

0.570

0.073

0a

propylcyclohexane

0.571

0.074

0a

n-dodecane

0.571

0.086

0a

decahydronaphthalene

0.574

0.056

0a

mesitylene

0.576

0.190

0a

n-pentadecane

0.578

0.068

0a

n-hexadecane

0.578

0.086

0a

cycloheptane

0.582

0.069

0a

tert-butylcyclohexane

0.585

0.074

0a

cyclooctane

0.590

0.077

0a

1,2,3,5-tetramethylbenzene

0.592

0.186

0a

cis-decahydronaphthalene

0.601

0.056

0a

tripropylamine

0.612

0.844

0a

m-xylene

0.616

0.162

0a

triethylamine

0.617

0.885

0a

p-xylene

0.617

0.160

0a

1-methylpiperidine

0.622

0.836

0a

tributylamine

0.624

0.854

0a

1,4-dimethylpiperazine

0.627

0.832

0a

hexafluorobenzene

0.629

0.119

0a

trimethylacetic acid

0.630

0.130

0.471

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Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents

SPP

SB

SA

dibutylamine

0.630

0.991

0a

di-n-hexyl ether

0.630

0.618

0a

1-methylpyrrolidine

0.631

0.918

0a

tetrachloromethane

0.632

0.044

0a

di-n-pentyl ether

0.636

0.629

0a

butylbenzene

0.639

0.149

0a

o-xylene

0.641

0.157

0a

isobutyric acid

0.643

0.281

0.515

isovaleric acid

0.647

0.405

0.538

ethylbenzene

0.650

0.138

0a

di-n-butyl ether

0.652

0.637

0a

hexanoic acid

0.656

0.304

0.456

toluene

0.655

0.128

0a

propylbenzene

0.655

0.144

0a

tert-butylbenzene

0.657

0.171

0a

N-methylbutylamine

0.661

0.960

0a

heptanoic acid

0.662

0.328

0.445

di-isopropyl ether

0.663

0.657

0a

N-methylcyclohexylamine

0.664

0.925

0a

N,N-dimethylcyclohexylamine

0.667

0.998

0a

benzene

0.667

0.124

0a

1,2,3,4-tetrahydronaphthlene

0.668

0.180

0a

ethylenediamine

0.674

0.843

0.047

di-n-propyl ether

0.676

0.666

0a

propionic acid

0.690

0.377

0.608

tert-butyl methyl ether

0.687

0.567

0a

diethyl ether

0.694

0.562

0a

2-methylbutyric acid

0.695

0.250

0.439

butyl methyl ether

0.695

0.505

0a

pentafluoropyridine

0.697

0.144

0a

1,4-dioxane

0.701

0.444

0.0

2-methyltetrahydrofuran

0.717

0.584

0.0

1-methylnaphthalene

0.726

0.156

0a

butylamine

0.730

0.944

0.0

632

9.3 Solvent effects based on pure solvent scales

Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents ethoxybenzene

SPP

SB

SA

0.739

0.295

0a

piperidine

0.740

0.933

0.0

1-undecanol

0.748

0.909

0.257

isoamyl acetate

0.752

0.481

0.0

1-decanol

0.765

0.912

0.259

fluorobenzene

0.769

0.113

0a

1-nonanol

0.770

0.906

0.270

tetrahydropyran

0.778

0.591

0.0

acetic acid

0.781

0.390

0.689

n-propyl acetate

0.782

0.548

0.0

n-butyl acetate

0.784

0.525

0.0

methyl acetate

0.785

0.527

0.0

1-octanol

0.785

0.923

0.299

chloroform

0.786

0.071

0.047

2-octanol

0.786

0.963

0.088

cyclohexylamine

0.787

0.959

0.0

trimethyl orthoformate

0.787

0.528

0.0

1,2-dimethoxyethane

0.788

0.636

0.0

pyrrolidine

0.794

0.990

0.0

ethyl acetate

0.795

0.542

0.0

1-heptanol

0.795

0.912

0.302

N,N,-dimethylaniline

0.797

0.308

0.0

methyl formate

0.804

0.422

0.0

2-buthoxyethanol

0.807

0.714

0.292

1-hexanol

0.810

0.879

0.315

3-methyl-1-butanol

0.814

0.858

0.315

propyl formate

0.815

0.549

0.0

1-pentanol

0.817

0.860

0.319

dibenzyl ether

0.819

0.330

0a

methoxybenzene

0.823

0.299

0.084

chlorobenzene

0.824

0.182

0a

bromobenzene

0.824

0.191

0a

cyclooctanol

0.827

0.919

0.137

2,6-dimethylpyridine

0.829

0.708

0.0

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Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents

SPP

SB

SA

2-methyl-2-propanol

0.829

0.928

0.145

2-pentanol

0.830

0.916

0.204

2-methyl-2-butanol

0.831

0.941

0.096

2-methyl-1-propanol

0.832

0.828

0.311

formamide

0.833

0.414

0.674

2,4,6-trimethylpyridine

0.833

0.748

0.0

3-hexanol

0.833

0.979

0.140

iodobenzene

0.835

0.158

0a

ethyl benzoate

0.835

0.417

0.0

dibutyl oxalate

0.835

0.549

0.0

methyl benzoate

0.836

0.378

0.0

1-chlorobutane

0.837

0.138

0a

1-butanol

0.837

0.809

0.341

2-methyl-1-butanol

0.838

0.900

0.289

tetrahydrofuran

0.838

0.591

0.0

pyrrole

0.838

0.179

0.387

cycloheptanol

0.841

0.911

0.183

2-butanol

0.842

0.888

0.221

1,3-dioxolane

0.843

0.398

0.0

3-methyl-2-butanol

0.843

0.893

0.196

2-hexanol

0.847

0.966

0.140

cyclohexanol

0.847

0.854

0.258

1-propanol

0.847

0.727

0.367

2-propanol

0.848

0.762

0.283

ethanol

0.853

0.658

0.400

1,2-dimethoxybenzene

0.854

0.340

0.0

2-methoxyethyl ether

0.855

0.623

0.0

methanol

0.857

0.545

0.605

methyl methoxyacetate

0.858

0.484

0.0

3-pentanol

0.863

0.950

0.100

cyclopentanol

0.865

0.836

0.258

cyclohexanone

0.874

0.482

0.0

propionitrile

0.875

0.365

0.030

allyl alcohol

0.875

0.585

0.415

634

9.3 Solvent effects based on pure solvent scales

Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents propiophenone

SPP

SB

SA

0.875

0.382

0a

triacetin

0.875

0.416

0.023

dichloromethane

0.876

0.178

0.040

2-methylpyridine

0.880

0.629

0.0

2-butanone

0.881

0.520

0.0

acetone

0.881

0.475

0.0

2-methoxyethanol

0.882

0.560

0.355

3-pentanone

0.883

0.557

0.0

benzyl alcohol

0.886

0.461

0.409

4-methyl-2-pentanone

0.887

0.540

0.0

trimethyl phosphate

0.889

0.522

0.0

1-methylpyrrole

0.890

0.244

0.0

1,2-dichloroethane

0.890

0.126

0.030

2-phenylethanol

0.890

0.523

0.376

2-chloroethanol

0.893

0.377

0.563

nitroethane

0.894

0.234

0.0

acetonitrile

0.895

0.286

0.044

chloroacetonitrile

0.896

0.184

0.445

N-methylacetamide

0.897

0.735

0.328

1,2-butanediol

0.899

0.668

0.466

valeronitrile

0.900

0.408

0.0

N-methylaniline

0.902

0.212

0.073

2,3-butanediol

0.904

0.652

0.461

acetophenone

0.904

0.365

0.044

nitromethane

0.907

0.236

0.078

cyclopentanone

0.908

0.465

0.0

triethyl phosphate

0.908

0.614

0.0

1,2-dichlorobenzene

0.911

0.144

0.033

tetrahydrothiophene

0.912

0.436

0a

2,2,2-trifluoroethanol

0.912

0.107

0.893

butyronitrile

0.915

0.384

0.0

N-methylformamide

0.920

0.590

0.444

isobutyronitrile

0.920

0.430

0.0

pyridine

0.922

0.581

0.033

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Table 9.3.1. The property parameters of solvents: Polarity/Polarizability SPP, Basicity SB, Acidity SA. Solvents

SPP

SB

SA

2-methyl-1,3-propanediol

0.924

0.615

0.451

1,2-propanediol

0.926

0.598

0.475

propylene carbonate

0.930

0.341

0.106

N,N-diethylacetamide

0.930

0.660

0.0

hexamethylphosphoric acid triamide

0.932

0.813

0a

1,2-ethanediol

0.932

0.534

0.565

N,N-diethylformamide

0.939

0.614

0.0

1,3-butanediol

0.944

0.610

0.424

1,2,3-propanetriol

0.948

0.309

0.618

1-methylimidazole

0.950

0.668

0.069

1,4-butanediol

0.950

0.598

0.424

1,3-propanediol

0.951

0.514

0.486

tetramethylurea

0.952

0.624

0.0

N,N-dimethylformamide

0.954

0.613

0.031

2-pyrrolidinone

0.956

0.597

0.347

benzonitrile

0.960

0.281

0.047

2,2,2-trichloroethanol

0.968

0.186

0.588

nitrobenzene

0.968

0.240

0.056

1-methyl-2-pyrrolidinone

0.970

0.613

0.024

N,N-dimethylacetamide

0.970

0.650

0.028

water

0.962

0.025

1.062

γ-butyrolactone

0.987

0.399

0.057

dimethyl sulfoxide

1.000

0.647

0.072

sulfolane

1.003

0.365

0.052

m-cresol

1.000

0.192

0.697

1,1,1,3,3,3-hexafluoro-2-propanol

1.014

0.014

1.000

α α α-trifluoro-m-cresol

1.085

0.051

0.763

a

Assumed value because it is considered non acid solvent. Assumed value because the first band of the TBSB spectra exhibits vibronic structure.

a

A brief analysis of these SPP data allows one to draw several interesting conclusion • Cyclohexane is used as the non-polar reference in many scales. In the SPP scale, the polarity gap between cyclohexane and the gas phase (0.557 SPP units) is as wide as that between cyclohexane and the highest polarity (0.443 SPP units).

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9.3 Solvent effects based on pure solvent scales

• •

Alkanes span a wide range of SPP values (e.g., 0.214 for perfluoro-n-hexane, 0.479 for 2-methylbutane and 0.601 for decalin). Unsaturation increases polarity in alcohols. Thus, the SPP values for n-propanol, allyl alcohol and propargyl alcohol are 0.847, 0.875 and 0.915, respectively.

9.3.5 SOLVENT BASICITY: THE SB SCALE72 As stated above, for a probe of solvent basicity to be usable in UV-Vis spectroscopy, it should meet a series of requirements. One is that it should be acidic enough in its electronic ground state to allow characterization of the basicity of its environment. In addition, its acidity should increase upon electronic excitation such that its electronic transitions will be sensitive to the basicity of the medium. This behavior will result in a bathochromic shift in the absorption band the magnitude of which will increase with increasing basicity of the environment. The probe should also be free of potential conformational changes that might influence the electronic transition to be evaluated. Finally, its molecular structure should be readily converted into a homomorph lacking the acid site without any side effects that might affect the resulting solvent basicity. 5-Nitroindoline (NI, 9) possesses the above-described electronic and structural features. It is an N−H acid with a single acid site borne by a donor group whose free rotation is hindered by an ethylene bridge on the ring. However, if charge transfer endows the compound with appropriate acid properties that increase with electronic excitation, the basicity of the acceptor (nitro) group will also increase and the polarity of the compound will be altered as a result. Both effects will influence the electronic transition of the probe that is to be used to evaluate basicity. Replacement of the acid proton (N−H) by a methyl group in this molecular structure has the same side effects; as a result, the compound will be similarly sensitive to the polarity and acidity of the medium, but not to its basicity owing to the absence of an acid site. Consequently, 1-methyl-5-nitroindoline (MNI, 10) possesses the required properties for use as a homomorph of 5-nitroindoline in order to construct our solvent basicity scale (SB). The suitability of this probe/homomorph couple is consistent with theoretical MP2/ 6-31G** data. Thus, both the probe and its homomorph exhibit the same sensitivity to solvent polarity/polarizability because of their similar dipole moments (µNI = 7.13, µMNI = 7.31 D) and polarizabilities (20.38 and 22.78 α/J-1C2m2 for NI and MNI, respectively). Both also have the same sensitivity to solvent acidity as their surface electrostatic potential minima are virtually coincident [VS,min(NI) = −47.49 kcal mol-1, VS,min(MNI) = −47.58 kcal mol-1]; according to Politzer et al.,71 this means that they exhibit the same hydrogenbonding basicity. In addition, the electrostatic potential surface in both molecules suggests that sole electrophilic sites are those on the oxygen atoms of the nitro group. Obviously, the difference in solvatochromism between NI and MNI [Δv(solvent) = vNI − vMNI] will cancel many spurious effects accompanying the basicity effect of the solvent. In addition, NI and MNI possess several advantageous spectral features; thus, they exhibit a sharp first absorption band that overlaps with no higher-energy band in any solvent, and both have the same spectral envelope in such a band (see Figure 1 in ref. 72), which facilitates comparison between the two spectra and the precise establishment of the basicity parameter, SB. The basicity of a solvent (SB) on a scale encompassing values

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between zero for the gas phase − the absence of solvent − and unity for tetramethylguanidine (TMG) can be directly obtained from the following equation: SB(solvent) = [Δv(solvent) − Δv(gas)]/[Δv(TMG) − Δv(gas)]

[9.3.10]

Table 9.3.1 lists the SB values for a wide range of solvents. All data were obtained from measurements made in our laboratory; most have been reported elsewhere70,72 but some are published here for the first time. A brief analysis of these SB data allows one to draw several interesting conclusions as regards structural effects on solvent basicity. Thus: • Appropriate substitution in compound families such as amines and alcohols allows the entire range of the solvent basicity scale to be spanned with substances from such families. Thus, perfluorotriethylamine can be considered non-basic (SB=0.082), whereas N,N-dimethylcyclohexylamine is at the top of the scale (SB=0.998). Similarly, hexafluoro-2-propanol is non-basic (SB=0.014), whereas 2-octanol is very near the top (SB=0.963). • The basicity of n-alkanols increases significantly with increase in chain length and levels off beyond octanol. • Cyclization hardly influences solvent basicity. Thus, there is little difference in basicity between n-pentane (SB=0.073) and cyclopentane (SB=0.063) or between n-pentanol (SB=0.869) and cyclopentanol (SB=0.836). • Aromatization decreases solvent basicity by a factor of 3.5-5.5, as illustrated by the following couples: pyrrolidine/pyrrole (0.99/0.18), N-methylpyrrolidine/Nethylpyrrole (0.92/0.22), tetrahydrofuran/furan (0.59/0.11), 2-methyltetrahydrofuran/2-methylfuran (0.56/0.16), cyclohexylamine/aniline (0.96/0.26), N-methylcyclohexylamine/N-methylaniline (0.92/0.21), N,N-dimethylcyclohexylamine/ N,N-dimethylaniline (0.99/0.30) and a structurally less similar couple such as piperidine/pyridine (0.93/0.58). The potential family-dependence of our SB scale was examined and published elsewhere.73

9.3.6 SOLVENT ACIDITY: THE SA SCALE74 As stated above, a probe for solvent acidity should possess a number of features to be usable in UV-Vis spectroscopy. One is that it should be basic enough in its electronic ground state to be able to characterize the acidity of its environment. In addition, its basicity should increase upon electronic excitation such that its electronic transitions will be sensitive to the acidity of the medium. This behavior will result in a bathochromic shift in the absorption band the magnitude of which will increase with increasing acidity of the environment. The probe should also be free of potential conformational changes that might influence the electronic transition to be evaluated. Finally, its molecular structure should be easily converted into a homomorph lacking the basic site without any side effects potentially affecting the resulting solvent acidity. Our group has shown24,75 that the extremely strong negative solvatochromism of the chromophore stilbazolium betaine dye (11), about 6500 cm-1, is not a result of a change in the non-specific effect of the solvent but rather of change in acidity. This was confirmed75

638

9.3 Solvent effects based on pure solvent scales

by a study of the solvatochromic effect of a derivative of (11), o,o’-di-tert-butylstilbazolium betaine dye (DTBSB) (12) in the same series of solvents. In this compound, the basic site in the betaine dye (its oxygen atom) is protected on both sides by bulky tertbutyl groups; the specific effect of the solvent is hindered and the compound exhibits only a small solvatochromic effect that can be ascribed to non-specific solvent effects.75 Since the carbonyl group of stilbazolium betaine possesses two lone pairs in the plane of the quinoid ring, one can have two (11), one (TBSB, 13) or no channels (DTBSB) to approach hydrogen bond-donor solvents, depending on the number of o-tert-butyl groups present in the molecular structure of the (11) derivative concerned. Our group24 has also shown that, for at least 20 alkanols, the wavenumber difference between the maximum of the first absorption bands for (11) and TBSB, and for TBSB and DTBSB, is virtually identical. These results show that an oxygen lone pair in (11) is basic enough, as a result of hydrogen bonding, for (11) to be used as an acidity probe in UV-Vis spectroscopy; thus, the absorption maximum for TBSB shifts by about 1000 cm-1 from 1-decanol to ethanol,24 whereas that for DTBSB shifts by only 300 cm-1. This sensitivity to acidity, and the structural likeness of the probe and its homomorph, which must endow them with a similar sensitivity to solvent basicity and dipolarity/polarizability, suggest that the two compounds make an appropriate probe-homomorph couple for developing a pure solvent acidity scale. For this purpose, the first visible absorption band for these compounds exhibits quite an interesting spectroscopic behavior. Thus, in a non-HBD solvent (i.e., one that cannot interact directly with the oxygen lone pair), the band is structured; on the other hand, the band loses its structure upon interaction with an HBD solvent.75 The SA acidity scale was established by comparing the solvatochromism of the probes TBSB and DTBSB using the method of Kamlet and Taft.18a In this method, the solvatochromism of DTBSB in a solvent is used as the reference for zero acidity. Consequently, non-acidic solvents obey the equation vTBSB = 1.409vDTBSB − 6288.7

[9.3.11]

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with n = 50, r = 0.961 and sd = 43.34 cm-1. Based on eq. [9.3.11] for non-acidic solvents, the SA value for a given solvent can be obtained from the following expression, where a value of 0.4 is assigned to ethanol, the acid solvatochromic behavior which is exhibited at 1299.8 cm-1: SA =[[vTBSB − (1.409vDTBSB − 6288.7)]/1299.8]0.4

[9.3.12]

Table 9.3.1 gives the SA values for a wide variety of C−H, N−H and O−H acid solvents. Data were all obtained from measurements made in our laboratory.74 The homomorph was insoluble in some solvents, which therefore could not be measured, so they where assumed not to interact specifically and assigned a zero SA value if the probe exhibited a structured spectrum in them. Evaluating the acidity of weakly acidic solvents entails using a probe basic enough to afford measurement of such an acidity; as a result, the probe is usually protonated by strongly acidic solvents and useless for the intended purpose. Stilbazolium betaines are subject to this constraint as they have pK values of about 10 − (11) and DTBSB have a pKa of 8.5776 and ca. 10,77 respectively, which makes them unsuitable for the evaluation of solvents more acidic than methanol. This forced us to find a suitable probe with a view to expanding the SA scale to more acidic solvents. This problem is not exclusive to our scale; in fact, it affects all acidity scales, which usually provide little information about strongly acidic solvents. The problem was solved thanks to the exceptional behavior of 3,6-diethyltetrazine70 (DETZ, 14). This compound possesses two lone electron pairs located on opposite sites of its hexagonal ring; the strong interaction be-tween the two pairs results in one antibonding n orbital in the compound lying at an anomalously high energy level; this, as shown below, has special spectroscopic implications. The π-electron system of DETZ is similar to that of benzene. Thus, the first π → π * transition in the two systems appears at λmax = 252 nm in DETZ and at 260 nm in benzene. On the other hand, the π → π * transition in DETZ is strongly shifted to the visible region ( λ max ≅ 550 nm), which is the origin of its deep color. This unique feature makes this compound a firm candidate for use as an environmental probe as the wide energy gap between the two transitions excludes potential overlap. Problems such as protonation of the DETZ probe by acid solvents can be ruled out since, according to Mason,78 this type of substance exhibits pK values below zero. The sensitivity of the n → π * transition in DETZ to the solvent is clearly reflected in its UV/Vis spectra in methylcyclohexane, methanol, trifluoromethanol, hexafluoro-2propanol, acetic acid and trifluoroacetic acid, with λmax values of 550, 536, 524, 517, 534 and 507 nm, respectively. In addition, the spectral envelope undergoes no significant change in the solvents studied, so a potential protonation of the probe (even a partial one) can be discarded. The shift in the n → π * band is largely caused by solvent acidity; however, an n → π * transition is also obviously sensitive to the polarity of the medium, the contribution of which must be subtracted if acidity is to be accurately determined. To this end, our group used the solvatochromic method of Kamlet and Taft18a to plot the frequency of the

640

9.3 Solvent effects based on pure solvent scales

absorption maximum for the n → π * transition against solvent polarity (the SPP value). As expected, non-acidic solvents exhibited a linear dependence [eq. (9.3.13)], whereas acidic solvents departed from this behavior − the more acidic the greater the divergence. This departure from the linear behavior described by eq. [9.3.13] is quantified by ΔvDETZ, vDETZ = 1.015SPP + 17.51

[9.3.13]

with n = 13, r = 0.983 and sd = 23 cm-1. The SA value of an acid solvent as determined by the DETZ probe is calculated using the expression established from the information provided by a series of solvents of increased acidity measurable by the TBSB/DTBSB probe/homomorph couple (viz. 1,2butanediol, 1,3,-butanediol, ethanol, methanol and hexafluoro-2-propanol); this gives rise to eq. [9.3.14], which, in principle, should only be used to determine SA for solvents with ΔvDETZ values above 100 cm-1: SA = 0.833ΔvDETZ + 0.339

[9.3.14]

with n = 6 and r = 0.987. Table 9.3.1 gives the SA values for a wide range of highly acidic solvents. Data were largely obtained from measurements made in our laboratory;70 some, however, are reported here for the first time. A brief analysis of these SA data allow one to draw several interesting conclusions from structural effects on solvent acidity. Thus: • Substitution into alcoholic compounds allows the entire range of the solvent acidity scale to be spanned. Thus, 2-octanol can be considered to be scarcely HBD (SA=0.088) and ethylene glycol to be highly HBD (SA=0.717). Perfluoroalkanols are even more highly HBD. • The acidity of 1-alkanols and carboxylic acids decreases significantly with increasing chain length but levels off beyond nonanol and octanoic acid, respectively. • Cyclization decreases solvent acidity. Thus, SA decreases from 0.318 to 0.257 between 1-pentanol and cyclopentanol, and from 0.298 to 0.136 between 1-octanol and cyclooctanol. • Aromatic rings make aniline (SA=0.131) and pyrrole (SA=0.386) more HBD than their saturated homologs: cyclohexylamine and pyrrolidine, respectively, both of which are non-HBD (SA=0). • The acidity of alkanols decreases dramatically with increasing alkylation at the atom that bears the hydroxyl group [e.g., from 1-butanol (SA=0.340) to 2-butanol (SA=0.221) to tert-butyl alcohol (SA=0.146)].

9.3.7 APPLICATIONS OF THE PURE SPP, SA, AND SB SCALES The SPP general solvent scale, and the SA and SB specific solvent scales, are orthogonal to one another, as can be inferred from the small correlation coefficients obtained in mutual fittings involving the 200 solvents listed in Table 9.3.1 [r2(SPP vs. SA) = 0.13, r2(SPP vs. SB) = 0.10 and r2(SA vs. SB) = 0.01]. These results support the use of these

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641

scales for the multi-parameter analysis of other solvent scales or data sets sensitive to the solvent effect on the basis of the following equation: P = aSPP + bSA + cSB + P0

[9.3.15]

where P is the quantity to be described in a given solvent; SPP, SA and SB are the corresponding polarity/polarizability, acidity and basicity values for such a solvent; coefficients a, b and c denote the sensitivity of P to such effects; and P0 is the P value in the absence of solvent (i.e., the gas phase, which is given a zero value in our scales). Each of these scales (SPP, SB and SA) has previously been compared with other reported solvent scales and found to be pure scales for the respective effects. However, eq. [9.3.15] is used below to perform a multi-parameter analysis of various reported scales and experimental data sets of interest. 9.3.7.1 Other reported solvents scales Reported scales for describing solvent polarity [f(ε,n),21,79 π*80 and S’60], basicity (DN20 and β18) and acidity (AN81 and α18) were previously analyzed against our SPP, SA and SB scales in the originating references, so no further comment is made here. Rather, this section analyses the behavior of reported single-parameter scales developed to describe the global behavior of solvents [viz. the Z, χR, Py, Φ, G and ET(30) scales] against the SPP, SB and SA scales on the basis of the 200 solvents listed in Table 9.3.1. The Y scale, established to describe the behavior of solvolysis-like kinetics, is dealt with in the section devoted to the description of kinetic data. The data used in this analysis were taken from the following sources: those for the Z scale from the review paper by Marcus;56 those for the χR, Φ and G scales from the compilation in Table 7.2 of Reichardt’s book;1 those for parameter Py from the paper by Dong and Winnik;50 and those for ET(30) from the review by Reichardt13 or Table 7.3 in his book.1 The Z value for the 51 solvents in Table 9.3.1 reported by Marcus allow one to establish the following equation: Z = 22.37(±4.85)SPP + 7.68(±1.64)SB + 31.27(±1.81)SA + 41.03(±4.15) [9.3.16] with r = 0.944 and sd = 3.03 kcal mol-1. This equation reveals that Z is largely the result of solvent acidity and polarity, and also, to a lesser extent, of solvent basicity. The strong delocalization of charge in the structure of the probe (4) upon electronic excitation, see scheme IV, accounts for the fact that the electronic transition of this probe is hypsochromically shifted by solvent polarity and acidity. The shift is a result of the increased stabilizing effect of the solvent − exerted via general and specific interactions − in the electronic ground state being partly lost upon electronic excitation through delocalization of the charge in the electronic excited state, which gives rise to decreased polarity and specific solvation. On the other hand, the small contribution of solvent basicity appears to have no immediate explanation. It should be noted that the three solvent effects (polarity, acidity and basicity) increase Z; also, as can be seen from Figure 9.3.1, the greatest imprecision in this parameter corresponds to solvents with Z values below 70 kcal mol-1.

642

9.3 Solvent effects based on pure solvent scales

Figure 9.3.1. Plot of Kosower’s Z values vs. the predicted Z values according to eq. [9.3.16].

Figure 9.3.2. Plot of Brooker’s χR values vs. the predicted χR values according to [eq. 9.3.17].

The 28 solvents in Table 9.3.1 with known values of χR reveal that this parameter reflects solvent polarity and, to a lesser extent, also solvent acidity:

χR = −15.81(±1.19)SPP − 4.74(±0.90)SA + 58.84(±0.94)

[9.3.17]

with r = 0.958 and sd = 0.78 kcal mol-1. It should be noted that the two solvent effects involved (polarity and acidity) contribute to decreasing χR. As can be seen from Figure 9.3.2, the precision in χR is similarly good throughout the studied range. The structure of the probe used to construct this scale (5) reveals that its electron-donor site (an amino group) is not accessible to the solvent, so the charge transfer involved in the electronic excitation does not alter its solvation; rather, it increases its polarity and localization of the charge on the acceptor sites of the compound (carbonyl groups), see scheme V, so increasing solvent polarity and acidity will result in a bathochromically shifted electronic transition by effect of the increased stabilization of the excited state through general and specific interactions.

Scheme V

The results of the multi-parameter analysis of Py suggests that its values are highly imprecise; even if the value for the gas phase is removed, this parameter only reflects (in an imprecise manner) solvent polarity, as is clearly apparent from eq. [9.3.18] (see Figure 9.3.3): Py = 2.30(±0.20)SPP − 0.57(±0.16)

[9.3.18]

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Figure 9.3.3. Plot of Dong and Winnick’s Py values vs. the predicted Py values according to eq. [9.3.18] (Point for gas phase,, is included in the plot, but not in the regression equation [9.3.18]).

Figure 9.3.4. Plot of Dubois and Bienvenüe’s Φ values vs. the predicted Φ values according to eq. [9.3.19].

Figure 9.3.5. Plot of Allerhand and Schleyer’s G values vs. the predicted G values according to eq. [9.3.20].

Figure 9.3.6. Plot of Reichardt’s ET(30) values vs. the predicted ET(30) values according to eq. [9.3.21].

with r = 0.839 and sd = 0.20. The difficulty of understanding the performance of the probe precludes rationalizing its spectral behavior. The 19 Φ values examined indicate that, based on eq. [9.3.19] and Figure 9.3.4, this parameter reflects mostly solvent acidity and, to a lesser extent, solvent polarity:

Φ = 0.18(±0.11)SPP + 0.38(±0.04)SA − 0.07(±0.08) with r = 0.941 and sd = 0.05.

[9.3.19]

644

9.3 Solvent effects based on pure solvent scales

The Φ scale is based on the solvatochromic behavior of an n → π * electronic transition, so it reflects a high hypsochromic sensitivity to solvent acidity (specific solvation between the lone pair involved in the electronic transition and solvent acidity is lost when one electron in the pair is electronically excited). An n → π * electronic transition is also known to decrease the polarity of the chromophore concerned,82 so an increase in SPP for the solvent will cause a hypsochromic shift in the electronic transition. Based on Figure 9.3.5 and the following equation, the values of G parameters are also dictated by solvent polarity and, to a lesser extent, solvent acidity: G = 102.96(±9.02)SPP + 78.20(±27.78)SA − 0.35(±6.28)

[9.3.20]

with r = 0.965 and sd = 7.6. It should be noted that the independent term for the gas phase is very small and highly imprecise in both the G scale and the Φ scale. For the 138 solvents with a known ET(30) value listed in Table 9.3.1, this parameter reflects mostly solvent acidity and polarity, and, to a lesser degree, also solvent basicity (see Figure 9.3.6): ET(30) = 0.62(±0.04)SPP + 0.12(±0.02)SB + 0.77(±0.02)SA − 0.31(±0.03)

[9.3.21]

with r = 0.965 and sd = 0.06. It should be noted that the three solvent effects (polarity, acidity and basicity) contribute to increasing ET(30), i.e., to a hypsochromic shift in the transition of the probe (see Figure 9.3.6). The spectroscopic behavior of the probe used to construct this scale (1) is typical of a structure exhibiting highly localized charge on its carbonyl group in the electronic ground state, see scheme III, and hence strong stabilization by effect of increased solvent polarity and acidity. The electronic transition delocalizes the charge and results in an excited state that is much less markedly stabilized by increased polarity or acidity in the solvent. The decreased dipole moment associated to the electronic transition in this probe also contributes to the hypsochromic shift. The small contribution of solvent basicity to the transition of the probe (1) is not so clear, however. 9.3.7.2 Treatment of the solvent effect in: 9.3.7.2.1 Spectroscopy Analyzing the SPP, SB and SA scales in the light of spectroscopic data that are sensitive to the nature of the solvent poses no special problem thanks to the vertical nature of the transitions, where the cybotactic region surrounding the chromophore is hardly altered. The papers where the SPP, SA and SB scales were reported discuss large sets of spectroscopic data in terms of the nature of the solvent. Some additional comments are made below. Recently, Fawcet and Kloss,83 analyzed the S=O stretching frequencies of dimethyl sulfoxide (DMSO) to explain behavior of 20 solvents and the gas phase. They found the frequency of this vibration in DMSO to be shifted by more than 150 cm-1 and to be correlated to the Gutmann acceptor number (AN) for the solvents. Based on our analysis, the frequency shift reflects the acidity and, to a lesser extent, the polarity of the solvent, according to the following equation:

Javier Catalan

vS=O = 38.90(±7.50)SPP − 89.67(±4.60)SA + 1099.1

645

[9.3.22]

with n = 21, r = 0.979 and sd = 6.8 cm-1. This fit is very good, taking into account that it encompasses highly polar solvents such as DMSO itself, highly acidic solvents such as trifluoroacetic acid (SPP=1.016, SA=1.307), and highly non-polar and non-acidic solvents such as the gas phase. Giam and Lyle84 determined the solvent sensitivity of the 19F NMR shifts on 4-fluoropyridine relative to benzene as an internal reference in 31 of the solvents listed in Table 9.3.1. If DMF is excluded on the grounds of its odd value, the chemical shifts for the remaining 30 solvents are accurately described by the following function of solvent acidity and polarity:

Δ4F = −1.66(±0.57)SPP − 6.84(±0.36)SA − 6.50(±0.45)

[9.3.23]

with r = 0.971 and sd = 0.34 ppm. Clearly, the acidity of the medium is the dominant factor in the chemical shift measured for this compound, which reveals the central role played by the lone electron pair in pyridine. Both absorption and emission electronic transitions are acceptably described by our scales, as shown by a recent study85 on the solvation of a series of probes containing an intramolecular hydrogen bond, so no further comment is made here other than the following: even if one is only interested in evaluating the change in dipole moment upon electronic excitation via solvatochromic analysis, a multi-parameter analysis must be conducted in order to isolate the shifts corresponding to the pure dipolar effect of the solvent.85 Lagalante et al.86 proposed the use of 4-nitropyridine N-oxide as a suitable solvatochromic indicator of solvent acidity. The hypsochromic shifts determined by these authors for 43 solvents in Table 9.3.1 are due largely to the acidity of solvent and, to a lesser extent, also to its basicity; based on the following equation, however, solvent polarity induces a bathochromic shift in the band: vmax = −0.92(±0.44)SPP + 0.68(±0.17)SB + 3.63(±0.23)SA +29.10(±0.31)[9.3.24] with r = 0.943 and sd = 0.31 kK. As can be seen from Figure 9.3.7, this probe classifies solvents in groups encompassing non-acidic solvents (below 29 kK), moderately acidic solvents (at about 30 kK) and highly acidic solvents (between 31 and 32 kK). Because the solvatochromism does not change gradually with increase in solvent acidity, the probe appears to be unsuitable for quantifying this effect. Davis87 determined the solvatochromism of a charge-transfer complex formed by tetra-n-hexylammonium iodide-nitrobenzene in 23 different solvents and, using the Z and ET(30) scales, observed a bilinear behavior in scarcely polar and highly polar solvents. A multi-parameter fit of the data for 22 of the solvents revealed that the solvatochromism is seemingly sensitive to solvent acidity only: vc.t. = 11.23(±0.75)SA + 21.41(±0.184)

[9.3.25]

646

9.3 Solvent effects based on pure solvent scales

Figure 9.3.7. Plot of the experimental UV/Vis absorption maxima, vmax, of 4-nitropyridine N-oxide vs. the predicted vmax values according to eq. [9.3.24].

Figure 9.3.8. Plot of the fluorescence maxima, vmax(em), for the Neutral Red in different solvents vs. the solvent polarity function Δf [Δf = (ε − 1)/(2ε + 1) − (n2 − 1)/(2n2 +1)].

Figure 9.3.9. Plot of the fluorescence maxima, vmax(em), for the Neutral Red in different solvents vs. the predicted, vmax(em), values according to eq. [9.3.26].

Figure 9.3.10. Plot of Grunwald and Wistein’s logktBuCl values vs. the predicted logktBuCl values according to eq. [9.3.29].

with n = 22, r = 0.959 and sd = 0.66 kK. An interesting situation is encountered in the analysis of electronic transitions that result from chromophores which, assisted by solvent polarity, can undergo a change in the electronic state responsible for the fluorescence emission; this is a frequent occurrence in systems involving a TICT mechanism.68,88-90 In this situation, a plot of Stokes shift against solvent polarity is a bilinear curve depending on whether the solvents are non-polar

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(where the fluorescence is emitted from the normal excited state of the chromophore) or polar enough for the transition to take place from the more polar state. Unless the solvents used are carefully selected, it is venturesome to assume that the electronic states will be inverted simply because the variation of solvatochromism with a function of solvent polarity is bilinear. Recently, Sapre et al.91 showed that a plot of the maximum fluorescence of Neutral Red (NR) against the solvent polarity function Δf is clearly bilinear (see Figure 9.3.8). Accordingly, they concluded that, in solvents with Δf > 0.37, the emitting state changes to a much more polar, ICT state. The analysis of this spectroscopic data in the light of our scales reveals that, in fact, the solvatochromism of NR is normal, albeit dependent not only on the polarity of the solvent (SPP), but also on its acidity (SA) (see Figure 9.3.9): NR

ν max = −4.31(±0.57)SPP − 1.78(±0.19)SA + 21.72(±0.47)

[9.3.26]

with r = 0.974 and sd = 0.21 kK. 9.3.7.2.2 Kinetics Kinetics so closely related to the solvent effect as those of the Menschutkin reaction between triethylamine and ethyl iodide [eq. (9.3.27)], the solvolysis of tert-butyl chloride [eq. (9.3.28)] or the decarboxylation of 3-carboxybenzisoxazole [eq. (9.3.29)], are acceptably described by our scales.15,92,93 The equation for the Menschutkin kinetics is logks/kHex = 8.84(±0.66)SPP + 1.90(±1.37)SA − 4.07(±0.53)

[9.3.27]

with n = 27, r = 0.947 and sd = 0.41. The rate of this reaction between triethylamine and ethyl iodide, which varies by five orders of magnitude from n-hexane (1.35x10-8 l mol-1 s-1) to DMSO (8.78x10-4 l mol-1 s-1), is accurately described by solvent polarity and acidity − the sensitivity to the latter is somewhat imprecise. The equation for the kinetics of solvolysis of tert-butyl chloride is: logk = 10.02(±1.14)SPP + 1.84(±0.99)SB + 8.03(±0.69)SA − 19.85(±0.70)

[9.3.28]

with n = 19, r = 0.985 and sd = 0.80. Based on eq. [9.3.28], all solvent effects increase the rate of solvolysis. However, the strongest contribution is that of polarity and the weakest one that of acidity. Although much less significant, the contribution of solvent basicity is especially interesting as it confirms that nucleophilicity also assists in the solvolytic process. Taking into account that it encompasses data spanning 18 orders of magnitude (from log k = −1.54 for water to log k = −19.3 for the gas phase), the fit is very good (see Figure 9.3.10). The equation for the kinetics of decarboxylation of 3-carboxybenzisoxazole is: logk = 10.37(±1.47)SPP + 2.59(±0.74)SB − 5.93(±0.58)SA − 9.74(±1.17) [9.3.29] with n = 24, r = 0.951 and sd = 0.73. Equation [9.3.29] reproduces acceptably well the sensitivity of the decarboxylation rate of 3-carboxybenzisoxazole in pure solvents observed by Kemp and Paul.7 In addition, it clearly shows that such a rate increases dramatically with increasing polarity and, also,

648

9.3 Solvent effects based on pure solvent scales

to a lesser degree, with solvent basicity. By contrast, it decreases markedly with increasing solvent acidity. This behavior is consistent with the accepted scheme for this decarboxylation reaction.93 9.3.7.2.3 Electrochemistry Gritzner94 examined the solvent effect on half-wave potentials and found those of K+ relative to bis(biphenyl)chromium(I)/(0), designated E1/2(BCr)K+, to be related to the Gutmann donor number (DN) for the solvents, so he concluded that K+ behaves as a Lewis acid against basic solvents. Based on the following equation, the behavior of E1/2(BCr)K+ is dictated largely by the basicity of the solvent but it is also dependent, however weakly, on its acidity: E1/2(BCr)K+ = −0.51(±0.05)SB + 0.12(±0.04)SA − 1.06(±0.03)

[9.3.30]

with n = 17, r = 0.941 and sd = 0.03 V. It should be noted that solvent basicity increases the half-wave potentials of K+ whereas solvent acidity decreases it. 9.3.7.2.4 Thermodynamics In order to compare the shifts of the conformational equilibrium position with solvent effects it is advisable to select species exhibiting negligible cavity effects on the equilibrium position. Two firm candidates in this respect are the Scheme VI. conformational equilibria of 1,2,2-trichloroethane and the equilibrium between the equatorial and axial forms of 2-chlorocyclohexanone; both are accurately described by our scales.15 Of special interest is also the equilibrium between the keto and enol tautomers of pentane-2,4-dione (see the scheme VI). The ΔG values for this equilibrium in 21 solvents reported by Emsley and Freeman95 are accurately reproduced by solvent polarity and acidity according to

ΔG = 18.45(±2.41)SPP + 4.22(±0.86)SA − 18.67(±1.96)

[9.3.31]

-1

with n = 21, r = 0.924 and sd = 1.34 kJ mol . The equilibrium position is mainly dictated by solvent polarity; however, there is clearly a specific contribution of solvent acidity from the carbonyl groups of the dione. 9.3.7.3 Mixtures of solvents. Understanding the preferential solvation model The solvation of a solute, whether ionic or neutral, in a mixture of solvents is even more complex than in a pure solvent.1 This is assumed to be so largely because a solvent mixture involves interactions not only between the solute and solvent but also among different molecules present in the mixture; the latter type of contribution also plays a central role in the solvation process. Among others, it results in significant deviations of the vapor pressure of a mixture with respect to the ideal behavior established by Raoult’s law.

Javier Catalan

649

Solvation studies of solutes in mixed solvents have led to the conclusion that the above-mentioned divergences may arise from the fact that the proportion of solvent components may be significantly different around the solute and in the solution bulk. This would be the case if the solute were preferentially surrounded by one of the mixture components, which would lead to a more negative Gibbs energy of solvation.1,96 Consequently, the solvent shell around the solute would have a composition other than the macroscopic ratio. This phenomenon is known as “preferential solvation”, a term that indicates that the solute induces a change with respect to the solvent bulk in its environment; however, such a change takes place via either non-specific solute-solvent interactions called “dielectric enrichment” or specific solute-solvent association (e.g. hydrogen bonding). Preferential solvation has been studied in the light of various methods, most of which are based on conductance and transference measurements,96 NMR measurements of the chemical shift of a nucleus in the solute97 or measurements of the solvatochromism of a solute in the IR98 or UV-Vis spectral region.99 Plots of the data obtained from such measurements against the composition of the bulk solvent (usually as a mole fraction) depart clearly from the ideal behavior and the deviation is ascribed to the presence of preferential solvation. Several reported methods aim to quantify preferential solvation;96-100 none, however, provides an acceptable characterization facilitating a clear understanding of the phenomenon. If preferential solvation is so strongly dictated by the polar or ionic character of the solute, then characterizing a mixture of solvents by using a molecular probe will be utterly impossible since any conclusions reached could only be extrapolated to solutes of identical nature as regards not only polarity and charge, but also molecular size and shape. However, the experimental evidence presented below allows one to conclude that this is not the case and that solvent mixtures can in fact be characterized in as simple and precise terms as can a pure a solvent. In the light of the previous reasoning, describing the solvolysis of tert-butyl chloride or the decarboxylation kinetics of 3-carboxybenzisoxazole in mixed solvents in terms of SPP, SB and SA for the mixtures appeared to be rather difficult owing to the differences between the processes concerned and the solvatochromism upon which the scales were constructed. However, the results are categorical as judged by the following facts: (a) The solvolysis rate of tert-butyl chloride in 27 pure solvents and 120 binary mixtures of water with methanol (31 mixtures), ethanol (31), isopropyl alcohol (1), trifluoroethanol (8), dioxane (13), acetone (27) and acetic acid (9), in addition to the datum for the gas phase, all conform to the following equation:92 logk = 10.62(±0.44)SPP + 1.71(±0.22)SB + 7.89(±0.17)SA − 20.07(±0.34)

[9.3.32]

with n = 148, r = 0.99 and sd = 0.40. (b) The decarboxylation rate of 3-carboxybenzisoxazole in 24 pure solvents and 36 mixtures of DMSO with diglyme (4 mixtures), acetonitrile (4), benzene (7), dichloromethane (6), chloroform (6) and methanol (9) are accurately described by the following expression:

650

9.3 Solvent effects based on pure solvent scales

logk = 10.03(±1.05)SPP + 2.41(±0.49)SB − 5.73(±0.40)SA − 9.58(±0.83) [9.3.33] with n = 60, r = 0.990 and sd = 0.60. Other evidence obtained in our laboratory using solvent mixtures and probes as disparate in size and properties as the cation Na+ and Reichardt’s ET(30), also confirm that solvent mixtures are no more difficult to characterize than pure solvents.

9.3.8 RESOLVING THE GENERAL SOLVENT EFFECT INTO ITS POLARIZABILITY AND DIPOLARITY COMPONENTS There have been several, unsuccessful attempts at empirically resolving the general solvent effect in the π* scale into its polarizability and dipolarity components.80-102 Thus, Kamlet, Abboud and Taft80,101 adapted their π* scale for increased flexibility to solvent polarizability by introducing a “polarizability correction term” δ ranging from 0.0 for nonchlorinated aliphatic solvents through 0.5 for polychlorinated solvents to 1.0 for aromatic solvents; in this way, they constructed the alternative (π* + dδ) scale. Similarly, Buncel and Rajogapal102 developed their well-known π*azo scale and, subsequently, Abe103 proposed his π*2 scale. In 1992, Drago14,104 used 27 different solvents to develop the S’ polarity scale, which is in fact a dipolarity scale. This dissatisfactory state of affairs led us to seek appropriate probes for measuring polarizability and then to resolve the solvent dipolarity component of solvatochromism in the probe DMANF. 9.3.8.1 The new SP scale The spectral properties of an effective molecular probe for measuring solvent polarizability should possess can be inferred by careful reading of the classic paper by Bayliss and McRae.105 Thus, the candidate probe should exhibit a strong, structured absorption band in the gas phase and the vibrational structure of the band should be retained in any type of solvent irrespective of its acidity, basicity of dipolarity; therefore, the energy of the band should only depend on the polarizability of the solvent. In 2004, Catalán and Hopf106 showed 3,20-di-tert-butyl-2,2,21,21-tetramethyl3,5,7,9,11,13,15,17,19-docosanonaene (ttbP9) (15) to strictly meet the previous requirements. They used the energy of the 0-0 component of the first absorption band for ttbP9 in various solvents to define solvent polarizability as SP = (vgas − vsolvent) /(vgas − vCS2)

[9.3.34]

SP ranging from 0 for the gas phase to 1 for CS2. These authors reported the SP values for a series of 99 solvents. Interestingly, they found the SPP values (a combination of solvent polarity and polarizability) for nondipolar solvents to exhibit highly linear correlation with its corresponding SP values (see Figure 4 in their paper). Also, they found very high correlation between the 0-0 component of the phosphorescence of the 1Δg singlet oxygen and SP in each solvent. In a subsequent paper, Catalán107 reported SP for a further 64 solvents. Table 9.3.2 lists the SP values for the 163 solvents studied.

Javier Catalan

651

Table 9.3.2. Empirical solvent parameters of polarizability (SP) and dipolarity (SdP). Number 1

Solvent gas-phase

SP

SdP

0.000

0.000

2

perfluoro-n-hexane

0.339

0.000

3

2-methylbutane

0.581

0.000

4

n-pentane

0.593

0.000

5

n-hexane

0.616

0.000

6

n-heptane

0.635

0.000

7

n-octane

0.650

0.000

8

n-nonane

0.660

0.000

9

n-decane

0.669

0.000

10

n-undecane

0.678

0.000

11

n-dodecane

0.683

0.000

12

n-tridecane

0.690

0.000

13

n-tetradecane

0.696

0.000

14

n-pentadecane

0.700

0.000

15

n-hexadecane

0.704

0.000

16

3-methylpentane

0.620

0.000

17

Isooctane

0.618

0.000

18

Cyclopentane

0.655

0.000

19

Cyclohexane

0.683

0.000

20

Cycloheptane

0.703

0.000

21

Cyclooctane

0.719

0.000

22

Methylcyclohexane

0.675

0.000

23

Decalin

0.744

0.000

24

cis-decalin

0.753

0.000

25

Squalane

0.714

0.000

26

Petroleum ether

0.593

0.005

27

Dichloromethane

0.761

0.769

28

Chloroform

0.783

0.614

29

Tetrachloromethane

0.768

0.000

30

1,2-dichloroethane

0.771

0.742

31

1,1,1-trichloroethane

0.737

0.500

32

1,1,2-trichlorotrifluoroethane

0.596

0.152

33

1,1,2,2-tetrachloroethane

0.845

0.792

652

9.3 Solvent effects based on pure solvent scales

Table 9.3.2. Empirical solvent parameters of polarizability (SP) and dipolarity (SdP). Number

Solvent

SP

SdP

34

1-chlorobutane

0.693

0.529

35

Benzene

0.793

0.270

36

Fluorobenzene

0.761

0.511

37

Chlorobenzene

0.833

0.537

38

Bromobenzene

0.875

0.497

39

(Trifluoromethyl)benzene

0.694

0.663

40

Hexafluorobenzene

0.623

0.252

41

1,2-dichlorobenzene

0.869

0.676

42

Toluene

0.782

0.284

43

Ethylbenzene

0.772

0.237

44

Propylbenzene

0.767

0.209

45

Butylbenzene

0.765

0.176

46

tert-butylbenzene

0.757

0.182

47

o-xylene

0.791

0.266

48

m-xylene

0.771

0.205

49

p-xylene

0.778

0.175

50

Mesitylene

0.775

0.155

51

1,2,3,5-tetramethylbenzene

0.784

0.203

52

Anisole

0.820

0.543

53

Veratrole

0.851

0.606

54

Dibenzyl ether

0.877

0.509

55

Aniline

0.924

0.956

56

Benzyl alcohol

0.861

0.788

57

Phenethyl alcohol

0.849

0.763

58

Ethoxybenzene

0.810

0.669

59

Methylbenzoate

0.824

0.654

60

Acetophenone

0.848

0.808

61

Benzonitrile

0.851

0.852

62

Nitrobenzene

0.891

0.873

63

Pyridine

0.842

0.761

64

Tetraline

0.838

0.182

65

1-methylnaphthalene

0.908

0.510

66

1-bromonaphthalene

0.964

0.669

67

Methanol

0.608

0.904

68

Ethanol

0.633

0.783

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653

Table 9.3.2. Empirical solvent parameters of polarizability (SP) and dipolarity (SdP). Number

Solvent

SP

SdP

69

n-propanol

0.658

0.748

70

n-butanol

0.674

0.655

71

n-pentanol

0.687

0.587

72

n-hexanol

0.698

0.552

73

n-heptanol

0.706

0.499

74

n-octanol

0.713

0.454

75

n-nonanol

0.717

0.429

76

n-decanol

0.722

0.383

77

n-undecanol

0.728

0.342

78

2-propanol

0.633

0.808

79

2-butanol

0.656

0.706

80

2-pentanol

0.667

0.665

81

2-hexanol

0.683

0.601

82

2-octanol

0.696

0.496

83

isobutanol

0.657

0.684

84

tert-butanol

0.632

0.732

85

Cyclopentanol

0.740

0.673

86

Cycloheptanol

0.770

0.546

87

Cyclooctanol

0.777

0.537

88

Allyl alcohol

0.705

0.839

89

Ethylene glycol

0.777

0.910

90

1,2-propanediol

0.731

0.888

91

1,2-butanediol

0.724

0.817

92

1,3-butanediol

0.739

0.873

93

1,4-butanediol

0.763

0.864

94

2,3-butanediol

0.714

0.877

95

Glycerin

0.828

0.921

96

2,2,2-trifluoroethanol

0.543

0.922

97

Acetic acid

0.651

0.676

98

Propionic acid

0.664

0.434

99

Butyric acid

0.675

0.333

100

Valeric acid

0.687

0.276

101

Hexanoic acid

0.698

0.245

102

Heptanoic acid

0.704

0.238

103

Isobutyric acid

0.659

0.302

654

9.3 Solvent effects based on pure solvent scales

Table 9.3.2. Empirical solvent parameters of polarizability (SP) and dipolarity (SdP). Number

Solvent

SP

SdP

104

2-methyl-butyric acid

0.686

0.261

105

3-methyl-butyric acid

0.670

0.310

106

Triethylamine

0.660

0.108

107

Butylamine

0.690

0.296

108

Dibutylamine

0.692

0.209

109

Tributylamine

0.689

0.060

110

Acetonitrile

0.645

0.974

111

Propionitrile

0.668

0.888

112

Butyronitrile

0.689

0.864

113

Valeronitrile

0.696

0.853

114

Chloroacetonitrile

0.763

1.024

115

Formamide

0.814

1.006

116

Dimethylformamide

0.759

0.977

117

Diethylformamide

0.745

0.939

118

Dimethylacetamide

0.763

0.987

119

Diethylacetamide

0.748

0.918

120

Piperidine

0.754

0.365

121

1-methylpiperidine

0.708

0.116

122

1-methylpyrrolidine

0.712

0.216

123

1-methylpyrrolidinone

0.812

0.959

124

1-methylimidazole

0.834

0.959

125

1,4-dimethylpiperazine

0.730

0.211

126

1,1,3,3-tetramethylguanidine

0.780

0.750

127

Tetramethylurea

0.778

0.878

128

Trimethyl phosphate

0.707

0.909

129

Hexamethylphosphoramine

0.744

1.10

130

Diethyl ether

0.617

0.385

131

Dipropyl ether

0.645

0.286

132

Dibutyl ether

0.672

0.175

133

Dihexyl ether

0.681

0.208

134

Diisopropyl ether

0.625

0.324

135

Butyl methyl ether

0.647

0.345

136

tert-butyl methyl ether

0.622

0.422

137

Tetrahydrofuran

0.714

0.634

138

2-methyltetrahydrofuran

0.700

0.768

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655

Table 9.3.2. Empirical solvent parameters of polarizability (SP) and dipolarity (SdP). Number

Solvent

SP

SdP

139

1,4-dioxane

0.737

0.312

140

Cineole

0.736

0.343

141

Triacetin

0.735

0.686

142

Methyl acetate

0.645

0.637

143

Ethyl acetate

0.656

0.603

144

Propyl acetate

0.670

0.559

145

Butyl acetate

0.674

0.535

146

Methyl salicylate

0.843

0.741

147

Ethyl salicylate

0.819

0.681

148

Ethyl formate

0.648

0.707

149

Propyl formate

0.667

0.633

150

Dimethyl carbonate

0.653

0.531

151

Propylene carbonate

0.746

0.942

152

Acetone

0.651

0.907

153

2-butanone

0.669

0.872

154

2-pentanone

0.689

0.783

155

3-pentanone

0.692

0.785

156

Cyclohexanone

0.766

0.745

157

γ-butyrolactone

0.775

0.945

158

Sulfolane

0.830

0.896

159

Nitromethane

0.710

0.954

160

Nitroethane

0.706

0.902

161

Dimethyl sulfoxide

0.830

1.000

162

Carbon disulfide

1.000

0.000

163

Water

0.681

0.997

The solvent polarizability scale has for the first time allowed the bathochromic shift in the first absorption band for BODIPYs, which is exclusively governed by the polarizability of the solvent, to be unambiguously explained.108 We recently showed that β-carotene does not fulfill the requirements for use as an effective polarizability probe.109 9.3.8.2 The new SdP scale As stated above, DMANF (7) is a very good choice for assessing dipolarity-dipolarizability interactions in solvents. This led us to use it in developing the SPP scale. Obviously, a plot of the maximum frequency of the first absorption band for DMANF against SP in nonpolar solvents should be linear. In fact, a plot of the data for 163 solvents revealed that 26 and the gas phase fitted the following equation:

656

9.3 Solvent effects based on pure solvent scales

v0solvt = −(4887.45 ± 44)SPsolv + (28224.6 ± 28)

[9.3.35]

with n = 27 and r = 0.9991. If the previous solvents are assumed to have zero dipolarity, then, clearly, departure from the line of the points for the other solvents will be proportional to their dipolarity. A solvent dipolarity scale can thus be established by using the following equation: SdP = (v0solv − vsolv)/(v0DMSO − vDMSO) = (v0solv − vsolv)/1611 0

[9.3.36]

0

where v solv and v DMSO represent the polarizability of the target solvent and DMSO, respectively, as calculated from eq. [9.3.35], and vsolv and vDMSO are frequencies of the first electronic transition of DMANF in the target solvent and DMSO, respectively. SdP ranges from 0 for the gas phase to 1 for DMSO. Table 9.3.2 lists the SdP values for the studied solvents. It should be noted that the S’ values originally used by Drago110,111 to describe the polarity of 27 solvents are well correlated with the corresponding values on our dipolarity (SdP) scale (n = 27, r = 0.961).

9.3.9 APPLICATIONS OF THE PURE SP, SDP, SA AND SB SCALES Before the polarizability (SP) and dipolarity (SdP) components resolved from the general solvent scale (SPP) were used to derive any conclusions, we checked whether the two new scales are in fact linearly independent. Least-squares fitting of the data for 163 solvents gave a coefficient r2 = 0.088, which confirms that the SP and SdP scales are linearly independent. In addition, the two scales are also linearly independent from the specific solvent scales SA and SB. Interestingly, the general solvent effect scale (SPP) is highly correlated with the polarizability (SP) and dipolarity (SdP) pure scales: SPP = (0.49 ± 0.03)SP + (0.38 ± 0.01)SdP + (0.21 ± 0.02)

[9.3.37]

with n = 159 and r = 0.9597. Based on this equation, SPP is a highly balanced combination of both effects, which is probably why it allows the general solvent effect to be accurately described − obviously, provided the target solute exhibits both effects. This is not the case with the π* scale, which exhibits not only more disparate polarizability and dipolarity coefficients, but also slight contamination with acidity and basicity effects as revealed by the following equation:

Π* = (1.48 ± 0.09)SP + (0.74 ± 0.03)SdP − (0.11 ± 0.03)SB + + (0.24 ± 0.18)SA + (2.66 ± 0.29)

[9.3.38]

with n = 78 and r = 0.9798. The fact that our scales allow solvent polarizability and dipolarity to be dealt with separately allowed us to revisit for the first time such interesting phenomena as dipolaritytriggered processes, which include charge transfer in biaryl compounds and the solvatochromism inversion in betaines. An analysis of the solvatochromism of biaryl compounds in terms of their polarity in various solvents (SPP)112,113 resulted in large standard deviations; by contrast, using

Javier Catalan

Figure 9.3.11. Correlation between the absorption and emission wavenumbers of BAC K and the dipolarity parameter SdP, see ref. 114.

657

Figure 9.3.12. Correlation between the absorption and emission wavenumbers of C9A and the dipolarity parameter SdP, see ref. 114.

SdP114 values led to much better statistics and exposed the TICT phenomenon. Figures 9.3.11 ad 9.3.12 illustrate the behavior of two prototypical biaryls: 9,9’-bisacridinyl (BAC) and el 9-(9’-anthracenyl)carbazole (C9A). As can be seen, the absorptive solvatochromism of both compounds exhibited a slight bathochromic shift throughout the dipolarity range (0-1.05). On the other hand, the emissive solvatochromism differed. Thus, BAC exhibited a bathochromic shift over the SdP range 0-0.8 (slope −435 ± 39), followed by an abrupt jump to a much higher slope (−7300 ± 447) over the SdP > 0.8 reflecting triggering of a TICT process in the excited electronic state. By contrast, C9A exhibited a sustained bathochromic shift (slope −2207 ± 48) throughout its dipolarity range. As can clearly be seen from Fig. 9.3.11, BAC in the excited state requires a dipolarity above 0.8 for the TICT process to be triggered; by contrast, C9A does not require a dipolar medium to undergo the process (see Fig. 9.3.12). Although inverted solvatochromism in betaines has been widely studied, no test clearly exposing the abrupt change from bathochromic solvatochromism to hypsochromic solvatochromism has so far been devised. Finding that the dipolarity of 1chlorobutane increases markedly with decreasing temperature115 allowed us to unambiguously expose this solvatochromic change116 (see Fig. 9.3.13). Resolving dipolarity and polarizability effects also allowed us to break down their contributions to n → π * transitions in Figure 9.3.13. Wavenumbers for the maxima of the first ketones;117 in addition, it allowed us to absorption band of DTBSB, dissolved in 1-chlorobudemonstrate their dependence on the size of tane and measured at temperatures over the range 34377K vs. the corresponding solvent dipolarity parameter the π backbone and also that the solvatochrSdP. omism of the first π → π * absorption band

658

9.3 Solvent effects based on pure solvent scales

for some polar compounds such as 1-methylindazole depends on the solvent polarizability alone.118 The following scales have been widely used in the last years for the solvatochromic analysis of a variety of chromophores. They permitted not only to establish the nature of solvents interactions with the chromophores, but also some studies have open new research directions. The synthetic efforts on the building a new derivative from PRODAN (6-propionyl2-dimethylaminophthalene) by Abelt’s group119-123 resulted in the creation of new solvatochromic scales and characterization of the nature of the interactions of PRODAN with a great variety of solvents. This is noteworthy for the reason that PRODAN was characterized by Weber and Farris124 as a fluorescent probe having micropolarity. Abelt et al. have synthesized derivatives of PRODAN that are highly sensitive sensors in the case of low solvent acidity.122 BODIPYs, abbreviation for boron-dipyrromethene, 4,4-difluoro-4-bora-3a,4a-diazas-indacene, exhibited the first absorption band easily characterized by an intense peakmaximum at about 500 nm and a corresponding emission band shifted slightly towards red. Solvatochromism of the BODIPY type molecules was not understood while taking into account solvent acidity, solvent basicity, and general solvent polarity represented, for example, by the parameter π* of Taft-Kamlet.80 The split by general solvent polarity into two contributions of solvent dipolarity (SdP)107 and solvent polarizability (SP)107 is the key point to a proper description of solvatochromism of BODIPYs. In 2009, Boens et al.125 showed that solvatochromism of two 3,5-dianilino-difluoroboron dipyrromethenes either on absorption or emission depended on the polarizability of the environment. This behavior was also typical of other two BODIPY derivatives,126 that is, 8-(4-bromophenyl)-3,4,4,5-tetracyano-4-bora-3a,4a,diaza-s-indacene and 8-(4-bromophenyl)3,5-dicyano-4,4-difluoro-bora-3a,4a,-diaza-sindacene. The polarizability dependence was attained a) by a series of conformationally constrained annulated BODIPY dyes,127 b) by a great number of 3-aryl and 3,5-diaryl substituted difluoroboron dipyrromethenes,128 c) several 8-haloBODIPY and 8-(C,N,O,S) substituted analogues,129 d) several alkylated BODIPY dyes,130,131 and e) by several BODIPYs benzylamine-substituted.132 Cole et al. analyzed the solvatochromism of thirteen coumarins (the so-called coumarins 1, 35, 102, 120, 151, 152, 153, 343, 445, 466, 522, 522B, and 314 T) in 17 solvents and found excellent fit with our solvatochromic scales for all of them, except for the coumarin 343, whose behavior was not adequately described. It was explained that coumarin 343 did not maintain the same molecular structure in all solvents used,134 and consequently the position of its absorption and emission peaks could not be consistently described by the solvatochromic scales. Proper solvatochromic adjustments for other coumarins have also been reported.135,136 Another important area of application of the solvatochromic scales is that of ionic liquids. In 2015 our group reported137 that our probes were adequate to establish the solvatochromic parameters (SA, SB, SdP and SP) of the ionic liquids 1-(1-butyl)-3-methylimidazolium tetrafluoroborate, [BMIM] [BF4] and 1-(1-butyl)-3-methylimidazolium

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hexafluorophosphate, [BMIM] [PF6], and also how, these varied by changing the temperature between 293 and 353 K. It is interesting to note that our solvatochromic parameters, SA, SB, SdP and SP for these ionic liquids change linearly with temperature. It is also important to mention the contributions made by Spange et al.138-141 Tiwari et al.142 successfully applied our scales for the first time to the eutectic liquids such as reline, ethaline and glycerin. These authors have also explored solvatochromic behavior in temperatures from 298 to 323K, which allowed them to understand the behavior of these solvents. The study of the solvatochromism of aromatic solutes in nonpolar solvents between 293 and 113K allowed us to set forth the following spectroscopic rule143 “an aromatic molecule, on Franck-Condon excitation can hardly generate an excited electronic state with lower polarizability than that of its ground electronic state”. This rule corrected the spectroscopic rule proposed by Renger et al.144 according to which “the larger the energy En of the excited state (of the solute), the larger the solvatochromic red shift”.

9.3.10 NEW RESEARCH DIRECTION IN MOLECULAR SOLVATOCHROMISM The unexplained solvatochromic behavior of 1-methyl-indazole with solvatochromic scales representing the general solvent effect behavior using a single global parameter was corrected by splitting the overall effect of the solvent into a dipolar contribution (SdP) and another due to polarizability (SP). With these unfolded scales, the solvatochromism of 1methyl-indazole only depends on the solvent polarizability.118 This unexpected conclusion for a polar solute indicates that any electronic transition generated from a non-bonding electron pair (nitrogen atom with sp2 hybridization of indazole) to a π system of one molecule of indazole depends mostly on the medium polarizability. This allows us to conclude that an electronic transition from π-localized system to a π-delocalized system, because of the molecular structure of the solute, involves a mostly electronic delocalization, and therefore, a bathochromic shift of the electronic transition.145 This increase in electronic delocalization could be expected to increase with increasing the size of the π system of the chromophore, consequently, it should be expected to increase from 1-methylpyrrole, to 1methylindole, and from this to 1-methylcarbazole.145 Consider that the π structure of these compounds formed from a pentagonal ring by adding one or two hexagonal rings. The solvatochromic equation found for 1-methylpyrrole is as follows:

ν abs = − (422±91) SP + (222±15) SdP + (46332±59) with a number of solvents n = 10, a correlation coefficient of r = 0.968, and a standard deviation of sd = 20 cm-1. For 1-methylindole the corresponding equation is as follows:

ν abs = − (762±71) SP + (80±37) SdP + (34492±43) with n = 17, r = 0.945, and sd = 25 cm-1, respectively. And, for 1-methylcarbazole, the following equation applies:

ν abs = − (1125±50) SP − (136±13) SdP + (29866±31)

660

9.3 Solvent effects based on pure solvent scales

with n = 17, r = 0.945, and sd = 25 cm-1, respectively. These adjustments confirm that the electronic delocalization in the first excited state increases with the size of the π-molecular system, thereby producing a bathochromic shift of the corresponding electronic transition. The first electronic transition is of the type π (loc) → π (deloc) as demonstrated for a number of molecules such as:145 BODIPYs, 1-methyl-indazol, 1-benzimidazole, 1-benzotriazol, DMABN (dimethylamino benzotriazol), DCS (trans-4-(dimethylamino)-4'-cyanostilbene), DMANF (dimethylaminonitrofluorene), MNI (1methyl-5-nitro-indole), metalloporphyrins, and 7-azaindole. It is noteworthy to point out that several of these compounds, showing singular spectral behavior, had their solvatochromism wrongly ascribed to a great extent to changes in their dipole moment on photoexcitation. Another interesting line of research appears to be the possibility of keeping the solvatochromism of a solute constant in a wide range of temperatures, such as between 182 and 77 K by using glycerol146 as a solvent. The four solvatochromic parameters representing the solvent polarizability, SP, the solvent dipolarity, SdP, the solvent basicity, SB, and the solvent acidity of glycerol can be regarded as constant when changing the temperature of glycerol between 182 and 77 K, as can be seen in Table 9.3.3 in which we provide the glycerol parameters obtained between 353 and 77 K. In Figure 9.3.14, the polarizability behavior of glycerol in this wide range of temperatures is given. Table 9.3.3. SP, SdP, SA, and SB values of glycerol, determined in the temperature range of 353 to 77K T/K

SP

SdP

SA

SB

353

0.828

0.932

0.786

0.267

343

0.829

0.932

0.792

0.275

333

0.831

0.931

0.799

0.283

323

0.832

0.928

0.800

0.289

313

0.833

0.929

0.801

0.298

303

0.834

0.924

0.808

0.302

293

0.835

0.921

0.814

0.309

283

0.836

0.916

0.815

0.314

273

0.837

0.915

0.820

0.320

263

0.838

0.901

0.823

0.328

253

0.839

0.897

0.824

0.331

243

0.841

0.882

0.827

0.343

233

0.843

0.873

0.833

0.351

223

0.845

0.855

0.832

0.358

213

0.847

0.844

0.832

0.370

203

0.850

0.826

0.837

0.374

193

0.853

0.808

0.841

0.381

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Table 9.3.3. SP, SdP, SA, and SB values of glycerol, determined in the temperature range of 353 to 77K T/K

SP

SdP

SA

SB

183

0.855

0.791

0.841

0.381

173

0.856

0.786

0.851

0.396

163

0.856

0.791

0.849

0.397

153

0.857

0.798

0.849

0.413

143

0.856

0.793

0.852

0.402

133

0.856

0.793

0.854

0.409

123

0.856

0.793

0.852

0.401

113

0.856

0.795

0.854

0.413

103

0.856

0.793

0.853

0.412

93

0.856

0.798

0.855

0.413

77

0.856

0.800

0.854

0.417

Figure 9.3.14. Polarizability of glycerol vs. temperature.

This unique behavior of glycerol is consistent with the conclusion reached in 1954 by Schulz147 that glycerol linearly increases its density when the temperature is lowered from 313 to 200K. Below 200 K, its density remains constant, in other words, its volume contraction stops, and its molecules remain in the crystalline form which does not change when the temperature is further decreased. When dissolving a solute in glycerol, it gets trapped and can be studied without changing its molecular structure below 182 K.

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9.3 Solvent effects based on pure solvent scales J. Phys. Chem., 97, 11199 (1993); R.D. Skwierczynski, K.A. Connors, J. Chem. Soc. Perkin Trans 2, 467(1994) M. Rosés, C. Ráfols, J. Ortega, E. Bosch, J. Chem. Soc. Perkin Trans 2, 1607 (1995); W. E. Acree Jr., J. R. Powell, S. A. Tucker, J. Chem. Soc. Perkin Trans 2, 529 (1995). R.W. Taft, J.L.M. Abboud, M.J. Kamlet, J. Am. Chem. Soc., 103, 1080 (1981). E. Buncel, S. Rajogapal, J. Org. Chem., 54, 798 (1989). T. Abe, Bull. Chem. Soc. Jpn., 63, 2328 (1990. R.S. Drago, J. Org. Chem., 57, 6547 (1992). N.S. Bayliss, E.G. McRae, J. Phys. Chem., 58, 1002 (1954). J. Catalán, H. Hopf, Eur. J. Org. Chem., 4694 (2004). J. Catalán, J. Phys. Chem. B, 113, 5951 (2009). W. Qin, M. Baruah, M. Sliva, M. Van Averaer, W.M. De Borggraeve, D. Beljonne, B. Van Averbeke, N. Boens, J. Phys. Chem. A, 112, 6104 (2008). J. Catalán, J. Phys. Org. Chem., 26, 948 (2013). R.S. Drago, J. Chem. Soc. Perkin Trans., 2, 1827 (1992). R.S. Drago, J. Org. Chem., 57, 6547 (1992). J. Catalán, C. Díaz, V. López, P. Pérez, R.M. Claramunt, J. Phys. Chem., 100, 18392 (1996). J. Catalán, C. Díaz, V. López, P. Pérez, R.M. Claramunt, Eur. J. Org. Chem., 1697 (1998). J. Catalán, C. Reichardt, J. Phys. Chem. A, 116, 4726 (2012). J. Catalán, J.L.M. de Paz, C. Reichardt, J. Phys. Chem. A, 114, 6226 (2010). J. Catalán, Dyes Pigm., 95, 180 (2012). J. Catalán, J.P. Catalán, Phys. Chem. Chem. Phys., 13, 4072 (2011). J. Catalán, Arkivoc, 2, 57 (2014). R.K.Everett, H.A.A. Nguyen, C.J. Abelt, J. Phys. Chem. A,, 114, 4946 (2010). N.A. Lopez, C.J. Abelt, J. Photochem. Photobiol A Chem., 238, 35 (2012). H. R. Naughton, C.J. Abelt, J. Phys. Chem. B, 117, 3323 (2013). A.H. Yoon, L.C. Whitworth, J.D. Wagner, C.J. Abelt, Molecules, 19, 6427 (2014). M. Daneri, C.J. Abelt, J. Photochem. Photobiol A Chem., 310, 106 (2015). G. Weber, F.J. Farris, Biochemistry, 18, 3075 (1979). N. Boens et al., J. Phys. Chem. C, 113, 11731 (2009). N. Boens et al. Photochem. Photobiol. Sci., 8, 1006 (2009). N. Boens et al, J. Phys. Chem. A, 116, 9621 (2012). N. Boens et al. Photochem. Photobiol. Sci., 12, 835 (2013). N. Boens et al. J. Phys. Chem. A, 118, 1576 (2014). N Boens et al. RSC Adv., 6, 89375 (2015). N Boens et al. RSC Adv., 6, 102899 (2016). N. Boens, Eur. J. Org. Chem., 2561 (2018). X. Liu, J.M. Cole, K.S. Low, J. Phys. Chem. C, 117, 14731 (2013). X. Liu, J.M. Cole, K.S. Low, J. Phys. Chem. C, 117, 14723 (2013). B. Maity, A. Chatterjee, D. Seth, Photochem. Photobiol., 90, 734 (20014) M. Rajeshirke, A. B. Tathe, N. Sekar, J. Mol. Liquids, 264, 358 (2018). J.C. del Valle, F. García Blanco, J. Catalán, J. Phys. Chem. B, 119, 4683 (2015). R. Lungwitz, V. Stremel, S. Spange, New. J. Chem., 34, 1135 (2010 S. Spange, R. Lungwitz, A. Schade, J. Mol. Liquids, 192, 137 (2014). A. Schade, N. Behme, S. Spange, Chem. Eur. J., 20, 2232 (2014). G. Thielemann, S. Spange, New. J. Chem., 41, 8561 (2017). A. Valvi, J. Dutta, S. Tiwari, J. Phys. Chem. B, 121, 11356 ( 2017). J. Catalán, J.C. del Valle, J. Phys. Chem. B, 118, 5168 (2014). T. Renger, B. Grundkötter, M.E.A. Madjet, F. Münh, Proc. Natl. Acad. Aci. U.S.A., 105, 13235 (2008). J. Catalám J. Phys. Org. Chem., 28, 497 (2015). J. Catalán, C. Reichardt, J. Phys. Chem. A, 121, 7114 (2017). A.K. Schulz, Kolloid-Zeitschrift, 138, 75 (1954).

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9.4 MODELING OF ACID-BASE PROPERTIES IN BINARY-SOLVENT SYSTEMS TADEUSZ MICHŁOWSKI,* BOGUSŁAW PILARSKI,** AGUSTIN G. ASUERO,*** ANNA M. MICHAŁOWSKA-KACZMARCZYK**** *Faculty of Engineering and Chemical Technology, Technical University of Cracow, 31-155 Cracow, Poland **P.P.H.U. Cerko s.c., 80 299 Gdansk, Afrodyty 9, Poland ***Department of Analytical Chemistry, The University of Seville, 41012 Seville, Spain ****Department of Oncology, The University Hospital in Cracow, 31-501 Cracow, Poland

9.4.1 INTRODUCTION After redox,1-4 acid-base reactions are among the most important types of reactions in chemistry and biochemistry. Acid-base reactions are usually coupled with redox reactions; + 2+ e.g., in reaction MnO 4 + 8H + 5e = Mn + 4H 2 O , the MnO 4 ion behaves like “octo+ 5 pus” towards the H ions; Br2 behaves as a weak acid in aqueous media; Na2S2O3 in reaction with KIO3 + KI acts as a strong base. Referring to the systems where only acid-base reactions occur, one can distinguish mono- and polyprotic acids.6,7 The acidic character of a monoprotic acid HL is expressed by its acidity constant, pK1 = −logK1, where K1 − dissociation constant +

-

[H ][L ] K 1 = ---------------------[ HL ]

[9.4.1]

which expresses the extent to which the acid dissociates in a solution; it is a valuable indication for estimating its physicochemical behavior at various pH. Dissociation of an acid HmL (m = 1,2,…) in solutions is defined by its pKi = −logKi value(s). For a molecular polyprotic acid, pK1 governs its acidic behavior and chemical reactivity, i.e., it has a decisive influence on the acid-base properties of polyprotic acids. The presence of functional proton-donor groups determines the biological and pharmacological activity (pharmacokinetic properties, such as bioavailability) of the molecules tested. Thus, the trans-membrane transport of drugs depends on the pKi values of the drug tested and the pH of the environment;8,9 so pKi values are crucial in understanding the biological activity. The pKi along with integrity, lipophilicity, solubility, and permeability has been considered as one of the five key physicochemical profiling screens10 to provide an understanding the key properties that affect ADME (Absorption, Dissociation, Metabolism, and Excretion) characteristics of drugs.11-13 The functional relationship between pKi and structure of the molecules is useful in rational drug study, and in the assessment of biological and pharmaceutical properties of molecules. In environmental chemistry and geology, pKi values determine the lipophilicity (solubility in non-polar solvents) of compounds and, therefore, their distribution in natural environment. Familiarity of physicochemical parameters concerning the dissociation, activity coefficient of hydrogen ions and

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9.4 Modeling of acid-base properties in binary-solvent systems

conductivity of components in electrolyte solutions where acid-base reactions occur, is important from the cognitive, as well as from an analytical point of view.14 Knowledge of pKi values helps in explaining the reactivity and the rate of chemical reactions, enzymes, tautomeric equilibria and also in the description of separation techniques.15,16 This behavior is also very important, among others, in chromatographic, partitioning, and phase-transition processes. The dissociation of acids and pH of the solution in binary-solvent systems affects the degree of separation of the analytes in reversed phase liquid chromatography (RPHPLC),17-24 ion chromatography (IC),25,26 or capillary zone electrophoresis (CZE)27,28 techniques. The pH and pKi values of acids also affect the shape of the UV-Vis and 1H NMR spectra of these acids. Suitable effects are averaged values of such quantities as the absorbance, A,29-32 the chemical shift, δ,33,34 retention time, tR, or reduced retention time tR',35-38 as well as effective mobility, μe;39,40 all of them are expressed by the formula41 q



H

x i × 10

log K i – i × pH

i=1

x = ---------------------------------------------------q

1+

[9.4.2]

H

 10

log K i – i × pH

i=1

where: x

= A, δ, tR, tR', μe; q ≥ m , and i

H log K i =



+

pK q + 1 – k, K q + 1 – k = [ H ] [ H k – 1 L

+k – 1 – n

] ⁄ [ Hk L

+k – n

]

k=1

The literature data on pKi values for acids refer mainly to aqueous solutions, and less frequently to solutions in organic or aqueous-organic solvents. In turn, a knowledge of the pKi changes resulting from a change in the composition of the binary-solvent systems are small, and often uncertain/wrong. Therefore, an important issue is to develop a relatively simple (and available in every research laboratory) methodology of mathematical modeling of the binary-solvent systems. This paper refers, among others, to some similarities inherent in the course of some normalized graphs plotted on the basis of titration curves obtained from PT and CT made for the pair of solutions: titrant (solution titrated, D), and titrant (titrating solution, T), containing the same acid HL, with identical concentration, C mol/L, in D and T; the only difference in D and T lies in the solvent composition that affects the changes in pH and conductivity of D+T mixture; it is the most principal novelty of the titrimetric procedure. The results obtained from PT and CT will be modeled, for comparative purposes, with use of polynomial functions. However, the modeling is made only to compare the experimental data obtained at different values of (a) initial volumes (V0) of D and (b) increments (ΔV) of T applied in PT and CT. Furthermore, after this introductory step, we aimed to apply the models with minimal or none additional parameters needed to compare the data in PT and CT.

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In order to prove/check the consistency of experimental data obtained in PT and CT, the principle of “triads”, raised first time elsewhere,41 will be presented in extended versions, with D and T as mixed-solvent systems, containing also some modifying agent Z, introduced intentionally, in order to extend the pH-range covered by experimental points, obtained in PT and CT. These modifications were introduced to extend the possibilities offered by the new method of gaining a physicochemical knowledge on acid-base properties of some (mono- and polyprotic) acids in binary-solvent media. Some relationships between parameters inherent in CT and PT are also considered. The functions expressing these relationships are modeled with use of functions that appeared to be quite accurate for different acids HmL and different organic co-solvents (S) applied in binary-solvent systems. Summarizing, the wealth of novelties inherent in this paper gives rise to a better knowledge of acid-base equilibria in binary-solvent media. In this study, the dependencies pKi = pKi(x) of the acidity parameters were formulated for the subsequent steps of dissociation of a weak acid HmL versus mole fraction x of the component: (1o) S2 in mixture S1+S2 or W+S2, or (2o) S1 in mixture W+S1, where: W = H2O, and S1, S2 − organic solvents. These relationships are obtained from results of the pH titration in the D+T system, see Table 9.4.1. The initial pH of the HmL solutions in D and T were determined by adding a base (NaOH, KOH, or NH3) or an acid (HCl) as a pH modifier. The composition and concentration of HmL and the modifier in D and T are identical, and the pH change during the titration is due only to the acid-base properties of the solvents used for preparation of D and T. The pKi = pKi(x) relationships were modeled using various functions, which allowed to calculate pKi(0) and pKi(1) values in solutions containing a single solvent for HmL, i.e., W, S1 or S2. The extension of this method allows for an internal validation criterion for pKi(0) and pKi(1) to be introduced, based on the use of three D+T pairs, with W, S1 and S2 as the solvents. In the models presented below, it is assumed that the D+T systems are homogeneous in the entire range of variation of the mole fraction x in the mixture; this means the unlimited, mutual solubility of solvents forming the binary-solvent system and the complete solubility of the substrates and reaction products, at pre-assumed concentrations of the solutes.

9.4.2 GENERAL CHARACTERISTICS OF ORGANIC SOLVENTS Organic solvents such as dimethyl sulfoxide (DMSO, (CH3)2SO), acetonitrile (CH3CN), tetrahydrofuran (THF, (CH2)4O), 1,4-dioxane ((CH2)4O2) or acetone, are widely used in chemical laboratory.42 Their properties make them fully miscible with water. Thus acetonitrile+water and tetrahydrofuran+water are widely used as mobile phases in reversephase liquid chromatography (RP-HPLC).43 Dimetylsulfoxide+water has been a popular medium for studying acid-base behavior for a long time,44 The pKi values of most pharmaceutical drugs and other compounds, too insoluble to be determined in water, can be determined in dimethylsulfoxide/water and then extrapolated to water.44,45 Generally, mixed solvents have been employed in different fields, including pharmaceutical and analytical sciences.46 The dissociation of an uncharged acid in a solvent requires the separation of two ions of opposite charges. The relative permittivity (ε) of a solvent is a physical property which

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9.4 Modeling of acid-base properties in binary-solvent systems

plays a fundamental role in dissociation reactions; it is a measure of solvent’s efficiency for separating the electrolytes into ions.46 The work required to separate these charges is inversely proportional to ε of the solvent. Solvents with high ε-value encourage complete dissociation of the electrolytes, whereas in solvents of low ε-value, considerable ion pairing occur.47 The energy required for dissociation is supplied by solvation of the ions and also the proton transfer from acid to the solvent molecule supplies an additional energy. In other words, media of high ε-values are strongly ionizing, whereas ionization at low εvalue proceeds to a lesser extent.48 The nature of the solvent is thus crucial for the strength of acids and bases. A measure of the solvent ability to solvate cations and Lewis acids is the donor number (DN).49 Water is a solvent of high solvating ability (DN=33, ε=78), which can dissociate the acid and stabilize the produced anion and proton (hydronium ion). Thus, it is expected that addition of methanol (DN=19, ε=32.6) into water, decreases the extent of interaction between the acid anion and proton with solvent, and thus decreases the acidity strength of an acidic solute. For lesser DN and ε values, more energy is required to separate the anion and cation and consequently the extent of dissociation of an acid will be lowered. By mixing solvents of different polarity in proper ratios, the ε-value of the medium can be varied and, at the same time, the strength of dissolved acids and bases varies too.

9.4.3 SOLVATION IN AQUEOUS AND BINARY-SOLVENT MEDIA The most popular solvent considered in electrolytic systems is water. The species present zi in such (aqueous) systems form hydrates, X i ⋅ n i H 2 O , where zi = 0, ±1, ±2,… is the charge of this species expressed in elementary charge units e = F/NA (F = Faraday conattached stant, NA = Avogadro number), and n i ≥ 0 is the mean number of water particles zi to this species, whose concentration [mol/L] in this system is denoted as [ X i ]. In further zi considerations, we start each time with the number Ni of the entities, denoted as X i (Ni, ni), for brevity. We refer also to some binary-solvent systems, composed of totally miscible solvents, exemplified by W = H2O, S1 = CH3OH and S2 = (CH3)2SO; W and S1 are polar protic solvents, and S2 is a polar aprotic solvent. In binary-solvent systems: (W,S1) and (W,S2), zi zi formation of the related mixed solvates: X i n i H 2 O ⋅ n iS1 S1 , X i n i H 2 O ⋅ n iS2 S2 ; n i ≥ 0, n iS1 ≥ 0, n iS2z ≥ 0 are the meanz numbers of molecules of the corresponding soli i X i n i H 2 O ⋅ n iS2 S2 ,formed in the system of solvents vents attached to X i . In particular, zi (W,S2) will be characterized as X i ( N i, n i, n iS2 ) , where Ni is the number of these entities. For example, N6 entities BrO 3 ·n6H2O·n6S2(CH3)2SO involve: N6 atoms of Br, N6·(2n6 + 6n6S2) atoms of H, N6·(3 + n6 + n6S2) atoms of O, N6·2n6S2 atoms of C, and N6 atoms of S. It is assumed here that the solvents molecules are not oxidized or reduced by the related solutes. 9.4.4 FORMULATION OF BALANCES FOR REDOX AND NON-REDOX BINARY-SOLVENT SYSTEMS The species in any electrolytic non-redox system are involved in charge and k concentration balances, referred to element(s) Xi ≠ H, O, or some clusters of atoms named as cores, involving Xi. In other words, charge and concentration balances, form a compatible

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set of k+1 equations needed for quantitative, algebraic description of non-redox systems. For redox systems, the new, compatible balance referred to electron transmission/distribution is needed. The principles of formulation of the k+2-th balance, known as the Generalized Electron Balance (GEB), were presented as Approaches I and II to GEB;1-4,50,51 both Approaches are equivalent. The Approach I to GEB is based on a “card game” principle, with electrons as “money”, electron-active elements as “players”, and electron-non-active elements as “fans”. In redox reactions, one (disproportionation, synproportionation) or more electronactive elements can be involved. The Approach I (named also as “short” version of GEB) can be applied for any redox system, where oxidation numbers for all elements in the species present in this system can easily be determined. The Approach II to GEB is based on the linear combination 2·f(O) − f(H) of the elemental balances: f(H) for H and f(O) for O. For a redox system, 2·f(O) − f(H) is linearly independent of the charge balance and other concentration balance(s) referred to element(s) Xi ≠ H, O in this system. This property is valid for redox systems of any degree of complexity. The balance 2·f(O) − f(H), referred to as a redox system, is named as a primary form of the Generalized Electron Balance (GEB) for this system, and denoted as prGEB = 2·f(O) − f(H). For a non-redox system, of any degree of complexity, 2·f(O) − f(H) is linearly dependent on the charge balance and other concentration balance(s) referred to this system. The dependency/independency property of the balance 2·f(O) − f(H) is then the criterion distinguishing between redox and non-redox systems. This criterion, valid primarily for aqueous media,1-4,50,51 can be extended to the systems where other solvents are involved, particularly to binary-solvent media. In this section, we refer to a relatively simple redox system, with aqueous solution of Br2 (C mol/L). For this system, the identity of equations for GEB, obtained according to Approaches I and II will be indicated. Then the identity of equations for GEB, formulated according to Approach II to GEB for aqueous (W) solutions and for the binary-solvent systems: (W,S1), (W,S2) and (S1,S2) will be proven. In aqueous solution, Br2 behaves as an acid, with a strength close to the strength of acetic acid, of the same concentration.52,53 Br2 in W N10 molecules of Br2 are mixed with N20 molecules of H2O and V mL of the solution is thus obtained. There are the following species: H2O (N1), H+ (N2, n2), OH- (N3, n3), HBrO3 (N4, n4), BrO3- (N5, n5), HBrO (N6, n6), BrO- (N7, n7), Br2 (N8, n8), Br3- (N9, n9), Br- (N11, n11) [9.4.3] On the basis of [9.4.3], we formulate the balances: • f(H) 2N1 + N2(1 + 2n2) + N3(1 + 2n3) + N4(1 + 2n4) + 2N5n5 + N6(1 + 2n6) + 2N7n7 + 2N8n8 + 2N9n9 + 2N11n11 = 2N20

[9.4.4]

670

9.4 Modeling of acid-base properties in binary-solvent systems

•

f(O) N2 + N2n2 + N3(1 + n3) + N4(3 + n4) + N5(3 + n5) + N6(1 + n6) + N7(1 + n7) + N8n8 + N9n9 + N11n11 = N20

•

2·f(O) − f(H) = pr-GEB

− N2 + N3 + 5N4 + 6N5 + N6 + 2N7 = 0 •

[9.4.6]

f(Br) N4 + N5 + N6 + N7 + 2N8 + 3N9 + N11 = 2N10

•

[9.4.5]

[9.4.7]

charge balance N2 − N3 − N5 − N7 − N9 − N11 = 0

[9.4.8]

Addition of [9.4.6] and [9.4.8] gives 5(N4 + N5) + N6 + N7 − N9 − N11 = 0

[9.4.9]

Subtraction of [9.4.9] from ZBr·f(Br) (see Eq. [9.4.7]) gives (ZBr − 5)(N4 + N5) + (ZBr − 1)(N6 + N7) + 2ZBrN8 + (3ZBr + 1)N9 + (ZBr + 1)N11 = 2ZBrN10

[9.4.10]

Applying the notations: zi

[ X i ]·V = 103·Ni/NA, C·V = 103·N10/NA

[9.4.11]

in [9.4.10], we get52 (ZBr − 5)([HBrO3] + [BrO3-]) + (ZBr − 1)([HBrO] + [BrO-]) + 2ZBr[Br2] + (3ZBr + 1)[Br3-] + (ZBr + 1)[Br-] = 2ZBrC

[9.4.12]

Note that application of Eq. [9.4.11] to Eq. [9.4.9] gives the simplest form of the GEB for C mol/L Br2 5([HBrO3] + [BrO3-]) + [HBrO] + [BrO-] − [Br3-] − [Br-] = 0

[9.4.13]

The pr-GEB (Eq. [9.4.6]) written in terms of concentrations is as follows

− [H+] + [OH-] + 5[HBrO3] + 6[BrO3-] + [HBrO] + 2[BrO-] = 0

[9.4.14]

Equations [9.4.12]-[9.4.14] can be treated as equivalent forms of GEB for C mol/L Br2.

Br2 in (W,S1) N10 molecules of Br2 are mixed with N20 molecules of H2O and N30 molecules of S1 = CH3OH, and V mL of the solution is thus obtained. There are the following species: H2O (N1), H+ (N2, n2, n2S1), OH- (N3, n3, n3S1), HBrO3 (N4, n4, n4S1),

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BrO3- (N5, n5, n5S1), HBrO (N6, n6, n6S1), BrO- (N7, n7, n7S1), Br2 (N8, n8, n8S1), Br3- (N9, n9, n9S1), Br- (N11, n11, n11S1), CH3OH (N12) [9.4.15] involved in balances: • f(H): 2N1 + N2(1 + 2n2 + 4n2S1) + N3(1 + 2n3 + 4n3S1) + N4(1 + 2n4 + 4n4S1) + N5(2n5 + 4n5S1) + N6(1 + 2n6 + 4n6S1) + N7(2n7 + 4n7S1) + N8(2n8 + 4n8S1) + N9(2n9 + 4n9S1) + N11(2n11 + 4n11S1) + 4N12 = 2N20 + 4N30 •

[9.4.16]

f(O): N1 + N2(n2 + n2S1) + N3(1 + n3 + n3S1) + N4(3 + n4 + n4S1) + N5(3 + n5 + n5S1) + N6(1 + n6 + n6S1) + N7(1 + n7 + n7S1) + N8(n8 + n8S1) + N9(n9 + n9S2) + N11(n11 + n11S2) + N12 = N20 + N30

[9.4.17]

Then we get −pr-GEB = f(H) − 2·f(O): N2(1 + 2n2S1) + N3(−1 + 2n3S1) + N4(−5 + 2n4S1) + N5(−6 + 2n5S1) + N6(−1 + 2n6S1) + N7(−2 + 2n7S1) + 2N8n8S1 + 2N9n9S1 + 2N11n11S1 + 2N12 = 2N30

[9.4.18]

Addition of [9.4.18] to charge balance [9.4.8a] and balance f(S1) = f(CH3OH) [9.4.19] 0 = N2 − N3 − N5 − N7 − N9 − N11

[9.4.8a]

2N30 = 2N2n2S1 + 2N3n3S1 + 2N4n4S1 + 2N5n5S1 + 2N6n6S1 + 2N7n7S1 + 2N8n8S1 + 2N9n9S1 + 2N11n11S1 + 2N12

[9.4.19]

gives the equation identical to [9.4.9] and then [9.4.12]. Br2 in (W,S2) N10 molecules of Br2 are mixed with N20 molecules of H2O and N30 molecules of S2 = (CH3)2SO, and V mL of the solution is thus obtained. There are the following species: H2O (N1), H+ (N2, n2, n2S2), OH- (N3, n3, n3S2), HBrO3 (N4, n4, n4S2), BrO3- (N5, n5, n5S2), HBrO (N6, n6, n6S2), BrO- (N7, n7, n7S2), Br2 (N8, n8, n8S2), Br3- (N9, n9, n9S2), Br- (N11, n11, n11S2), (CH3)2SO (N12)[9.4.20] involved in the balances: • f(H) 2N1 + N3(1 + 2n3 + 6n2S2) + N4(1 + 2n4 + 6n4S2) + N5(1 + 2n5 + 6n5S2)

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9.4 Modeling of acid-base properties in binary-solvent systems

+ N6(2n6 + 6n6S2) + N7(1 + 2n7 + 6n7S2) + N8(2n8 + 6n8S2) + N9(2n8 + 6n9S2) + N11(2n11 + 6n11S2) + N12(2n12 + 6n12S2) + 6N2 = 2N20 + 6N30 [9.4.21] •

f(O) N1 + N3(n3 + n3S2) + N4(1 + n4 + n4S2) + N5(3 + n5 + n5S2) + N6(3 + n6 + n6S2) + N7(1 + n7 + n7S2) + N8(1 + n8 + n8S2) + N9(n9 + n9S2) + N11(n11 + n11S2) + N12(n12 + n12S2) + N2 = N20 + N30

[9.4.22]

Then we get −pr-GEB = f(H) − 2·f(O) N2(1 + 4n2S2) + N3(−1 + 4n3S2) + N4(−5 + 4n4S2) + N5(−6 + 4n5S2) + N6(−1 + 4n6S2) + N7(−2 + 4n7S2) + 4N8n8S2 + 4N9n9S2 + 4N11n11S2 + 4N12 = 4N30

[9.4.23]

Addition of [9.4.23] to [9.4.8] and 4·f((CH3)2SO) 4N30 = 4N2 + 4N3n3S2 + 4N4n4S2 + 4N5n5S2 + 4N6n6S2 + 4N7n7S2 + 4N8n8S2 + 4N9n9S2 + 4N11n11S2 + 4N12n12S2

[9.4.24]

gives the equation identical to [9.4.9], and then [9.4.12]. Br2 in (S1,S2) N10 molecules of Br2 are mixed with N20 molecules of S1 = CH3OH, N30 molecules of S2 = (CH3)2SO, and V mL of the solution is thus obtained. There are the following species: CH3OH (N1), H+ (N2, n2S1, n2S2), OH- (N3, n3S1, n3S2), HBrO3 (N4, n4S1, n4S2), BrO3- (N5, n5S1, n5S2), HBrO (N6, n6S1, n6S2), BrO- (N7, n7S1, n7S2), Br2 (N8, n8S1, n8S2), Br3- (N9, n9S1, n9S2), Br- (N11, n11S1, n11S2), (CH3)2SO (N12)

[9.4.25]

involved in balances: • f(H) 4N1 + N2(1 + 4n2S1 + 6n2S2) + N3(1 + 4n3S1 + 6n3S2) + N4(1 + 4n4S1 + 6n4S2) + N5(4n5S1 + 6n5S2) + N6(1 + 4n6S1 + 6n6S2) + N7(4n7S1 + 6n7S2) + N8(4n8S1 + 6n8S2) + N9(4n9S1 + 6n9S2) + N11(4n11S1 + 6n11S2) + 6N12 = 4N20 + 6N30 •

f(O) N1 + N2(n2S1 + n2S2) + N3(1 + n3S1 + n3S2) + N4(3 + n4S1 + n4S2)

[9.4.26]

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673

+ N5(3 + n5S1 + n5S2) + N6(1 + n6S1 + n6S2) + N7(1 + n7S1 + n7S2) + N8(n8S1 + n8S2) + N9(n9S1 + n9S2) + N11(n11S1 + n11S2) + N12 = N20 + N30 [[9.4.27] Then we get −pr-GEB = f(H) − 2·f(O) 2N1 + N2(1 + 2n2S1 + 4n2S2) + N3(−1 + 2n3S1 + 4n3S2) + N4(−5 + 2n4S1 + 4n4S2) + N5(−6 + 2n5S1 + 4n5S2) + N6(−1 + 2n6S1 + 4n6S2) + N7(−2 + 2n7S1 + 4n7S2) + N8(1 + 2n8S1 + 4n8S2) + N9(1 + 2n9S1 + 4n9S2) + N11(1 + 2n11S1 + 4n11S2) + 4N12 = 2N20 + 4N30

[9.4.28]

Addition of [9.4.28] to [9.4.8a], 2·f(CH3OH) [9.4.19], and 4·f((CH3)2SO) [9.4.24] and application of further operations as above, gives Eq. [9.4.9] and then [9.4.12]. This way it is proven that the GEB obtained for C mol/L Br2 in aqueous (W) and in binary-solvent media: (W,S1), (W,S2) and (S1,S2) are identical. This principle can be extended on the solutions where more solvents are involved. Some comments referred to the examples presented above are needed. It would seem, at first sight, that the components CH3OH2+ and CH3O- were omitted in [9.4.15] and [9.4.25]; CH3OH has amphiprotic (protophilic and protogenic) properties, like water. However, one can rearrange the elements and charges within the fragments in some parts of the related species in:15 H+ (N21, n2, n2S1), CH3OH2+ (N22, n2, n2S1 − 1), and OH- (N31, n3, n3S1), CH3O- (N32, n3 + 1, n3S1 − 1) (from transformation CH3OH + OH- = CH3O- + H2O) respectively, where N2 = N21 + N22, and N3 = N31 + N32

[9.4.29] +

The fragments of equations [9.4.16] and [9.4.17], involved with H and OH-, are rewritten as follows: • f(H):

… + N21(1 + 2n2 + 4n2S1) + N22(5 + 2n2 + 4(n2S1 − 1)) + N31(1 + 2n3 + 4n3S1) + N32(3 + 2(n3 + 1) + 4(n3S1 − 1))... =... •

[9.4.16a]

f(O):

… + N21(n2 + n2S1) + N22(1 + n2 + (n2S1 − 1)) + N31(1 + n3 + n3S1) + N32(1 + (n3 + 1) + (n3S1 − 1)) … = …

[9.4.17a]

From [9.4.16a] and [9.4.17a] we calculate −pr-GEB = f(H) − 2·f(O):

… + N21(1 + 2n2S1) + N22(1 + 2n2S1) + N31(−1 + 2n3S1) + N32(−1 + 2n3S1) +... = …

[9.4.30]

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9.4 Modeling of acid-base properties in binary-solvent systems

and then applying [9.4.29], from [9.4.30], we get the segment

… + N2(1 + 2n2S1) + N3(−1 + 2n3S1) + … = …

[9.4.31]

identical to the one given in Eq. [9.4.18]. As indicated in the examples presented above, the formulation of f(H) − 2·f(O) needs only a knowledge of the chemical composition and external charge of the species present in the related electrolytic system. The connections of individual elements and their valences (oxidation numbers) within the species are not considered in this respect. This property is of capital importance, particularly when referred to complex species participating in redox reactions, where calculation of valences of particular elements is at least difficult task. Within GATES/GEB, the terms: oxidant and reductant are not ascribed a priori to particular species. Similar balancing can also be applied to non-redox systems. For this purpose let us take, as an example, a system (V mL) composed of N10 molecules of benzoic acid, BA=C6H5COOH, N20 molecules of H2O and N30 molecules of S1 = CH3OH. In the system thus formed we have the following species: H2O (N1), CH3OH (N2), H+ (N3, n3, n3S1), OH(N4, n4, n4S1), C6H5COOH (N5, n5, n5S1), C6H5COO- (N6, n6, n6S1). The related elemental balances for H and O are as follows: • f(H): 2N1 + 4N2 + N3(1 + 2n3 + 4n3S1) + N4(1 + 2n4 + 4n4S1) + N5(6 + 2n5 + 4n5S1) + N6(5 + 2n6 + 4n6S1) = 6N10 + 2N20 + 4N30 •

[9.4.32]

f(O): N1 + N2 + N3(n3 + n3S1) + N4(1 + n4 + n4S1) + N5(2 + n5 + n5S1) + N6(2 + n6 + n6S1) = 2N10 + N20 + N30

f(H))

[9.4.33]

From Eqs. [9.4.32] and [9.4.33], we get the equation for f(H) − 2·f(O) = − (2·f(O) − 2N2 + N3(1 + 2n3S1) + N4(−1 + 2n4S1) + N5(2 + 2n5S1) + N6(1 + 2n6S1) = 2N10 + 2N30

[9.4.34]

It should be noticed that the selection of f(H) − 2·f(O) (not of 2·f(O) − f(H)) balance is a matter of choice only. Simply, f(H) − 2·f(O) involves lesser number of components with negative signs (“aesthetic” point of view). Addition of Eq. [9.4.34] to charge balance [9.4.35] and balances: 4·f(CH3O) for S1 [9.4.36], and 2·f(C6H5COO) for C6H5COO [9.4.37] 0 = N 3 − N4 − N6

[9.4.35]

2N30 = 2N2 + 2N3n3S1 + 2N4n4S1 + 2N5n5S1 + 2N6n6S1

[9.4.36]

2N10 = 2N5 + 2N6

[9.4.37]

gives the identity, 0 = 0, see.4 Note that the balance f(C) for C

Tadeusz Michałowski et al.

N2 + N3n3S1 + N4n4S1 + N5(6 + n5S1) + N6(6 + n5S1) = 6N10 + N30

675

[9.4.38]

is the linear combination 6·f(C6H5COO) + f(CH3OH) of f(CH3OH) and f(C6H5COO), i.e., N2 + N3n3S1 + N4n4S1 + N5n5S1 + N6n5S1 = N30 and N5 + N6 = N30. Note that 2·f(O) − f(H) (= − (f(H) − 2·f(O))) does not involve N20, N1 and ni (i = 2,…,6) values, referred to the numbers of water molecules − free or involved in hydrates. In other words, water molecules are cancelled in the balance [9.4.34]. Similar property is valid for any non-redox and redox system, of any degree of complexity. In other words, for non-redox systems, of any degree of complexity, the balance f(H) − 2·f(O) (or equivalently, the balance 2·f(O)−f(H)) does not provide a new, linearly independent equation and then any non-redox system is described with use of k+1 balances, composed of charge balance and k concentration balances.1-4

9.4.5 POTENTIOMETRIC AND CONDUCTOMETRIC METHODS OF pK i DETERMINATION Potentiometric (pH) and conductometric titrations (PT and CT) stand among the main electrochemical methods of titrimetric analyses, where titrant T is added in consecutive portions into titrand D, and D+T system is thus formed. Investigation of acid-base equilibria in aqueous, non-aqueous54 and mixed-solvent media with use of PT and CT methods of analysis is of perpetual interest in scientific literature referred to electrolytic systems, owing to the fact that PT and CT belong to the most accurate physicochemical measurements made in such media.55 Modeling the systems tested with use of CT and PT methods was outlined elsewhere.6,56 In particular, the equations derived by Fuoss-Hsia,57 Lee and Wheaton58 and their extended versions,59,60 were applied, among others, for modeling of acid-base equilibria, tested according to CT in mixed-solvent media,61-65 where the solvent composition is characterized by mole fraction x of one of solvents composing the system. CT is a (complementary against PT) technique, applied for determination of stability constants of complexes66,67 and proto-complexes, in particular. The knowledge of physico-chemical parameters related to dissociation of mono- and polyprotic acids HmL in electrolytic systems is important both from cognitive and analytical viewpoints.68 Dissociation of the acids in such systems is characterized by pKi = −logKi values for acidity parameters. In binary-solvent systems, the acidity parameters at the ends of x-scale (i.e., x = 0 and 1) are called as acidity constants,41,69,70 referred to solutions in pure (mono-component) solvent: S1 (pKiS1), S2 (pKiS2), and W (pKiW), where S1, S2 − organic solvents, W − water. We refer later to the solvents characterized by mutual miscibility, in all proportions, within the pairs: W+S1, W+S2, and S1+S2. The pKi values, considered as acidity constants, refer mainly to aqueous solutions (pKi = pKiW), and − more rarely − to the solutions in organic or mixed, water+organic solvents. In turn, the papers on changes in pKi values, resulting from changes in the solvent composition in binary-solvent systems, are scarce. The main aim of this issue is the elaboration of a simple methodology that enables the binary-solvent electrolytic systems to be studied, with use of mathematical modeling applied. In the present contribution, the acidity parameters pKi = pKi(x), for successive dissociation steps of a weak acid HmL, are presented as a function of a mole fraction x of (a) co-

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9.4 Modeling of acid-base properties in binary-solvent systems

solvent S2 in mixture of solvents S1+S2 or W+S2, or (b) co-solvent S1 in W+S1 mixture. Such an approach is, in several aspects, a novelty when compared with ones practiced hitherto. This acid-acid titration has some similarities to titrations made for determination of pK values according to the new, isohydric method suggested by Michałowski and presented in the previous papers.70-73

9.4.6 MODELING OF THE SYSTEMS TESTED 9.4.6.1 Basic relationships The dissociation of weak acids HL in binary-solvent media was also considered in the recently published papers.41,69,70 Particularly, the “triads” of different solvents (W, S1, S2) are considered in the D+T systems: HL/S1 ↔ HL/W; HL/S2 ↔ HL/W, and HL/ S1 ↔ HL/S2, where W = water, S1, S2 − organic solvents having total mutual miscibility, and totally miscible with W; HL/X denotes HL dissolved in pure solvent X = W, S1, or S2, and symbol “ ↔ ” signifies reciprocal pH titration within particular systems, where the roles of D and T are inverted. In each of the D+T systems, concentration of HL in HL/ X (X = W, S1, S2) is identical and equal to C mol/L. In the formulae involved, it is also assumed that correction on non-additivity in volumes of the solutions mixed can be neglected when collated with an error in pH measurement made during pH titration. The C value is then assumed constant at any point of the titration, where pH values in D+T result only from difference in the solvents applied in D and T. The pH titration curves, pH = pH(V), obtained for different pairs of solutions were recalculated (converted) into the curves pK1 = pK1(x), where pK1 = −logK1 expressed by the formula41,69,70 pK 1 = 2pH + log ( C – 10

– pH

)

[9.4.39]

is named as dissociation parameter, whose value depends on the mole fraction x of one of the solvents in the pair of solvents, K1 as in Eq. [9.4.1]. To arrange the notation, it is assumed that molar masses MS [g/mol] of solvents X = W, S1, S2 fulfill the relation MW < MS1 < MS2 and x is the mole fraction of the solvent with higher MS value, i.e. x = xS2 in the systems HL/S2 ↔ HL/W and HL/S1 ↔ HL/S2, and x = xS1 in the system HL/ S1 ↔ HL/W. Assuming that V mL of T is added into V0 mL of D, we have the expressions for x specified in Table 9.4.1. In expressions for χWS1, χWS2, and χS1S2, the molar masses and densities of the corresponding solvents are involved; for example, χS1S2 = 1.7517 for S1 = CH3OH and S2 = (CH3)2SO. It is tacitly assumed that the densities of the diluted solutions are equal to the densities of the related solvents. Reciprocal titrations are done in order to cover the whole (or possibly wide) x range, e.g., x ∈ for the mole fraction x in the systems presented in Table 9.4.1. Table 9.4.1. Expressions for the mole fraction x for defined pairs: (W, S1), (W, S2) and (S1, S2), within the triad (W, S1, S2); ρX, MX − density [g/mL] and molar mass [g/mol] of the solvent X = W, S1, S2. No.

T (V) → D (V0)

x

χ ρ W M S1 χ WS1 = -------------------ρ S1 M W

1a

HL/S1 → HL/W

xS1 = V/(V + χWS1·V0)

1b

HL/W → HL/S1

xS1 = V0/(V0 + χWS1·V)

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677

Table 9.4.1. Expressions for the mole fraction x for defined pairs: (W, S1), (W, S2) and (S1, S2), within the triad (W, S1, S2); ρX, MX − density [g/mL] and molar mass [g/mol] of the solvent X = W, S1, S2. No.

T (V) → D (V0)

x

χ ρ W M S2 χ WS2 = -------------------ρ S2 M W

2a

HL/S2 → HL/W

xS2 = V/(V + χWS2·V0)

2b

HL/W → HL/S2

xS2 = V0/(V0 + χWS2·V)

3a

HL/S2 → HL/S1

xS2 = V/(V + χS1S2·V0)

3b

HL/S1 → HL/S2

xS2 = V0/(V0 + χS1S2·V)

ρ S1 M S2 χ S1S2 = --------------------ρ S2 M S1

Within the pH interval where C >> 10-pH, Eq. [9.4.39] is simplified into the form pK = 2pH + log C

[9.4.40]

We refer also to titrations made in the systems HL/W+S ↔ HL/W, where S = S1 or S2 is the organic co-solvent for water (W). Applying the notation as in Table 9.4.1 and assuming the additivity in volumes, we obtain the formulae for mole fraction of S in D+T: qV x = ---------------------------------------------------------------qV + χ WS ( V 0 + ( 1 – q ) V )

for HL (C)/W+S ↔ HL (C)/W [9.4.41]

qV 0 x = ----------------------------------------------------------------qV 0 + χ WS ( V + ( 1 – q ) V 0 )

for HL (C)/W ↔ HL (C)/W+S [9.4.42]

where q is the volume fraction of S in W+S, χWS = 2.2431 for S = S1 = CH3OH, χWS = 3.9293 for S = S2 = (CH3)2SO. For q = 1, Eqs [9.4.41] and [9.4.42] are identical with the ones given in Table 9.4.1, no. 3, 4. The experimental results, used to formulate the pKi = pKi(x) and κ = κ(x) relationships, were obtained according to PT and CT principles, where the corresponding solutions were applied as D and T (Figure 9.4.1), with the composition presented in Table 9.4.1. In Figure 9.4.2 (left) lower lines at each pair of D+T systems correspond to pH titration HL (C)/W+S2 → HL (C)/W, and upper lines to titration HL (C)/W → HL (C)/W+S2. In Figure 9.4.2 (right) upper lines at each pair correspond to the conducFigure 9.4.1. The plots for κ = κ(V) relationships obtained for titrations: (1) Py-3CA (C)/W+S1 → Py- tometric titration HL (C)/W+S2 → HL 3CA (C)/W (upper line) and (2) Py-3CA (C)/W → (C)/W and lower lines to titration HL (C)/ Py-3CA (C)/W+S1 (lower line); C = 0.01 mol/L for pyridine-3-carboxylic acid (HL = Py-3CA), V0 = 3 mL; S1 W → HL (C)/W+B; it results from lower = CH3OH. conductivity of S2 = Me2SO than that of

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9.4 Modeling of acid-base properties in binary-solvent systems

Figure 9.4.2. Comparison of (left) pH = pH(V) in PT and (right) κ = κ(V) in CT curves; C = 0.01 mol/L HL = BA (benzoic acid); V0 = 3 mL, ΔV = 0.01 mL in (left), and V0 = 4 mL, ΔV = 0.02 mL in (right); numbers at the curves indicate q-values.

water. The specific conductivities (at 20oC) reported for Me2SO are: 0.02 μS/cm in ref.74 and 0.03 μS/cm in ref.75 The related values reported in refs.76,77 are: 0.5 μS/cm for distilled water and 0.055 μS/cm for totally pure water. For comparison, the conductivity of distilled water applied in our measurements was 0.18 μS/cm. The D+T systems of different complexity are considered in Table 9.4.2. In particular, the systems no. 1 and 2 refer to the solutions of an acid HmL (m ≥ 1) in pure solvents, X: W, S1 or S2; it is also assumed that the acid HmL used for preparation of D and T is not a hydrate, e.g., phthalic acid, H2L (m=2). System 3 refers to the case with hydrate of HmL involved, e.g., citric acid, H3L·H2O (m=3); this hydrate introduces water as the minor (against S = S1, S2) component; this fact is denoted by the symbol w+S. In all the cases considered, concentration C of HmL assumed in D and T is relatively small, e.g., C = 0.01 mol/L. In such instances, the quantity of water introduced by H3L·H2O is comparable with the contents (ca. 0.5%) of admixtures (e.g., H2O) entering S = S1, S2 used in the analyses; these admixtures are also omitted in considerations. In the system 4, the W = H2O contents, introduced by aqueous solution Z used as pH-modifying agent, is much more greater than that in the system 3. System 5 is the most general (in this context) quasi-binary solvent system, where water is the minor solvent, for which the wide range of molar ratio x = xW for W is not considered. In the systems 4 and 5, the D and T composition is modified by a base (Z = NaOH, KOH, NH3) or strong acid (Z = HCl). The presence of Z enables to attain the pH range, where determination of pre-assumed parameters of the related systems is possible. In particular, the use of Z = NH3 is advised e.g. in the cases where sodium or potassium salts of the corresponding acids are precipitated in S1, S2 and/or S1+S2, whereas ammonium salts are soluble in these media. However, the use of Z = NH3 is limited in consideration to pH-range where [NH3]/[NH4+] m. On the stage of D and T preparation, the agent Z is supplied as an aqueous solution. Generally, the minimization of water content in the solutions HmL/w+S (S = S1, S2) is advised/required. Therefore, solid HmL (or its salt) is introduced as solid (not as aqueous solution), and Z is added as relatively concentrated (ca. 1-2 mol/L) aqueous solution of a base or acid. Table 9.4.2. The D+T systems of different complexity considered in this contribution. System no.

D (V0)

T (V)

1

a

HmL/W

HmL/S2

b

HmL/S2

HmL/W

a

HmL/S1

HmL/S2

b

HmL/S2

HmL/S1

a

HmL/W

HmL/w+S2

b

HmL/w+S2

HmL/W

a

HmL+Z/W

HmL+Z/w+S2

2 3 4 5

b

HmL+Z/w+S2

HmL+Z/W

a

HmL+Z/w+S1

HmL+Z/w+S2

b

HmL+Z/w+S2

HmL+Z/w+S1

The functions pKi = pKi(x) obtained after conversion of PT experimental data are the basis for calculation of pKi(0) and pKi(1) values for successive acidity parameters (pKi) referred to HmL in pure organic solvents, HmL/S (S = S1, S2). Functions x = x(V) for the systems with a pH-modifying agent Let us consider the system 5a (Table 9.4.2), formed of HmL (C) + Z (Cbi) /W+S1 (as D, volume V0 mL) and HmL (C) + Z (Cbi)/W+S2 (as T, volume V mL), Z = base. We denote: n S2 x = x S2 = ----------------------------------n S2 + n S1 + n W

[9.4.43]

V0S1 + V0W = V0, VS2 + VW = V, VS1 + VW = V, V0S2 + V0W = V0

[9.4.44]

rS1S2 = VS1/VS2 = V0S1/V0S2, rWS1 = VW/VS1 = V0W/V0S1

[9.4.45]

and xWS2, xS1S2 as ones specified in Table 9.4.1; nX, ρX, MX − numbers of mmoles, density [g/mL] and molar masses [g/mol] of X; V0X and VX − volumes [mL] of X = W, S1, S2 in D and T. The relationships [9.4.44] express the simplifying assumption of additivity in volumes of the components forming D, T and D+T systems. Moreover, we assume that VW μe.1,105 Another contribution to the described interactions, the dispersion one, is significant both in polar and nonpolar solvents. Its relevancy is related to the fact, that, even in the case of the molecules possessing no permanent dipole moment, the fluctuations of the electron cloud results in a small induced dipole moment that can influence the charge of the neighboring species. It is well established that the dispersion effect leads to the red shift, as the molecule in the excited state is more susceptible to the perturbation induced by external electric field than in the ground state.1,15,19,106-109 The magnitude of this shift depends on the solvent refractive index, the transition intensity and the size of the solute molecule.1 Similar situation is met, when in the polar solvent the nonpolar solute is placed, however in this case also the quadrupole/solvent dipole interactions need to be considered.1 The electrostatic contribution is more prominent than the dispersion one, so in the case of dipolar molecules the induced bathochromic shift strengthens the one resulting from electrostatic interaction or is prevailed by electrostatically induced blue shift. The most difficult to predict is the influence of the hydrogen bond, as it can affect the energies of various states in a different way. However, in the literature, some empirically or theoretically examined examples of a specific groups characterized by one type of shift can be found, for example the case of n → π * transition in carbonyl-group/protic-solvent interaction, where the blue shift is observed.1,15,19,106-107,110-113 A completely separate issue is the matter of the solvent influence on the UV-Vis absorption band intensity. Attempts of describing this effect were made since the beginning of 20th century, however still this problem is not fully solved. A pioneering work was reported by Chako, who utilized a classical Lorentz local field theory placing the molecule inside a spherical cavity.114 He related the oscillator strength of the molecule in the gas phase with the oscillator strength of the molecule in the solution.114-115 However, his equation always predicts the increase of the oscillator strength with the increasing index of refraction.115 The second attempt was made by Schuyer.116 It was based on the Onsager theory and resulted in derivation of the formula relating a molar extinction coefficient of the solution to the vapor one,116-117 which was later found by Bakhshiev to be a more adequate relation.118-120 Another authors, Weigang118 and Liptay,121 independently reported expressions of integrated intensity.117 More recent are the works of Abe117 and Birge et al.115 Abe also used the Onsager cavity field and included the transition energies of the solute in solution and in the gas phase. However, his work was later criticized by Birge as predicting always a decrease of oscillator strength with the increasing index of refraction.115 Another approach was proposed by Birge et al. and was based on the work of Weigang.118 However, in order to simplify the final expression they have neglected solutesolute interactions, and assumed no permanent dipole moments, so their derivations describe only the dispersion effect.115 Although further Abe and Birge in their com-

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10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

ments,122-123 have argued about some aspects of expressions presented by Birge, a comparison of the experimental and theoretical data based on the Birge model gave a satisfactory qualitative prediction.115 A few years later Abe and Iweibo presented another theoretical model of solvent effect on the absorption intensities.124-126 The latest report have been published in 2005 by Figure 10.3.5. Schematic illustration of the two-photon Valée et al., where a microscopic model is a) positive and b) negative solvatochromism. proposed.127 However, authors focus on another topic and the solvent influence on the oscillator strength is considered as a secondary issue. Unfortunately, according to our best knowledge, to date no new model was developed, nor the dispute was settled.

10.3.3 SOLVENT EFFECT ON THE TWO-PHOTON ABSORPTION As it has been already indicated in the introduction, that until recently the solvatochromic behavior of a variety of organic dyes was examined mostly in the field of the linear spectroscopy. In the available literature the spectacular examples of red and blue shifts as well as changes in the intensity of the absorption or emission bands are systematically reported. Quantitative analysis of this phenomenon allows for the discussion of conformational changes of molecules placed in different environments, evaluation of the origins of intermolecular interactions, determination of the dipole moments and polarizabilities as well as other molecular properties. With no doubt solvatochromism of the chemical species provides a lot of valuable data about their electronic structure and other properties. In this context, measurements of the electronic spectra of different systems in a variety of solvents are a powerful research tool. Like in the case of one-photon, the two-photon solvatochromism can be discussed in two frames of reference. Firstly, how the solvent influences the 2PA band position and secondly how it alters its intensity. Sources of the solventinduced absorption band shift are the same as in the case of one-photon absorption. When considering the dipolar CT molecules the 2PA band is expected to be on the position of twice larger wavelengths than in the case of the linear absorption. Furthermore, the solvent will cause the shift exactly the same like in the case of 1PA (cf. Figures 10.3.3 and 10.3.5). It is related to the fact, that in both types of the absorption strictly the same excited state is populated and the way of the excitation does not play any role. A more complicated issue concerns the solvent influence on the 2PA cross-section. In general, inspection of the electronic spectra published for a set of molecules in solutions show, that the effect of the solvent on the intensity of the 2PA bands is more important than its effect on 1PA. This conclusion is especially supported by investigations presented by Drobizhev et al. for the fluorescent proteins.58 In particular, the authors have demonstrated a significant sensitivity of the σ2PA of the polar chromophore to local electric field generated by different “Fruit” proteins, while for the same systems, the 1PA extinction coefficient varied only slightly. These observations have been rationalized with the help of the two-level model (Eq. 10.3.2). For our considerations, the presented example indicates

715

that the 2PA cross-section can be manipulated by changing the chemical environment of the investigated molecule. From the historical point of view, probably the first theoretical and experimental description of the solvent effect on the 2PA of molecules was published already in 1971 by Aslanidi et al.32 The measurement method applied in that work was different than presently used and interpretation of the obtained results is difficult. However, based on the units adopted by authors, the changes related to the environmental influence are clearly visible. Another historical work published in 1988 by Mohler and Wirth presents the solvent effect on the excited state symmetry of the randomly oriented molecules by 2PA.128 In this very important paper, using the perturbation theory and continuum reaction field models, authors show, that solvent perturbations on the excited state symmetry of the fluorene molecule contain an information about the macroscopic properties of the solvent environment. Another systematic analysis was conducted, based on the two- and three-level models as well as the semi-empirical quantum chemical calculations, pointing out the possible directions of changes for both the 2PA cross-sections and hyperpolarizabilities of the D-π-A molecules.19 In this work the problem of the solvent effect on the σ2PA is considered in the strictly theoretical way based on the δeg parameter. In this approach, based on the concept proposed by Monson and Mcclain,129 the two-photon transition probability is derived from the theoretically calculated values. Here also the twostate approximation is used. The model defined within the Taylor convention is as follows:19 2

24 f ( μ e – μ g ) TL δ eg = ------ -------------------------3 5 ω

[10.3.4]

eg

where (μe − μg) is the difference between the dipole moment of the solute at its ground and excited states, f is the oscillator strength and the ωeg denotes the energy transition from the ground to the excited state. However, using the Eq. 10.3.4 in the presented form for the comparison of theoretically derived and experimentally measured data is not possible. In order to obtain the results in GM units, usually the following formula is used:47 2 5

2

8 π a 0 αω TL TL - δ eg σ eg = -----------------------cΓ

[10.3.5]

In this equation a0 is the Bohr radius, c is the speed of light, α is the fine structure constant, ω = ω eg ⁄ 2 is the angular frequency of the incident light. The meaning of Γ is the same like in the case of Eq. 10.3.2. It should be noticed that from the theoretical point of view, if the pure electronic transitions are considered, i.e., the vibronic effects are neglected (Eqs. 10.3.4 and 10.3.5), Γ may be defined as FWHM (full width at half maximum) of the absorption band. In this case, the normalized Lorentzian (or Gaussian) profile of the absorption band is usually assumed. According to the purely theoretical approach (Eq. 10.3.4), in the case of chromophores exhibiting large negative solvatochromism, the presence of polar environment leads to the substantial decrease of the 2PA cross-section values, as the denominator in the (Eq. 10.3.4) is here the predominant factor. Opposite tendencies should be observed for the chromophores exhibiting positive solvatochromism.

716

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

However, this theoretical picture is restricted for 2PA from the ground to the CT excited state. Moreover, in the quoted study, discussion concerning the possible changes of the broadening of the final excited state (Γ) in different solvents as well as the influence of the vibronic coupling on 2PA is not included. Before the significance of the Γ factor was appreciated, it was substituted by 0.1 eV value,71 what have led to an oversimplification of this approach, causing the overestimation of the energy difference significance and, what, in some cases, can be more important, some subtle effects were ignored. Another relevant factor, the influence of the vibronic coupling on 2PA together with the solvent effects, can be taken into consideration based on the theoretical formalism derived from the essentialstate description of the electronic structure of chromophores. This approach has been developed and it is gradually supplemented by Terenziani et al.130 This chapter mainly focuses on the presentation of the experimental results obtained for the molecular systems representing different types of symmetry and electronic structures. Therefore in the Tables 10.3.1 and 10.3.2 (see tables at the end of the this contribution) the experimental data concerning the σ2PA as a function of the solvent polarity32-50 are collected. Data are taken from the published reports, however, the presented works may not be all that have been published until the present day. In order to unify the data quoted from the original papers as well as to clearly present the interactions of the twophoton absorbing molecules (cf. Figures 10.3.6-10.3.9) with its polar and nonpolar environment, we have adapted the well-known polarity scale, based on the empirical Solvent Polarity Parameter, ET(30), which is defined as follows:1 hc E T ( 30 ) = N A ----------λ max

[10.3.6]

where NA is the Avogadro constant, h is the Planck constant and c is the speed of light. It should be noticed that ET(30) is expressed in kcal/mol and λmax is the maximum wavelength of the CT solvatochromic absorption band of the pyridinium N-phenolate betaine dye (Figure 10.3.4). Up to now a relatively few works, describing the influence of solvent on the 2PA of the organic molecules were published.32-51 However, this restricted amount of data enables to outline the currently available knowledge. Quoted works, as they are presented by unrelated researchers, have a separate aims and character, what, altogether with the lack of the coherent research plan, makes the 2PA solvatochromism still not sufficiently explained. Investigated systems are radically different. Some of them have a high symmetry with the center of inversion, so according to the Laporte rules, two-photon absorption can occur to the 1PA-forbidden excited state (1,5-12,20-22 in Tables 10.3.1 and 10.3.2 (chemical structures of numbered molecules are given in Figures 10.3.6 to 10.3.9 below)). In other papers both protic and aprotic solvents were used (5-14,37) whereas the intermolecular interactions in both cases can be of different nature. Also in order to obtain the molecule soluble in water, some parts of the molecule’s ligands were exchanged (5-14) what leads to difficulties in comparing the reported data (changes in the structure of the molecule can alter the conjugation path, which in turn may influence two-photon absorption cross-section value). In other reports experimental data were provided only for a one or a limited quan-

717

tity of wavelengths (15-18,20-26,36,37), forcing us to a special care in our attempt to interpret those data, as the change of the σ2PA can be related not only to the solvent effect on the 2PA cross-section but also to the shift of the band. All mentioned differences in the research methodologies, altogether with the different architectures and symmetry types of the investigated species, make the overall tendencies ambiguous and difficult to interpret. Therefore, based on the available data, it is challenging to draw any general conclusions. However, it is possible to sum up the currently existing reference material and build a preliminary picture of the phenomenon. Namely, among the adduced data there is a group of the compounds for which the σ2PA value increases together with the polarity of the solvent (16-18,23-25,27,30,35,36). The most significant change of the maximum value of σ2PA depending on the solvent was reported for molecule 30. The change of the absolute value was about 3200 GM, however, the relative increase from toluene to dichloromethane was by a factor of about three. Other works present the negative solvent effect on the 2PA when the solvent polarity increases (2-10,13,14,20,26,32,34). In this case the largest change of the absolute value was observed by Belfield et al.34 for molecule 4. In this case the relative change − about 1.5 times − is moderate. On the other hand, the most significant relative change, approximately 4.5 times, was reported by Rodriguez et al.46 (32), with the absolute difference being 82 GM. For other molecules the non-monotonic behavior has been reported (1,11,12,15,21,22,28,29,31,33). In this case, both the largest absolute (3990 GM) and relative change (factor of about 6.5) was observed for molecule 31, moved from tetrahydrofurane to dichloromethane.45 Presented ability of solvents to induce a massive changes in the σ2PA value could be the one of the most desired properties of two-photon absorption process. Until recently the enhancement of the 2PA absorption crosssection were designed by a structural changes, mostly by enlarging the molecule’s size. As it turns out in the case of some applications, like the biological applications related to the transfer of the particle through the cell membrane or in the case of the molecular photostability, this approach can be a dead end. Taking it to the consideration, the environment effect can bring a new quality. However, the study on the solvent effect on the 2PA process is still in its early stage. The published experimental32-51 and theoretical131-138 results indicate a lack of consensus, therefore, in order to try to address this issue, the examples of a model solvatochromic molecules with known properties44,47 will be used. First examined molecule will be a well known push-pull type 4-dimethylamino-4'-nitrostilbene (DANS)44 (28). It is characterized by a moderate positive solvatochromism. The obtained experimental results show, that, with the increase of the solvent polarity, the changes of σ2PA are non-monotonic. The maximum of the 2PA response was reached for the solvent of intermediate polarity (dichloromethane) and a further increase of the solvent polarity (dimethyl sulfoxide) resulted in the reduction of σ2PA. This result is inconsistent with the purely theTL oretical two-state model (Eq. 10.3.4) which, in this case, predicts an increase of the δ eg probability maximum value with the increase of the solvent polarity. In this approach only the energy gap difference, oscillator strength between the ground and excited state and the difference between the dipole moment of the molecule in its ground and excited states are taken into account. The positive solvent shift causes the decrease of the denominator while the polar solvent-DANS interaction leads to the increase of Δμge.71 As a result, the δeg also

718

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

increases. However, as it was mentioned before, experimental data indicate that the changes of the σ2PA are non-monotonic, reaching its maximum for a moderate polarity solvent. These data have confirmed a more sophisticated theoretical results obtained with the help of the hybrid DFT/MM method, where the effect of non-monotonic σ2PA behavior was predicted for DANS in chloroform, dimethyl sulfoxide and water.71 The authors of this work have included the Γ parameter in their considerations. As it can be seen from the equations 10.3.2 and 10.3.5, in this approach the energy gap loses its importance. In this case ΔEeg value is still inversely proportional to σ2PA but only to the power of one. This relation and the fact that DANS is only a moderately solvatochromic molecule, makes Γ one of the most decisive parameters, which permits proper prediction of its non-monotonic behavior.44,71 Another aspect was reported in the combined experimental and theoretical work describing the solvent effect on the two-photon absorption of Reichardt's dye47 (34), which is well known because of its extraordinary negative solvatochromism.1,15-17 This time, like in the case of the 1PA, the σ2PA decreases with the increase of the solvent polarity. This dependence was observed both experimentally and theoretically. Carrying out a similar analysis as for DANS, it is possible to notice that, in the Eq. 10.3.1, the denominator increases with the increase of the solvent polarity. However, the situation in the numerator is more complicated. The difference between the dipole moment in the ground and excited states increases, but it is multiplied by the decreasing oscillator strength. From the above, it can be concluded that also in this case the value of the two-photon absorption probability σ2PA depends on how the individual values in the Eq. 10.3.4 will compete. In turn, if the relation 10.3.5 is considered, also the parameter Γ needs to be taken into TL account. According to the quantum chemical calculations reported in the ref.47, the σ 2PA is decreased with the solvent polarity increasing, what is consistent with the experimental results. Presented relationships indicate, that in this case the increase of the denominator together with the decrease of the oscillator strength prevail causing increase in (μe − μg) and, as a result, the 2PA cross-section value is being suppressed. As a result, it is possible to conclude, that a simple two-state model is able to predict properly the tendency of the 2PA cross-section changes for molecules exhibiting such strong negative solvatochromism. Based on the presented research it can be stated, that the excited state line width parameter has an important influence on the σ2PA in the case of the moderate positive solvatochromic molecules, as the individual parameters may cancel each other. In the case of strongly negative solvatochromic molecule, the Γ probably just confirmed the tendency established by the three other parameters. The research is still in progress and every year even more data is published. Among the available works an attentive reader can find a very interesting pieces of research. For example Vivas et al. published the research on the influence of solvent on the induction of coil to helix conformational change generating the modification of the σ2PA values.43 Kavitha et al.,139 have presented the solvent effect on the 2PA of ZnO nanoparticles. Also, other than solvent types of environmental influences attract attention of scientists. Woo et al.,36 and, more recently, Bairu et al.50 have demonstrated that the micellar systems, in

719

particular their concentration36 and different micropolarity of the micelle's Stern layers,50 can have a substantial influence on the σ2PA. One more idea, worth to be taken into consideration, is the issue of the solvent effect on the three-photon absorption cross-section. A pioneering works, both in the theoretical and experimental area, have been already published.140-141 Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

Solvent

ET(30) kcal/mol

σ2PA GM

1

33

p-xylene toluene THF DMF

33.1 33.9 37.4 43.2

596 480 666 234

2

34

hexane cyclohexanone

31.0 39.8

240 ~100**

3

34

hexane cyclohexanone

31.0 39.8

710 ~400**

Diagram

720

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

Solvent

ET(30) kcal/mol

σ2PA GM

4

34

hexane cyclohexanone

31.0 39.8

6800 ~4550**

5 6

35

toluene water

33.9 63.1

1290 370

7 8

35

toluene water

33.9 63.1

2080 690

9 10

35

toluene water

33.9 63.1

1690 700

Diagram

721 Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Solvent

ET(30) kcal/mol

σ2PA GM

37

toluene THF acetone DMSO DMSO water

33.9 37.4 42.2 45.1 45.1 63.1

910 1540 1200 ~800** ~900 330

13 14

37

toluene water

33.9 63.1

890 360

15

38

toluene THF DCM DMF

33.9 37.4 40.7 43.2

83 84 110 69

16

39

toluene THF DMF

33.9 37.4 43.2

40 41 43

Molecule Ref. # #

11

12

Diagram

722

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

17

39

18

Solvent

ET(30) kcal/mol

σ2PA GM

toluene THF DMF

33.9 37.4 43.2

58 81 125

toluene THF DMF

33.9 37.4 43.2

101 188 280

19

40

hexane THF

31.0 37.4

~110 ~120**

20

41

cyclohexane toluene THF benzonitrile

30.9 33.9 37.4 41.5

1679 1365 1461 1297

Diagram

723 Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

Solvent

ET(30) kcal/mol

σ2PA GM

21

41

cyclohexane toluene THF benzonitrile

30.9 33.9 37.4 41.5

574 990 822 663

22

41

cyclohexane toluene benzonitrile acetonitrile

30.9 33.9 41.5 45.6

335 587 722 235

23

42

toluene acetonitrile

33.9 45.6

1400 3200

24

42

toluene acetonitrile

33.9 45.6

850 920

Diagram

724

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

Solvent

ET(30) kcal/mol

σ2PA GM

25

42

toluene acetonitrile

33.9 45.6

360 450

26

42

toluene acetonitrile

33.9 45.6

1900 1800

27

43

hexane

31

chloroform

39.1

90(550 mm) 50(620 mm) 160(550 mm) 100(620 mm)

chloroform

39.1 40.7 45.1

28

44

dichloromethane

DMSO

126 129 107

Diagram

725 Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

Solvent

ET(30) kcal/mol

σ2PA GM

29

45

toluene THF chloroform DCM

33.9 37.4 39.1 40.7

1033 2439 5250 1984

30

45

toluene THF chloroform DCM

33.9 37.4 39.1 40.7

1564 3531 3475 4743

31

45

toluene THF chloroform DCM

33.9 37.4 39.1 407

2294 4711 2904 721

32

46

hexane toluene THF

31 33.9 37.4

105 81 23

Diagram

726

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

Table 10.3.1. Summary of the published data concerning the influence of solvent on the 2PA cross-section of a variety of chromophores (see chemical structures of chromophores in Figures 10.3.6 to 10.3.9 below). Molecule Ref. # #

Solvent

ET(30) kcal/mol

σ2PA GM

33

46

hexane toluene THF acetone acetonitrile methanol

31.0 33.9 37.4 42.2 45.6 55.4

317 819 1000 660 238 236

34

47

chloroform DMF DMSO

39.1 43.2 45.1

38 26 25

35

48

DMF DMSO

43.2 45.1

517 668

36

49

THF DMSO

37.4 45.1

2300 2421

Diagram

*Water soluble analogs of (5), (7), (9), (11), (13). **Data were taken from the graphs provided in the published reports. THF − tetrahydrofuran, DMF − dimethylformamide, DMSO − dimethyl sulfoxide, DCM − dichloromethane.

727

Table 10.3.2. Summary of the published data concerning the influence of the different environment types on the 2PA cross-section of a variety of chromophores. Molecule Ref. # #

37

32

Molecule Ref. # #

8*

36

Molecule Ref. # #

38

50

Solvent

ET(30) kcal/mol

σ2PA cm2

1-chloronaphthalene

37.0

2x10-21

acetophenone

40.6

5x10-21

ethanol

51.9

5x10-22

diethylene glycol

53.8

5x10-22

water

63.1

5x10-22

Micellar Environment

Concentration mM

σ2PA GM

SDS

0.2

820

Micellar Environment

50

2020

100

2050

Micropolarity ** ET(30), kcal/mol

σ2PA GM

Tx-100

48.1

35

SDS

57.1

33

CTAB

57.5

29

Water

63.1

31

Diagram

Diagram

Diagram

*Water soluble analog of (7) **Data available in Supporting Information attached to Ref. 50

728

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

Figure 10.3.6. Molecules 1-8* described in Tables 10.3.1 and 2.

729

Figure 10.3.7. Molecules 9-18 described in Table 10.3.1.

730

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

Figure 10.3.8. Molecules 20-28 described in Table 10.3.1.

731

Figure 10.3.9. Molecules 29-38 described in Tables 10.3.1 and 10.3.2.

732

10.3 Solvent effects on the two-photon absorption cross-section of organic molecules

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M. Wielgus, W. Bartkowiak and M. Samoc, Chem. Phys. Lett., 554, 113 (2012). Y. Tan, Q. Zhang, J. Yu, X. Zhao, Y. Tian, Y. Cui, X. Hao, Y. Yang and G. Qian, Dyes Pigm., 97, 58 (2013). J. Rodriguez-Romero, L. Aparicio-Ixta, M. Rodriguez, G. Ramos-Ortiz, J. Luis Maldonado, A. Jimenez-Sanchez, N. Farfan and R. Santillan, Dyes Pigm., 98, 31 (2013). M. Wielgus, R. Zalezny, N. A. Murugan, J. Kongsted, H. Ågren, M. Samoc and W. Bartkowiak, ChemPhysChem, 14, 3731 (2013). D. Li, D. Yu, Q. Zhang, S. Li, H. Zhou, J. Wu and Y. Tian, Dyes Pigm., 97, 278 (2013). H. Xiao, C. Mei, B. Li, N. Ding, Y. Zhang and T. Wei, Dyes Pigm., 99, 1051 (2013). S. Bairu and G. Ramakrishna, J. Phys. Chem. B, 117, 10484 (2013). M. Zawadzka, J. Wang, W. J. Blau and M. O. Senge, Photochem. Photobiol. Sci., 12, 1811 (2013). M. Göppert-Mayer, Ann. Phys., 401, 273 (1931). M. Göppert-Mayer, Ann. Phys., 18, 466 (2009). P. A. M. Dirac, Proc Roy Soc., A114, 243 (1927). W. Kaiser and C. Garrett, Phys. Rev. Lett., 7, 229 (1961). M. Drobizhev, S. Tillo, N. S. Makarov, T. E. Hughes and A. Rebane, J. Phys. Chem. B, 113, 855 (2009). E. Kamarchik and A. I. Krylov, J. Phys. Chem. Lett., 2, 488 (2011). M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes and A. Rebane, Nat. Methods, 8, 393 (2011). M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes and A. Rebane, J. Phys. Chem. B, 116, 1736 (2012). H. Hosoi, S. Yarnaguchi, H. Mizuno, A. Miyawaki and T. Tahara, J. Phys. Chem. B, 112, 2761 (2008). Y. Ai, G. Tian and Y. Luo, Mol. Phys., 111, 1316 (2013). M. Samoc, A. Samoc, G. T. Dalton, M. P. Cifuentes, M. G. Humphrey and P. A. Fleitz in Multiphoton Processes in Organics and Their Application, I. Rau and F. Kajzar, Eds., Old City Publishing, Philadelphia, 2011, pp. 341-355. F. Terenziani, C. Katan, E. Badaeva, S. Tretiak and M. Blanchard-Desce, Adv. Mater., 20, 4641 (2008). R. W. Boyd, Nonlinear Optics, Academic Press, San Diego, California, 2008. D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics, Dover Publications, Mineola, N.Y., 1998. M. Sheik-Bahae, A. Said, T. Wei, D. Hagan and E. Van Stryland, IEEE J. Quantum Electron., 26, 760 (1990). B. Orr and J. Ward, Mol. Phys., 20, 513 (1971). M. Pawlicki, H. A. Collins, R. G. Denning and H. L. Anderson, Angew. Chem.-Int. Ed., 48, 3244 (2009). M. M. Alam, M. Chattopadhyaya and S. Chakrabarti, Phys. Chem. Chem. Phys., 14, 1156 (2011). D. L. Silva, N. A. Murugan, J. Kongsted, Z. Rinkevicius, S. Canuto and H. Ågren, J. Phys. Chem. B, 116, 8169 (2012). N. A. Murugan, J. Kongsted, Z. Rinkevicius, K. Aidas, K. V. Mikkelsen, and H. Ågren, Phys. Chem. Chem. Phys., 13, 12506 (2011). J. Olesiak-Banska, K. Matczyszyn, R. Zalezny, N. A. Murugan, J. Kongsted, H. Ågren, W. Bartkowiak and M. Samoc, J. Phys. Chem. B, 117, 12013 (2013). D. W. Silverstein and L. Jensen, J. Chem. Phys., 136, 064111 (2012). R. Fortrie and H. Chermette, J. Chem. Phys., 124, 204104 (2006). V. Hughes and L. Grabner, Phys. Rev., 79, 314 (1950). C. Xu and W. W. Webb, J. Opt. Soc. Am. B-Opt. Phys., 13, 481 (1996). E. W. Van Stryland and M. Sheik-Bahae in Characterization Techniques and Tabulations for Organic Nonlinear Materials, M. G. Kuzyk and C. W. Dirk, Eds., Marcel Dekker, Inc., New York, 1998, pp. 655-692. R. L. Sutherland, D. G. McLean and S. Kirkpatrick, Handbook of Nonlinear Optics, Marcel Dekker, Inc., New York, 2003. J. Hermann and J. Ducuing, Phys. Rev. A, 5, 2557 (1972). K. D. Belfield, M. V. Bondar, A. R. Morales, X. Yue, G. Luchita, O. V. Przhonska and O. D. Kachkovsky, ChemPhysChem, 13, 3481 (2012). D. Parthenopoulos and P. Rentzepis, Science, 245, 843 (1989). J. Strickler and W. Webb, Opt. Lett., 16, 1780 (1991). A. Dvornikov and P. Rentzepis, Opt. Commun., 119, 341 (1995). B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I. Y. S. Lee, D. McCord-Maughon, J. Q. Qin, H. Rockel, M. Rumi, X. L. Wu, S. R. Marder and J. W. Perry, Nature, 398, 51 (1999). W. Denk, J. Strickler, and W. Webb, Science, 248, 73 (1990).

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10.3 Solvent effects on the two-photon absorption cross-section of organic molecules C. Xu, W. Zipfel, J. B. Shear, R. M. Williams and W. W. Webb, Proc. Natl. Acad. Sci. U. S. A., 93, 10763 (1996). G. C. Cianci, J. R. Wu and K. M. Berland, Microsc. Res. Tech., 64, 135 (2004). G. McConnell, E. Gu, C. Griffin, C. W. Jeon, H. W. Choi, A. M. Gurney, J. M. Girkin and M. D. Dawson in Microscopy of Semiconducting Materials 2003, A. G. Cullis and P. A. Midgley, Eds., IOP Publishing Ltd., Bristol, 2003, pp. 341-344. F. Helmchen and W. Denk, Nat. Methods, 2, 932 (2005). S. Maruo, O. Nakamura and S. Kawata, Opt. Lett., 22, 132 (1997). S. Kawata, H. B. Sun, T. Tanaka and K. Takada, Nature, 412, 697 (2001). W. H. Zhou, S. M. Kuebler, K. L. Braun, T. Y. Yu, J. K. Cammack, C. K. Ober, J. W. Perry and S. R. Marder, Science, 296, 1106 (2002). A. Fisher, A. Murphree and C. Gomer, Lasers Surg. Med., 17, 2 (1995). J. D. Bhawalkar, N. D. Kumar, C. F. Zhao and P. N. Prasad, J. Clin. Laser Med. Surg., 15, 201 (1997). S. Kim, T. Y. Ohulchanskyy, H. E. Pudavar, R. K. Pandey and P. N. Prasad, J. Am. Chem. Soc., 129, 2669 (2007). W. R. Dichtel, J. M. Serin, C. Edder, J. M. J. Frechet, M. Matuszewski, L. S. Tan, T. Y. Ohulchanskyy and P. N. Prasad, J. Am. Chem. Soc., 126, 5380 (2004). M. Blanchard-Desce, Comptes Rendus Phys., 3, 439 (2002). K. Konig, J. Microsc., 200, 83 (2000). M. D. Cahalan, I. Parker, S. H. Wei and M. J. Miller, Nat. Rev. Immunol., 2, 872 (2002). D. Kanis, M. Ratner and T. Marks, Chem. Rev., 94, 195 (1994). J. Oudar and D. Chemla, J. Chem. Phys., 66, 2664 (1977). L. R. Dalton, P. A. Sullivan and D. H. Bale, Chem. Rev., 110, 25 (2010). H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S.-T. Ho, E. C. Brown, M. A. Ratner and T. J. Marks, J. Am. Chem. Soc., 129, 3267 (2007). G. S. He, J. Zhu, A. Baev, M. Samoc, D. L. Frattarelli, N. Watanabe, A. Facchetti, H. Ågren, T. J. Marks and P. N. Prasad, J. Am. Chem. Soc., 133, 6675 (2011). A. Botrel, A. Lebeuze, P. Jacques and H. Strub, J. Chem. Soc.-Faraday Trans. II, 80, 1235 (1984). J. Li, C. J. Cramer and D. G. Truhlar, Int. J. Quantum Chem., 77, 264 (2000). C. J. Cramer and D. G. Truhlar, Chem. Rev., 99, 2161 (1999). J. Tomasi and M. Persico, Chem. Rev., 94, 2027 (1994). F. C. Grozema and P. T. van Duijnen, J. Phys. Chem. A, 102, 7984 (1998). J. Gao, J. Am. Chem. Soc., 116, 9324 (1994). T. Fox and N. Rosch, Chem. Phys. Lett., 191, 33 (1992). H. McConnell, J. Chem. Phys., 20, 700 (1952). G. Brealey and M. Kasha, J. Am. Chem. Soc., 77, 4462 (1955). N. Q. Chako, J. Chem. Phys., 2, 644 (1934). A. Myers and R. Birge, J. Chem. Phys., 73, 5314 (1980). J. Schuyer, Recl. Trav. Chim. Pays-Bas-J. R. Neth. Chem. Soc., 72, 933 (1953). T. Abe, Bull. Chem. Soc. Jpn., 43, 625 (1970). O. Weigang, J. Chem. Phys., 41, 1435 (1964). B. Neporent and N. Bakhshiev, Opt. Spektros., 5, 634 (1958). N. Bakhshiev, Opt. Spektros., 5, 646 (1958). W. Liptay, Z. Naturforschung Part -Astrophys. Phys. Phys. Chem., A 21, 1605 (1966). T. Abe, J. Chem. Phys., 77, 1074 (1982). R. Birge, J. Chem. Phys., 77, 1075 (1982). T. Abe and I. Iweibo, J. Chem. Phys., 83, 1546 (1985). T. Abe and I. Iweibo, Bull. Chem. Soc. Jpn., 59, 2381 (1986). I. Iweibo, N. Obiegbedi, P. Chongwain, A. Lesi and T. Abe, J. Chem. Phys., 93, 2238 (1990). R. A. L. Vallée, M. Van Der Auweraer, F. C. De Schryver, D. Beljonne and M. Orrit, ChemPhysChem, 6, 81 (2005). C. Mohler and M. Wirth, J. Chem. Phys., 88, 7369 (1988). P. Monson and W. Mcclain, J. Chem. Phys., 53, 29 (1970). C. Sissa, V. Parthasarathy, D. Drouin-Kucma, M. H. V. Werts, M. Blanchard-Desce and F. Terenziani, Phys. Chem. Chem. Phys., 12, 11715 (2010). C. K. Wang, K. Zhao, Y. Su, Y. Ren, X. Zhao and Y. Luo, J. Chem. Phys., 119, 1208 (2003). Y. Luo, P. Norman, P. Macak and H. Ågren, J. Phys. Chem. A, 104, 4718 (2000). R. Zalezny, W. Bartkowiak, S. Styrcz and J. Leszczynski, J. Phys. Chem. A, 106, 4032 (2002).

735 134 W. Bartkowiak, B. Skwara and R. Zalezny, J. Comput. Methods Sci. Eng., 4, 551 (2004). 135 F. Terenziani, A. Painelli, C. Katan, M. Charlot and M. Blanchard-Desce, J. Am. Chem. Soc., 128, 15742 (2006). 136 K. Zhao, L. Ferrighi, L. Frediani, C.-K. Wang and Y. Luo, J. Chem. Phys., 126, 204509 (2007). 137 M. J. Paterson, J. Kongsted, O. Christiansen, K. V. Mikkelsen and C. B. Nielsen, J. Chem. Phys., 125, 184501 (2006). 138 P. C. Ray and J. Leszczynski, J. Phys. Chem. A, 109, 6689 (2005). 139 M. K. Kavitha, P. C. Haripadmam, P. Gopinath, B. Krishnan and H. John, Mater. Res. Bull., 48, 1967 (2013). 140 N. Lin, L. Ferrighi, X. Zhao, K. Ruud, A. Rizzo and Y. Luo, J. Phys. Chem. B, 112, 4703 (2008). 141 I. Cohanoschi, K. D. Belfield, C. Toro and F. E. Hernandez, J. Chem. Phys., 125, 161102 (2006).

11

Other Properties of Solvents, Solutions, and Products Obtained from Solutions George Wypych ChemTec Laboratories, Inc., Toronto, Canada

11.1 RHEOLOGICAL PROPERTIES The modification of rheological properties is one of the main reasons for adding solvents to various formulations. Rheology is also a separate complex subject which requires an indepth understanding that can only be accomplished by studying specialized sources such as monographic books on rheology fundamentals.1-3 Rheology is such a vast subject that the following discussion will only outline some of the important effects of solvents. When considering the viscosity of solvent mixtures, solvents can be divided into two groups: interacting and non-interacting solvents. The viscosity of a mixture of non-interacting solvents can be predicted with good approximation by a simple additive rule: i–n

log η =

 φi log ηi

[11.1]

i=1

where:

η i φi ηi

viscosity of solvent mixture iteration subscript for mixture components (i = 1, 2, 3,..., n) fraction of component i viscosity of component i.

Interacting solvents contain either strong polar solvents or solvents which have the ability to form hydrogen bonds or influence each other on the basis of acid-base interactions. Solvent mixtures are complex because of the changes in the interaction that occur with changes in the concentration of the components. Some general relationships describe viscosity of such mixtures but none is sufficiently universal to replace measurement. Further details on solvent mixtures are included in Chapter 8. The addition of solute(s) further complicates rheology because in such mixtures solvents may not only interact among themselves but also with the solute(s). There are also

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11.1 Rheological properties

interactions between solutes and the effect of ionized species with and without solvent participation. Only very dilute solutions of low molecular weight substances exhibit Newtonian viscosity. In these solutions, the viscosity is a constant, proportionality factor of shear rate and shear stress. The viscosity of these solutions is usually well described by the classical, Einstein's equation:

η = η ( 1 + 2.5 φ ) where:

ηi φ

[11.2]

solvent viscosity volume fraction of spheres (e.g. suspended filler) or polymer fraction

If φ is expressed in solute mass concentration, the following relationship is used: NVc φ = -----------M

[11.3]

where: N V c M

Avogadro's number molecular volume of solute ((4/3)πR3) with R − radius solute mass concentration molecular weight

Combination of equations [11.2] and [11.3] gives:

η – ηs 2.5NV --------------- = ---------------ηs c M

[11.4]

The results of studies of polymer solutions are most frequently expressed in terms of intrinsic, specific, and relative viscosities and radius of gyration; the mathematical meaning of these and the relationships between them are given below:

η–η [ η ] = lim  ---------------s  c → 0 ηs c 

[11.5]

η sp 2 ------= [ η ] + k1 [ η ] c + … c

[11.6]

ln η ----------r = [ η ] – k' 1 [ η ] 2 c + … c

[11.7]

η η = η sp + 1 = ----ηs

[11.8]

where: [η] ηsp η k1 k' 1

intrinsic viscosity specific viscosity relative viscosity the coefficient of direct interactions between pairs of molecules the coefficient of indirect (hydrodynamic) interactions between pairs of molecules

George Wypych

739

Figure 11.1. Viscosity vs. shear rate for 10% solution of polyisobutylene in pristane. [Data from C R Schultheisz, G B McKenna, Antec '99, SPE, New York, 1999, p 1125.]

Figure 11.2. Viscosity of polyphenylene solution in pyrrolidone. [Data from F. Motamedi, M Isomaki, M S Trimmer, Antec, 98, SPE, Atlanta, 1998, p. 1772.]

In Θ solvents, the radius of gyration of unperturbed Gaussian chain enters the following relationship: 3

Φ 0 R g, 0 [ η ] 0 = ---------------M where:

[11.9]

Φ0 coefficient of intramolecular hydrodynamic interactions = 3.16±0.5x1024 Rg,0 radius of gyration of unperturbed Gaussian chain

In good solvents, the expansion of chains causes an increase in viscosity as described by the following equation: 3

3

Φ 0 α η R g, 0 [ η ] = ----------------------M where:

[11.10]

αη = [η]1/3/[η]01/3 is an effective chain expansion factor.

Existing theories are far from being universal and precise in the prediction of experimental data. A more complex treatment of measurement data is needed to obtain characteristics of these “rheological” liquids. Figure 11.1 shows that the viscosity of a solution depends on shear rate. These data come from the development of a standard for instrument calibration by NIST to improve the accuracy of measurements by application of nonlinear liquid standards.4 Figure 11.2 shows the effect of polymer concentration on the viscosity of a solution of polyphenylene in N-methyl pyrrolidone.5 Two regimes are clearly visible. The regimes are divided by a

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Figure 11.3. Viscosity of 40% polystyrene in di-2-ethyl hexyl phthalate. [Data from G D J Phillies, Macromolecules, 28, No.24, 8198-208 (1995).]

11.1 Rheological properties

Figure 11.4. Shear rate of polystyrene in DOP vs. molecular weight. [Data from M Ponitsch, T Hollfelder, J Springer, Polym. Bull., 40, No.2-3, 345-52 (1998).]

critical concentration above which viscosity increases more rapidly due to the interaction of chains leading to aggregate formation. These two sets of data show that there are considerable departures from the simple predictions of the above equations because, based on them, the viscosity should be a simple function of molecular weight. Figure 11.3 shows, in addition, that the relationship between viscosity of the solution and the molecular weight is nonlinear.6 Also, the critical shear rate, at which aggregates are formed, is a non-linear function of molecular weight (Figure 7 11.4). Figure 11.5. Energy release from PDMS polymer containing unreactive PDMS liquids vs. crack velocity. 0 − Solvent (plasticizer) molecular weight control, 5970 − low molecular weight liquid, 308,000 − also affects mechanical properties of polyhigh molecular weight liquid. [Data from R A Mrozek, 8 P J Cole, K J Otim, K R Shull, J L Lenhart, Polymer, 52, mer gel as evident from Figure 11.5. When 3422-30 (2011). solvent molecular weight is larger than its entanglement weight (in this case molecular weight of entanglement is 29,000 g/mol), solvent entangles with polymer network and increases energy release as compared with control which does not contain solvent (and vice versa).8

George Wypych

Figure 11.6. Viscosity of PMMA solutions in different solvents vs. PMMA concentration. Basic solvents: tetrahydrofuran, THF, and dioxane, DXN; neutral: toluene, TOL and CCl4; acidic: 1,2-dichloroethane, DCE, CHCl3, and dichloromethane, DCM. [Adapted, by permission, from M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994).]

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Figure 11.7. Relative viscosity of block copolymers with and without segments capable of forming complexes vs. concentration. [Data from I C De Witte, B G Bogdanov, E J Goethals, Macromol. Symp., 118, 237-46 (1997).]

These departures from simple relationships are representative of simple solutions. The relationships for viscosities of solution become even more complex if stronger interactions are included, such as the presence of different solvents, the presence of interacting groups within the polymer, combinations of polymers, or the presence of electrostatic interactions between ionized structures within the same or different chains. Figure 11.6 gives one example of the complex behavior of a polymer in solution. The viscosity of PMMA dissolved in different solvents depends on concentration but there is no one consistent Figure 11.8. Intrinsic viscosity of PS/PVAc mixtures in methyl-ethyl-ketone, MEK, and toluene. [Data from relationship (Figure 11.6). Instead, three H Raval, S Devi, Angew. Makromol. Chem., 227, separate relationships exist each for basic, 27-34 (1995).] neutral, and acidic solvents, respectively. This shows that solvent’s acid-base properties have a very strong influence on viscosity. Figure 11.7 shows two different behaviors for non-associated and associated block copolymers. The first type has a linear relationship between viscosity and concentration whereas, in the case of the second type, there is a rapid increase in viscosity as concentra-

742

Figure 11.9. Viscosity of poly(ethylene oxide), PEO, poly(acrylic acid), PAA, and their 1:1 mixture in aqueous solution vs. pH. [Adapted, by permission, from I C De Witte, B G Bogdanov, E J Goethals, Macromol. Symp., 118, 237-46 (1997).]

11.1 Rheological properties

Figure 11.10. Effect of pH and zein type on zein gelation time. 1 − zein sample rich in α-zein at pH=12, 2 − zein sample rich in γ-zein at pH=2, 3 − zein sample rich in γ-zein at pH=6, 4 − zein sample rich in γ-zein at pH=12. [Data from P Nonthanum, Y Lee, G W Padua, J. Cereal Sci., 58, 76-81 (2013).]

tion increases. This is the best described as a power law function.9 Two polymers in combination have different reactions when dissolved in different solvents (Figure 11.8). In MEK, intrinsic viscosity increases as polymer concentration increases. In toluene, intrinsic viscosity decreases as polymer concentration increases.10 The polymer-solvent interaction term for MEK is very small (0.13) indicating a stable compatible system. The interaction term for toluene is much larger (0.58) which indicates a decreased compatibility of polymers in toluene and lower viscosity of the mixture. Figure 11.9 explicitly shows that the behavior of individual polymers does not necessarily have a bearing on the viscosity of their solutions. Both poly(ethylene oxide) and poly(propylene oxide) are not affected by solution pH but, when used in combination, they become sensitive to solution pH. A rapid increase of viscosity at a lower pH is ascribed to the intermolecular complex formation. This behavior can be used for thickening of formulations.9 A mixture of water and ethanol is the best solvent for zein.11 Zein, a corn protein, is a mixture of the polypeptides α-, γ-, β-, and δ-zein, with α- and γ-zeins comprising 70-85% and 10-20% of total zein, respectively.11 Figure 11.10 shows that concentration of ethanol affects gelation time (as well as the flow behavior) of zein solutions, but there is also the substantial influence of pH.11 The last is explained by chemical structures of different zeins. α-Zein solutions were nearly Newtonian while those containing γ-zein showed shear thinning behavior.11 It is because high pH promotes formation of disulfide bonds in γ-zein because γ-zein is rich in cysteine which contributes to formation of these bonds.11 Figures 11.11 and 11.12 show one potential application in which a small quantity of solvents can be used to lower melt viscosity during polymer processing. Figure 11.11 shows that not only can melt viscosity be reduced but also that the viscosity is almost

George Wypych

Figure 11.11. Apparent melt viscosity of original PET and PET containing 20% 1-methyl naphthalene vs. shear rate. [Adapted, by permission, from S Tate, S Chiba, K Tani, Polymer, 37, No.19, 4421-4 (1996).]

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Figure 12.1.12. Viscosity behavior of PS with and without CO2. [Data from M Lee, C Tzoganikis, C B Park, Antec.99, SPE, New York, 1999, p 2806.]

independent of shear rate.12 In environmentally friendly processes, the supercritical fluids can be used to reduce melt viscosity. Rheological behavior of water-based conductive pastes was adjusted by using alcohol co-solvents.15 The viscosity was increased with the number of hydroxyl groups in cosolvent which also affected thixotropy.15 Co-solvent with two hydroxyl groups was the best in inducing Marangoni flow.15 The above data illustrate that the real behavior of solutions is much more complex than it is intuitively predicted based on simple models and relationships. The proper selection of solvent can be used to tailor the properties of the formulation to the processing and application needs. Solution viscosity can be either increased or decreased to meet process technology requirements or to give the desired material properties.

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A Ya Malkin, Rheology Fundamentals, ChemTec Publishing, Toronto, 1994; A. Ya Malkin, A I Isayev, Rheology. Concepts, Methods, and Applications, 3rd Ed., ChemTec Publishing, Toronto, 2017. Ch W Macosko, Rheology. Principles, Measurements, and Applications, VCH Publishers, New York, 1994. R I Tanner, K. Walters, Rheology: a Historical Perspective, Elsevier, Amsterdam, 1998. C R Schultheisz, G B McKenna, Antec '99, SPE, New York, 1999, p 1125. F Motamedi, M Isomaki, M S Trimmer, Antec '98, SPE, Atlanta, 1998, p. 1772. G D J Phillies, Macromolecules, 28, No.24, 8198-208 (1995). M Ponitsch, T Hollfelder, J Springer, Polym. Bull., 40, No.2-3, 345-52 (1998). R A Mrozek, P J Cole, K J Otim, K R Shull, J L Lenhart, Polymer, 52, 3422-30 (2011). I C De Witte, B G Bogdanov, E J Goethals, Macromol. Symp., 118, 237-46 (1997). H Raval, S Devi, Angew. Makromol. Chem., 227, 27-34 (1995). P Nonthanum, Y Lee, G W Padua, J. Cereal Sci., 58, 76-81 (2013). S Tate, S Chiba, K Tani, Polymer, 37, No.19, 4421-4 (1996). M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994). M Lee, C Tzoganikis, C B Park, Antec '99, SPE, New York, 1999, p 2806. C Hua, X Li, L Shen, H Lei, X Guo, Z Liu, Q Kong, L Xie, C-M Chen, Particuology, 33, 35-41, 2017.

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11.2 Aggregation

11.2 AGGREGATION The development of materials with an engineered morphological structure, such as selective membranes and nanostructures, employs principles of aggregation in these interesting technical solutions. Here, we consider some basic principles of aggregation, methods of studies, and outcomes. The discipline is relatively new, therefore, for the most part, only exploratory findings are available. The theoretical understanding is still to be developed and this development is essential for the control of industrial processes and development of new materials. Methods of study and data interpretation still require further work and refinement. Several experimental techniques are used, including microscopy (TEM, SEM);1,2 dynamic light scattering3-6 using laser sources, goniometers, and digital correlators; spectroscopic methods (UV, CD, fluorescence);7,8 fractionation; solubility and viscosity measurements;9 and acid-base interaction.10 Dynamic light scattering is the most popular method. Results are usually expressed by the radius of gyration, Rg, the second viral coefficient, A2, the association number, p, and the number of arms, f, for starlike micelles. Zimm's plot and equation permit Rg and A2 to be estimated: 2

16 R KC 1 -------- = -------- 1 + ------ π 2 -----2g- sin 2 θ + … + 2A 2 C + … 3 λ Rθ Mw 0

[11.11]

where: K C Rθ Mw λ0 θ

optical constant polymer concentration Rayleigh ratio for the solution weight average molecular weight wavelength of light scattering angle.

The following equations are used to calculate p and f: M agg -; p = ----------M1

M agg = KI q → 0 ⁄ C

[11.12]

where: Magg M1 I Rgarm v

mass of aggregates mass of free copolymers scattered intensity radius of gyration of linear polymer excluded volume exponent.

Three major morphological features are under investigation: starlike, crew-cut, and polymer brushes (Figure 11.13). Morphological features have been given nick-names characterizing the observed shapes, such as “animals” or “flowers” to distinguish between various observed images.6 Figure 11.14 shows four morphologies of aggregates formed by polystyrene, PS, poly(acrylic acid), PAA, diblock copolymers.1 The morphology produced was a direct result of the ratio between lengths of blocks of PS and PAA (see Figure

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Figure 11.13. Morphological features: starlike and crew-cut. The bottom drawing illustrates polymer brush. [Adapted, by permission from G Liu, Macromol. Symp., 113, 233 (1997).]

Figure 11.15. PS-PAA aggregates of different morphologies depending on its concentration in DMF: A − 2, B − 2.6, C − 3, D − 4 wt%. [Adapted, by permission, from L Zhang, A Eisenberg, Macromol. Symp., 113, 221-32 (1997).]

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Figure 11.1.14. Morphological features of PS-PAA copolymer having different ratios of PS and PAA block lengths: A − 8.3, B- 12, C − 20.5, and D − 50. [Adapted, by permission, from L Zhang, A Eisenberg, Macromol. Symp., 113, 221-32 (1997).]

Figure 11.16. TEM micrograph of nanospheres. [Adapted, by permission, from G Liu, Macromol. Symp., 113, 233 (1997).]

11.14). When this ratio is low (8.3), spherical micelles are formed. With a slightly higher ratio (12), rod-like micelles result which have a narrow distribution of diameter but variable length. Increasing ratio even further (20.5) causes vesicular aggregates to form. With the highest ratio (50), large spherical micelles are formed. One of the reasons for the differences in these formations is that the surface tension between the core and the solvent varies widely. In order to decrease interfacial tension between the core and the solvent, the aggregate increases the core size.1 The polymer concentration in solution also affects aggregate formation as Figure 11.15 shows. As polymer concentration increases, spherical micelles are replaced by a mixture of rod-like structures and vesicles. With a further

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Figure 11.17. TEM micrograph of assemblies of cylindrical aggregates. [Adapted, by permission, from G Liu, Macromol. Symp., 113, 233 (1997).]

Figure 11.19. TEM micrograph of knots and strands formed in carbohydrate amphiphile. [Adapted, by permission, from U Beginn, S Keinath, M Moller, Macromol. Chem. Phys., 199, No.11, 2379-84 (1998).]

11.2 Aggregation

Figure 11.18. TEM micrograph of nanofibers. [Adapted, by permission, from G Liu, Macromol. Symp., 113, 233 (1997).]

increase in concentration, the rod-like shapes disappear and only vesicles remain. Figures 11.16-11.18 show a variety of shapes. These include nanospheres, assemblies of cylindrical aggregates, and nanofibers.11 Nanospheres were obtained by the gradual removal of the solvent by dialysis, fibers were produced by a series of processes involving dissolution, crosslinking, and annealing. Figure 11.19 sheds some light on the mechanism of aggregate formation. Two elements are clearly visible from micrographs: knots and strands. Based on studies of carbohydrate amphiphiles, it is concluded that knots are formed early in the process by spinodal decomposition. Formation of strands between knots occurs much later.2 A similar course of events occurs with the molecular aggregation of PVC solutions.5 Figure 11.20 gives more details on the mechanism of aggregate formation.5 PVC dissolved in bromobenzene, BrBz, undergoes a coil to globule transition which does not occur in dioxane, DOA, solution. Bromobenzene has a larger molar volume than dioxane and the polymer chain must read-

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Figure 11.20. Radius of gyration vs. temperature for PVC solutions in bromobenzene, BrBz, and dioxane, DOA. [Adapted, by permission, from Hong Po-Da, Chen Jean-Hong Chen, Polymer, 40, 4077-4085, (1999).]

Figure 11.21. Specific viscosity of PVC in bromobenzene solution vs. concentration. [Adapted, by permission, from Hong Po-Da, Chen Jean-Hong Chen, Polymer, 40, 4077-4085, (1999).]

Figure 11.22. Diblock copolymer association number vs. its concentration. [Adapted, by permission, from D Lairez, M Adam, J-P Carton, E Raspaud, Macromolecules, 30, No.22, 6798-809 (1997).]

Figure 11.23. Fluorescence intensity ratio vs. concentration of polyimide in chloroform. [Data from H Luo, L Dong, H Tang, F Teng, Z Feng, Macromol. Chem. Phys., 200, No.3, 629-34 (1999).]

just to the solvent molar volume in order to interact. Figure 11.21 shows that two regimes of aggregation are involved which are divided by a certain critical value. Below the critical value, chains are far apart and do not interact due to contact self-avoidance. At the critical point, knots, similar to shown in Figure 11.19, begin to form and the resultant

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11.2 Aggregation

aggregation increases viscosity. As the polymer concentration increases, the association number, p, also increases, but then levels off (Figure 11.22). Fluorescence studies (Figure 11.23) show that there are two characteristic points relative to concentration. Below the first point, at 0.13 g/dl, in a very dilute solution, molecules are highly expanded and distant from one another and fluorescence does not change. Between the two points, individual chain coils begin to sense each other and become affected by the presence of neighbors forming intermolecular associations. Above the second point, coils begin to overlap leading to a dense packing.8 These data are essentially similar to those presented in Figure 11.22 but cover a broader concentration range. Tuning aggregation of microemulsion droplets and silica nanoparticles can be achieved using solvent mixtures.12 The state of aggregation can be correlated with the effective molecular volume of the solvent mixture.12 This is because the droplet diffusion coefficient increases and the apparent diameter of microemulsion droplets decreases when the effective molar volume of the solvent mixture decreases.12 Attractive interactions are increased, when the effective molar volume of the solvent is increased.12 Proteins are inherently unstable and may produce degraded forms which are harmful when used in the treatment of human diseases.13 On the other hand, protein-based therapeutic preparations are the fastest growing new drugs under development.13 This calls for use of aggregation suppressing additives which reduce the risk of instability.13 Theory of aggregation prevention and practical applications of preventive measures are broadly discussed in this review.13 Molecular dynamics simulations were performed to demonstrate the application of the dimension map.14 The map can be separated into three regions representing three groups of structures: one-dimensional rod-like structures; two-dimensional planar structures or short-cylinder-like structures; and three-dimensional sphere-like structures.14 Examining the location of the aggregates on the dimension map its changes with solvent type and solute material parameter provides an effective way to study solubility and mechanism of aggregation.14 The above studies show that there are many means of regulating aggregate size and shape which is likely to become an essential method of modifying materials by morphological engineering.

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14

L Zhang, A Eisenberg, Macromol. Symp., 113, 221-32 (1997). U Beginn, S Keinath, M Moller, Macromol. Chem. Phys., 199, No.11, 2379-84 (1998). P A Cirkel, T Okada, S Kinugasa, Macromolecules, 32, No.2, 531-3 (1999). K Chakrabarty, R A Weiss, A Sehgal, T A P Seery, Macromolecules, 31, No.21, 7390-7 (1998). Hong Po-Da, Chen Jean-Hong Chen, Polymer, 40, 4077-4085, (1999). D Lairez, M Adam, J-P Carton, E Raspaud, Macromolecules, 30, No.22, 6798-809 (1997). R Fiesel, C E Halkyard, M E Rampey, L Kloppenburg, S L Studer-Martinez, U Scherf, UHF Bunz, Macromol. Rapid Commun., 20, No.3, 107-11 (1999). H Luo, L Dong, H Tang, F Teng, Z Feng, Macromol. Chem. Phys., 200, No.3, 629-34 (1999). A Leiva, L Gargallo, D Radic, J. Macromol. Sci. B, 37, No.1, 45-57 (1998). S Bistac, J Schultz, Macromol. Chem. Phys., 198, No. 2, 531-5 (1997). G Liu, Macromol. Symp., 113, 233 (1997). A Salabat, J Eastoe, K J Mutch, R F Tabor, J. Colloid Interface Sci., 318, 244-51, (2008). D Shukla, C P Schneider, B L Trout, Adv. Drug Delivery Rev., 63, 1074-85 (2011). C Jian, T Tang, S Bhattacharjee, J. Molec. Graphics Model., 58, 10-15, 2015.

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11.3 PERMEABILITY The phenomenon of solvent transport through solid barriers has three aspects which are discussed under the heading of permeability. These are the permeation of solvent through materials (films, containers, etc.); the use of pervaporation membranes to separate organic solvents from water or water from solvents; and the manufacture of permeate selective membranes. The permeability of different polymers and plastics to various solvents can be found in an extensive, specialized database published as a book and as a CD-ROM.1 The intrinsic properties of polymers can be modified in several ways to increase their resistance and reduce their permeability to solvents. The development of plastic gas tanks was a major driving force behind these developments and now various plastic containers are manufactured using similar processes. Fluorination of plastics, usually polypropylene or polyethylene, is by far the most common modification. Containers are typically manufactured by a blow molding process. Then, they are protected by a fluorination process applied on the line or, more frequently, off the line. The first patent2 for this process was issued in 1975 and numerous other patents have contributed to further improvements of the process.3 The latest processes use a reactive gas containing 0.1 to 1% fluorine to treat parison within the mold after it was expanded.3 Containers treated by this process have a barrier to polar liquids, hydrocarbon fuels, and carbon fuels containing polar liquids such as alcohols, ethers, amines, carboxylic acids, ketones, etc. Superior performance is achieved when a hydrogen purge precedes the exposure of the container to oxygen. In another development,4 containers are being produced from a blend of polyethylene and poly(vinylidene fluoride) with aluminum stearate as a compatibilizer. This process eliminates the use of the toxic gas fluorine and by-products which reduces environmental pollution and disposal problems. It is argued that fluorinated containers may not perform effectively when the protective layer becomes damaged due to stress cracking. Such a blend is intended as a replacement for previous blends of polyamide and polyethylene used in gas tanks and other containers. These older blends were exposed to a mixture of hydrocarbons but now oxygenated solvents (e.g., methanol) have been added which cause an unacceptable reduction of barrier properties. A replacement technology is needed. Improved barrier properties in this design4 come from increased crystallinity of the material brought about by controlling the laminar thickness of polyethylene crystals and processing material under conditions which favor the crystallization of poly(vinylidene fluoride). Another approach involves the use of difunctional telechelic polyolefins with ester, hydroxyl, and amine terminal groups.5 Telechelic polyolefins can be used to make polyesters, polyamides, and polyurethanes with low permeability to solvents and gases. Separation processes such as ultrafiltration and microfiltration use porous membranes which allow the passage of molecules smaller than the membrane pore size. Ultrafiltration membranes have pore sizes from 0.001 to 0.1 μm while microfiltration membranes have pore sizes in the range of 0.02 to 10 μm. The production of these membranes is almost exclusively based on non-solvent inversion method which has two essen-

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11.3 Permeability

tial steps: the polymer is dissolved in a solvent, cast to form a film, and then the film is exposed to a nonsolvent. Two factors determine the quality of the membrane: pore size and selectivity. Selectivity is determined by how narrow the distribution of pore size is.6,7 In order to obtain membranes with good selectivity, one must control the non-solvent inversion process so that it inverts slowly. If it occurs too fast, it causes the formation of pores of different sizes which will be non-uniformly distributed. This can be prevented either by an introduction of a large number of nuclei, which are uniformly distributed in the polymer membrane or by the use of a solvent combination which regulates the rate of solvent replacement. Figure 11.24. PEI fiber from NMP. Typical solvents used in the membrane produc[Adapted, by permission from D Wang, tion include N-methylpyrrolidinone, N,N-dimethyK Li, W K Teo, J. Appl. Polym. Sci., 71, No.11, 1789-96 (1999).] lacetamide, N,N-dimethylformamide, dimethylsulfoxide, tetrahydrofuran, dioxane, dichloromethane, methyl acetate, ethyl acetate, and chloroform. They are used alone or in mixtures.6 These are used most frequently as non-solvents: methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, and tbutanol. Polymers involved include polysulfone, polyethersulfone, polyamide, polyimide, polyetherimide, polyolefins, polycarbonate, polyphenyleneoxide, poly(vinylidene fluoride), polyacrylonitrile, and cellulose and its derivatives. The second method of membrane preparation is based on the thermally-induced phase separation process.8 The goal of this process is to produce a Figure 11.25. PEI fiber from DMF. [Adapted, membrane which has an ultrathin separation layer by permission from D Wang, (to improve permeation flux) and uniform pores.9 In K Li, W K Teo, J. Appl. Polym. Sci., 71, this process, the polymer is usually dissolved in a No.11, 1789-96 (1999).] mixture of solvents which allow the mixture to be processed either by spinning or by coating. The desired membrane morphology is obtained through cooling to induce phase separation of polymer/solvent/non-solvent system. One practice in use is the addition of non-solvents to the casting solution.10 The mixture should be designed such that homogeneous casting is still possible but the thermodynamic condition approaches phase separation. Because of cooling and/or evaporation of one of the solvents, demixing occurs before material enters coagulation bath.10 Figures 11.24 and 11.25 explain technical principles behind the formation of the efficient and selective membrane. Figure 11.24 shows a micrograph of hollow PEI fiber pro-

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Figure 11.26. Precipitation value for PEI/NMP system with different non-solvents vs. temperature. [Data from D Wang, Li K,WK Teo, J. Appl. Polym. Sci., 71, No.11, 1789-96 (1999).]

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Figure 11.27. Skin thickness vs. evaporation time during formation of asymmetric membrane from polysulfone. [Data from A Yamasaki, R K Tyagi, A E Fouda, T Matsura, K Jonasson, J. Appl. Polym. Sci., 71, No.9, 1367-74 (1999).]

duced from N-methyl-2-pyrrolidone, NMP, which has thin surface layer and uniform pores and Figure 11.25 shows the same fiber obtained from a solution in dimethylformamide, DMF, which has a thick surface layer and fewer uniform pores.9 The effect depends on the interaction of polar and non-polar components. The compatibility of components was estimated based on their Hansen's solubility parameter difference. The compatibility increases as the solubility parameter difference decreases.9 Adjusting temperature is another method of control because the Hansen's solubility parameters decrease as the temperature increases. A procedure was developed to determine precipitation values by titration with non-solvent to a cloud point.9 Use of this procedure aids in selecting a suitable non-solvent for a given polymer/solvent system. Figure 11.26 shows the results of the application of this method.9 Successful membrane production by either non-solvent inversion or thermally-induced phase separation requires careful analysis of the compatibilities between polymer and solvent, polymer and non-solvent, and solvent and non-solvent. Also, the processing regime, which includes temperature control, removal of volatile components, uniformity of solvent replacement must be carefully controlled. Efforts must be made to select solvents of low toxicity and to minimize solvent consumption. An older method of producing polyetherimide membranes involved the use of a mixture of two solvents: dichloromethane (very volatile) and 1,1,2-trichloroethane together with a mixture of non-solvents: xylene and acetic acid. In addition, large amounts of acetone were used in the coagulation bath. A more recent process avoided environmental problems by using tetrahydrofuran and γ-butyrolactone in a process in which water is used in the coagulating bath (membrane quality remained the same).10

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11.3 Permeability

Figure 11.28. Pervaporation transport parameters: A/l (liquid transport) and B/l (vapor transport) vs. evaporation time during membrane preparation from aromatic polyamide. [Data from A Yamasaki, R K Tyagi, A Fouda, T Matsuura, J. Appl. Polym. Sci., 57, No.12, 1473-81 (1995).]

Figure 11.29. Separation factor vs. solubility of solvents in water. [Adapted, by permission, from M Hoshi, M Kobayashi, T Saitoh, A Higuchi, N Tsutomu, J. Appl. Polym. Sci., 69, No.8, 1483-94 (1998).]

Figure 11.30. Effect of triclene concentration in feed solution on its pervaporation flux through acrylic membrane. [Data from M Hoshi, M Kobayashi, T Saitoh, A Higuchi, N Tsutomu, J. Appl. Polym. Sci., 69, No.8, 1483-94 (1998).]

Figure 11.31. Effect of hexane concentration in feed solution on its concentration in permeate through acrylic membrane. [Data from M Hoshi, M Kobayashi, T Saitoh, A Higuchi, N Tsutomu, J. Appl. Polym. Sci., 69, No.8, 1483-94 (1998).]

Thermally-induced phase separation has been applied to the production of polysilane foams.11 Variation of polymer concentration, solvent type, and cooling rate have been used to refine the macrostructure. Both membrane production methods rely on the formation of aggregates of controlled size and shape as discussed in the previous section.

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Figure 11.27 shows the effect of solvent evaporation time on the skin layer thickness. It is only at the beginning of the process that skin thickness does not increase. Thereafter a rapid skin thickness growth is observed. Polymer concentration is the other important determinant of skin thickness. Figure 11.28 shows that during very short evaporation times (5 min.), even though the skin is thin, the diameter of pores is so small that the pervaporation parameters A/l and B/l, which characterize liquid and vapor transport, respectively, do not increase. Longer evaporation times bring about a gradual decrease in transport properties.12,13 Figure 11.29 shows the relationship between the separation factor and the solubility of solvents in water. The separation of the solvent by a pervaporation membrane occurs less efficiently as solvent solubility increases.The more concentrated the solution of solvent, the faster is the separation (Figure 11.30). Separation of hexane from a mixture with heptane is similar (Figure 11.31). The acrylic membrane shows good selectivity. These examples demonstrate the usefulness of pervaporation membranes in solvent recovery processes. Skin permeation experiments were conducted with model solutes (corticosterone, urea, mannitol, glycerol, triamcinolone acetonide, and estradiol) and model solvents (ethanol, butanol, water, and propylene glycol) using Franz diffusion cells and human epidermal membrane.15 Solvents did not act solely as a vehicle for spreading the solutes during solvent deposition.15 The solute permeation mechanism with the volatile solvent was related to solute dissolution on the skin surface and its diffusion across the skin.15 The decreased moisture uptake on treatment with chloroform/methanol results with sample reaching equilibrium in shorter times which indicates a deterioration of the stratum corneum tissue which is the primary barrier to body water loss.16 With acetone treatment, a decreased permeability is observed and stratum corneum barrier functions are improved.16

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

L McKeen, Permeability and Other Film Properties, Plastics Design Library, Norwich, 2011. US Patent 3,862,284, 1975. J P Hobbs, J F DeiTos, M Anand, US Patent 5,770,135, Air Products and Chemicals, Inc., 1998 and US Patent 5,244,615, 1992. R T Robichaud, US Patent 5,702,786, Greif Bros. Corporation, 1997. P O Nubel, H B Yokelson, US Patent 5,731,383, Amoco Corporation, 1998 and US Patent 5,589,548, 1996. J M Hong, S R Ha, H C Park, Y S Kang, K H Ahn, US Patent 5,708,040, Korea Institute of Science and Technology, 1998. K-H Lee, J-G Jegal, Y-I Park, US Patent 5,868,975, Korea Institute of Science and Technology, 1999. J M Radovich, M Rothberg, G Washington, US Patent 5,645,778, Althin Medical, Inc., 1997. D Wang, Li K, W K Teo, J. Appl. Polym. Sci., 71, No.11, 1789-96 (1999). K-V Peinemann, J F Maggioni, S P Nunes, Polymer, 39, No.15, 3411-6 (1998). L L Whinnery, W R Even, J V Beach, D A Loy, J. Polym. Sci.: Polym. Chem. Ed., 34, No.8, 1623-7 (1996). A Yamasaki, R K Tyagi, A Fouda, T Matsuura, J. Appl. Polym. Sci., 57, No.12, 1473-81 (1995). A Yamasaki, R K Tyagi, A E Fouda, T Matsura, K Jonasson, J. Appl. Polym. Sci., 71, No.9, 1367-74 (1999). M Hoshi, M Kobayashi, T Saitoh, A Higuchi, N Tsutomu, J. Appl. Polym. Sci., 69, No.8, 1483-94 (1998). R Intarakumhaeng, A Wanasathop, S K Li, Int. J. Pharmac., 536, 1, 405-13, 2018. C Barba, C Alonso, M Martí, A Manich, L Coderch, Biochim. Biophys. Acta - Biomembranes, 1858, 8, 1935-43, 2016.

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11.4 Molecular structure and crystallinity

11.4 MOLECULAR STRUCTURE AND CRYSTALLINITY The gelation of polymer-solvent systems was initially thought of as a process which occurs only in poor solvents which promote chain-chain aggregation. Further studies have revealed that many polymers also form gels in good solvents. This has prompted research which attempts to understand the mechanisms of gelation. These efforts have contributed the current understanding of the association between molecules of solvents and polymers.1 Studies on isotactic, iPS, and syndiotactic, sPS, polystyrenes2-6 have confirmed that, although both polymers have the same monomeric units, they are significantly different in terms of their solubility, gelation, and crystallization. In systems where sPS has been dissolved in benzene and carbon tetrachloride, gelation is accomplished in a few minutes whereas in chloroform it takes tens of hours. Adding a small amount of benzene to the chloroform accelerates the gelation process. There is also evidence from IR which shows that the orientation of the ring plane is perpendicular to the chain axis. This suggests that there is a strong interaction between benzene and sPS molecules. The other interesting observation came from studies on decalin sPS and iPS systems. iPS forms a transparent gel and then becomes turbid, gradually forming trigonal crystallites of iPS. sPS does not convert to a gel but the fine crystalline precipitate particles instead. This shows that the molecular arrangement depends on both the solvent type and on the molecular structure of the polymer.2 Figure 11.32 shows how benzene molecules align themselves parallel to the phenyl rings of polystyrene and how they are housed within the helical form of the polymer structure which is stabilized by the presence of solvent.1 Work on poly(ethylene oxide) gels7 indicates that the presence of solvents such as chloroform and carbon disulfide contributes to the formation of a uniform helical conformation. The gelation behavior and the gel structure depend on the solvent type which, in turn, is determined by solvent-polymer interaction. In a good solvent, polythiophene molecules exist in coiled conformation. In a poor solvent, the molecules form aggregates through the short substituents.8 Figure 11.32. Molecular model of polystyPolyvinylchloride, PVC, which has a low crysrene and benzene rings alignment. [Adapted by permission, from J M Guenet, Macromol. tallinity, gives strong gels. Neutron diffraction and Symp., 114, 97 (1997).] scattering studies show that these strong gels result from the formation of PVC-solvent complexes.9 This indicates that the presence of solvent may affect the mechanical properties of such a system. Figure 11.33 shows that the presence of dichloromethane in sPS changes the

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Figure 11.33. Stress-strain behavior at 130oC of glassy sPS with and without immersion in dichloromethane. [Data from C Daniel, L Guadagno, V Vittoria, Macromol. Symp., 114, 217 (1997).]

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Figure 11.34. Carbonyl frequency vs. molar fraction of solvent. [Adapted, by permission, from J M Gomez-Elvira, P Tiemblo, G Martinez, J Milan, Macromol. Symp., 114, 151 (1997).]

mechanical characteristic of the material. A solvent-free polymer has a high elongation and yield value. An oriented polymer containing dichloromethane has lower elongation, no yield value, and approximately four times greater tensile strength.10 The interaction of polymer-solvent affects rheological properties. Studies on a divinyl ether-maleic anhydride copolymer show that molecular structure of the copolymer can be altered by the solvent selected for synthesis.11 Studies have shown that the thermal and UV stability of PVC is affected by the presence of solvents.12-14 Figure 12.1.34 shows that solvent type and its molar fraction affect the value of the carbonyl frequency shift. This frequency shift occurs at a very low solvent concentration. The slope angles for each solvent are noticeably different.15 Similar frequency shifts were reported for various solvents in polyetheretherketone, PEEK, solutions.16 These associations are precursors of further ordering by crystallization. Figure 11.35 shows different crystalline structures of poly(ethylene oxide) with various solvents.17 Depending on the solvent type, a unit cell contains a variable number of monomers and molecules of solvent stacked along the crystallographic axis. In the case of dichlorobenzene, the molecular complex is orthorhombic with 10 monomers and 3 solvent molecules. Figure 11.36 shows optical micrograph of spherulite formed from unit cells having 8 monomers and 4 molecules of solvent. The unit cell of the triclinic crystal, formed with nitrophenol, is composed of 6 monomers and 4 molecules of solvent. This underlines the importance of solvent selection in achieving the desired structure in the formed material. The technique is also advantageous in polymer synthesis, in improving polymer stability, etc. Temperature is an essential parameter in the crystallization process.18 Rapid cooling of a polycarbonate, PC, solution in benzene resulted in extremely high crystallinity

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11.4 Molecular structure and crystallinity

Figure 11.35. Crystal structure of poly(ethylene oxide) molecular complex with: (a) p-dichlorobenzene, (b) resorcinol, (c) p-nitrophenol. [Adapted, by permission, from M Dosiere, Macromol. Symp., 114, 51 (1997).]

(46.4%) as compared to the typical PC crystallinity of about 30%. Polymer-solvent interaction combined with the application of an external force leads to the surface crazing of materials. The process is based on similar principles as discussed in this section formation of fibrillar crystalline structures. The surface molecular structure of spin cast polymer films is important for the rational design of surface properties.20 The surface molecular structure of spin cast homopolymers containing phenyl groups has been influenced by the solvent aromaticity.20 If phenyl groups were located in a linear polymer backbone, the spin casting with aromatic solvents enhanced sum Figure 11.36. Optical micrograph of PEO-resorcifrequency generation vibrational spectroscopy nol complex. [Adapted, by permission, from signal of the phenyl as compared to a non-aroM Dosiere, Macromol. Symp., 114, 51 (1997).] matic solvent.20 This suggests that the aromatic solvent caused ordering the surface phenyl groups and placed them perpendicular to the film surface.20 The effect of solvent aromaticity on phenyl ordering at spin cast film surfaces was explained by the differences in molecular structures of polymer chains at solvent/air interfaces, preferential solvation of functional groups during evaporation, and reorientation of bulky side groups at the polymer film/air interface.20

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In the processing of biomass, the pretreatment and dissolution of cellulose are important steps.21 A good solvent for cellulose has high diffusivity, aggressiveness in decrystallization, and capability of disassociating the cellulose chains.21 The cellulose fibers remain crystalline almost until the end of the dissolution process.21 Decreasing the fiber crystallinity by pretreatment would result in a considerable increase in the dissolution rate.21 Although research on molecular structure and crystallization is yet to formulate a theoretical background which might predict the effect of different solvents on the fine structure of different polymers, studies have uncovered numerous issues which cause concern but which also point out to new applications. A major concern is the effect of solvents on craze formation and on thermal and UV degradation. Potential applications include engineering of polymer morphology by synthesis in the presence of selected solvent under a controlled thermal regime, polymer reinforcement by interaction with smaller molecules, better retention of additives, and modification of surface properties to change adhesion or to improve surface uniformity, etc.

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

J M Guenet, Macromol. Symp., 114, 97 (1997). M Kobayashi, Macromol. Symp., 114, 1-12 (1997). T Nakaoki, M Kobayashi, J. Mol. Struct., 242, 315 (1991). M Kobayashi, T Nakoaki, Macromolecules, 23, 78 (1990). M Kobayashi, T. Kozasa, Appl. Spectrosc., 47, 1417 (1993). M. Kobayashi, T Yoshika, M Imai, Y Itoh, Macromolecules, 28, 7376 (1995). M Kobayashi, K Kitagawa, Macromol. Symp., 114, 291 (1997). P V Shibaev, K Schaumburg, T Bjornholm, K Norgaard, Synthetic Metals, 97, No.2, 97-104 (1998). H Reinecke, J M Guenet, C. Mijangos, Macromol. Symp., 114, 309 (1997). C Daniel, L Guadagno, V Vittoria, Macromol. Symp., 114, 217 (1997). M Y Gorshkova, T L Lebedeva, L L Stotskaya, I Y Slonim, Polym. Sci. Ser. A, 38, No.10, 1094-6 (1996). G Wypych, Handbook of Material Weathering, 6th Edition, ChemTec Publishing, Toronto, 2018. G Wypych, PVC Degradation and Stabilization, 3rd Edition, ChemTec Publishing, Toronto, 2015. G Wypych, Handbook of UV Degradation and Stabilization, 2nd Edition, ChemTec Publishing, Toronto, 2015. J M Gomez-Elvira, P Tiemblo, G Martinez, J Milan, Macromol. Symp., 114, 151 (1997). B H Stuart, D R Williams, Polymer, 36, No.22, 4209-13 (1995). M Dosiere, Macromol. Symp., 114, 51 (1997). G Ji, F Li, W Zhu, Q Dai, G Xue, X Gu, J. Macromol. Sci. A, A34, No.2, 369-76 (1997). I V Bykova, E A Sinevich, S N Chvalun, N F Bakeev, Polym. Sci. Ser. A, 39, No.1, 105-12 (1997). J N Myers, C Zhang, C Chen, Z Chen, J. Colloid. Interface Sci., 423, 60-6, 2014. M Ghasemi, M Tsianou, P Alexandridi, Bioresource Technol., 228, 330-8, 2017.

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Figure 11.37. Peroxide formation from tetrahydrofuran during irradiation at 254 nm. [Data from J F Rabek, T A Skowronski, B Ranby, Polymer, 21, 226 (1980).]

11.5 Other properties affected by solvents

Figure 11.38. Spectral intensity of n-octane radical formed during irradiation of PE at −196oC for 30 min vs. concentration of p-xylene. [Adapted, by permission, from H Kubota, M Kimura, Polym. Deg. Stab., 38, 1 (1992).]

11.5 OTHER PROPERTIES AFFECTED BY SOLVENTS Many other properties of solutes and solutions are affected by solvents. Here, we will discuss material stability and stabilization, some aspects of reactivity (more information on this subject appears in Chapter 12), physical properties, some aspects of electrical and electrochemical properties (more information on this subject appears in Chapter 10), surface properties, and polarity and donor properties of solvents. Degradative processes have long been known to be promoted by the products of solvent degradation. Tetrahydrofuran is oxidized to form a peroxide which then dissociates to two radicals initiating a chain of photooxidation reactions. Figure 11.37 shows the kinetics of hydroperoxide formation.1 Similar observations, but in a polymer system, were made in xylene by direct determination of the radicals formed using ESR.2 An increased concentration in trace quantities of xylene contributed to the formation of n-octane radicals by abstracting hydrogen from polyethylene chain in an α-position to the double bond (Figure 11.38). 3-Hydroperoxyhexane cleaves with the formation of carboxylic acid and hydrocarbon radical (ethylene or propylene).3 These known examples show that the presence of even traces of solvents may change the chemistry and the rate of photooxidative processes because of radical formation. In another aspect of photooxidative processes, solvents influence the reactivity of small molecules and chain segments by facilitating the mobility of molecules and changing the absorption of light, the wavelength of emitted fluorescent radiation, and the lifetime of radicals. Work on anthraquinone derivatives, which are common photosensitizers,

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has shown that when photosensitizer is dissolved in isopropanol (hydrogen-donating solvent) the half-life of radicals is increased by a factor of seven compared to acetonitrile (a non-hydrogen-donating solvent).4 This shows that the ability of a photosensitizer to act in this manner depends on the presence of a hydrogen donor (frequently the solvent). In studies on another group of photosensitizers − 1,2-diketones, the solvent cyclohexane increased the absorption wavelength of the sensitizer in the UV range by more than 10 nm compared with solutions in ethanol and chloroform.5 Such a change in absorption may benefit some systems because the energy of absorbed radiation will become lower than the energy required to disrupt existing chemical bonds. But it may also increase the potential for degradation by shifting radiation wavelength to the range absorbed by a particular material. Presence of water may have a plasticizing action which increases the mobility of chains and their potential for interactions and reactions.6 PVC was decomposed in tetralin and decalin at 300-400oC.7 In the first step, dehydrochlorination has occurred both in solvents and without their presence.7 Dehydrochlorination products differed.7 Without solvent, oil and solid carbon were produced by degradation and condensation.7 In the presence of a solvent, the dehydrochlorinated PVC was converted to oil.7 Decomposition was accelerated in tetralin.7 Solvents having different hydrogen-donating capabilities have been used in thermal cracking of HDPE to increase production of C5-C32 α-olefins used by chemical industry.8 Good hydrogen-donating solvents, such as 9,10-dihydroanthracene and tetralin gave lowest yields of hydrocarbons.8 Poor hydrogen donating solvents, such as 1-methylnaphthalene and decalin, gave the highest C5-C32 yields.8 These solvents suppress reactions between intermediate radicals and α-olefins, which are responsible for the increased content of α-olefins.8 Studies on photoresists, based on methacryloyethyl-phenylglyoxylate, show that, in aprotic solvents, the main reaction mechanism is a Norrish type II photolysis leading to chain scission.9 In aprotic solvents, the polymer is photoreduced and crosslinks are formed. The polarity of the solvent determines quantum yields in polyimides.10 The most efficient photocleavage was in medium-polar solvents. The selection of solvent may change the chemical mechanism of degradation and the associated products of such reactions. Singlet oxygen is known to affect material stability by its ability to react directly with hydrocarbon chains to form peroxides. The photosensitizers discussed above are capable of generating singlet oxygen. Solvents, in addition to their ability to promote photosensitizer action, affect the lifetime of singlet oxygen (the time it has to react with molecules and form peroxides). Singlet oxygen has a very short lifetime in water (2 μs) but much longer times in various solvents (e.g., 24 μs in benzene, 200 μs in carbon disulfide, and 700 μs in carbon tetrachloride).11 Solvents also increase the oxygen diffusion coefficient in a polymer. It was calculated12 that in solid polystyrene only less than 2% of singlet oxygen is quenched compared with more than 50% in solution. Also, the quantum yield of singlet oxygen was only 0.56 in polystyrene and 0.83 in its benzene solution.12 It is confirmed by experimental studies that the lifetime of gaseous molecular oxygen in its excited state on UV exposure in solvents depends on dipolarity/polarizability,

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11.5 Other properties affected by solvents

Figure 11.39. Effect of viscosity on molecular weight of polyethylene wax obtained by thermolysis in the presence of phenylether at 370oC. [Adapted, by permission, from L Guy, B Fixari, Polymer, 40, No.10, 2845-57 (1999).]

Figure 11.40. Yield of condensation products depending on solvent. [Adapted, by permission, from J Jeczalik, J. Polym. Sci.: Polym. Chem. Ed., 34, No.6, 1083-5 (1996).]

SPP, basicity, SB, and acidity, SA, of solvent.13 The variation of rate constant of phosphorescence, kp, in solvents mixtures is described by the equation:13 log k p = ( 0.703 ± 0.11 ) SPP + ( 1.10 ± 0.07 ) SB – ( 0.60 ± 0.02 ) SA – ( 1.38 ± 0.11 ) The photostabilizer must be durable. It was found that salicylic stabilizers are efficiently degraded by singlet oxygen in polar alkaline media but in a less polar, non-alkaline solvents these stabilizers are durable.14 In hydrogen-bonding solvents, the absorption spectrum of UV absorbers is changed.15 Thermal decomposition yield and composition of polystyrene wastes is affected by the addition of solvents.16 Solvents play two roles: First, they stabilize radicals and, second, by lowering solution viscosity, they contribute to homogeneity, increase the mobility of components, and increase of reactivity. The 85% benzyl and phenoxy radicals were stabilized by hydrogens from tetralin.15 In polyethylene thermolysis, the use of a solvent to reduce viscosity resulted in obtaining lower molecular weight, narrow molecular weight distribution and high crystallinity in resultant polyethylene wax.17 Figure 11.39 illustrates the relationship between molecular weight and viscosity of solutions of polyethylene in phenylether as a solvent.17 Figure 11.40 shows that polymerization yield depends on the solvent selected for the polymerization reaction. The polymerization yield increases as solvent polarity increases.18 Work on copolymerization of methyl methacrylate and N-vinylpyrrolidone shows that the solvent selected regulates the composition of the copolymer.19 The smaller the polarity of the solvent and the lower the difference between the resonance factors of the two monomers the more readily they can copolymerize. Work on electropolymeriza-

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tion20 has shown an extreme case of solvent effect in the electrografting of polymer on metal. If the donocity of the monomer is too high compared with that of the solvent, no electrografting occurs. If the donocities are low, a high relative permittivity of solvent decreases grafting efficiency. This work, which may be very important in corrosion protection, illustrates that a variety of influences may affect the polymerization reaction. Solvent has a plasticizing effect on the polymer. The increase in free volume has a further influence on the glass transition temperature of the polymer. Figure Figure 11.41. Glass transition temperature of perfluoro 11.41 shows the effect of methyl-isobutylpolyoxyalkylene oligomers vs. MIBK concentration. ketone, MIBK, at various concentrations on [Data from S Turri, M Scicchitano, G Gianotti, C glass transition temperature.21 Several solTonelli, Eur. Polym. J., 31, No.12, 1227-33 (1995).] vents were used in this study21 to determine if the additivity rule can be useful to predict the glass transition temperature of a polymersolvent system. The results, as a rule, depart from the linear relationship between glass transition temperature and solvent concentration. Generally, the better the solvent for a particular polymer, the higher the departure. Hydrogen bond formation as a result of the interaction of the polymer with solvent was found to contribute to changes in the electric properties of polyaniline.22 Hydrogen bonding caused changes in the conformal structure of polymer chains. This increased the electrical conductivity of polyaniline. Water was especially effective in causing such changes but other hydrogen bonding solvents also affected conductivity.22 This phenomenon is applied in antistatic compounds which require a certain concentration of water to perform their function. Surface properties such as smoothness and gloss are affected by the rheological properties of coatings and solvents play an essential role in these formulations. The surface composition may also be affected by the solvent. In some technological processes, the surface composition is modified by small additions of polydimethylsiloxane, PDMS, or its copolymers. The most well-known application of such technology has been the protection of the external surface of the space shuttle against degradation using PDMS as the durable polymer. Other applications use PDMS to lower the coefficient of friction. In both cases, it is important that PDMS forms a very high concentration on the surface (possibly 100%). Because of its low surface energy, it has the intrinsic tendency to migrate to the surface, consequently, the surface concentrations as high as 90% can be obtained without special effort. It is more difficult to further increase this surface concentration. Figure 11.42 shows the effect of a chloroform/toluene mixture on the surface segregation of PDMS. When the poor solvent for PDMS (toluene) is mixed with chloroform, the decrease in the

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Figure 11.42. Surface DMS vs. toluene concentration for two bulk contents of DMS in polystyrene. [Data from Jiaxing Chen, J A Gardella, Macromolecules, 31, No.26, 9328-36 (1998).]

11.5 Other properties affected by solvents

Figure 11.43. Surface DMS vs. cyclohexanone concentration for two bulk contents of DMS in polystyrene. [Data from J Chen, J A Gardella, Macromolecules, 31, No.26, 9328-36 (1998).]

mobility of the PDMS segments makes the cohesive migration of the polystyrene, PS, segments more efficient and the concentration of PDMS on the surface increases as the concentration of toluene increases. Increase in PDMS concentration further improves its concentration on the surface to almost 100%. This shows the influence of polymer-solvent interaction on surface segregation and demonstrates a method of increasing the additive polymer concentration on the surface. Solvents with higher boiling points also increase surface concentration of PDMS because they extend the time of the segregation process.23 Figure 11.43 shows the effect of the addition of cyclohexanone to chloroform.23 This exemplifies yet another phenomenon which can help to increase the surface concentration of PDMS. Cyclohexanone is more polar solvent than chloroform (solubility parameter, δp, is 3.1 for chloroform and 6.3 for cyclohexanone). The solvation of cyclohexanone molecules will selectively occur around PDMS segments which helps in the segregation of PDMS and in the cohesive migration of PS. But the figure shows that PDMS concentration initially increases then decreases with further additions of cyclohexanone. The explanation of this behavior is in the amount of cyclohexanone required to better solvate PDMS segments. When cyclohexanone is in excess, it also increases the solvation of PS and the effect which produces an increased surface segregation is gradually lost. The surface smoothness of materials is important in solvent welding. It was determined that a smooth surface on both mating components substantially increases the strength of the weld.24 This finding may not be surprising since weld strength depends on close surface contact but it is interesting to note that the submicrostructure may have an influence on phenomena normally considered to be influenced by features which have a larger dimensional scale. Non-blistering primer is another example of a modification which tailors surface properties.25 The combination of resins and solvents used in this

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invention allows the solvent to escape through the surface of the cured primer before the material undergoes transitions that occur at high temperatures. Additional information on this subject can be found in Chapter 7. A review paper26 examines the nucleophilic properties of solvents. It is based on accumulated data derived from calorimetric measurements, equilibrium constants, Gibbs free energy, nuclear magnetic resonance, and vibrational and electronic spectra. Parameters characterizing Lewis-donor properties are critically evaluated and tabulated for a large number of solvents. The explanation of the physical meaning of polarity and discussion of solvatochromic dyes as the empirical indicators of solvent polarity are discussed (see more on this subject in Chapter 9).26 Interactions between nanodiamonds and solvent molecules influence surface properties and solvent organization.27 In water, these interactions depend on the nanodiamonds surface chemistry.27 The graphitized and hydrogenated surfaces chemically react with the solvent, while hydroxylated and carboxylated surfaces seem less reactive, although they affect the water hydrogen bond network.27

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

J F Rabek, T A Skowronski, B Ranby, Polymer, 21, 226 (1980). H Kubota, M Kimura, Polym. Deg. Stab., 38, 1 (1992). G Teissedre, J F Pilichowski, J Lacoste, Polym. Degrad. Stability, 45, No.1, 145-53 (1994). M Shah, N S Allen, M Edge, S Navaratnam, F Catalina, J. Appl. Polym. Sci., 62, No.2, 319-40 (1996). P Hrdlovic, I Lukac, Polym. Degrad. Stability, 43, No.2, 195-201 (1994). M L Jackson, B J Love, S R Hebner, J. Mater. Sci. Materials in Electronics, 10, No.1, 71-9 (1999). T Kamo, Y Kondo, Y Kodera, Y Sato, S Kushiyama, Polym. Deg. Stab., 81, 187-96 (2003). D P Serano, J Aguado, G Vicente, N Sanchez, J. Anal. Appl. Pyrolysis, 78, 194-99 (2007). H Shengkui, A Mejiritski, D C Neckers, Chem. Mater., 9, No.12, 3171-5 (1997). H Ohkita, A Tsuchida, M Yamamoto, J A Moore, D R Gamble, Macromol. Chem. Phys., 197, No.8, 2493-9 (1996). G Wypych, Handbook of Material Weathering, 6th Ed. ChemTec Publishing, Toronto, 2017. R D Scurlock, D O Martire, P R Ogilby, V L Taylor, R L Clough, Macromolecules, 27, No.17, 4787-94 (1994). J Catala, C Diaz, L Barrio, Chem. Phys., 300, 33-39 (2004). A T Soltermann, D de la Pena, S Nonell, F Amat-Guerri, N A Garcia, Polym. Degrad. Stability, 49, No.3, 371-8 (1995). K P Ghiggino, J. Macromol. Sci. A, 33, No.10, 1541-53 (1996). M Swistek, G Nguyen, D Nicole, J. Appl. Polym. Sci., 60, No.10, 1637-44 (1996). L Guy, B Fixari, Polymer, 40, No.10, 2845-57 (1999). J Jeczalik, J. Polym. Sci.: Polym. Chem. Ed., 34, No.6, 1083-5 (1996). W K Czerwinski, Macromolecules, 28, No.16, 5411-8 (1995). N Baute, C Calberg, P Dubois, C Jerome, R Jerome, L Martinot, M Mertens, P Teyssie, Macromol. Symp., 134, 157-66 (1998). S Turri, M Scicchitano, G Gianotti, C Tonelli, Eur. Polym. J., 31, No.12, 1227-33 (1995). E S Matveeva, Synthetic Metals, 79, No.2, 127-39 (1996). J Chen, J A Gardella, Macromolecules, 31, No.26, 9328-36 (1998). F Beaume, N Brown, J. Adhesion, 47, No.4, 217-30 (1994). M T Keck, R J Lewarchik, J C Allman, US Patent 5,688,598, Morton International, Inc., 1996. Ch Reichardt, Chimia, 45(10), 322-4 (1991). T Petit, Interactions with solvent in Nanodiamonds, Elsevier, 2017, pp. 301-21.

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Effect of Solvents on Chemical Reactions and Reactivity 12.1 SOLVENT EFFECTS ON CHEMICAL REACTIVITY Wolfgang Linert, Markus Holzweber*, and Roland Schmid+ Institute of Applied Synthetic Chemistry, Vienna University of Technology, Getreidemarkt 9/163-AC, A-1060 Vienna, Austria *BAM − Federal Institute for Materials Research and Testing, Division 6.8 Surface Analysis and Interfacial Chemistry, Under den Eichen 44-46, D-12203 Berlin, Germany

12.1.1 INTRODUCTION More than a century ago, it was discovered that the solvent can dramatically change both the rate and the thermodynamics of chemical reactions.1 Since then, the generality and importance of solvent effects on chemical reactivity (rate constants or equilibrium constants) have been widely acknowledged. It can be said without much exaggeration that studying solvent effects is one of the most exciting topics of chemistry. In the course of its development, there are few topics in chemistry in which so many controversies and changes in interpretation have arisen as in solute-solvent and solvent-solvent interactions.2 Historically, the “dielectric approach” (still terms like “polar” and “non-polar” solvents are commonly used) has been seen in conflict with “chemical approaches” (like Lewis acid-base concepts), which, however, has grown together by later results and become closer to a “physical approach” That what follows is not intended just to give a complete overview of existing ideas, but to filter seminal conceptions and to take up more fundamental ideas. It should be mentioned that solvent relaxation phenomena, i.e., dynamic solvent effects, are omitted. On the other hand, recent investigations of thermochromism and solvatochromism in solution have also been considered as a rapidly expanding field applicable to both, easy characterization of solvent properties as well as in technological applications. Such methods can be used to investigate mutual solute-solvent and solvent-solvent interactions for example in case of ions in solutions as well as in ionic liquids. ________________________________________________________________________ + This chapter is considerably based on the section written by Roland Schmid, published in the first edition of this Handbook, who sadly passed away in April 2004”

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12.1.2 THE DIELECTRIC APPROACH It has soon been found that solvent effects are particularly large for reactions in which charge is either developed or localized or vice versa, that is, the disappearance of charge or delocalization of charge. In the framework of electrostatic considerations, which have been around since Berzelius, these observations led to the concept of solvation. Weak electrostatic interactions simply created a loose solvation shell around a solute molecule. It was in this climate of opinion that Hughes and Ingold3 presented the first satisfactory qualitative account of solvent effects on reactivity by the concept of activated complex solvation. The first solvent property applied to correlate reactivity data was the static relative permittivity ε (also termed εs) in the form of dielectric functions as suggested from elementary electrostatic theories such as those by Born (1/ε), Kirkwood (ε−1)/(2ε+1), ClausiusMosotti (ε−1)/(ε+2), and (ε−1)/ (ε+1). A successful correlation is shown in Figure 12.1.1 for the rate of the SN2 reaction of p-nitrofluorobenzene with piperidine.4 The classical dielectric function preFigure 12.1.1. Relationship between second-order rate constants at dicts that reactivity changes level 50°C of the reaction of p-nitrofluorobenzene and piperidine and the out for relative permittivities say solvent dielectric properties. [Data from Y. Marcus, M. J. Kamlet, above 30. For instance, the Kirkand R. W. Taft, J. Phys. Chem., 92, 3613 (1988).] wood function has an upper limiting value of 0.5, with the value of 0.47 reached at ε = 25. The insert in Figure 12.1.1 illustrates this point. Therefore, since it has no limiting value, the logε function may be preferred. A theoretical justification has been given in the framework of the dielectric saturation model of Block and Walker.5 However, the main criticism of such approaches was that ε is rather a macroscopic property not really describing the situation on a molecular level, where a continuous parameter like ε loses its meaning. Picturing the solvent as a homogeneous dielectric continuum essentially means to neglect the solvent molecule’s size as well as its movement. The adequate physical realization would be a lattice of permanent point dipoles that can rotate but are not able to perform translational movements. 12.1.3 THE CHEMICAL APPROACH Due to the often-observed inadequacies of the dielectric approach, that is, using the relative permittivity to influence reactivity changes, the problem of correlating solvent effects was next tackled by the use of empirical solvent parameters measuring some solvent-sensitive physical property of a solute chosen as the model compound. Of these, spectral properties such as solvatochromic and NMR shifts have made a spectacular contribution.

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Other important scales are based on enthalpy data, with the best-known example being the donor number (DN) measuring solvent's Lewis basicity. In the intervening years, there is a proliferation of solvent scales that is really alarming. It was the merit particularly of Gutmann and his group to disentangle the great body of empirical parameters on the basis of the famous donor-acceptor concept or the coordination-chemical approach.6 This concept has its roots in the ideas of Lewis going back to 1923, with the terms donor and acceptor introduced by Sidgwick.7 In this framework, the two outstanding properties of a solvent are its donor (nucleophilic, basic, cation-solvating) and acceptor (electrophilic, acidic, anion-solvating) abilities, and solute-solvent interactions are considered as acid-base reactions in the Lewis' sense. Actually, many empirical parameters can be lumped into two broad classes, as judged from the rough interrelationships found between various scales.8 The one class is more concerned with cation (or positive dipole's end) solvation, with the most popular solvent basicity scales being the Gutmann DN, the Kamlet and Taft β, and the Koppel and Palm B. The other class is said to reflect anion (or negative dipole's end) solvation. This latter class includes the famous scales π*, α, ET(30), Z, and last but not least, the acceptor number AN. Summed up: Cation solvation (or interactions with the positive dipole's end) Gutmann Kamlet and Taft Koppel and Palm

DN (and DN derived from solvatochromism)9,10 β B (B*)

Anion solvation (or interaction with the negative dipole’s end) Gutmann Dimroth and Reichardt Kosower Kamlet and Taft

AN (AN-values derived from solvatochromism)11,12 ET(30) Z α, π*

These two sets of scales agree in their general trend but are often at variance when values for any two particular solvents are taken. Some inter-correlations have been presented by Taft et al., e.g., the parameters ET, AN and Z can be written as linear functions of both α and π*.13 Originally, the values of ET and π* were conceived as microscopic polarity scales reflecting the “local” polarity of the solvent in the neighborhood of solutes (“effective” relative permittivity in contrast to the macroscopic one). In the framework of the donor-acceptor concept, however, they obtained an alternative meaning, based on the interrelationships found between various scales. Along these lines, the common solvents may be separated into specified classes as follows. A plot of AN versus ET is shown in Figure 12.1.2. While there is a quite good agreement for a large number of “well behaved” solvents (and likely for the nonpolar aliphatic

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12.1 Solvent effects on chemical reactivity

solvents), the other classes are considerably off-line.14 This behavior may be interpreted in terms of the operation of different solvation mechanisms such as electronic polarizability, dipole density, and/or hydrogenbonding (HB) ability. For instance, the main physical difference between π* and ET(30), in the absence of HB interactions, is claimed to lie in different Figure 12.1.2. Plot of AN vs. ET for 56 solvents. The full line refers responses to solvent polarizability to the previously reported linear relationship (1) between ET(30) effects. Likewise, in the relationand AN: Group 1: well behaved solvents; Group 2: alcohols; Group ship between the π* scale and the 3: aromatics; Group 4: alkanes; Group 5: amines; open circles: remaining solvents where no temperature dependent data are avail- reaction field functions of the able to perform a significant IKR analysis.19-22 refractive index (whose square is called the optical relative permittivity ε ∞ ) and the relative permittivity, the aromatic and the halogenated solvents were found to constitute special cases.15 This feature is also reflected by the polarizability correction term in eqn. [12.1.1] below. For the selected solvents, the various “polarity” scales are more or less equivalent. An account of the various scales has been given by Marcus,16 and in particular of π* by Laurence et al.,17 and of ET by Reichardt.18 The separation into these different groups is strongly supported by the observed thermochromism of the pyridinium N-phenoxide betaine dyes, betaine 1 and betaine 2.19 They have been studied in different solvents, over a range of temperatures, and shown to yield isoparametric (isokinetic) relationships (IKR).21,22 (The use of the more lipophilic betaine 2 enabled the range of solvents to be extended to cover very apolar solvents in which betaine 1 is insoluble.) These IKR’s led to the identification of the given five different groups of solvents, each group showing different solute-solvent and solvent-solvent mechanisms and being characterized by their functional groups. These groups are reflected in the relationship between Reichardt's ET values and Gutmann's acceptor numbers (AN) which is re-investigated and each group is shown to lie on one of a series of parallel lines in the ET vs. AN plot. This demonstrated that acceptor parameters depend strongly on the donor properties of the probe used to obtain them. However, solvation is not the only mode of action taken by the solvent on chemical reactivity. Since chemical reactions are typically accompanied by changes in volume, even reactions with no alteration of charge distribution are sensitive to the solvent. The solvent dependence of a reaction, where both reactants and products are neutral species (“neutral” pathway), is often treated in terms of either of two solvent properties. The one is the cohesive energy density εc or cohesive pressure measuring the total molecular cohesion per unit volume,

ε c = ( Δ H v – RT ) ⁄ V

[12.1.1]

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+ where:

ΔHv V

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molar enthalpy of vaporization represents molar liquid volume

The square root of εc is termed the Hildebrand solubility parameter δH, which is the solvent property measuring the work necessary to separate the solvent molecules (disrupt and reorganize solvent/solvent interactions) to create a suitably sized cavity for the solute. The other quantity in use is the internal pressure Pi which is a measure of the change in internal energy U of the solvent during a small isothermal expansion, Pi = ( ∂ U/ ∂ V)T. Interesting, and long-known, is the fact that for the highly dipolar and particular for protic solvents, values of εc are far in excess of Pi.23 This is interpreted to mean that a small expansion does not disrupt all of the intermolecular interactions associated with the liquid state. It has been suggested that Pi does not detect hydrogen bonding but only weaker interactions. At first, solvent effects on reactivity were studied in terms of some particular solvent parameter. Later on, more sophisticated methods via multiparameter equations were applied such as24 XYZ = XYZ o + s ( π * + d δ ) + a α + b β + h δ H

[12.1.2]

where XYZo, s, a, b, and h are solvent-independent coefficients characteristic of the process and indicative of its sensitivity to the accompanying solvent properties. Further, δ is a polarizability correction term equal to 0.0 for nonchlorinated aliphatic solvents, 0.5 for polychlorinated aliphatics, and 1.0 for aromatic solvents. The other parameters have been given above, viz. π*, α, β, and δH are indices of solvent dipolarity/polarizability, Lewis acidity, Lewis basicity, and cavity formation energy, respectively. For the latter, instead of δH, δH2 should be preferred as suggested from regular solution theory.25 Let us just mention two applications of the linear solvation energy relationship (LSER). The one concerns the solvolysis of tertiary butyl-halides26 2

t

log k ( Bu Cl ) ) = – 14.60 + 5.10 π * + 4.17 α + 0.73 β + 0.0048 δ H (r=0.9973) and the other deals with the transfer of tetramethylammonium iodide through solvents with methanol as the reference solvent,25

ΔGtr° = 10.9 − 15.6π* − 6.2α + 0.022δH

(r = 0.997)

A lot of insight into solute-solvent interactions can be gained from the fact that several metal complexes can be used as color indicators to visualize and to measure Lewis basicities and Lewis acidities of solvents.27-30 For example Cu(tmen)(acac)ClO4, where tmen = N,N,N’,N’-tetramethylethylendiamine and acac = acetylacetonate, has be successfully used as a Lewis-basicity indicator, and Fe(phen)2(CN)2, where phen = 1,10-phenanthroline, as a Lewis-acidity indicator. The physical origin of the underlying color changes is sketched in the Figure 12.1.3, as modified from ref.27,29 These color indicators can be applied as a quick method for assessing the coordination properties of solvents, solvent mixtures, and solutes not yet measured.

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12.1 Solvent effects on chemical reactivity

Figure 12.1.3. Left hand side: Relative orbital energy levels for Cu(tmen)(acac)2+ in square planar, tetragonal, and octahedral environments.27,29 The insert shows the energy levels for the analogous Ni(tmen)(acac)2+ complex. Due to the change in the spin-state this complex does not show a continuous color change in various solvents but the equilibrium between discrete square-planar and octahedral species and acts like commonly used acid base indicators. Right hand side: Simplified orbital scheme for the charge transfer transition in Fe(phen)2(CN)2 varying with solvation. The diagram, not drawn to scale, is adjusted so that π* is constant.27-29 The insert shows the energy levels for the analogous Fe(phen)2(CN)2+ species, showing a reversed solvatochromic behavior associated with different solubility and adsorption properties.31-33

This is very expedient since some classical parameters, particularly the donor numbers, are arduously amenable. Equation [12.1.3] correlates the wave numbers vo (in cm-1) of the visible band of Cu(tmen)(acac)+ and the solvent donor numbers (Figure 12.1.4).11,12,30 –3

10 ν max, Cu = 20.0 – 0.103DN (r = 0.99)

[12.1.3]

Similarly, the acceptor numbers are expressed as a function of the wave numbers of the long wavelength absorption of Fe(phen)2(CN)2 (Figure 12.1.5). –3

10 ν max, Fe = 15.0 – 0.076DN (r = 0.99)

[12.1.4]

12.1.4 THE DIELECTRIC APPROACH VERSUS THE CHEMICAL APPROACH Although the success of the empirical solvent parameters has tended to downgrade the usefulness of the dielectric approach, there are correlations that have succeeded as exemplified by Scheme 12.1.1. It is commonly assumed that the empirical solvent parameters are superior to dielectric estimates because they are sensitive to short-range phenomena not captured in dielectric measurements. This statement may not be generalized, however, since it depends strongly on the chemical reaction investigated and the choice of solvents. For instance, the rate of the Menschutkin reaction between tripropylamine and methyl

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

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iodide in select solvents correlates better with the logε function than with the solvent acceptor number.34 Thus the solution chemists were puzzled for a long time over the question about when and when not the dielectric approach is adequate. In the meantime, this issue has been unraveled, in that dielecS cheme 12.1.1. Example for the usefulness of the Donor-Aceptor tric estimates have no relevance to the solvation of positive (partial) charge. Thus, there is no relationship between the free energies of transfer for cations and the relative permittivity.8 Likewise, note the solvent-dependence of the solubilities of the sodium-cation (Table 12.1.1). For instance, the pairs of solvents H2O/PC and DMF/MeCN have similar ε’s but vastly different abilities to dissolve NaCl. In Figure 12.1.4. Correlation of the wave numbers v of the maximum similar terms, the inclusion of a of the visible band of Cu(tmen)(acac)+ dissolved in several solvents donor number term improves versus the solvent’s donor numbers.9,11 somewhat the correlation in Figure 12.1.1, as may be seen in Figure 12.1.5. This would suggest that the hydrogen of piperidine in the activated complex becomes acidic and is attacked by the strong donor solvents DMF, DMA, and DMSO.

Figure 12.1.5. Linear relationship between the absorption maxima of Fe(phen)2(CN)2 and the Acceptor Number. A plot of these values vs. ET(30) is given in the insert.19

772

12.1 Solvent effects on chemical reactivity

Table 12.1.1. Standard free energies of solution of sodium chloride in various solvents at 25°C. Data of ΔGsol are from reference34 ΔGsol, kJ mol-1

Σε

DN

AN

H2O

-9.0

78.4

18

55

FA

-0.4

109

24

40

Solvent

NMF

3.8

182

27

32

MeOH

14.1

32.6

19

41

DMSO

14.9

46.7

30

19

DMF

26.8

36.7

26

16

PC

44.7

65

15

18

MeCN

46.8

36

14

19

On the other hand, if negative charge is solvated in the absence of positive charge capable of solvation, the relative permittivity is often a pretty good guide to ranking changes in reactivity. As a consequence, the dielectric approach has still its place in organic chemistry while it is doomed to complete failure in inorganic reactions where typically cation solvation is involved. For selected solvents, ultimately, the relative permittivity is related to the anion-solvating properties of solvents according to the regression equation5 Figure 12.1.6. Multiparameter correlation of the reaction given in Scheme 12.1.1.36

logε = 0.32 + 0.073 (ANE)

(r = 0.950)

[12.1.5]

where: ANE are ET-based acceptor numbers taken according to “well behaved solvents”, with ANE = −40.52 + 1.29ET

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This equation works also quite well for the aromatics and the halogenated solvents, but it does not hold for the protic solvents. For these, the predicted values of the relative permittivities are orders of magnitude too large, revealing how poorly the associates are dissociated by the macroscopically attainable fields. A correlation similar to [12.1.5] has been proposed35 between the gas phase dipole moment and π*

μ(D) = 4.3π* − 0.1

(r = 0.972)

[12.1.6]

Along these lines, the dielectric and the chemical approach are brought under one roof.5,36 The statement, however, that the terms “good acceptor solvent” and “highly polar solvent” may be used synonymously would seem, though true, to be provocative. The determination of donor and acceptor numbers for ions in non-aqueous solvents can also be conducted with solvatochromic indicators such as the metal complexes described above. The approach, however, is not so straight-forward as for common sol-

Figure 12.1.7. Absorption maxima of Cu(acac)(tmen)+ in various solvents in the presence of anions versus the absorption maximum observed in DCE solutions.

vents, since the ability of anions (cations) to act as electron pair donors (electron pair acceptors) influences the donor and acceptor properties of a solvent. To circumvent the ionic influence, anions such as perchlorates and tetraphenylborates were often used as counter ions as they are assumed to have a low basicity and thus not influencing the donor and acceptor properties of solvents significantly.37,12 The first estimation of donor numbers for anions was based on the measurement of the free energies (i.e., equilibrium constant) of the reaction [VO(acac)2(MeCN)] + D ↔ [VO(acac)2D] +

774

12.1 Solvent effects on chemical reactivity

MeCN where D was either an anion or a solvent of comparable donor strength and acac = acetylacetonate. This was then further improved for anions and cations using the indicators Cu(tmen)(acac)+ and Fe(phen)2(CN)2 respectively.9,11 The behavior of the absorption maxima of Cu(acac)(tmen)+ in various solvents in the presence of anions as shown in Figure 12.1.7 can be explained as follows. The interaction of the anions with the copper indicator depends on both the donor and acceptor properties of the solvent. If the donor strength of the solvent is higher than that of the anion, the solvent coordinates preferably with the copper complex, however, if the acceptor strength of the solvent is too high, it will compete with the indicator for the coordination of the anion and no change in the absorption maximum is found (solvent dependent part). If the donor strength of the anion exceeds the donor strength of the solvent, a shift of the absorption maximum can be observed (ion-dependent part). For strong acceptor solvents like water and methanol even strong donating anions cannot coordinate to the copper complex as they are preferentially solvated by such solvents (see Figure 12.1.7.). The ascending part of the curves depends, therefore, on both the acceptor and donor number of the respective solvent. The following relationship can therefore be expressed as

ν˜ max ( solv ) = ν˜ max ( DCE ) + a ( DN solv – DN DCE ) + b ( AN solv – AN DCE ) [12.1.8] in which donor and acceptor number for dichloroethane (DCE) (DN = 0, AN = 16.7) is known. A multiple regression analysis of the data yields for a = 63 and for b = 91 (r = 0.986). Measuring the absorption maximum of Cu(acac)(tmen)+ for a large number of solvents, a linear correlation with solvent donor numbers is found leading to the expression –3 10 ν˜ max = 20 – 0.103DN solv

[12.1.9]

Equalizing expressions [12.1.8] and [12.1.9] gives the condition for the intersection of the curve in Figure 12.1.7. At this intersection point, both the donor properties of the solvent and those of the anion are equal, and the donor number thus obtained is defined as the donor number of the anion dissolved in that particular solvent (DNX,solv). DN X, solv = 129.6 – 0.548AN solv – 0.00602 ν˜ max ( DCE )

[12.1.10]

Table 12.1.2. Donor Numbers of some anions in dependence of the respective solvent as resulting from equation [12.1.10]. Only values in bold are representing “active” Donor Numbers of anions, others are “hidden” due to the stronger solvent’s Donor properties. Anion BPh 4 BF 4 ClO 4 2CO 3

(DNx,solv)

DNx DCE

Ac

DMF

DMSO

An

0.00

2.31

0.39

−1.42

−1.20

6.03

8.33

6.42

4.61

4.83

8.44

10.7

8.83

7.02

7.24

13.3

15.6

13.6

11.8

12.1

EtOH

H2O

MeOH

−2.07

−11.6

−20.9

−13.6

[3.95]

−5.69

−14.8

−7.56

6.36

−3.18

−12.4

−5.15

11.2

1.64

−7.62

−0.33

NM

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

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Table 12.1.2. Donor Numbers of some anions in dependence of the respective solvent as resulting from equation [12.1.10]. Only values in bold are representing “active” Donor Numbers of anions, others are “hidden” due to the stronger solvent’s Donor properties. Anion CF 3 SO 3 NO 3 -

DNx

(DNx,solv)

DCE

Ac

DMF

DMSO

An

NM

EtOH

H2O

MeOH

16.9

[19.2]

17.3

15.5

[15.7]

14.8

5.26

−4.00

3.29

21.1

23.4

21.5

19.7

19.9

19.0

9.47

0.21

7.50

CN

27.1

29.4

[27.5]

25.7

25.9

25.0

15.5

6.24

13.5

-

28.9

31.2

29.3

27.5

27.7

26.8

17.3

8.04

15.3

29.5

31.8

29.9

[28.1]

28.3

27.4

17.9

8.65

15.9

31.9

34.2

32.3

30.5

30.7

29.9

[20.3]

11.1

18.3

33.7

36.0

34.1

32.3

32.5

31.7

22.1

12.9

[20.2]

34.3

36.6

34.7

32.9

33.1

32.3

22.7

13.5

20.8

34.9

37.2

35.3

33.5

33.7

32.9

23.3

14.1

21.4

36.2

38.5

36.5

34.7

34.9

34.1

24.5

15.3

22.6

40.4

42.7

40.8

38.9

39.2

38.3

28.8

[19.5]

26.8

DNsolv

0.0

17.0

26.6

29.8

14.1

2.7

19.0

19.5

19.1

ANsolv

16.7

12.5

16.0

19.3

18.9

20.5

37.9

54.8

41.5

I

Ac

-

SCN Br

-

-

-

N3 OH Cl

-

-

NCO

-

The same concept can be applied to determine the acceptor number of cations in solution.11 Figure 12.1.8 depicts the absorption maxima of Fe(phen)2(CN)2 in the presence of a cation in a solvent versus the absorption maxima under the same conditions using nitromethane (NM) as a solvent. A similar behavior is found for cations as it was observed for anions. If the solvent is a stronger Lewis acid than the cation, the solvent interacts solely with the indicator, or the solvent is a Lewis base strong enough to solvate the cations making an interaction between indicator and cation impossible. In these two cases, no significant change in the absorption maximum is found as the influence of the dissolved cation is negligible (solvent dependent part). An increase of Lewis acidity and therefore an increase of acceptor properties of the cation lead to a shift of the absorption maximum to lower energies (ion dependent part). This part depends on the acceptor and donor properties of the respective solvent and can be, using nitromethane as reference solvent (DN = 2.7, AN = 20.5), expressed as ˜ ( NM ) + A ( DN ν˜ max ( solv ) = ν max solv – DN NM ) + B ( AN solv – AN NM ) [12.1.11] A multiple regression analysis of the data yields for A = −48.7 and for B = −5.62 (r=0.960). Measuring the absorption maximum of Fe(phen)2(CN)2 for a large number of solvents a linear correlation with solvent donor numbers is found leading to the expression –3 10 ν˜ max = 15.08 + 0.076AN solv

[12.1.12]

776

12.1 Solvent effects on chemical reactivity

Figure 12.1.8. Absorption maxima of Fe(phen)2(CN)2 in various solvents in the presence of cations versus the absorption maximum observed in NM solutions. In the case of some transition metal ions in a given solvent (EtOH, DMF and DMSO) an apparent constant displacement can be observed. In these cases the solvated species are coordinated to the indicator by an outer sphere mechanism, i.e. the cations are separated from the indicator by a solvent molecule.

Equalizing expressions [12.1.11] and [12.1.12] gives the condition for the intersection of the curve in Figure 12.1.8. At this intersection point, both the acceptor properties of the solvent and those of the cation are equal and the acceptor number thus obtained is defined as the acceptor number of the cation dissolved in that particular solvent (ANM,solv). AN M, solv = – 181 – 0.595DN solv + 0.0122 ν˜ max ( NM )

[12.1.13]

The validity of the approach for donor and acceptor numbers for ions in non-aqueous solvents is given in several examples. The solvatochromism of the analogous complex Ru(phen)2(CN)2 is linearly related to the absorption maxima obtained with Fe(phen)2(CN)2.11,10 The logarithm of formation constants of metal ion EDTA complexes in aqueous solutions is found to be related to the apparent AN of metal ions in the respective solvent.11 By transferring a given ion from one solvent to another the free energy of transfer can be considered as a characteristic parameter for the solvation of ions. Thus a linear relationship was found for the free energy of transfer from water to various solvents and the solvent dependent donor numbers of anions.10 The logarithm of the rate constants

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+ 2+

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777 +

for the reaction of Ni + X + terpy → [ NiX ( terpy ) ] in acetonitrile is found to correlate with the DN of the anions in the respective solvent.9 Table 12.1.3. Acceptor Numbers of some cations in dependence of the respective solvent as resulting from equation [12.1.13]. Only values in bold are representing “active” Acceptor Numbers of Cations, others are “hidden” due to the stronger solvent’s acceptor properties. Cation +

Bu4N Na

+

ANM

(ANM,solv)

NM

AA*

MeCN

PC

AC

H2O

MeOH

THF

EtOH

DMF

DMSO

HMPT

34.5

29.9

27.7

27.1

26.0

25.4

24.8

24.2

24.2

20.3

18.4

[13.0]

35.3

30.6

28.5

27.9

26.8

26.2

25.6

25.0

25.0

21.1

[19.2]

13.8

K+

38.6

33.9

31.8

31.2

30.0

29.4

28.9

28.3

28.3

24.3

22.4

17.1

Li+

44.6

39.9

37.8

37.2

36.0

35.5

34.9

34.3

34.3

30.3

28.4

23.1

Ba2+

50.7

46.0

43.9

43.3

42.1

41.6

[41.0]

40.4

[40.4]

36.4

34.5

29.2

Mg

2+

54.3

49.7

47.5

46.9

45.8

45.2

44.6

44.0

44.0

40.1

38.2

32.8

Ni2+

57.1

[52.5]

50.3

49.7

48.6

48.0

47.4

46.8

48.6

42.9

41.0

35.6

Mn2+

62.4

57.7

55.6

55.0

53.9

53.3

52.7

52.1

52.1

48.1

46.2

40.9

Ce3+

63.3

58.7

56.6

56.0

54.8

[54.2]

53.6

53.1

53.1

49.1

47.2

41.9

2+

Co

66.4

61.8

59.6

59.0

57.9

57.3

56.7

56.1

56.1

52.2

50.3

44.9

Fe2+

69.0

64.3

62.2

61.6

60.4

59.9

59.3

58.7

58.7

54.7

52.8

47.5

2+

Cu

71.0

66.4

64.2

63.7

62.5

61.9

61.3

60.7

60.7

56.8

54.9

49.6

Cr3+

75.4

70.8

68.6

68.0

66.9

66.3

65.7

65.1

65.1

61.2

59.3

53.9

2+

79.8

75.2

73.0

72.4

71.3

70.7

70.1

69.5

69.5

65.6

63.7

58.3

51

37

50

Zn

SSa DN

2.70

10.5

14.1

15.1

17.0

18.0

19.0

20.0

20.0

26.6

29.8

38.8

AN

20.5

52.9

18.9

18.3

12.5

54.8

41.5

8.0

37.9

16.0

19.3

10.6

*AA − acetic acid, SS − solvated species, a − estimated values for Ni2+, Mn2+, Co2+, and Zn2+

The most important point of these result is that donor and acceptor properties of a solvated species depend upon their molecular environments, namely the solvents properties. This is especially of importance when investigating ionic liquids as will be discussed below.

12.1.5 CONCEPTUAL PROBLEMS WITH EMPIRICAL SOLVENT PARAMETER A highly suspect feature behind the concept of empirical solvent parameters lies in the interpretation of the results in that condensed phase matters are considered from the narrow viewpoint of the solute only with the solvent's viewpoint notoriously neglected. However, the solute is actually probing the overall action of the solvent, comprising two modes of interactions: solute-solvent (solvation) and solvent-solvent (restructuring) effects of unknown relative contribution. Traditionally, it is held that solvent structure only assumes

778

12.1 Solvent effects on chemical reactivity

importance when highly structured solvents, such as water, are involved.38 But this view increasingly turns out to be erroneous. In fact, ignoring solvent-solvent effects, even in aprotic solvents, can lead to wrong conclusions as follows. In the donor-acceptor approach, solutes and solvents are divided into donors and acceptors. Accordingly, correlations found between some property and the solvent donor (acceptor) ability are commonly thought to indicate that positive (negative) charge is involved. In the case of solvent donor effects, this statement is actually valid. We are unaware, in fact, of any exception to the rule saying: “Increase in reaction rate with increasing solvent DN implies that positive charge is developed or localized and vice versa”.36 In contrast, correlations with the acceptor number or related scales do not simply point to anion solvation, though this view is commonly held. An example of such type of reasoning concerns the medium effect on the intervalence transition (IT) energy within a certain binuclear, mixed-valence, 5+ cation.39 As the salt effect was found to vary with the solvent AN, anion, that is counterion, solvation in ion pairs was invoked to control the IT energy. A conceptual problem becomes obvious by the at first glance astonishing result that the reduction entropies of essentially non-donor cationic redox couples such as Ru(NH3)63+/2+ are correlated with the solvent AN.40 These authors interpreted this solvent dependence as reflecting changes in solvent-solvent rather than solvent-ligand interactions. That the acceptor number might be related to the solvent structure is easy to understand since all solvents of high AN always are good donors (but not vice versa!) and therefore tend to be increasingly self-associated.36 There is since growing evidence that the solvent’s AN and related scales represent ambiguous solvent properties including solvent structural effects instead of measuring anion solvation in an isolated manner. Thus, correlations between Gibbs energies of cation transfer from water to organic solvents and the solvent DN are improved by the inclusion of a term in ET (or a combination of α and π*)41 Consequently Marcus et al. rightly recognized that “ET does not account exclusively for the electron pair acceptance capacity of solvents”.42 In more work,43 a direct relationship has been found between the solvent reorganizational energy accompanying the excitation of ruthenium(II) cyano complexes and the solvent acceptor number. In the basicity scales, on the other hand, complications by the solvent structure are not as obvious. If the restriction is to aprotic solvents, as is usual, various scales though obtained under different conditions, are roughly equivalent.36,5 There is, for instance, a remarkably good relationship between the DN scale (obtained in dilute dichloromethane solution, i.e. with medium effects largely excluded) and the B scale (derived from measurements performed with 0.4 M solutions of MeOD in the various solvents).5 The relationship between β and B, on the other hand, separates out into families of solvents.35 Donor measures for protic solvents eventually are hard to assess and often are at considerable variance from one scale to another.44,45 To rationalize the discrepancies, the concept of “bulk donicity” was introduced8 but with little success. Instead, the consideration of structure changes accompanying solvation might better help tackle the problem. Another suspect feature of the common method of interpreting solvent-reactivity correlations is that it is notoriously done in enthalpic (electronic, bond-strength etc) terms.

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This way of thinking goes back to the Hughes-Ingold theory. However, many reactions in solution are not controlled by enthalpy changes but instead by entropy. Famous examples are the class of Menschutkin reactions and the solvolysis of t-butyl halides. Both these reaction types are characterized by the development of halide ions in the transition state, which can be considered as ion-pair like. In view of this, rate acceleration observed in good acceptor (or, alternatively, highly polar) solvents seems readily explainable in terms of solvation of the developing halide ion with concomitant carbon-halogen bond weakening. If this is true, most positive activation entropies and highest activation enthalpies should be expected to occur for the poor acceptor solvents. However, a temperature dependence study of the t-butyl halide solvolysis revealed just the opposite.26 This intriguing feature points to changes in solvent structure as a major determinant of the reaction rate with the ionic transition state acting as a structure maker in poor acceptor solvents, and as a structure maker in the protic solvents. It is rather ironic that the expected increase in rate with increasing solvent acceptor strength is a result of the coincidence of two, from the traditional point of view, unorthodox facts: (i) The intrinsic solvation of the developing halide ion disfavors the reaction via the entropy term. However, (ii), the extent of that solvation is greater in the poorly coordinating solvents (providing they are polarizable such as the aromatic solvents and the polyhalogenated hydrocarbons). In keeping with this interpretation, the Menschutkin reaction between benzyl bromide and pyridine is characterized by more negative activation volumina (i.e., stronger contraction of the reacting system in going to the activated complex) in poor acceptor (but polarizable) solvents.46 The importance is evident of studying temperature or pressure dependences of solvent effects on the rate in order to arrive at a physically meaningful interpretation of the correlations. Another problem with the interpretation of multiparameter equations such as [12.1.2] arises since some of the parameters used are not fully independent of one another. As to this, the trend between π* and α has already been mentioned. Similarly, the δH parameter displays some connection to the polarity indices.47,48 Virtually, the various parameters feature just different blends of more fundamental intermolecular forces (see below). Because of this, the interpretations of empirical solvent-reactivity correlations are often based more on intuition or preconceived opinion than on physically defined interaction mechanisms. As it turns out, polar solvation has traditionally been overemphasized relative to nonpolar solvation (dispersion and induction), which is appreciable even in polar solvents. The conceptual problems of the empirical solvent parameters summarized: • The solvent acceptor number and other “polarity” scales include appreciable, perhaps predominant, contributions from solvent structure changes rather than merely measuring anion solvation. • Care is urged in a rash interpretation of solvent-reactivity correlations in enthalpic terms, instead of entropic, before temperature-dependence data are available. Actually, free energy alone masks the underlying physics and fails to provide predictive power for more complex situations. • Unfortunately, the parameters used in LSER's sometimes tend to be roughly related to one another, featuring just different blends of more fundamental inter-

780

12.1 Solvent effects on chemical reactivity

molecular forces. Not seldom, fortuitous cancellations make molecular behavior in liquids seemingly simple (see below). Further progress would be gained if the various interaction modes could be separated by means of molecular models. This scheme is, in fact, taking shape in current years giving rise to a new era of tackling solvent effects as follows.

12.1.6 THE PHYSICAL APPROACH There was a saying that the nineteenth century was the era of the gaseous state, the twentieth century of the solid state, and that perhaps by the twenty-first century we may understand something about liquids.49 Fortunately, this view is unduly pessimistic, since theories of the liquid state have actively been making breathtaking progress. In the meantime, not only equations of state of simple liquids, that is in the absence of specific solvent-solvent interactions,50-52 but also calculations of simple forms of intermolecular interactions are becoming available. On this basis, a novel approach to treating solvent effects is emerging, which we may call the physical approach. This way of description is capable of significantly changing the traditionally accepted methods of research in chemistry and ultimately will lay the foundations of the understanding of chemical events from first principles. The guiding principle of these theories is recognition of the importance of packing effects in liquids. It is now well-established that short-ranged repulsive forces implicit in the packing of hard objects, such as spheres or dumbbells, largely determine the structural and dynamic properties of liquids.53 It may be noted in this context that the roots of the idea of repulsive forces reach back to Newton who argued that an elastic fluid must be constituted of small particles or atoms of matter, which repel each other by a force increasing in proportion as their distance diminishes. Since this idea stimulated Dalton, we can say that the very existence of liquids helped to pave the way for formulating the modern atomic theory with Newton granting the position of its “grandfather”.54 Since the venerable view of van der Waals, an intermolecular potential composed of repulsive and attractive contributions is a fundamental ingredient of modern theories of the liquid state. While the attractive interaction potential is not precisely known, the repulsive part, because of changing sharply with distance, is treatable by a common formalism in terms of the packing density η, that is the fraction of space occupied by the liquid molecules. The packing fraction is the key parameter in liquid state theories and is in turn related in a simple way to the hard sphere (HS) diameter σ in a spherical representation of the molecules comprising the fluid: 3

η = πρσ ⁄ 6 = ρ V HS where:

η ρ N/V σ VHS

is the packing density the number density number of particles per unit volume HS diameter the HS volume.

[12.1.14]

For the determination of σ (and hence η), the most direct method is arguably based on inert gas solubility data.55,56 However, in view of the arduousness involved and the

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

781

uncertainties in both the extrapolation procedure and the experimental solubilities, it is natural to look out for alternatives. From the various suggestions,57,58 a convenient way is to adjust σ such that the computed value of some selected thermodynamic quantity, related to σ, is consistent with experiment. The hitherto likely best method59 is the following: To diminish effects of attraction, the property chosen should probe primarily repulsive forces rather than attractions. Since the low compressibility of the condensed phase is due to short-range repulsive forces, the isothermal compressibility βT = −(1/V)( ∂ V/ ∂ P)T might be a suitable candidate, in the framework of the generalized van der Waals (vdW) equation of state

βT(RT/V)Qr = 1

[12.1.15]

where: Qr

the density derivative of the compressibility factor of a suitable reference system.

In the work referred to, the reference system adopted is that of polar-polarizable spheres in a mean field, 2

3

5η – 2η– 1 – 2Z μ Q r = 2 ----------------------4 (1 – η) where: Zμ

[12.1.16]

compressibility factor due to dipole-dipole forces,59 which is important only for a few solvents such as MeCN and MeNO2.

The HS diameters so determined are found to be in excellent agreement with those derived from inert gas solubilities. It may be noted that the method of Ben-Amotz and Willis,60 also based on βT, uses the nonpolar HS liquid as the reference and, therefore, is applicable only to liquids of weak dipole-dipole forces. Of course, as the reference potential approaches that of the real liquid, the HS diameter of the reference liquid should more closely approximate the actual hard-core length. Finally, because of its popularity, an older method should be mentioned that relies on the isobaric expansibility αp as the probe, but this method is inadequate for polar liquids. It turns out that solvent expansibility is appreciably determined by attractions. Some values of η and σ are shown in Table 12.1.4 including the two extreme cases. Actually, water and n-hexadecane have the lowest and the highest packing density, respectively of the common solvents. There is an appreciable free volume, which may be expressed by the volume fraction η − ηo, where ηo is the maximum value of η calculated for the face-centered cubic packing of HS molecules where all molecules are in contact with each other is ηo = π 2 /6 = 0.74. Thus, 1 − ηo corresponds to the minimum of unoccupied volume. Since η typically is around 0.5, about a quarter of the total liquid volume is empty enabling solvent molecules to change their coordinates and hence local density fluctuations occur.

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12.1 Solvent effects on chemical reactivity

Packing density, h minimum

maximum

≈0

0.4 to 0.6

0.74

perfect gas

liquids

cubic close-packed

Table 12.1.4. Packing densities in some liquids. η

Liquid

free volume, %

H2O

0.41

59

n-C6

0.50

50

Benzene

0.51

49

MeOH

0.41

59

Et2O

0.47

53

n-C16

0.62

38

These considerations ultimately offer the basis of a genuinely molecular theory of solvent effects, as compared to a mean-field theory. Thus, packing and repacking effects accompanying chemical reactions have to be taken into account for any realistic view of the solvent’s role played in chemical reactions to be attained. The well-known cavity formation energy is the work done against intermolecular repulsions. At present, this energy is calculated for spherical cavities by the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) mixed HS equation of state.61,62 3 2 2 Δ G rep ηd ηd ηd(– d + d + 1) -------------- = 2 ------------------- + 3 ------------------- + 3 ---------------------------------------- + 3 2 (1 – η) RT (1 – η) (1 – η) 3

2

+ ( – 2d + 3d – 1 ) ln ( 1 – η ) where:

d = σo/σ σo σ

[12.1.17]

the relative solute size the solute HS diameter the solvent diameter.

Quite recently, a modification of this equation has been suggested for high liquid densities and large solute sizes.63 Notice that under isochoric conditions the free energy of

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cavity formation is a totally entropic quantity. Ravi et al.64 have carried out an analysis of a model dissociation reaction ( Br 2 → 2Br ) dissolved in a Lennard-Jones solvent (Ne, Ar, and Xe). This and the previous work65 demonstrated that solvent structure contributes significantly to both chemical reaction volumes (which are defined as the pressure derivatives of reaction free energies) and free energies, even in systems containing no electrostatic or dispersion long-ranged solvent-solute interactions. Let us now turn to the more difficult case of intermolecular attractive forces. These may be subdivided into:

Long-ranged or unspecific

Short-ranged or specific

dispersion

electron overlap (charge transfer)

induction

H-bonding

dipole-dipole higher multipole

For the first three ones on the left (dispersion, induction, dipole-dipole forces) adequate calculations are just around the corner. Let us give some definitions. Dispersion forces are the result of the dipolar interactions between the virtually excited dipole moments of the solute and the solvent, resulting in a nonzero molecular polarizability. Although the average of every induced dipole is zero, the average of the product of two induced dipoles is nonzero. Induction forces are caused by the interaction of the permanent solvent dipole with the solvent dipoles induced by the solute and solvent field. Figure 12.1.9. Dispersion forces as a result Sometimes it is stated that dispersion is a quanof dipolar interactions between the virtually tum mechanical effect and induction is not. Thus, excited dipole moments of solute and solvent. some clarifying comments are at place here. From the general viewpoint, all effects including polarizability are quantum mechanical in their origin because the polarizability of atoms and molecules is a quantum mechanical quantity and can be assessed only in the framework of quantum mechanics. However, once calculated, one can think of polarizability in classical terms representing a quantum molecular object as a classical oscillator with the mass equal to the polarizability, which is not specified in the classical framework. This is definitely wrong from a fundamental viewpoint, but, as it usually appears with harmonic models, a quantum mechanical calculation and such a primitive classical model give basically

784

12.1 Solvent effects on chemical reactivity

the same results about the induction matter. Now, if we implement this classical model, we would easily come up with the induction potential. However, the dispersion interaction will be absent. The point is that to get dispersions, one needs to switch back to the quantum mechanical description where both inductions and dispersions naturally appear. Thus the quantum oscillator may be used resulting in both types of potentials.66 If, in the same procedure, one switches to the classical limit (which is equivalent to putting the Plank constant zero) one would get only inductions. The calculation of the dispersive solvation energy is based on perturbation theories following the Chandler-AnderFigure 12.1.10. Induction forces sen-Weeks67 or Barker-Henderson68 formalisms, in which are caused by the interaction of a long-range attractive interactions are treated as perturbations permanent solvent dipole with solvent dipoles induced by solute to the properties of a hard body reference system. Essentially, and solvent fields. perturbation theories of fluids are a modern version of van der Waals theory.69 In the papers reviewed here, the Barker-Henderson approach was utilized with the following input parameters: Lennard-Jones (LJ) energies for the solvent, for which reliable values are now available, the HS diameters of solvent and solute, the solvent polarizability, and the ionization potentials of solute and solvent. A weak point is that in order to get the solute-solvent LJ parameters from the solute and solvent components, some combining rules have to be utilized. However, the commonly applied combining rules appear to be adequate only if solute and solvent molecules are similar in size. For the case of particles appreciably different both in LJ energy and size, the suggestion has been made to use an empirical scaling by introducing empirical coefficients so as to obtain agreement between calculated and experimental solvation energies for selected inert gases and nonpolar large solutes.70 In the paper,70 the relevance of the theoretical considerations has been tested on experimental solvation free energies of nitromethane as the solute in select solvents. The total solvation energy is a competition of the positive cavity formation energy and the negative solvation energy of dispersion and dipolar forces,

ΔG = ΔGcav + ΔGdisp + ΔGdipolar

[12.1.18]

where the dipolar term includes permanent and induced dipole interactions. The nitromethane molecule is represented by the parameters of the HS diameter σ = 4.36 Å, the gas-phase dipole moment μ = 3.57 D, the polarizability α = 4.95 Å, and the LJ energy ε LJ ⁄ k = 391 K. Further, the solvent is modeled by spherical hard molecules of spherical polarizability, centered dipole moment, and central dispersion potential. To calculate the dipolar response, the Padé approximation was applied for the chemical potential of solvation in the dipolar liquid and then extended to a polarizable fluid according to the procedure of Wertheim. The basic idea of the Wertheim theory is to replace the polarizable liquid of coupled induced dipoles with a fictitious fluid with an effective dipole moment calculated in a self-consistent manner. Further, the Padé form is a simple analytical way to describe the dependence of the dipolar response on solvent polarity, solvent density, and

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solute/solvent size ratio. The theory/experiment agreement of the net solvation free energy is acceptable as seen in Table 12.1.5 where solvent ordering is according to the relative permittivity. Note that the contribution of dispersion forces is considerable even in strongly polar solvents. Table 12.1.5. Thermodynamic potentials (kJ/mol) of dissolution of nitromethane at 25°C. Data are from reference71 εs

ΔGcav

ΔGdisp

ΔGdipolar

ΔG(calc)

ΔG(exp)

n-C6

1.9

23.0

−32.9

−2.2

−12.1

−12.1

c-C6

2.0

28.1

−38.1

−2.8

−12.7

−12.0

Solvent

Et3N

2.4

24.2

−33.5

−2.9

−12.2

−15.2

Et2O

4.2

22.6

−33.4

−5.8

−16.5

−17.5

EtOAc

6.0

28.0

−38.5

−9.7

−20.1

−21.2

THF

7.5

32.5

−41.5

−12.2

−21.1

−21.3

c-hexanone

15.5

35.1

−39.8

−17.9

−22.6

−21.8

2-butanone

17.9

28.3

−33.9

−18.9

−24.5

−21.9

Acetone

20.7

27.8

−31.2

−22.1

−25.5

−22.5

DMF

36.7

38.1

−32.1

−28.5

−22.5

−23.7

DMSO

46.7

41.9

−31.1

−31.0

−20.2

−23.6

Scheme 12.1.2. ET(30) and n* are based on the solvent-induced shift of electronic absorption transitions.

With an adequate treating of simple forms of intermolecular attractions becoming available, there is currently great interest in making a connection between the empirical scales and solvation theory. Of course, the large, and reliable, experimental databases on empirical parameters are highly attractive for theoreticians for testing their computational models and improving their predictive power. At present, the solvatochromic scales are

786

12.1 Solvent effects on chemical reactivity

under considerable scrutiny. Thus, in a recent thermodynamic analysis, Matyushov et al.71 analyzed the two very popular polarity scales, ET(30) and π*, based on the solventinduced shift of electronic absorption transitions (see Scheme 12.1.2). Solvatochromism has its origin in changes in both dipole moment and polarizability of the dye upon electronic excitation provoking differential solvation of the ground and excited states. The dipole moment, μe, of the excited state can be either smaller or larger than the ground state value μg. In the former case one speaks about a negatively solvatochromic dye such as betaine-30, whereas the π* dye 4-nitroanisole is positively solvatochromic. Thus, polar solvent molecules produce a red shift (lower energy) in the former and a blue shift (higher energy) in the latter. On the other hand, polarizability arguably always increases upon excitation. Dispersion interactions, therefore, would produce a red shift proportional to Δα = αe − αg of the dye. In other words, the excited state is stabilized through the strengthening of dispersive coupling. Finally, the relative contributions of dispersion and dipolar interactions will depend on the size of the dye molecules with dispersive forces becoming increasingly important the larger the solute. Along these lines, the dye properties entering the calculations are given in Table 12.1.6. The purpose of the analysis was to determine how well the description in terms of “trivial” dipolar and dispersion forces can reproduce the solvent dependence of the absorption energies (and thereby, by difference to experiment, expose the magnitude of specific forces), h ω abs = Δ + Δ E rep + Δ E disp + Δ E dipolar + Δ E ss

[12.1.19]

where: hω abs Δ ΔErep ΔEdisp ΔEdipolar ΔEss

absorption energy vacuum energy gap shift due to repulsion solute-solvent interactions (taken to be zero) shift due to dispersion interactions shift due to dipolar forces of permanent and induced dipoles solvent reorganization energy

Table 12.1.6. Dye properties used in the calculations. Data from reference73 Molecular parameter

Betaine-30

4-Nitroanisole

Vacuum energy gap (eV)

1.62

4.49

R0 (Å)

6.4

4.5

αg (Å)

68

15

Δα (Å)

61

6

mg (D)

14.8

4.7

me (D)

6.2

12.9

Δμ (D)

−8.6

8.2

For the detailed and arduous calculation procedure, the reader may consult the paper cited. Here, let us just make a few general comments. The solvent influence on intramolecular optical excitation is treated by implementing the perturbation expansion over the

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solute-solvent attractions. The reference system for the perturbation expansion is chosen to be the HS liquid with the imbedded hard core of the solute. It should be noted for clarity that ΔEdisp and ΔEdipolar are additive due to different symmetries: dispersion force is nondirected (i.e. is a scalar quantity), and dipolar force is directed (i.e. is a vector). In other words, the attractive intermolecular potential can be split into a radial and an angle-dependent part. In modeling the solvent action on the optical excitation, the solute-solvent interactions have to be dissected into electronic (inertia-less) (dispersion, induction, chargetransfer) and molecular (inertial) (molecular orientations, molecular packing) modes. The idea is that the inertial modes are frozen on the time scale of the electronic transition. This is the Franck-Condon principle with such types of transitions called vertical transitions. Thus the excited solute is to be considered as a Frank-Condon state, which is equilibrated only to the electronic modes, whereas the inertial modes remain equilibrated to the ground state. According to the frozen solvent configuration, the dipolar contribution is represented as the sum of two terms corresponding to the two separate time scales of the solvent, (i) the variation in the solvation potential due to the fast electronic degrees of freedom, and (ii) the work needed to change the solute permanent dipole moment to the excited state value in a frozen solvent field. The latter is calculated for accommodating the solute ground state in the solvent given by orientations and local packing of the permanent solvent dipoles. Finally, the solvent reorganization energy, which is the difference of the average solvent-solvent interaction energy in going from the ground state to the excited state, is extracted by treating the variation with temperature of the absorption energy. Unfortunately, the experimental thermochromic coefficients are available for a few solvents only. The following results of the calculations are relevant. While the contributions of dispersions and inductions are comparable in the π* scale, inductions are overshadowed in the ET(30) values. Both effects reinforce each other in π*, producing the well-known red shift. For the ET(30) scale, the effects due to dispersion and dipolar solvation have opposite signs making the red shift for nonpolar solvents switch to the blue for polar solvents. Furthermore, there is an overall reasonable agreement between theory and experiment for both dyes, as far as the nonpolar and select solvents are concerned, but there are also discrepant solvent classes pointing to other kinds of solute-solvent interactions not accounted for in the model. Thus, the predicted ET(30) values for protic solvents are uniformly too low, revealing a decrease in H-bonding interactions of the excited state with lowered dipole moment. Another intriguing observation is that the calculated π* values of the aromatic and chlorinated solvents are throughout too high (in contrast to the ET(30) case). Clearly, these deviations, reminiscent of the shape of the plots such as in Figure 12.1.2, may not be explained in terms of polarizability as traditionally done (see above), since this solvent property has been adequately accommodated in the present model via the induction potential. Instead, the theory/experiment discord may be rationalized in either of two ways. One reason for the additional solvating force can be sought in terms of solute-solvent π overlap resulting in exciplex formation. Charge-transfer (CT) interactions are increased between the solvent and the more delocalized excited state.71 The alternative, and arguably more

788

12.1 Solvent effects on chemical reactivity

reasonable, view considers the quadrupole moment which is substantial for both solvent classes.72 Recently, this latter explanation in terms of dipole-quadrupole interactions is favored.

Figure 12.1.11. Depiction of simple multipoles

It is well-known that the interaction energy falls off more rapidly the higher the order of the multipole. Thus, for the interaction of an n-pole with an m-pole, the potential energy n+m+1 varies with distance as E ∝ 1 ⁄ r . The reason for the faster decrease is that the array of charges seems to blend into neutrality more rapidly with distance the higher the number of individual charges contributing to the multipole. Consequently, quadrupolar forces die off faster than dipolar forces. It has been calculated that small solute dipoles are even more effectively solvated by solvent quadrupoles than by solvent dipoles.73 In these terms it is understandable that quadrupolar contributions are more important in the π* than in the ET(30) scale. Similarly, triethylphosphine oxide, the probe solute of the acceptor number scale, is much smaller than betaine(30) and thus might be more sensitive to quadrupolar solvation. Thus, at long last, the shape of Figure 12.1.2 and similar ones seems rationalized. Note by the way that the quadrupole and CT mechanisms reflect, respectively, inertial and inertia-less solvation pathways, and hence could be distinguished by a comparative analysis of absorption and fluorescence shifts (Stokes shift analysis). However, for 4-nitroanisole fluorescence data are not available. Reverting once more to the thermodynamic analysis of the π* and ET(30) scales referred to above, it should be mentioned that there are also other theoretical treatments of the solvatochromism of betaine(30). Actually, in a very recent computer simulation,74 the large polarizability change Δα (nearly 2-fold, see Table 12.1.6 upon the excitation of betaine(30) has been (correctly) questioned). (According to a rule of thumb, the increase in polarizability upon excitation is proportional to the ground state polarizability, on the order Δα ≈ 0.25 α g .66) Unfortunately, Matyushov et al.71 derived this high value of Δα = 61 Å3 from an analysis of experimental absorption energies based on aromatic, instead of alkane solvents as nonpolar reference solvents. A lower value of Δα would diminish the importance of dispersion interactions. Further theoretical and computational studies of betaine(30) of the ET(30) scale are reviewed by Mente and Maroncelli.74 Despite several differences in opinion obvious in these papers, an adequate treatment of at least the nonspecific components of solvatochromism would seem to be “just around the corner”. Finally, a suggestion should be men-

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tioned on using the calculated π* values taken from ref.71 as a descriptor of nonspecific solvent effects.75 However, this is not meaningful since these values are just a particular blend of inductive, dispersive, and dipole-dipole forces.

12.1.7 SOME HIGHLIGHTS OF RECENT INVESTIGATIONS The like dissolves like rule The buzzword “polarity”, derived from the dielectric approach, is certainly the most popular word dealing with solvent effects. It is the basis for the famous rule of thumb “similia similibus solvuntur” (“like dissolves like”) applied for discussing solubility and miscibility. Unfortunately, this rule has many exceptions. For instance, methanol and toluene, with relative permittivities of 32.6 and 2.4, respectively, are miscible, as are water (78.4) and isopropanol (18.3). The problem lies in exactly what is meant by a “like” solvent. Originally, the term “polarity” was meant to be an abbreviation of “static dipolarity” and was thus associated with solely the dielectric properties of the solvent. Later on, with the advent of the empirical solvent parameters, it has assumed a broader meaning, sometimes even that of the overall solvating power.18 With this definition, however, the term “polarity” is virtually superfluous. Clearly, neither the relative permittivity nor the dipole moment is an adequate means to define polarity. The reason is that there are liquids whose constituent molecules have no net dipole moment, for symmetry reasons, but nevertheless have local polar bonds. This class of solvents, already mentioned above, comprises just the notorious troublemakers in solvent reactivity correlations, namely the aromatic and chlorinated solvents. These solvents, called “nondipolar” in the literature,76 stabilize charge due to higher solvent multipoles (in addition to dispersive forces) like benzene (“quadrupolar”) and carbon tetrachloride (“octupolar”). Of this class, the quadrupolar solvents are of primary importance. Thus, the gas-phase binding energy between K+ and benzene is even slightly greater than that of K+ and water. The interaction between the cation and the benzene molecule is primarily electrostatic in nature, with the ion-quadrupole interaction accounting for 60% of the binding energy.77 This effect is size-dependent: Whereas at K+ benzene will displace some water molecules from direct contact with the ion, Naaq+ is resistant towards dehydration in an aromatic environment, giving rise to selectivity in some K+ channel proteins.78 For the polarity of the C−H bonds, it should be remembered that electronegativity is not an intrinsic property of an atom, but instead varies with hybridization. Only the C(sp3)−H bond can be considered as truly nonpolar, but not so the C(sp2)−H bond.79 Finally, ethine has hydrogen atoms that are definitely acidic. It should further be mentioned that higher moments or local polarities cannot produce a macroscopic polarization and thus be detected in infinite wavelength dielectric experiments yielding a static relative permittivity close to the squared refractive index. Because of their short range, quadrupolar interactions do not directly contribute to the relative permittivity, but are reflected only in the Kirkwood gK factor that decreases due to breaking the angular dipole-dipole correlations with increasing quadrupolar strength.

790

12.1 Solvent effects on chemical reactivity

In these terms it is strongly recommended to redefine the term polarity. Instead of meaning solely dipolarity, it should also include higher multipolar properties, polarity = dipolarity + quadrupolarity + octupolarity

[12.1.20]

This appears to be a better scheme than distinguishing between truly nonpolar and nondipolar solvents.72 A polar molecule can be defined as having a strongly polar bond, but need not necessarily be a dipole. In this framework, the solvating power of the “nondipolar” solvents need no longer be viewed as anomalous or as essentially dependent on specific solvation effects.15 Beyond this it should be emphasized that many liquids have both a dipole moment and a quadrupole moment, water for example. However, for dipolar solvents such as acetonitrile, acetone, and dimethyl sulfoxide, the dipolar solvation mechanism will prevail. For less dipolar solvents like tetrahydrofurane, quadrupoles and dipoles might equally contribute to the solvation energetics.73 Notwithstanding this modified definition, the problem with polarity remains in that positive and negative charge solvation is not distinguished. As already pointed out above, there is no general relationship between polarity and the cation solvation tendency. For example, although nitromethane (MeNO2) and DMF have the same relative permittivity, the extent of ion pairing in MeNO2 is much greater than that in DMF. This observation is attributed to the weak basicity of MeNO2 which poorly solvates cations. As a result, ion pairing is stronger in MeNO2 in spite of the fact that long-range ion-ion interactions in the two solvents are equal. Finally, a potential problem with polarity rests in the fact that this term is typically associated with enthalpy. But caution is urged in interpreting the like-dissolves-like rule in terms of enthalpy. It is often stated for example that nonpolar liquids such as octane and carbon tetrachloride are miscible because the molecules are held together by weak dispersion forces. However, spontaneous mixing of the two phases is driven not by enthalpy, but by entropy. Water's anomalies The outstanding properties and anomalies of water have fascinated and likewise intrigued physicists and physical chemists for a long time. During the past decades much effort has been devoted to finding phenomenological models that explain the (roughly ten) anomalous thermodynamic and kinetic properties, including the density maximum at 4°C, the expansion upon freezing, the isothermal compressibility minimum at 46°C, the high heat capacity, the decrease of viscosity with pressure, and the remarkable variety of crystalline structures. Furthermore, isotope effects on the densities and transport properties do not possess the ordinary mass or square-root-mass behavior. Some of these properties are known from long ago, but their origin has been controversial. From the increasingly unmanageable number of papers that have been published on the topic, let us quote only a few those which appear to be essential. Above all, it seems to be clear that the exceptional behavior of water is not simply due to hydrogen bonding, but instead due to additional “trivial” vdW forces being present in any liquid. A hydrogen bond occurs when a hydrogen atom is shared between generally two electronegative atoms; vdW attractions arise from interactions among fixed or induced dipoles. The super-

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

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imposition and competition of both are satisfactorily accommodated in the framework of a “mixture model”. The mixture model for liquid water, promoted in an embryonic form by Röntgen80 over a century ago, but later discredited by Kauzmann81 and others,82 is increasingly gaining ground. Accordingly there are supposed to be two major types of intermolecular bonding configurations, an open bonding form, with a low density, such as occurs in ice one h, plus a dense bonding form, such as occurs in the most thermodynamically stable dense forms of ice, e.g., ice-II, -III, -V, and -VI.83 In these terms, water has many properties of the glassy states associated with multiple hydrogen-bond network structures.84 Clearly, for fluid properties, discrete units, (H2O)n, which can move independently of each other are required. The clusters could well be octamers dissociating into tetramers, or decamers dissociating into pentamers.85,86 (Note by the way that the unit cell of ice contains eight water molecules.) However, this mixture is not conceived to be a mixture of ices, but rather is a dynamic (rapidly fluctuating) mixture of intermolecular bonding types found in the polymorphs of ice. A theoretical study of the dynamics of liquid water has shown that there exist local collective motions of water molecules and fluctuation associated with hydrogen bond rearrangement dynamics.84 The half-life of a single H-bond estimated from transition theory is about 2x10-10 s at 300K.87 In view of this, tiny lifetime it seems more relevant to identify the two mixtures not in terms of different cluster sizes, but rather in terms of two different bonding modes. Thus, there is a competition between dispersion interactions that favor random dense states and hydrogen bonding that favors ordered open states. Experimental verification of the two types of bonding has been reviewed by Cho et al.88 From X-ray and neutron scattering, the open structure is characterized by an inner tetrahedral cage of four water molecules surrounding a central molecule, with the nearestneighbor O…O distance of about 2.8 Å. This distance, as well as the nearest-neighbor count of four, remains essentially intact in both in all crystalline ice polymorphs and in the liquid water up to near the boiling point. In this open tetrahedral network, the secondneighbor O…O distance is found at 4.5 Å. However, and most intriguing, another peak in the O…O radial distribution function (RDF), derived from a nonstandard structural approach (ITD), is found near 3.4 Å,89 signaling a more compact packing than in an ordinary H-bonding structure. This dense bonding form is affected by dispersive O…O interactions supplanting H-bonding. Note, however, that in this array the H-bonds may not be envisaged of being really broken but instead as being only bent. This claim is substantiated by a sophisticated analysis of vibrational Raman spectra90 and mid-IR spectra86 pointing to the existence of essentially two types of H-bonds differing in strength, with bent H-bonds being weaker than normal (i.e., linear) H-bonds. It should be mentioned that the 3.4 Å feature is hidden by the ordinary minimum of open tetrahedral contributions to the RDF. Because of this, the ordinary integration procedure yields coordination numbers greater than four,91 which confuses the actual situation. Instead, it is the outer structure that is changing whereas the inner coordination sphere remains largely invariant. Even liquid water has much of the tetrahedral H-bonding network of ice I.

792

12.1 Solvent effects on chemical reactivity

As temperature, or pressure, is raised, the open tetrahedral hydrogen bonding structure becomes relatively less stable and begins to break down, creating more of the dense structure. Actually all the anomalous properties of water can be rationalized on the basis of this open → dense transformation. An extremum occurs if two opposing effects are superimposed. The density maximum, for instance, arises from the increase in density due to the thermal open → dense transformation and the decrease in density due to a normal thermal expansion.88 As early as in 1978, Benson postulated that the abnormal heat capacity of water is due to an isomerization reaction.92 A clear explanation of the density anomaly is given by Silverstein et al.93 “The relatively low density of ice is due to the fact that H-bonding is stronger than the vdW interactions. Optimal H-bonding is incommensurate with the tighter packing that would be favored by vdW interactions. Ice melts when the thermal energy is sufficient to disrupt and disorder the H-bonds, broadening the distribution of H-bond angles and lengths. Now among this broadened H-bond distribution, the vdW interactions favor those conformations of the system that have a higher density. Hence liquid water is denser than ice. Heating liquid water continues to further deform hydrogen bonds and increases the density up to the density anomaly temperature. Further increase in temperature beyond the density anomaly weakens both H-bonds and vdW bonds, thus reducing the density, as in simpler liquids.” The same authors commented on the high heat capacity of water as follows: “Since the heat capacity is defined as CP = ( ∂ H/ ∂ T)P the heat capacity describes the extent to which some kinds of bonds are broken (increasing enthalpy) with increasing temperature. Breaking bonds is an energy storage mechanism. The heat capacity is low in the ice phase because the thermal energy at those temperatures is too small to disrupt the H-bonds. The heat capacity peaks at the melting temperature where the solid-like H-bonds of ice are weakened to become the liquid-like H-bonds of liquid water. The reason liquid water has a higher heat capacity than the vdW liquids is because water has an additional energy storage mechanism, namely the H-bonds that can also be disrupted by thermal energies.” Summed up, it appears that any concept to be used in a realistic study of water should have, as a fundamental ingredient, the competition between expanded, less dense structures, and compressed, denser ones. Thus, the outer structure in the total potential of water should be characterized by a double minimum: an open tetrahedral structure with a second-neighbor O…O distance of 4.5 Å and a bent H-bond structure with an O…O non-Hbonded distance of about 3.4 Å. Actually, according to a quite recent theoretical study, all of the anomalous properties of water are qualitatively explainable by the existence of two competing equilibrium values for the interparticle distance.94 Along these lines, the traditional point of view as to the structure of water is dramatically upset. Beyond that, also the classical description of the hydrogen bond needs revision. In contrast to a purely electrostatic bonding, quite a recent Compton X-ray scattering studies have demonstrated that the hydrogen bonds in ice have substantial covalent character,95 as already suggested by Pauling in the 1930s.96 In overall terms, a hydrogen bond is comprised of electrostatic, dispersion, charge-transfer, and steric repulsion interactions. Similarly, there are charge-transfer interactions between biological complexes and water97 that could have a significant impact on the understanding of biomolecules in aqueous solution.

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Finally, we return to the physical meaning of the large difference, for the protic solvents, between the cohesive energy density εc and the internal pressure Pi, quoted in section 12.1.3. For water, this difference is highest with the factor εc/Pi equal to 15.3. At first glance, this would seem explainable in the framework of the mixture model if H-bonding is insensitive to a small volume expansion. However, one should have in mind the whole pattern of the relationship between the two quantities. Thus, εc − Pi is negative for nonpolar liquids, relatively small (positive or negative) for polar non-associated liquids, and strongly positive for H-bonded liquids. A more rigorous treatment57 using the relations, Pi = ( ∂ U/ ∂ V)T = T( ∂ P/ ∂ T)V − P and the thermodynamic identity ( ∂ S/ ∂ V)T = ( ∂ P/ ∂ T)V reveals that the relationship is not as simple and may be represented by the following equation with dispersion detached from the other types of association, U disp RT - – ρ U ass + ρ 2 T ( ∂ S ass ⁄ ∂ρ ) ε c – P i = P – -------- Z o + ----------RT V

[12.1.21]

where: P V Zo Udisp Uass ρ Sass

external pressure liquid volume compressibility factor due to intermolecular repulsion potential of dispersion potential of association excluding dispersion the liquid number density entropy of association excluding dispersion

With the aid of this equation we readily understand the different ranges of εc − Pi found for the different solvent classes. Thus, for the nonpolar liquids, the last two terms are negligible, and for the usual values, Zo ≈ 10, −Udisp/RT ≈ 8, and V ≈ 150 cm3, we obtain the typical order of εc − Pi ≈ −(300 − 400) atm (equal to −(30 − 40) J cm-3, since 1 J cm-3 ≡ 9.875 atm). For moderately polar liquids, only the last term remains small, while the internal energy of dipolar forces is already appreciable −ρUpolar ≈ (200-500) atm giving the usual magnitude of εc − Pi. For H-bonded liquids, ultimately, the last term turns out to dominate reflecting the large increase in entropy of a net of H-bonds upon a small decrease in liquid density. The hydrophobic effect In some respects, the hydrophobic effect may be considered as the converse of the likedissolves-like rule. The term hydrophobic effect refers to the unusual behavior of water towards nonpolar solutes. Unlike simple organic solvents, the insertion of nonpolar solutes into water is (1) strongly unfavorable though slightly favored by enthalpy, but (2) strongly opposed by a large, negative change in entropy at room temperature, and (3) accompanied by a large positive heat capacity. An example is given in Table 12.1.7 for the thermodynamic properties of methane dissolved in water and in carbon tetrachloride. In dealing with the entropy (and free energy) of hydration, a brief remark on the choice of standard states is in order.

794

12.1 Solvent effects on chemical reactivity

Table 12.1.7. Solution thermodynamics of methane in water and carbon tetrachloride at 25°C. Data from Refs. 98, 125. Water

CCl4

ΔS*, J/mol K

−64.4

−7.1

300ΔS*, kJ/mol

−19.3

−2.1

ΔH , kJ/mol

−10.9

−1.2

ΔG*, kJ/mol

8.4

0.9

ΔCp, J/mol K

217.5

0 to 42

o

The standard molar entropy of dissolution, ΔsolvS° pertains to the transfer from a 1 atm gas state to a 1 mol L-1 solution and hence includes compression of the gas phase from 1 mol contained in 24.61 L (at 300 K) to 1 mol present in 1 L. Since theoretical calculations disregard volume contributions, it is proper to exclude the entropy of compression equal to −R ln 24.61 = −26.63 J K-1 mol-1, and instead to deal with ΔSsolv*.99 Thus,

ΔsolvS* = ΔsolvS° + 26.63 J K-1 mol-1

[12.1.22]

ΔsolvG*300 = ΔsolvH° − 300 ΔsolvS*

[12.1.23]

and Hydrophobicity forms the basis for many important chemical phenomena including the cleaning action of soaps and detergents, the influence of surfactants on surface tension, the immiscibility of nonpolar substances in water,100 the formation of biological membranes and micelles,101,102 the folding of biological macromolecules in water,103 clathrate hydrate formation,104 and the binding of a drug to its receptor.105 Of these, particularly intriguing is the stabilization of protein structure due to the hydrophobicity of nonpolar groups. Hydrophobic interactions are considerably involved in self-assembly, leading to the aggregation of nonpolar solutes, or equivalently, to the tendency of nonpolar oligomers to adopt chain conformations in water relative to a nonpolar solvent.106 Ever-increasing theoretical work during the last years unveils secrecy of the molecular details of the hydrophobic effect, a subject of vigorous debate. Specifically, the scientific community would eagerly like to decide whether the loss in entropy stems from the water-water or the water-solute correlations. There are two concepts. The older one is the clathrate cage model reaching back to the “iceberg” hypothesis of Frank and Evans,107 and the other, newer one, is the cavity-based model. It should be stressed here that the vast literature on the topic is virtually impossible to survey comprehensively. In the following, we will cite only a few papers (and references therein) that paved the way to the present state of the art. The clathrate cage model states that the structure of water is strengthened around a hydrophobic solute, thus causing a large unfavorable entropic effect. The surrounding water molecules adopt only a few orientations (low entropy) to avoid “wasting” hydrogen

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bonds, with all water configurations fully H-bonded (low energy). There is experimental evidence of structure strengthening, such as NMR and FTIR studies,108 NMR relaxation,109 dielectric relaxation,110 and HPLC.111 A very common conclusion is that the small solubility of nonpolar solutes in water is due to this structuring process. In the cavity-based model, the hard core of water molecules is more important to the hydrophobic effect than H-bonding of water. The process of solvation is dissected into two components, the formation of a cavity in the water to accommodate the solute and the interaction of the solute with the water molecules. The creation of a cavity reduces the volume of the translational motion of the solvent particles. This causes an unfavorable entropic effect. The total entropy of cavity formation at constant pressure70

Δ S cav, P = ρα p ( ∂Δ G cav ⁄ ∂ρ ) T – Δ G cav ⁄ T where:

ΔScav, P ρ ΔGcav

[12.1.24]

is the cavity formation entropy at constant pressure, the liquid number density, the free energy of cavity formation.

is the result of the opposing nature of the (positive) liquid expansibility term and the (negative) chemical potential summand. Along these lines the large and negative entropy of cavity formation in water is traced to two particular properties of water: the small molecular size (σ = 2.87 Å) and the low expansibility (αp = 0.26x10-3 K-1), with the latter having the greater impact. It is interesting to note that in both aspects water is extraordinary. Water's low expansibility reflects the fact that chemical bonds cannot be stretched by temperature. There is also a recent perturbation approach showing that it is more costly to accommodate a cavity of molecular size in water than in hexane for example.112 Considering the high fractional free volume of water, it is concluded that the holes in water are distributed in smaller packets.113 Compared to H-bonding network, a hard-sphere liquid finds more ways to configure its free volume in order to make a cavity. In the cavity-based model, large perturbations in water structure are not required to explain hydrophobic behavior. This conclusion arose out of the surprising success of the scaled particle theory (SPT),55 which is a hard-sphere fluid theory, to account for the free energy of hydrophobic transfers. Since the theory only uses the molecular size, density, and pressure of water as inputs and does not explicitly include any special features of Hbonding of water, the structure of water is arguably not directly implicated in the hydration thermodynamics. (However, the effect of H-bonds of water is implicitly taken into account through the size and density of water.) The proponents of this hypothesis argue that the entropic and enthalpic contributions arising from the structuring of water molecules largely compensate each other. In fact, there is thermodynamic evidence of enthalpyentropy compensation of solvent reorganization.114-117 Furthermore, recent simulations118,119 and neutron scattering data120-122 suggest that solvent structuring might be of much lower extent than previously believed. Also, a recent MD study report123 stated that the structure of water is preserved, rather than enhanced, around hydrophobic groups.

796

12.1 Solvent effects on chemical reactivity

Finally, the contribution of solute-water correlations to the hydrophobic effect may be displayed, for example, in the framework of the equation

Δ G sol = Δ G cav + Δ G att where

ΔGsol ΔGcav ΔGatt

[12.1.24]

free energy of dissolution free energy of cavity formation free energy of attractive interactions

This equation has been used by de Souza and Ben-Amotz124 to calculate values of ΔGatt from the difference between experimental solubilities of rare gases, corresponding to ΔGsol, and ΔGcav assessed from eqn. [12.1.24], i.e., using a hard-sphere fluid (HF) model. The values of ΔGatt so obtained have been found to correlate with the solute polarizabilities suggesting a dispersive mechanism for attractive solvation. It is interesting to note that, in water, the solubility of the noble gases increases with increasing size, in contrast to the aliphatic hydrocarbons whose solubility decreases with size. This differential behavior is straightforwardly explained in terms of the high polarizability of the heavy noble gases having a large number of weakly bound electrons, which strengthens the vdW interactions with water. It can be shown that for noble gases, on increasing their size, the vdW interactions increase more rapidly than the work of cavity creation, enhancing solubility. On the contrary, for the hydrocarbons, on increasing the size, the vdW interactions increase less rapidly than the work of cavity creation, lowering the solubility.125 We have seen that there is evidence of both, the clathrate cage model and the cavitybased model. Hence the importance of water structure enhancement in the hydrophobic effect is equivocal. The reason for this may be twofold. First, theoretical models have many adjustable parameters, so their physical bases are not always clear. Second, the free energy alone masks the underlying physics in the absence of a temperature dependence study, because of, amongst other things, the entropy-enthalpy compensation noted above. In place of the free energy other thermodynamic derivatives are more revealing. Of these, the study of heat capacity changes arguably provides a better insight into the role of changes in water structure upon hydration than analysis of entropy or enthalpy changes alone. Note that heat capacity is the most complex of the four principal thermodynamic parameters describing solvation (ΔG, ΔH, ΔS, and ΔCp), with the following connections, 2

∂Δ S ∂Δ H 2 ∂ ΔG Δ C p = ----------- = T ---------- = – T ------------2 ∂ T ∂T ∂T

[12.1.25]

It should be stressed that the negative entropy of hydration is virtually not the main characteristic feature of hydrophobicity, since the hydration of any solute, polar, nonpolar, or ionic, is accompanied by a decrease in entropy.126 The qualitative similarity in hydration entropy behavior of polar and nonpolar groups contrasts sharply with the opposite sign of the heat capacity change in polar and nonpolar group hydration. Nonpolar solutes have a large positive heat capacity of hydration, while polar groups have a smaller, negative one. Thus, the large heat capacity increase might be what truly distinguishes the hydrophobic effect from other solvation effects.127

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Recently, this behavioral difference of nonpolar and polar solutes could be reproduced by heat capacity calculations using a combination of Monte Carlo simulations and the random network model (RNM) of water.127-129 It was found that the hydrogen bonds between the water molecules in the first hydration shell of a nonpolar solute are shorter and less bent (i.e., are more ice-like) compared to those in pure water. The opposite effect occurs around polar solutes (the waters become less ice-like). The increase in H-bond length and angle has been found to decrease the water heat capacity contribution, while decreases in length and angle have been found to cause the opposite effect. Note further that a large heat capacity implies that the enthalpy and entropy are strong functions of temperature, and the free energy vs. temperature is a curved function, increasing at low temperatures and decreasing at higher temperatures. Hence there will be a temperature at which the solubility of nonpolar species in water is at a minimum. The low solubility of nonpolar species in water at higher temperatures is caused by unfavorable enthalpic interactions, not unfavorable entropy changes. Some light on these features has been shed by using a “simple” statistical mechanical MB model of water in which the water molecules are represented as Lennard-Jones disks with hydrogen bonding arms.130 (The MB model is called this because of the resemblance of each model water to the Mercedes-Benz logo.) As an important result, the insertion of a nonpolar solute into cold water causes ordering and strengthening of the H-bonds in the first shell, but the reverse applies in hot water. This provides a physical interpretation of the crossover temperatures TH and TS, where the enthalpy and entropy of transfer equal zero. TH is the temperature at which H-bond reorganizations are balanced by solute-solvent interactions. On the other hand, TS is the temperature at which the relative H-bonding strengths and numbers of shell and bulk molecules reverse roles. Although the large positive free energy of mixing of hydrocarbons with water is dominated by entropy at 25°C, it is dominated by enthalpy at higher temperatures (112°C from Baldwin’s extrapolation for hydrocarbons, or 150°C from the measurements of Crovetto for argon)130 where the disaffinity of oil for water is maximal. Ironically so, where hydrophobicity is strongest, entropy plays no role. For this reason, models and simulations of solutes that focus on cold water, around or below 25°C, miss much of the thermodynamics of the oil/water solvation process. Also, a clathrate-like solvation shell emerged from a recent computer simulation study of the temperature dependence of the structural and dynamical properties of dilute O2 aqueous solutions.131 In the first hydration shell around O2, water-water interactions are stronger and water diffusional and rotational dynamics slower than in the bulk. This calls to one’s mind an older paper by Hildebrand132 showing that at 25°C, methane’s diffusion coefficient in water is 40% less than it is in carbon tetrachloride (D(H2O) = 1.42x10-5 cm2/s vs. D(CCl4) = 2.89x10-5 cm2/s). Presumably, the loose clathrate water cages serve to inhibit free diffusion of the nonpolar solute. From these data, it seems that both the nonpolar solute and the aqueous solvent experience a decrease in entropy upon dissolving in water. It should also be mentioned in this context that pressure increases the solubility. The effect of pressure on the entropy was examined and it was found that increase in the pressure causes a reduction of orientational correlations, in agreement with the idea of pressure as a “structure breaker” in water.133 Actually,

798

12.1 Solvent effects on chemical reactivity

frozen clathrate hydrates trapped beneath oceans and arctic permafrost may contain more than 50% of the world's organic carbon reserves.134,135 Likewise, the solubility of aromatics is increased at high pressure and temperature, with π bond interactions involved.136 Only at first glance, the two approaches, the clathrate cage model and the cavitybased model, looked very different, the former based on the hydrogen bonding of water, and the later on the hard core of water. But taken all results together it would appear that both are just different perspectives on the same physics with different diagnostics reporting consequences of the same shifted balance between H-bonds and vdW interactions. Actually, in a very recent paper, a unified physical picture of hydrophobicity based on both the hydrogen bonding of water and the hard-core effect has been put forward.137 Hydrophobicity features an interplay of several factors. The Structure of Liquids A topic of abiding interest is the issue of characterizing the order in liquids which may be defined as the entropy deficit due to preferential orientations of molecular multipoles relative to random orientations (orientational order) and nonuniformly directed intermolecular forces (positional order). Phenomenologically, two criteria are often claimed to be relevant for deciding whether or not a liquid is to be viewed as ordered: the Trouton entropy of vaporization or Trouton quotient and the Kirkwood correlation factor gK.138 Strictly speaking, however, both are of limited relevance to the issue. The Trouton quotient is related to the structure of the liquids only at their respective boiling points, of course, which may markedly differ from their structures at room temperature. This should be realized especially for the high-boiling liquids. As these include the highly dipolar liquids such as HMPA, DMSO, and PC, the effect of dipole orientation to produce order in the neat liquids remains obscure. All that can be gleaned from the approximate constancy of the Trouton quotient for all sorts of aprotic solvents is that at the boiling point the entropy of attractions becomes unimportant relative to the entropy of unpacking liquid molecules, that is repulsions.139 In terms of the general concept of separating the interaction potential into additive contributions of repulsion and attraction, the vaporization entropy can be expressed by

Δ v H ⁄ T b = Δ v S = Δ S o – S att

[12.1.26]

where: ΔvH represents the vaporization enthalpy at the boiling point Tb, ΔSo the entropy of depacking hard spheres = entropy of repulsion, Satt the entropy of attraction, ΔSo can be separated into the entropy fo(η) of depacking hard spheres to an ideal gas at the liquid volume V, and the entropy of volume expansion to Vg = RT/P,

Δ S o ⁄ R = f o ( η ) + ln ( V g ⁄ V )

[12.1.27]

Further, fo(η) can be derived from the famous Carnahan-Starling equation as59 3

fo ( η ) = ( 4 η – 3 η ) ⁄ ( 1 – η )

2

[12.1.28]

It can, in fact, be shown that, for the nonpolar liquids, ΔvS/R is approximately equal to fo(η).139 Along these lines, Trouton's rule is traced to two facts: (i) The entropy of

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depacking is essentially constant, a typical value being ΔSo/R ≈ 9.65, due to the small range of packing densities encompassed. In addition, the entropies of HS depacking and of volume change vary in a roughly compensatory manner. (ii) The entropy of attraction is insignificant for all the aprotics. Only for the protics, the contributions of Satt may not be neglected. Actually, the differences between ΔvS and ΔSo reflect largely the entropy of hydrogen bonding. However, the application of the eqns. [12.1.26] to [12.1.28] to room temperature data reveals, in contrast to boiling point conditions, not unimportant contributions of Satt even for some aprotic liquids (see below). On the other hand, the gK factor is, loosely speaking, a measure of the deviation of the relative permittivity of the solvent with the same dipole moment and polarizability would have if its dipoles were not correlated by its structure. However, the gK factor is only the average cosine of the angles between the dipole moments of neighboring molecules. There may thus be orientational order in the vicinity of a molecule despite a gK of unity if there are equal head-to-tail and antiparallel alignments. Furthermore, the gK factor is not related to the positional order. The better starting point for assessing order would be experimental room temperature entropies of vaporization upon applying the same method as described above for the boiling point conditions. (Note, however, that the packing density, and hence the molecular HS diameter, varies with temperature. Therefore, in the paper139 the packing densities have been calculated for near boiling point conditions.) Thus we choose the simplest fluid as the reference system. This is a liquid composed of spherical, nonpolar molecules, approximated to a HS gas moving in a uniform background or mean field potential provided by the attractive forces.59 Since the mean field potential affects neither structure nor entropy, the excess entropy Sex S ex ⁄ R = ln ( V g ⁄ V ) + f o ( η ) – Δ v H ⁄ RT

[12.1.29]

may be viewed as an index of orientational and positional order in liquids. It represents the entropy of attractions plus the contributions arising from molecular nonsphericity. This latter effect can be estimated by comparing the entropy deficits for spherical and hard convex body repulsions in the reference system. Computations available for three n-alkanes suggest that only ≈ 20% of Sex are due to nonsphericity effects. Table 12.1.8. Some liquid properties concerning structure. Data are from ref.71 and ref. 145 (gK) ΔvH/RT

ΔvSo/R

−Sex/R

c-C6

18.21

17.89

0.32

THF

12.83

12.48

0.35

CCl4

13.08

12.72

0.36

n-C5

10.65

10.21

0.44

CHCl3

12.62

12.16

0.46

Solvent

CH2Cl2

11.62

11.14

0.48

Ph-H

13.65

13.08

0.57

gK

800

12.1 Solvent effects on chemical reactivity

Table 12.1.8. Some liquid properties concerning structure. Data are from ref.71 and ref. 145 (gK) ΔvH/RT

ΔvSo/R

−Sex/R

Ph-Me

15.32

14.62

0.70

n-C6

12.70

11.89

0.81

Et2O

10.96

10.13

0.83

c-hexanone

18.20

17.30

0.90

Py

16.20

15.22

0.98

MeCN

13.40

12.37

1.03

1.18 1.49

Solvent

gK

Me2CO

12.50

11.40

1.10

MeOAc

13.03

11.79

1.24

EtCN

14.53

13.25

1.28

1.15

PhNO2

22.19

20.89

1.30

1.56

MeNO2

15.58

14.10

1.48

1.38

NMP

21.77

20.25

1.52

1.52

EtOAc

14.36

12.76

1.60

DMSO

21.33

19.30

2.03

1.67

DMF

19.19

17.04

2.15

1.60

DMA

20.26

18.04

2.22

1.89 1.44

HMPA

24.65

22.16

2.49

PhCN

21.97

19.41

2.56

NMF

22.69

19.75

2.94

n-C11

22.76

19.66

3.10

4.52

FA

24.43

21.26

3.17

2.04

H2O

17.71

14.49

3.22

2.79

MeOH

15.10

11.72

3.38

2.99

n-C13

26.72

22.51

4.21

EtOH

17.07

12.85

4.22

3.08

PC

26.33

22.06

4.27

1.86

n-PrOH

19.14

14.29

4.85

3.23

n-BuOH

21.12

15.90

5.22

3.26

The calculations for some common liquids are given in Table 12.1.8 ordered according to decreasing Sex. An important result is an appreciable order produced by the hydrocarbon chain relative to polar groups and hydrogen-bonding effects. For instance, Sex would project for water the same degree of order as for undecane. In like terms, ethanol is comparable to tridecane. However, the same magnitude of the excess entropy does by no means imply that ordering is similar. Much of the orientational ordering in liquids composed of elongated molecules is a consequence of efficient packing such as the intertwin-

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ing of chains. In contrast, the structure of water is largely determined by strong electrostatic interactions leading to sharply-defined directional correlations characteristic of H-bonding. Although contrary to chemical tradition, there are other indications that the longer-chain hydrocarbon liquids are to be classified as highly structured as judged from thermodynamic140,141 and depolarized Rayleigh scattering data,142,143 and vibrational spectra.144 For nonprotic fluids, as Table 12.1.8 further shows, the vaporization entropy is strongly dominated by the entropy of HS depacking. This is an at least qualitative representation of the longstanding claim that repulsions play the major role in the structure of dense fluids.53 This circumstance is ultimately responsible for the striking success of the description of neutral reactions in the framework of a purely HS liquid, as discussed in Section 12.1.6. Also included in the Table are values of gK as determined in the framework of a generic mean spherical approximation.145 Since these values differ from those from other sources,146,138 because of differences in theory, we refrain from including the latter. It is seen that the gK parameter is unsuited to scale order since the positional order is not accounted for. On the other hand, values of gK exceed unity for the highly dipolar liquids and thus both Sex and gK attest to some degree of order present in them. Solvent reorganization energy in ET Electron transfer (ET) reactions in condensed matter continue to be of considerable interest to a wide range of scientists. The reasons are twofold. Firstly, ET plays a fundamental role in a broad class of biological and chemical processes. Secondly, ET is rather simple and very suitable to be used as a model for studying solvent effects and to relate the kinetics of ET reactions to thermodynamics. Two circumstances make ET reactions particularly appealing to theoreticians: • Outer-sphere reactions and ET within rigid complexes of well-defined geometry proceed without changes in the chemical structure since bonds are neither formed nor broken. • The long-ranged character of interactions of the transferred electron with the solvent's permanent dipoles. As a consequence of the second condition, a qualitative (and even quantitative) description can be achieved upon disregarding (or reducing through averaging) the local liquid structure changes arising on the length of molecular diameter dimensions relative to the charge-dipole interaction length. Because of this, it becomes feasible to use for outersphere reactions in strongly polar solvents the formalism first developed in the theory of polarons in dielectric crystals.147 In the treatment, the polar liquid is considered as a dielectric continuum characterized by the high-frequency ε ∞ and static εs relative permittivities, in which the reactants occupy spherical cavities of radii Ra and Rd, respectively. Electron transitions in this model are supposed to be activated by inertial polarization of the medium attributed to the reorientation of permanent dipoles. Along these lines, Marcus148 obtained his well-known expression for the free energy ΔF of ET activation

802

12.1 Solvent effects on chemical reactivity 2

( Δ Fo + Er ) Δ F = --------------------------4E r

[12.1.30]

where ΔFo is the equilibrium free energy gap between products and reactants and Er is the reorganization energy equal to the work applied to reorganize inertial degrees of freedom changing in going from the initial to the final charge distribution and can be dissected into inner-sphere and solvent contributions: Er = Ei + Es

[12.1.31]

where: inner-sphere reorganization energy solvent reorganization energy

Ei Es

For outer-sphere ET the solvent component Es of the reorganization energy 2

Es = e co g

[12.1.32]

is the product of the medium-dependent Pekar factor co = 1/ ε ∞ − 1/εs and a reactantdependent (but solvent independent) geometrical factor g = 1 ⁄ 2R a + 1 ⁄ 2R d – 1 ⁄ R

[12.1.33]

where: R

the donor-acceptor separation and e is the electron charge.

Further advancements included calculations of the rate constant preexponent for nonadiabatic ET,149 an account of inner-sphere150 and quantum intramolecular151-153 vibrations of reactants and quantum solvent modes.154,155 The main results were the formulation of the dependencies of the activation energy on the solvent dielectric properties and reactant sizes, as well as the bell-shaped relationship between ΔF and ΔFo. The predicted activation energy dependence on both the solvent dielectric properties156,157 and the donor-acceptor distance158 has, at least qualitatively, been supported by experiment. A bell-shaped plot of ΔF vs. ΔFo was obtained for ET in exciplexes,159 ion pairs,160 intramolecular,161 and outer-sphere162 charge shift reactions. However, the symmetric dependence predicted by eq. [12.1.31] has not yet been detected experimentally. Instead, always asymmetric plots of ΔF against ΔFo are obtained or else, in the inverted region (ΔFo < −Er), ΔF was found to be nearly invariant with ΔFo.163 A couple of explanations for the asymmetric behavior are circulating in the literature (see, e.g., the review by Suppan164). The first one165,166 considered vibrational excitations of high-frequency quantum vibrational modes of the donor and acceptor centers. Another suggestion167 was that the frequencies of the solvent orientational mode are significantly different around the charged and the neutral reactants. This difference was supposed to be brought about by dielectric saturation of the polar solvent. This model is rightly questioned168 since dielectric saturation cannot affect curvatures of the energy surface at the equilibrium point. Instead, dielectric saturation displays itself in a nonlinear deviation of the free energy surface from the parabolic form far

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

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from equilibrium. Hence, other sources of this behavior should be sought. Nevertheless, both concepts tend to go beyond the structureless description advocating a molecular nature of either the donor-acceptor complex or the solvent. Nowadays, theories of ET are intimately related to the theories of optical transitions. While formerly both issues have developed largely independently, there is now growing desire to get a rigorous description in terms of intermolecular forces shifting the research of ET reactions toward model systems amenable to spectroscopic methods. It is the combination of steady-state and transient optical spectroscopy that becomes a powerful method of studying elementary mechanisms of ET and testing theoretical concepts. The classical treatments of ET and optical transition have been facing a serious problem when extended to weakly polar and eventually nonpolar solvents. Values of Eop (equal to Es in eq [12.1.32]) as extracted from band-shape analyses of absorption spectra were found to fall in the range 0.2 − 0.4 eV. Upon partitioning these values into internal vibrations and solvent degrees of freedom, although this matter is still ambiguous, the contribution of the solvent could well be of the order of 0.2 − 0.3 eV.169-171 Unfortunately, all continuum theories predict zero solvent reorganization energies for ET in nonpolar liquids. It is evident that some new mechanisms of ET, alternatively to permanent dipoles' reorientation, are to be sought. It should be emphasized that the problem cannot be resolved by treatments of fixed positions of the liquid molecules, as their electronic polarization follows adiabatically the transferred electron and thus cannot induce electronic transitions. On the other hand, the displacement of molecules with induced dipoles are capable of activating ET. In real liquids, as we have stated above, the appreciable free volume enables the solvent molecules to change their coordinates. As a result, variations in charge distribution in the reactants concomitantly alter the packing of liquid molecules. This point is corroborated by computer simulations.172 Charging a solute in a Stockmayer fluid alters the inner coordination number from 11.8 for the neutral entity to 9.5 for the positively charged state, with the process accompanied by a compression of the solvation shell. It is therefore apparent that solvent reorganization involves reorganization of liquid density, in addition to the reorientational contribution. This concept has been introduced by Matyushov,173 who dissected the overall solvent reorganization energy Es into a dipole reorganization component Ep and a density reorganization component Ed, Es = Ep + Ed

[12.1.34]

It should be mentioned that the two contributions can be completely separated because they have different symmetries, i.e., there are no density/orientation cross terms in the perturbation expansion involved in the calculations. The density component comprises three mechanisms of ET activation: (i) translations of permanent dipoles, (ii) translations of dipoles induced by the electric field of the donor-acceptor complex (or the chromophore), and (iii) dispersion solute-solvent forces. On the other hand, it appears that in the orientational part only the permanent dipoles (without inductions) are involved. With this novel molecular treatment of ET in liquids, the corundum of the temperature dependence of the solvent reorganization energy is straightforwardly resolved. Dielectric continuum theories predict an increase of Es with temperature paralleling the

804

12.1 Solvent effects on chemical reactivity

decrease in the relative permittivities. In contrast, experimental results becoming available quite recently show that Es decreases with temperature. Also, curved Arrhenius plots eventually featuring a maximum are being reported, in weakly polar174 and nonpolar175 solvents. The bell-shaped temperature dependence in endergonic and moderately exergonic regions found for ET quenching reactions in acetonitrile176 was attributed to a complex reaction mechanism. Analogously, the maximum in the Arrhenius coordinates, peculiar to the fluorescence of exciplexes formed in the intramolecular177 and bimolecular178 pathways, is commonly attributed to a temperature dependent competition of exciplex formation and deactivation rates. A more reasonable explanation can be given in terms of the new theory as follows. A maximum in the Arrhenius coordinates follows from the fact that the two terms in eq. [12.1.34] depend differently on temperature. Density fluctuation around the reacting pair is determined mainly by the entropy of repacking hard spheres representing the repulsive part of the intermolecular interaction. Mathematically, the entropy of activation arises from the explicit inverse temperature dependence Ed ∝ 1/T. Since the liquid is less packed at a higher temperature, less energy is needed for reorganization. Repacking of the solvent should lead to larger entropy changes than those of dipoles' reorientation that is enthalpic in nature due to the long-range character of dipole-dipole forces. The orientational component increases with temperature essentially as predicted by continuum theories. In these ways, the two solvent modes play complementary roles in the solvent's total response. This feature would lead to curved Arrhenius plots of ET rates with slight curvatures in the normal region of ET (−ΔFo < Er), but even a maximum in the inverted region (−ΔFO > Er).179,180 The maximum may, however, be suppressed by intramolecular reorganization and should, therefore, be discovered particularly for rigid donor-acceptor pairs. Photoinduced ET in binuclear complexes with localized electronic states provides at the moment the best test of theoretical predictions for the solvent dependent ET barrier. This type of reaction is also called metal-metal charge-transfer (MMCT) or intervalence transfer (IT). The application of the theory to IT energies for valence localized biruthenium complexes and the acetylene-bridged biferricenium monocation181 revealed its superiority to continuum theories. The plots of Es vs. Eop are less scattered, and the slopes of the best-fit lines are closer to unity. As a major merit, the anomalous behavior of some solvents in the continuum description − in particular HMPA and occasionally water − becomes resolved in terms of the extreme sizes, as they appear at the opposite ends of the solvent diameter scale. Recently, it became feasible for the first time, to measure experimentally for a single chemical system, viz. a rigid, triply linked mixed-valence binuclear iron polypyridyl complex, [Fe(440)3Fe]5+, the temperature dependencies of both the rate of thermal ET and the optical IT energy (in acetonitrile-d3).182 The net Er associated with the intramolecular electron exchange in this complex is governed exclusively by low frequency solvent modes, providing an unprecedented opportunity to compare the parameters of the theories of thermal and optical ET in the absence of the usual complications and ambiguities. The acceptable agreement was obtained only if solvent density fluctuations around the reacting system were taken into account. In these ways, the idea of density fluctuations is achiev-

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

805

ing experimental support. The two latest reports on negative temperature coefficients of the solvent reorganization energy (decrease in Es with temperature) should also be mentioned.183,184 Thus, two physically important properties of molecular liquids are absent in the continuum picture: the finite size of the solvent molecules and thermal translational modes resulting in density fluctuations. Although the limitations of the continuum model are long known, the necessity for a molecular description of the solvent, curiously, was first recognized in connection with solvent dynamic effects in ET. Solvent dynamics, however, affects the preexponent of the ET rate constant and, therefore, influences the reaction rate much less than does the activation energy. From this viewpoint, it is suspicious that the ET activation energy has so long been treated in the framework of continuum theories. The reason for this affection is the otherwise relative success of the latter, traceable to two main features. First, the solvents usually used are similar in molecular size. Second, there is a compensation because altering the size affects the orientational and translational parts of the solvent barrier in opposite directions. The solution ionic radius The solution ionic radius is arguably one of the most important microscopic parameters. Although detailed atomic models are needed for a full understanding of solvation, simpler phenomenological models are used to interpret the results for more complex systems. The most famous model in this respect is that of Born, originally proposed in 1920,185 representing the simplest continuum theory of ionic solvation. For a spherical ion, the Born excess free energy ΔGB of solvation was derived by considering the free energy change resulting from the transfer of an ion from vacuum to solvent. The equation has a very simple dependence on the ionic charge z, the radius rB, and the solvent relative permittivity ε 2 2

1 –e z * Δ G B = -------------  1 – ---  ε 2r B

[12.1.35]

While Born assumes that the dielectric response of the solvent is linear, nonlinear effects such as dielectric saturation and electrostriction should occur due to the high electric field near the ion.186 Dielectric saturation is the effect that the dipoles are completely aligned in the direction of the field so that any further increase in the field cannot change the degree of alignment. Electrostriction, on the other hand, is defined as the volume change or compression of the solvent caused by an electric field, which tends to concentrate dipoles in the first solvation shell of an ion. Dielectric saturation is calculated to occur at field intensities exceeding 104 V/cm while the actual fields around monovalent ions are on the order of 108 V/cm.187 In the following, we concentrate on ionic hydration that is generally the focus of attention. Unaware of nonlinear effects, Latimer et al.188 showed that the experimental hydration free energies of alkali cations and halide anions were consistent with the simple Born equation when using the Pauling crystal radii rP increased by an empirical constant Δ equal to 0.85 Å for the cations and 0.1 Å to the anions. In fact three years earlier a similar relationship was described by Voet.189 The distance rP + Δ was interpreted as the radius of the cavity formed by the water dipoles around the ion. For cations, it is the ion-oxygen dis-

806

12.1 Solvent effects on chemical reactivity

tance while for anions it is the ion-hydrogen distance of the neighboring water molecules. From those days onwards, the microscopic interpretation of the parameters of the Born equation has continued to be a corundum because of the ambiguity of using either an effective radius (that is a modification of the crystal radii) or an effective relative permittivity. Indeed, the number of modifications of the Born equation is hardly countable. Rashin and Honig,190 as an example, used the covalent radii for cations and the crystal radii for anions as the cavity radii, on the basis of electron density distributions in ionic crystals. On the other hand, Stokes191 put forward that the ion's radius in the gas-phase might be appreciably larger than that in solution (or in a crystal lattice of the salt of the ion). Therefore, the loss in self-energy of the ion in the gas-phase should be the dominant contributor. He could show indeed that the Born equation works well if the vdW radius of the ion is used, as calculated by a quantum mechanical scaling principle applied to an isoelectronic series centering around the crystal radii of the noble gases. More recent accounts of the subject are available.192,193 Irrespective of these ambiguities, the desired scheme of relating the Born radius with some other radius is facing an awkward situation: Any ionic radius depends on arbitrary divisions of the lattice spacings into anion and cation components, on the one hand, and on the other, the properties of individual ions in condensed matter are derived by means of some extra-thermodynamic principle. In other words, both properties, values of r and ΔG*, to be compared with one another, involve uncertain apportionments of observed quantities. Consequently, there are so many different sets of ionic radii and hydration free energies available that it is very difficult to decide which to prefer. In a most recent paper,99 a new table of absolute single-ion thermodynamic quantities of hydration at 298K has been presented, based on conventional enthalpies and entropies upon implication of the thermodynamics of water dissociation. From the values of ΔhydG* the Born radii were calculated from rb(Å) = −695z2/ΔhydG*(kJ)

[12.1.36]

as given in Table 12.1.9 This is at first a formal definition whose significance may be tested in the framework of the position of the first maximum of the radial distribution function (RDF) measured by solution X-ray and neutron diffraction.194 However, the procedure is not unambiguous as is already reflected by the names given to this quantity, viz. (for the case of a cation) ion-water195 or ion-oxygen distance. The ambiguity of the underlying interpretation resides in the circumstance that the same value of 1.40 Å is assigned in the literature to the radius of the oxide anion, the water molecule, and the vdW radius of the oxygen atom. Table 12.1.9. Some radii (Å). Data are from ref.99 Atom

rB

raq

rmetal

Li

1.46

1.50

1.52

Na

1.87

1.87

1.86

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

807

Table 12.1.9. Some radii (Å). Data are from ref.99 Atom

rB

raq

K

2.33

2.32

Rb

2.52

rmetal 2.27 2.48

Cs

2.75

2.58

2.65

Be

1.18

1.06

1.12

Mg

1.53

1.52

1.60

Ca

1.86

1.86

1.97

Sr

2.03

2.02

2.15

Ba

2.24

2.27

2.17

F

1.39

1.29

Cl

1.86

1.85

Br

2.00

2.00

I

2.23

2.30

It seems that many workers would tend to equate the distance (d) corresponding to the first RDF peak with the average distance between the center of the ion and the centers of the nearest water molecules, d = rion + rwater. Actually, Marcus196,197 presented a nice relationship between d, averaged over diffraction and simulation data, and the Pauling crystal radius in form d = 1.38 + 1.102 rp. Notwithstanding this success, it is preferable to implicate not the water radius but instead the oxygen radius. This follows from the close correspondence between d and the metal-oxygen bond lengths in crystalline metal hydrates.99 The gross coincidence of the solid and solution state distances is strong evidence that the value of d measures the distance between the nuclei of the cation and the oxygen rather than the center of the electron cloud of the whole ligand molecule. Actually, first RDF peaks for ion solvation in water and in nonaqueous oxygen donor solvents are very similar despite the different ligand sizes. Examples include methanol, formamide, and dimethyl sulfoxide.197 Nevertheless, the division of d into ion and ligand components is still not unequivocal. Since the traditional ionic radius is often considered as a literal measure of size, it is usual to interpret crystallographic metal-oxygen distances in terms of the sum of the vdW radius of oxygen and the ionic radius of the metal. It should be emphasized, however, that the division of bond lengths into “cation” and “anion” components is entirely arbitrary. If the ionic radius is retained, the task remains to seek a connection to the Born radius, an issue that has a long-standing history beginning with the work of Voet.189 Of course, any addition to the ionic radius necessary to obtain good results from the Born equation needs a physical explanation. This is typically done in terms of the water radius, in addition to other correction terms such as a dipolar correlation length in the MSA (mean spherical approximation).198-200 In this case, however, proceeding from the first RDF peak, the size of the water moiety is implicated twice.

808

12.1 Solvent effects on chemical reactivity

It has been shown99 that the puzzle is unraveled if the covalent (atomic) radius of oxygen is subtracted from the experimental first peak position of the cation-oxygen radial distribution curve (strictly, the upper limits instead of the averages). The values of raq so obtained are very close to the Born radius, d ( cation – O ) – r cov ( O ) = r aq ≈ r B

[12.1.37]

Similarly, for the case of the anions, the water radius, taken as 1.40 Å, is implicated, d ( anion – O ) – r ( water ) = r aq ≈ r B

[12.1.38]

Furthermore, also the metallic radii (Table 12.1.9) are similar to values of raq. This correspondence suggests that the positive ion core dimension in a metal tends to coincide with that of the corresponding rare gas cation. The (minor) differences between raq and rmetal for the alkaline earth metals may be attributed, among other things, to the different coordination numbers (CN) in the metallic state and the solution state. The involvement of the CN is apparent in the similarity of the metallic radii of strontium and barium which is obviously a result of the cancellation of the increase in the intrinsic size in going from Sr to Ba and the decrease in CN from 12 to 8. Along these lines, a variety of radii are brought under one umbrella, noting, however, a wide discrepancy to the traditional ionic radii. Cation radii larger than the traditional ionic radii would imply smaller anion radii so as to meet the (approximate) additivity rule. In fact, the large anion radii of the traditional sets give rise to at least two severe inconsistencies: (i) the dramatic differences of the order of 1 Å between the covalent radii and the anion radii are hardly conceivable in view of the otherwise complete parallelism displayed between ionic and covalent bonds.201 (ii) It is implausible that non-bonded radii202 should be smaller than ionic radii. For example, the ionic radius of oxygen of 1.40 Å implies that oxygen ions should not approach each other closer than 2.80 Å. However, non-bonding oxygen-oxygen distances as short as 2.15 Å have been observed in a variety of crystalline environments. “(Traditional) ionic radii most likely do not correspond to any physical reality,” Baur notes.203 It should be remarked that the scheme of reducing the size of the anion at the expense of that of the cation has been initiated by Gourary and Adrian, based on the electron density contours in crystals.204 The close correspondence seen between rB and raq supports the idea that the Born radius (in aqueous solution) is predominantly a distance parameter without containing dielectric, i.e., solvent structure, contributions. This result could well be the outcome of a cancellation of dielectric saturation and electrostriction effects as suggested recently from simulations.205-208 It should be emphasized, however, that the present discussion might be confined to water as the solvent. Recent theoretical treatments advise the cavity radius not to be considered as an intrinsic property of the solute, but instead to vary with solvent polarity, with orientational saturation prevailing at low polarity and electrostriction at high polarity.208,209 It would appear that the whole area of nonaqueous ion solvation deserves more methodical attention. It should, in addition, be emphasized that the cavity radius is sensitive to temperature. Combining eq. [12.1.35] with

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

∂Δ G* o Δ H = Δ G* + T  ---------------  ∂T 

809

[12.1.39]

one obtains194

∂ε T ∂r T o Δ H = Δ G* 1 + -------------------  ------ – ---  ------ ( ε – 1 )ε  ∂ T P r  ∂ T P

[12.1.40]

The derivation of ( ∂ r/ ∂ T)P from reliable values of ΔH° and ΔG* is interesting, because nominally the dielectric effect (−0.018 for water) is smaller than the size effect ( – 0.069 for chloride), a result that has not given previously the attention due to it. Consequently, as Roux et al.194 stated unless a precise procedure for evaluating the dependence of the radius on the temperature is available, the Born model should be restricted to the free energy of solvation. Notwithstanding this, beginning with Voet,189 the Born model has usually been tested by considering the enthalpies of hydration.210 The reason for the relative success lies in the fact that ion hydration is strongly enthalpy controlled, i.e., ΔH° ∼ ΔG*. The discussion of radii given here should have implications for all calculations involving aqueous ionic radii, for instance, the solvent reorganization energy in connection with eq. [12.1.32]. Thus, treatments using the crystal radii as an input parameter211-214 may be revisited. The donor-acceptor approach to ionic liquids: Mutual influence of cations and anions The same concept as for ions in non-aqueous solutions can be applied for the determination of donor and acceptor numbers of ionic liquids.30 As mentioned in above cations and anions influence the donor and acceptor properties of a solvent thus shifting the absorption maximum of a solvatochromic dye. In the case of ionic liquids, the assumption is made that cations are solvated by anions and vice versa. The anions, therefore, are acting as a solvent for the cations and the cations as a solvent for the anions. Hence there is a mutual influence of the ions on their donating and accepting ability. A system of equations can be established in order to reflect the ionic influence.

ν˜ max, Cu ( IL ) – ν˜ max, Cu ( DCE ) = a ( DN IL – DN DCE ) + b ( AN IL – AN DCE ) [12.1.41] ν˜ max, Fe ( IL ) – ν˜ max, Fe ( NM ) = a ( DN IL – DN NM ) + b ( AN IL – AN NM )

[12.1.42]

By solving this system of equations, using the constants (a, b and A, B) determined previously for ion in a non-aqueous solvent, donor and acceptor numbers for neat ionic liquids can be obtained. Using dichloroethane (DCE) and nitromethane (NM) as reference solvents the DNs and ANs are on the same scale as Gutmann’s DN and AN for solvents.6 Solving equations [12.1.41] and [12.1.42] and inserting parameters, acceptor and donor numbers for neat ionic liquids can easily be determined: A a AN IL = --------------------  Δν˜ max, Cu + ---- Δν˜ max, Fe + 1200.56  Ab – Ba  A

[12.1.43]

810

12.1 Solvent effects on chemical reactivity

B b DN IL = --------------------  Δν˜ max, Cu + ---- Δν˜ max, Fe – 2474.91  aB – bA  B

[12.1.44]

Figure 12.1.12. Linear relation of DN with AN for [C4C1im][X], where X is the variation of the anion; correlation r = 0.94.

In case of ionic liquids, both the anions and the cations influence the absorption spectra of the indicator and the summary effect can be seen. Table 12.1.10 summarizes the absorption band maximum of the complexes and the obtained donor and acceptor numbers in neat 1-butyl-3-methylimidazolium (C4C1im+) based ionic liquids. Figure 12.1.12 shows a linear dependence of the donor and acceptor number. In conventional solvents where a solvent molecule can act as donor and/or as acceptor, e.g. methanol is a strong acceptor but can also donate electrons from the lone pairs of the oxygen, and no such correlation can be found. In contrast, in ionic liquids without functional groups the cation is only acting as electron pair acceptor and the anion only as electron pair donor (additional functional groups can of course also act as acceptor and/or donor). Table 12.1.10. Absorption maxima of the solvatochromic indicators and calculated donor and acceptor numbers for 1-butyl-3-methylimidazolium (C4C1im+) based neat ionic liquids. Cation C4C1im

+

Anion Cl

−

λmax(Fe)

λmax(Cu)

AN

DN

ΔH2

593.1

−

−

−

10.31

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

811

Table 12.1.10. Absorption maxima of the solvatochromic indicators and calculated donor and acceptor numbers for 1-butyl-3-methylimidazolium (C4C1im+) based neat ionic liquids. Cation C4C1im

+

C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

Anion −

CH3COO −

λmax(Fe)

λmax(Cu)

AN

DN

ΔH2

590.0

702.0

−54.38

11.32

10.27

590.0

−

−

−

9.94

CF3COO−

585.1

638.0

−35.15

6.23

9.74

−

588.9

684.0

−49.44

10.14

9.68

586.2

659.0

−41.58

7.59

9.68

Br

NO2 I−

−

586.9

645.0

−37.96

7.58

9.57

n-C8H17SO4−

586.2

617.0

−29.24

6.16

9.32

CH3SO4− −

587.9

596.0

−23.20

6.49

9.21

585.1

690.0

−49.26

7.86

9.15

−

(CN)2N

584.1

941.0

−35.56

5.66

8.96

CF3SO3−

580.0

601.5

−21.47

1.57

8.91

−

NO3

SCN

578.0

540.0

2.07

−2.38

8.64

NTf2−

576.0

546.0

0.56

−3.44

8.56

PF6−

577.0

516.5

12.59

−4.21

8.38

BF4

The negative AN (DN) might imply that the cation (the anion) is actually a donor, but this seems to be a matter of referencing. In the donor-acceptor approach, an arbitrarily referencing system is used. DN represents the negative ΔH value of the reaction of SbCl5 with a solvent molecule L to the adduct SbCl5·L in high dilution of DCE. Here DCE has been defined as reference solvent with DN = 0 (despite the fact that it itself shows very low donor ability, which was neglected). For commonly used solvents this reaction is exotherm so that ΔH turns out to be positive and usual values are in the range between 0 (DN) and 100. AN, on the contrary, is defined as the NMR chemical shift of the 31P nucleus in Et3PO in the respective solvent (undiluted). To obtain comparable values with the DN scale, this NMR shifts (measured in ppm) have been re-normated to become 100 for the (DN-important) probe SbCl5. Negative AN (DN) just means that the ionic liquid in question is a weaker acceptor (donor) than nitromethane (dichloroethane). For example, in acetone (AN = 12.5) Cl− is a strong donor (DN = 38.5); upon changing to a solvent with a higher AN, the donicity of Cl− shrinks (DN in methanol is only 22.6). In [C4C1im][Cl] the solvation shell consists of C4C1im+ cations which are accepting most of the electrons from Cl− and the cation is, therefore, a very weak acceptor and the Cl− is a weaker donor than in acetone or methanol. [BF4] − exhibits in acetone a donor strength of 8.33 and in methanol −7.56; in C4C1im+ the DN is −4.18, having approximately the same donicity as [CF3SO3]− in water (DN = −4.0).9 It can also be shown that the Kamlet-Taft solvent parameter β (i.e., a measure of the hydrogen bond accepting (HBA) ability is linearly correlated to the H-2 hydrogen NMR chemical shift δH2 of 1-butyl-3-methylimidazolium C4C1im+ based ionic liquids.33,215 In our consideration the DN value should also be correlated linearly. Figure [12.1.13] shows

812

12.1 Solvent effects on chemical reactivity

Figure 12.1.13. Linear correlation of DN with δH2 for [C4C1im][X], where X is the variation of the anion.

such a behavior. The electronic environment of the “theoretically isolated” cation C4C1im+ is fixed. Any alteration on the electron density is therefore dependent on the nature of the anion. As there is no additional NMR sensitive probe molecule in the ionic liquid (the shift of a NMR probe like triethylphosphine oxide should be dependent on donor and acceptor properties as do the solvatochromic indicators) the donor properties of the anion can be screened solely by the shift of H-2, i.e. the H-2 proton acts as “built-in” indicator.215 From a linear correlation of δH2 with DN and a linear correlation of AN with DN, it is possible to determine donor and acceptor numbers for (in this case) C4C1im+ based ionic liquids where a solvatochromic approach is not feasible (e.g., high melting, colored or hydrolysis sensitive ionic liquids): DN IL = k 1 δ H2 + d 1

(r = 0.82)

[12.1.45]

AN IL = k 2 DN IL + d 2

(r = 0.97)

[12.1.46]

with k1 = 8.4667, d1 = −73.7101, k2 = −4.1043 and d2 = −9.7339. Table 12.1.11 summarizes the results calculated from the NMR shift. These are in agreement with the results for the anion variation of C4C1im+ ionic liquids determined by solvatochromic indicators. In the series of chloroaluminate anions, it can be seen, that an ionic liquid with a low mole fraction of added AlCl3 exhibits strong donating abilities, whereas the donor properties are

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

813

reduced as the mole fraction rises (i.e. the “basicity” of the anion decreases by increasing the amount of the Lewis acid AlCl3). Table 12.1.11. Calculated donor and acceptor numbers for 1-butyl-3-methylimidazolium based neat ionic liquids based on the correlation of δ with DN and AN with DN Cation C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im+ C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

C4C1im+ C4C1im+ C4C1im+ C4C1im

+

C4C1im+ C4C1im

+

Anion SnCl3− BBr4− TiCl5− SbCl6− I3− SnCl5− I5− WCl7− MoCl6− AlCl4− AlCl4− AlCl4− AlCl4− AlCl4− Al2Cl7− Al2Cl7− Al2Cl7− Al2Cl7− Al2Cl7−

X AlCl

3

δH2, ppm

AN

DN

9.24

−28.29

4.52

9.04

−21.31

2.83

8.99

−19.61

2.41

8.68

−8.83

−0.22

8.66

−8.14

−0.39

8.59

−5.71

−0.98

8.52

−3.27

−1.57

8.50

−2.58

−1.74

8.06

12.71

−5.47

0.17

10.29

−64.78

13.41

0.29

10.05

−56.44

11.38

0.38

9.62

−41.50

7.74

0.44

9.06

−22.04

3.00

0.50

8.39

1.24

−2.67

0.55

8.37

1.94

−2.84

0.58

8.34

2.98

−3.10

0.62

8.30

4.37

−3.44

0.64

8.27

5.41

−3.69

0.67

8.23

6.80

−4.30

Figure 12.1.14 shows the variation of the cation two different correlations. Less steric demanding cations (N1;1;1;4+, S2;2;2+, C4py+, C1C4pyrr+, C2C1im+, C4C1im+, C6C1im+ and C8C1im+) give a steeper slope than cations with a high steric demand (P6;6;6;14+, C8thiaz+). Although choline is not sterically demanding it does not correlate with the other less sterically demanding cations. The reason for this could be the functional group OH which gives an additional possibility of interaction (e.g., hydrogen bridge bonding, the interaction of the free electron pairs of the oxygen) with a given anion. Table 12.1.12 summarizes the absorption maxima of the solvatochromic indicators and calculated donor and acceptor numbers for bis(trifluoromethylsulfonyl)imide based neat ionic liquids. The current state of knowledge from the available data allows the conclusion that the influence of

814

12.1 Solvent effects on chemical reactivity

Figure 12.1.14. Linear correlation of DN with AN for [C][NTf2] (squares) and [C][PF6] (stars), where C is the variation of the cation.

the cation is driven by steric hindrance and the nature (and the number of) additional functional groups. Table 12.1.12. Absorption maxima of the solvatochromic indicators and calculated donor and acceptor numbers for bis(trifluoromethylsulfonyl)imide based neat ionic liquids. Cation

Abbr.

Anion [nm]

λmax (Fe) [nm]

λmax (Cu) [nm]

AN

DN

butyltrimethylammonium

N1,1,1,4+

NTf2−

573.2

546.0

1.89

−5.35

triethylsulfonium

S2,2,2+ C4py+

NTf2−

585.9

591.3

−4.00

3.09

NTf2− NTf2− NTf2− NTf2− NTf2−

587.8

548.0

−5.60

4.41

586.1

545.0

−3.64

3.17

580.6

573.7

4.60

−1.10

597.3

669.2

−32.55

13.08

553.0

535.8

32.61

−21.98

butylpyridinium

1-butyl-1-methylpyrrolidinium C1C4pyrr+ 3-octylthiazolium

C8thiaz

+

trihexyltetradecylphosphonium P6,6,6,14+ choline

+

chol

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

815

Figure 12.1.15. Dependence of the side chain length in [CnC1im][NTf2] and [CnC1im][PF6] on AN.

Table 12.1.13. Absorption maxima of the solvatochromic indicators and calculated donor and acceptor numbers for imidazolium-based neat ionic liquids with a fixed anion. Cation

Anion

λmax (Fe), nm λmax (Cu), nm

AN

DN

12.61

−4.23

PF6

−

577.0

516.5

PF6

−

579.0

516.5

11.66

−2.87

C8C1im+

PF6−

578.0

516.5

12.13

−3.54

C10C1im+

C4C1im

+

C6C1im

+

PF6−

581.1

516.5

10.74

−1.53

C2C1im

+

NTF2−

579.0

547.0

−1.21

−1.41

C4C1im

+

NTF2− NTF2− NTF2−

576.0

546.0

0.58

−3.46

579.0

547.0

−1.23

−1.38

581.1

548.5

−2.75

0.03

C6C1im+ C8C1im

+

The interpretation of the influence of the side chain length is not straightforward. Considering a virtual, from anions unaffected CnC1im cation, a linear decrease of AN would be expected due to the increasing inductive effect of a longer side chain. From the available data, the results show local minima and maxima respectively for DN and AN in dependence of the chain length. The DN and AN values are still linearly correlated but not

816

12.1 Solvent effects on chemical reactivity

in the order as it would be expected from the increasing inductive effect (see Figure 12.1.15 and Table 12.1.13). Despite the different anion size and donor strength from PF6− and NTf2− a parallel displacement of the linear correlation can be observed. Influences from the sterical hindrance of the side chain or the size of the anion ( r PF- ≥ r NTf- ) and an 6 2 ordering effect from side chain stacking must be taken into account. More data for different anions and especially for the structure of ionic liquids in the liquid state is needed for a correct interpretation. Acceptor numbers determined from Kamlet-Taft parameters,33 Raman spectroscopy216 and 31P-NMR217-219 were already reported for ionic liquids. Table 12.1.14 compiles some values for AN from literature. The apparent donor and acceptor numbers established by our approach do not resemble the previously reported values for ionic liquids. The main difference lies in the mutual influence of cations and anions, which are not taken into account by the other authors. Calculating acceptor numbers without considering the influence of the counter ion ANs comparable to values determined by other methods are obtained. Polarity scales like Kamlet-Abboud-Taft and Reichardt's ET do not consider this ionic interaction. The same is true for the calculation of AN for ionic liquids by 31PNMR. Any probe molecule dissolved in an ionic liquid is dependent on the donor and acceptor properties of the ionic liquid. Therefore the chemical shift (δP) of the probe triethylphosphine oxide is dependent on the solvent used. Using conventional solvents the donor property of a solvent is negligible, but not in ionic liquids, were the solvation shell of the probe molecule coordinated to the cation (Lewis acid) consists of anions (Lewis base). Therefore all previously reported acceptor numbers are too high since the lowering effect of the anion is not considered. To visualize the importance of mutual interactions to acid-base considerations, one might compare AN and DN (representing Lewis acidities and basicities) with “simple” Brønsted relations. Table 12.1.14. Comparison of AN values determined by different approaches. Cation

Anion

AN ref.218

AN ref.33

AN calc. Eq. E

AN ref.216

AN calc. Eq. I

NTF2−

30.05

25.99

25.20

2.37

C4C1im

+

BF4−

29.26

28.77

26.90

4.55

C4C1im

+

PF6− −

29.66

29.18

27.70

12.37

23.41

−

26.90

−

C4C1im+

C4C1im+ C8C1im

+

C8C1im+ C8C1im

+

Cl

Cl-AlCl3− Cl-GaCl3− Cl-InCl3−

91.81 45.85 57.11

Taking H3BO3 for example, which is a very weak acid in aqueous solutions (i.e., its grade of deprotonation is very low) becomes strongly deprotonated in liquid ammonia and is acting in reactions accordingly in such media. On the other hand, strong bases will lose their basicity in liquid ammonia. The situation obviously becomes reversed using acidic media like water-free acetic acid as solvents.

Wolfgang Linert, Markus Holzweber*, and Roland Schmid+

817

These results indicate that ionic liquid cations and anions cannot be discussed separately; the mutual influence of the counter ion has to be considered. That means that the acceptor (donor) properties are not only a function of the cation (anion), as it is usually suggested for the Kamlet-Taft parameters α and β, but also a function of the anion (cation). Increasing the basicity, e.g., from [BF4]− to [Cl]− the accepting ability is reduced. Increasing the acidity, e.g., from [S2;2;2]+ to [chol]+ the donating ability of [NTf2]− is reduced. The polarity of ionic liquids is often described to behave, depending on the ion combination, like conventional solvents220 e.g., C4C1im+ based ionic liquids are usually compared to lower alcohols.221 The presented results clearly show that ionic liquids cannot be considered to behave like conventional solvents; they have to be regarded as a unique class of solvents. DN and AN of cations and anions are influenced by the solvent.11,9 Based on this fact and considering ionic liquids as cations (anions) solvated by anions (cations) the simple concept of mutual interactions in ionic liquids has to be considered. For solvent describing scales this has not been taken into account (as for most reactions this can be neglected), however, it leads to the fact that basicity and acidity related scales are usually not in a simple relationship. For example, without this mutual interaction, DN and AN are not simply related (for example linearly dependent) to each other like pKA and corresponding pKB values are pKA + pKB = pKSolvent (i.e., the negative log of the ion-product) for protic solvents.

12.1.8 THE FUTURE OF THE PHENOMENOLOGICAL APPROACH Originally, the empirical solvent parameters have been introduced to provide guidelines for the comparison of different solvent qualities and for an orientation in the search for an understanding of the complex phenomena in solution chemistry. Indeed, the choice of the right solvent for a particular application is an everyday decision for the chemist: which solvent should be the best to dissolve certain products, and what solvent should lead to increased reaction yields and/or rates of a reaction? In the course of time, however, a rather sophisticated scheme has developed of quantitative treatments of solute-solvent interactions in the framework of LSERs.222 The individual parameters employed were imagined to correspond to a particular solute-solvent interaction mechanism. Unfortunately, as it turned out, the various empirical polarity scales feature just different blends of fundamental intermolecular forces. As a consequence, we note, alas with melancholy, that the era of combining empirical solvent parameters in multiparameter equations, in a scientific context, is beginning to fade away. As a matter of fact, solution chemistry research is increasingly being occupied by theoretical physics in terms of molecular dynamics (MD) and Monte Carlo (MC) simulations, the integral equation approach, etc. In the authors’ opinion, it seems that further use of the empirical parameters should more return to the originally intended purpose, emphasizing more the qualitative aspects rather than to devote too much effort to multilinear regression analyses based on parameters quoted to two decimal places. Admittedly, such a scheme may nevertheless still be used to get some insight concerning the nature of some individual solvent effect as in the

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12.1 Solvent effects on chemical reactivity

recent case of an unprecedented positive wavelength shift in the solvatochromism of an aminobenzodifuranone.223 The physical approach, though still in its infancy, has been helping us to see the success of the phenomenological approach in a new light. Accordingly, the reason for this well documented and appreciated success can be traced back to the following features • The molecular structure and the molecular size of many common solvents are relatively similar. The majority belongs to the so-called select solvents having a single dominant bond dipole, which, in addition, is typically hard, viz. an O− or N− donor. For example, if also soft donors (e.g., sulfur) had been employed to a larger extent, no general donor strength scale could have been devised. Likewise, we have seen that solvents other than the select ones complicate the issue. • As it runs like a thread through the present treatment, various cancellations and competitions (enthalpy/entropy, repulsion/attraction, etc.) appear to be conspiring to make molecular behavior in complex fluids seemingly simple. Notwithstanding this, the phenomenological approach will remain a venerable cornerstone in the development of unraveling solvent effects. Only time will tell whether a new generation of solvent indices will arise from the physical approach.

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L. Perera and M. L. Berkowitz, J. Chem. Phys., 96, 3092 (1992). D. V. Matyushov, Mol. Phys., 79, 795 (1993). H. Heitele, P. Finckh, S. Weeren, F. Pöllinger, and M. E. Michel-Beyerle, J. Phys. Chem., 93, 5173 (1989). E. Vauthey and D. Phillips, Chem. Phys., 147, 421 (1990). H. B. Kim, N. Kitamura, Y. Kawanishi, and S. Tazuke, J. Am. Chem. Soc., 109, 2506 (1987). F. D. Lewis and B. E. Cohen, J. Phys. Chem., 98, 10591 (1994). A. M. Swinnen, M. Van der Auweraer, F. C. De Schryver, K. Nakatani, T. Okada, and N. Mataga, J. Am. Chem. Soc., 109, 321 (1987). D. V. Matyushov and R. Schmid, Chem. Phys. Lett., 220, 359 (1994). D. V. Matyushov and R. Schmid, Mol. Phys., 84, 533 (1995). D. V. Matyushov and R. Schmid, J. Phys. Chem., 98, 5152 (1994). C. M. Elliott, D. L. Derr, D. V. Matyushov, and M. D. Newton, J. Am. Chem. Soc., 120, 11714 (1998). D. L. Derr and C. M. Elliott, J. Phys. Chem. A, 103, 7888 (1999). P. Vath, M. B. Zimmt, D. V. Matyushov, and G. A. Voth, J. Phys. Chem. B, 103, 9130 (1999). M. Born, Z. Phys., 1, 45 (1920). B. E. Conway, Ionic Hydration in Chemistry and Biophysics, Elsevier, Amsterdam, 1981. J. F. Böttcher, Theory of Electric Polarization, Elsevier, Amsterdam, 1973, Vol. 1. W. M. Latimer, K. S. Pitzer, and C. M. Slansky, J. Chem. Phys., 7, 108 (1939). A. Voet, Trans. Faraday Soc., 32, 1301 (1936). A. A. Rashin and B. Honig, J. Phys. Chem., 89, 5588 (1985). R. H. Stokes, J. Am. Chem. Soc., 86, 979 (1964); J. Am. Chem. Soc., 86, 982 (1964). K. J. Laidler and C. Pegis, Proc. R. Soc., A241, 80 (1957). B. E. Conway and E. Ayranci, J. Solution Chem., 28, 163 (1999). B. Roux, H. A. Yu, and M. Karplus, J. Phys. Chem., 94, 4683 (1990). M. Mezei and D. L. Beveridge, J. Chem. Phys., 74, 6902 (1981). Y. Marcus, J. Solution Chem., 12, 271 (1983). Y. Marcus, Chem. Rev., 88, 1475 (1988). D. Y. C. Chan, D. J. Mitchell and B. W. Ninham, J. Chem. Phys., 70, 2946 (1979). L. Blum and W. R. Fawcett, J. Phys. Chem., 96, 408 (1992). W. R. Fawcett, J. Phys. Chem., 97, 9540 (1993). A. M. Pendás, A. Costales, and V. Luana, J. Phys. Chem. B, 102, 6937 (1998). M. O'Keeffe and B. G. Hyde, Structure and Bonding in Crystals, Academic Press, New York, 1981, Vol. 1, p. 227. W. H. Baur, Cryst. Rev., 1, 59 (1987). B. S. Gourary and F. J. Adrian, Solid State Phys., 10, 127 (1960). S. W. Rick and B. J. Berne, J. Am. Chem. Soc., 116, 3949 (1994). J. K. Hyun and T. Ichiye, J. Chem. Phys., 109, 1074 (1998). J. K. Hyun and T. Ichiye, J. Phys. Chem. B, 101, 3596 (1997). D. V. Matyushov and B. M. Ladanyi, J. Chem. Phys., 110, 994 (1999). A. Papazyan and A. Warshel, J. Chem. Phys., 107, 7975 (1997). D. W. Smith, J. Chem. Educ., 54, 540 (1977). G. E. McManis, A. Gochev, R. M. Nielson, and M. J. Weaver, J. Phys. Chem., 93, 7733 (1989). I. Rips, J. Klafter, and J. Jortner, J. Chem. Phys., 88, 3246 (1988). W. R. Fawcett and L. Blum, Chem. Phys. Lett., 187, 173 (1991). H. Heitele, P. Finckh, S. Weeren, F. Pollinger, and M. E. Michel-Beyerle, J. Phys. Chem., 93, 325 (1990). R. Lungwitz and S. Spange, ChemPhysChem., 13, 1910 (2012) T. Fujisawa, M. Fukuda, M. Terazima and Y. Kimura, J. Phys. Chem. A, 110, 6164 (2006) T. A. Zawodzinski and R. A. Osteryoung, Inorg. Chem., 28, 1710 (1989) J. Estager, A. A. Oliferenko, K. R. Seddon and M. Swadzba-Kwasny, Dalton Trans., 39, 11382 (2010) M. Schmeisser, P. Illner, R. Puchta, A. Zahl and R. van Eldik, Chem. Eur. J., 18, 10969 (2012) C. Reichardt, Green. Chem., 7, 339 (2005) L. Crowhurst, P. R. Mawdsley, J. M. Perez-Arlandis, P. A. Salter and T. Welton, Phys. Chem. Phys., 5, 2790, (2003) Quantitative Treatments of Solute/Solvent Interactions, P. Politzer and J. S. Murray, Eds., Elsevier, Amsterdam, 1994. A. A. Gorman, M. G. Hutchings, and P. D. Wood, J. Am. Chem. Soc., 118, 8497 (1996).

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12.2 SOLVENT EFFECTS ON FREE RADICAL POLYMERIZATION Michelle L. Coote and Leesa M. Smith Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia

12.2.1 INTRODUCTION Free radical polymerization is one of the most useful and lucrative fields of chemistry ever discovered − recent years have seen a tremendous increase in research into this area once considered a mature technological field. Free radical synthetic polymer chemistry is tolerant of diverse functionality and can be performed in a wide range of media. Emulsion and suspension polymerizations have been established as important industrial processes for many years. More recently, the 'green' synthesis of polymers has diversified from aqueous media to supercritical fluids and the fluorous biphase. Moreover, the last few decades has seen the development of techniques such as nitroxide mediated polymerization (NMP),1-3 atom transfer radical polymerization (ATRP),4-6 and reversible addition fragmentation chain transfer (RAFT)7-9 polymerization, which can allow for intricate control of the polymer molecular weight distribution and chain architecture,10 as well as considerable progress towards stereocontrolled radical polymerization using Lewis acids, polar solvents and other additives.11 An enduring feature of the research literature on free radical polymerization has been studies into specific solvent effects. In many cases the influence of solvent is small, however, it is becoming increasingly evident that solvent effects can be used to assist in controlling the polymerization reaction, both at the macroscopic and at the molecular levels. The purpose of this chapter is to give a brief introduction to the types of specific solvent effect that can be achieved in both free radical homo- and copolymerizations. 12.2.2 HOMOPOLYMERIZATION Free radical polymerization can be conveniently codified according to the classical chain reaction steps of initiation, propagation, transfer and termination. In cases where a significant solvent effect is operative then the effect is normally exerted in all of these steps. However, for the purpose of facilitating discussion this chapter is broken down into these specific reaction steps. 12.2.2.1 Initiation Solvent effects on the initiation reaction are primarily on the rate of decomposition of initiator molecules into radicals and in the efficiency factor, f, for polymerization. However, in some instances the solvent plays a significant role in the initiation process, for example, in initiation reactions with t-butoxy radical where the primary radical rarely initiates a chain but instead abstracts a hydrogen atom from the solvent medium, which subsequently initiates the chain.12 The consequence of this is that the polymer chains contain fragments of solvent. As the stability of the chains to thermal and photochemical degradation is governed, in part, by the nature of the chain ends then the solvent moieties within the chain can have a substantial impact on the material performance of the polymer. The efficiency factor, f, decreases as the viscosity of the reaction medium increases.13 This is caused by

824

12.2 Solvent effects on free radical polymerization

an increase in the radical lifetime within the solvent cage, leading to an increased possibility of radical-radical termination. In this regard the diffusion rates of the small radicals becomes an important consideration and Terazima and co-workers,14,15 have published results indicating that many small radicals diffuse slower than expected. They have attributed this to specific interactions between radical and solvent molecules. 12.2.2.2 Propagation and stereochemistry The ability of solvents to affect the homopropagation rate of many common monomers has been widely documented. In the 1960s, Bamford and Brumby16 showed that the propagation rate (kp) of methyl methacrylate (MMA) at 25°C was sensitive to a range of aromatic solvents. Burnett et al.17 found that the kp of styrene (STY) was depressed by increasing concentrations of benzonitrile, bromobenzene, diethyl phthalate, dinonyl phthalate, and diethyl malonate, while in other studies,18,19 they found that the kp for MMA was enhanced by halobenzenes and naphthalene. Zammit et al.20 have shown that solvents capable of hydrogen-bonding, such as, benzyl alcohol and N-methyl pyrrolidone have a small influence on both the activation energy (Ea) and pre-exponential factor (A) in STY and MMA homopropagation reactions. These are but a few of the many instances of solvent effects in the homopolymerization reactions of two typical monomers, STY and MMA. For these monomers, solvent effects are relatively small, and this is indicative of the majority of homopropagation reactions. A summary of available literature data for STY and MMA is provided in Tables 12.2.1 and 12.2.2, respectively. Table 12.2.1. Solvent effects on the propagation rate coefficient (kp, L.mol-1.s-1) of styrene Temperature, oC

kp

Reference

Bulk

25

86

21

Ethanol (25-75%)

25

76-101

22

Methanol (25%)

25

70

22

Diethyl malonate (44%, 72%)

26.5

101,134

20

Diethyl phthalate (44%, 72%)

26.5

91,88

20

Bromobenzene (44%, 72%)

26.5

87,88

20

Benzonitrile (44%, 72%)

26.5

80,84

20

Chlorobenzene (44%, 72%)

26.5

85,82

20

DMSO (44%)

26.5

85

20

Benzyl alcohol (44%, 72%)

Solvent

26.5

108, 137

20

Acetonitrile (50%)

25

70

23

Dimethyl formamide (50%)

25

70

23

Toluene (50%)

25

80

23

Anisole (50%)

25

77

23

Methyl isobutyrate (50%)

25

73

23

Bromobenzene (50%)

25

75

23

Michelle L. Coote and Leesa M. Smith

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Table 12.2.1. Solvent effects on the propagation rate coefficient (kp, L.mol-1.s-1) of styrene Temperature, oC

kp

Reference

Benzene (50%)

25

77

23

Mesitylene (50%)

25

82

23

1,2-Dichloroethane (50%)

25

74

23

Cyclohexane (50%)

25

97

23

Solvent

Table 12.2.2. Solvent effects on the propagation rate coefficient (kp, L.mol-1.s-1) of methyl methacrylate Solvent Bulk Ethanol (25%, 75%)

Temperature, o C

kp

Reference

25

323

24

25

292-414

22

Diethyl malonate (35%, 67%)

26.5

383, 293

20

Diethyl phthalate (35%, 67%)

26.5

342, 405

20

Bromobenzene (35%, 67%)

26.5

274, 358

20

Benzonitrile (35%, 67%)

26.5

344, 374

20

Chlorobenzene (35%, 67%)

26.5

282, 315

20

DMSO (35%, 67%)

26.5

433, 550

20

Benzyl alcohol (35%, 67%)

26.5

446, 405

20

Acetonitrile (50%)

25

295

23

Dimethyl formamide (50%)

25

321

23

Toluene (50%)

25

269

23

Anisole (50%)

25

293

23

Methyl isobutyrate (50%)

25

258

23

Bromobenzene (50%)

25

304

23

Benzene (50%)

25

266

23

Mesitylene (50%)

25

285

23

1,2-Dichloroethane (50%)

25

267

23

Bulk

25

300

23

Methyl isobutyrate (27%, 57%, 58%)

40

537, 593, 597

25

Methyl isobutyrate (57%)

30

538

25

Phenylethyl isobutyrate (25%, 57%, 79%)

40

606, 714, 819

25

Phenylethyl isobutyrate (27%, 79%)

60

993, 1308

25

Phenylethyl isobutyrate (25%, 79%)

80

1524, 1947

25

826

12.2 Solvent effects on free radical polymerization

Table 12.2.2. Solvent effects on the propagation rate coefficient (kp, L.mol-1.s-1) of methyl methacrylate Solvent

Temperature, o C

kp

Reference

Tetralin (15%, 36%, 56%, 68%, 78%)

40

538, 595, 676, 687, 726, 815

25

Toluene (14%, 36%, 56%, 79%)

40

526, 561, 596, 628, 639

25

Toluene (14%, 36%, 56%, 79%)

25

377

25

THF (15%, 35%, 57%, 68%, 79%)

40

524, 548, 551, 583, 561

25

Bulk

40

527

25

1-Butyl-3-methylimidazolium hexafluorophosphate ([bmin][PF6]) (0%, 10%, 20%, 50%, 60%)

25

337, 375, 436, 683, 806

26, 27

([bmin][PF6]) (0%, 20%, 50%)

40

674, 832, 1249

26

([bmin][PF6]) (0%, 20%, 50%)

50

496, 646, 988

26

([bmin][PF6]) (0%, 20%, 50%)

60

855, 1069, 1630

26

While most solvent effects on propagation in radical polymerization are relatively small, in some instances much larger effects are observed, especially in cases where specific interactions such as H-bonding or ionization occur. Examples of this type include the polymerization of N-vinyl-2-pyrrolidone (where water has been found to dramatically increase kp)28 and the polymerization of acrylamide29 and acrylic acid30 (where pH plays a strong role). The largest solvent effects observed on kp for homopropagations have been for vinyl acetate31 and for α-(hydroxymethyl) ethyl acrylate.33 In the former case, the radical is highly unstable and some form of π-complexation between the vinyl acetate radical and aromatic solvents seems plausible. However, the large solvent effect cannot be explained by a simple radical stabilization argument (because of the early transition state for free radical propagation reactions)32 and again the evidence points towards a change in the geometry of the transition state. The solvent effects on π-(hydroxymethyl) ethyl acrylate are in the order of 300% on kp and there are large changes in both the Arrhenius parameters as the solvent medium is changed.33 More generally, there is only limited data available for the Arrhenius parameters for homopropagation reactions in different solvents but this typically indicates that both the activation energy and pre-exponential factor are affected by solvent.20,33 Solvent effects on propagation can be loosely divided into two categories. The first is when the solvent causes genuine changes to the rate of the propagation step through, for example, its ability to stabilize or destabilize the transition state of the reaction via electrostatic effects, H-bonding and so forth. The wide variation in the propagation rate coefficient of the (meth)acrylic acids and their salts with solvent, pH and, were relevant counterion, are an example of this,30 as are most if not all of the other examples outlined

Michelle L. Coote and Leesa M. Smith

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above. When the solvent molecules directly interact with the transition state, there is the potential for solvents to affect the stereochemistry of the resulting polymer. This has at times been exploited to achieve some degree of stereocontrol. For example, bulky fluoroalcohols have been used to increase the syndiotacticity of methacrylate polymers through hydrogen bonding to their ester side chains and increasing their effective steric bulk.34 Conversely, aromatic solvents can be used to disrupt π bonding networks between bulky aromatic side chains and thereby reverse the inherent stereocontrol in such systems.35 The nature of the solvent can have a dramatic impact on the effectiveness of Lewis acids as stereocontrol agents,36 due to their ability to competitively coordinate or solvate the Lewis acid and thereby alter the ability of the Lewis acid to coordinate with the polymer radical.30,37 The second category of solvent effects on propagation occurs when the solvent affects the measured propagation rate coefficient, without actually changing the genuine propagation rate coefficient itself. This can occur if there is preferential solvation of either the monomer (which is always present as a solvent) or the added solvent around the growing polymer chain. As a result, the local concentration “seen” by the propagating radical is different to the (known) bulk monomer concentration, and hence the propagation rate is higher or lower than expected based on the rate coefficient and the bulk concentration. This type of effect has been termed a “Bootstrap” effect in the literature.38 It has also been suggested that in some instances the growing polymer coil can “shield” the radical chainend resulting in a low monomer concentration. This shielding effect would be expected to be greatest in poor solvents (hence a tighter coil).39 For methyl methacrylate and styrene, the largest solvent effects on propagation seem to be in the order of a 40% change in kp.23,40 In some solvents there seems to be reasonably strong evidence that the solvent does cause changes to the geometry of the transition state (e.g., dimethylformamide and acetonitrile in styrene polymerization40 and in liquid carbon dioxide it appears that the 40% change in kp for methyl methacrylate can be ascribed to the poor solvent medium).41 Finally, it is worth bearing in mind that occasionally measured solvent effects on kp values can be caused by artifacts from the pulsed laser polymerization (PLP) experiment used to determine them. A good example of this is in acrylate polymerizations where back-biting reactions lead to a mixture of chain-end and mid-chain propagation reactions occurring, each with distinct rate coefficients.42 The observed overall propagation rate coefficient depends on the fraction of each type of process present, and this in turn can be altered by the conditions of the experiment used to determine kp. In particular, at very fast laser flashing rates, the probability of back-biting becomes minimal and end-chain propagation dominates, while at slower laser flashing rates mixtures are observed. In this latter case, even an inert solvent can affect the relative populations of end-chain and mid-chain radicals, simply by diluting the monomer and allowing (unimolecular) back-biting to better compete with (bimolecular) propagation. This dilution effect can thus cause a change to the observed kp without actually changing the individual rate coefficients values for any of the reactions. As a result, early PLP studies showed significant effects of toluene on the kp values for homologous series of acrylate monomers to the extent that, in bulk these values increased with the size of the ester side chain, while in toluene they decreased by a

828

12.2 Solvent effects on free radical polymerization

similar amount.43,44 When faster lasers became available the experiments were repeated at 500Hz, at which rate end-chain propagation is dominant irrespective of monomer concentration, these solvent effects completely disappeared, confirming that the earlier results were an artifact of the experiment.42 12.2.2.3 Transfer Many solvents undergo chain transfer with propagating radicals and thus participate as a reagent in free-radical polymerization. Table 12.2.3 shows some typical chain transfer coefficients for various solvents with styrene and with methyl methacrylate.45 As seen in this table, Cs varies over many orders of magnitude with changes to both the solvent and the monomer. Broadly speaking, in abstraction reactions, the size of the transfer coefficient depends largely on the type of bond being broken, the relative stabilities of the reactant and product radicals, and also importantly the polarity of the transition state.46 In particular, Odian47 has suggested that polar interactions contribute to the high transfer coefficient for styrene with carbon tetrachloride, and more recent work supports this idea.48 Table 12.2.3. Chain transfer coefficients (Cs = ktr/kp) for various solvents with styrene and methyl methacrylate45 Cs x104 (60°C) Carbon tetrachloride Chloroform

Styrene

Methyl methacrylate

90

2.40

0.5

1.77

Toluene

0.125

0.20

Cyclohexane

0.031

0.10*

Benzene

0.023

0.040

*80oC

Solvent effects on the rate coefficients for chain transfer have not received much attention. Significant solvent effects have been observed in catalytic chain transfer reactions using cobaloximes where the transfer reaction appears (in some cases at least) to be diffusion controlled and therefore the speed of the reaction is governed, in part, by the viscosity of the polymerizing medium.49 In transfer reactions involving organometallic reagents then solvent effects may become important where ligand displacement may occur. This is thought to happen in catalytic chain transfer when pyridine is utilized as a solvent.50 There have been only limited studies of the effect of solvent on chain transfer to monomer (CM), and these indicate some minor effects in some solvents, especially those that differ in their polarity to that of the monomer. Examples for transfer to methyl methacrylate and are summarized in Table 12.2.4.

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Table 12.2.4. Chain transfer to monomer (CM) for various solvents with styrene and methyl methacrylate Solvent

Temperature, oC

CMx104

Reference

Methyl methacrylate None

70

0.20, 0.23, 0.265, 0.30, 0.45

51, 52, 53, 54, 55

Ethyl acetate

70

0.17

54

Toluene

70

0.29

54

None

75

0.33

54

Ethyl acetate

75

0.27

54

Methyl ethyl ketone

75

0.60

54

Benzene

75

0.70

54

None

70

0.6, 0.6, 0.96, 1.16, 1.35

52, 55, 56, 57

Ethyl acetate

70

0

54

Benzene

70

2.0

54

None

75

1.6

54

Ethyl acetate

75

0

54

Methyl ethyl ketone

75

5.0

54

Benzene

75

5.0

54

Styrene

12.2.2.4 Termination The solvent effects on the termination reaction have been extensively studied. In early work, it was established that the radical-radical termination reaction is diffusion controlled and the efficacy of termination was found to have a strong relationship with the solvent viscosity.58 Subsequently, more complex models have been developed accounting for the quality of the solvent (hence the size of the polymer coil).59 The current debate centers on the relative roles played by segmental and translational diffusion at different stages of conversion for a variety monomers. Clearly in both cases the nature of the solvent becomes important. Solvent effects are known to play a significant role in determining the strength and onset conversion of the gel effect. This work originated in the classical paper by Norrish and Smith60 who reported that poor solvents cause an earlier gel effect in methyl methacrylate polymerization. Careful studies of the gel effect by Torkelson and coworkers61 have reinforced observations made by Cameron and Cameron62 over four decades ago concluding that termination is hindered in poor solvents due to formation of more tightly coiled polymer radicals.

12.2.3 COPOLYMERIZATION When solvent effects on the propagation step occur in free-radical copolymerization reactions, they result not only in deviations from the expected overall propagation rate, but

830

12.2 Solvent effects on free radical polymerization

also in deviations from the expected copolymer composition and microstructure. This may be true even in bulk copolymerization, if either of the monomers exerts a direct effect or if strong cosolvency behavior causes preferential solvation. A number of models have been proposed to describe the effect of solvents on the composition, microstructure and propagation rate of copolymerization. In deriving each of these models, an appropriate base model for copolymerization kinetics is selected (such as the terminal model or the implicit or explicit penultimate models), and a mechanism by which the solvent influences the propagation step is assumed. The main mechanisms by which the solvent (which may be one or both of the comonomers) can affect the propagation kinetics of free-radical copolymerization reactions are as follows: (1) Polarity effect (2) Radical-solvent complexes (3) Monomer-solvent complexes (4) Bootstrap effect In this chapter we explain the origin of these effects, show how copolymerization models for these different effects may be derived, and review the main experimental evidence for and against these models. Throughout this review the baseline model for copolymerization is taken as the terminal or Mayo-Lewis model.63 This model can be used to derive well-known expressions for copolymer composition and copolymerization propagation kinetics. Deviations from this model have often been interpreted in terms of either solvent effects or penultimate unit effects, although the two are by no means mutually exclusive. Deviations which affect both the copolymer composition and propagation kinetics have been termed explicit effects by Fukuda64 in deriving penultimate unit models, whereas deviations from the kinetics without influencing the copolymer composition have been termed implicit effects. In this review we use the same terminology with respect to solvent effects: that is, a solvent effect on kp only is termed an implicit solvent effect, while a solvent effect on composition, microstructure and kp is termed explicit. The relatively recent discovery by Fukuda and co-workers65 of the seemingly general failure of the terminal model to predict kp, even for bulk copolymerizations that follow the terminal model composition equation, led them to propose an implicit penultimate unit effect as a general phenomenon in free-radical copolymerization kinetics. We conclude this review with a brief examination of the possibility that an implicit solvent effect, and not an implicit penultimate unit effect, may instead be responsible for this failure of the terminal model kp equation. 12.2.3.1 Polarity effect 12.2.3.1.1 Basic mechanism One type of solvent effect on free-radical addition reactions such as the propagation step of free-radical polymerization is the so-called “polarity effect”. This type of solvent effect is distinguished from other solvent effects, such as complexation, in that the solvent affects the reactivity of the different types of propagation steps without directly participating in the reaction. The mechanism by which this could occur may be explained as follows. The transition states of the different types of propagation steps in a free-radical copolymerization may be stabilized by charge transfer between the reacting species. The

Michelle L. Coote and Leesa M. Smith

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amount of charge transfer, and hence the amount of stabilization, is inversely proportional to the energy difference between the charge transfer configuration, and the product and reactant configurations that combine to make up the wave function at the transition state.66 Clearly, the stability of the charge transfer configuration would differ between the crossand homopropagation reactions, especially in copolymerization of highly electrophilic and nucleophilic monomer pairs. Hence, when it is significant, charge transfer stabilization of the transition state occurs to different extent in the cross- and homopropagation reactions, and thus exerts some net effect on the monomer reactivity ratios. Now, it is known that polar solvents can stabilize charged species, as seen in the favorable effect of polar solvents on both the thermodynamics and kinetics of reactions in which charge is generated.67 Therefore, when charge transfer in the transition state is significant, the stability of the charge transfer species and thus the transition state would be affected by the polarity of the solvent, and thus a solvent effect on reactivity ratios would result. 12.2.3.1.2 Copolymerization model There are two cases to consider when predicting the effect of solvent polarity on copolymerization propagation kinetics: (1) the solvent polarity is dominated by an added solvent and polarity is thus independent of the comonomer feed ratio, or (2) the solvent polarity does depend on the comonomer feed ratio, as it would in a bulk copolymerization. In the first case, the effect on copolymerization kinetics is simple. The monomer reactivity ratios (and additional reactivity ratios, depending on which copolymerization model is appropriate for that system) would vary from solvent to solvent, but, for a given copolymerization system they would be constant as a function of the monomer feed ratios. Assuming of course that there were no additional types of solvent effect present, these copolymerization systems could be described by their appropriate base model (such as the terminal model or the explicit or implicit penultimate models), depending on the chemical structure of the monomers. In the second case, the effect of the solvent on copolymerization kinetics is much more complicated. Since the polarity of the reacting medium would vary as a function of the comonomer feed ratios, the monomer reactivity ratios would no longer be constant for a given copolymerization system. To model such behavior, it would be first necessary to select an appropriate base model for the copolymerization, depending on the chemical structure of the monomers. It would then be necessary to replace the constant reactivity ratios in this model by functions of the composition of the comonomer mixture. These functions would need to relate the reactivity ratios to the solvent polarity, and then the solvent polarity to the comonomer feed composition. The overall copolymerization kinetics would therefore be very complicated, and it is difficult to suggest a general kinetic model to describe these systems. However, it is obvious that such solvent effects would cause deviations from the behavior predicted by their appropriate base model and might therefore account for the deviation of some copolymerization systems from the terminal model composition equation. 12.2.3.1.3 Evidence for polarity effects in propagation reactions The idea of charge separation in the transition state of the propagation step of free radical polymerization reactions, as suggested by Price,68 was discounted by Mayo and Walling69

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12.2 Solvent effects on free radical polymerization

and many subsequent workers.70 Their rejection of this idea was based upon the absence of any unambiguous correlation between the reactivity ratios of a system and the relative permittivity of the solvent. For instance, in the copolymerization of STY with MMA, it was reported that the reactivity ratios were independent of small quantities of water, ethylbenzene, dodecyl mercaptan or hydroquinone, or the presence or absence of air63,71,72 and were thus unaffected by the relative permittivity of the system. In contrast, other studies have found a relationship between relative permittivity and the reactivity ratios in specific systems.73,74 The apparent lack of a general relationship between the relative permittivity of the system and the monomer reactivity ratios does not necessarily discount a polarity effect on reactivity ratios. A polarity effect is only expected to occur if the charge transfer configurations of the transition state are sufficiently low in energy to contribute to the ground state wave function. Since this is not likely to occur generally, a comprehensive correlation between reactivity ratios and the solvent relative permittivity is unlikely. Furthermore, even in systems for which a polarity effect is operating, a correlation between solvent relative permittivity and monomer reactivity ratios may be obscured by any of the following causes. • The operation of additional types of solvent effects, such as a Bootstrap effect, that would complicate the relationship between solvent polarity and reactivity ratios. • Errors in the experimental database from which the correlation was sought. • The recognized inadequacy of simple reactivity − relative permittivity correlations, that take no account of specific interactions between the solvent and solute molecules.67 In fact, recent theoretical66 and experimental studies75 of small radical addition reactions indicate that charge separation does occur in the transition state when highly electrophilic and nucleophilic species are involved. It is also known that copolymerization of electron donor-acceptor monomer pairs are solvent sensitive, although this solvent effect has in the past been attributed to other causes, such as a Bootstrap effect (see Section 12.2.3.4). Examples of this type include the copolymerization of styrene with maleic anhydride76 and with acrylonitrile.77 Hence, in these systems, the variation in reactivity ratios with the solvent may (at least in part) be caused by the variation of the polarity of the solvent. In any case, this type of solvent effect cannot be discounted, and should thus be considered when analyzing the copolymerization data of systems involving strongly electrophilic and nucleophilic monomer pairs. 12.2.3.2 Radical-solvent complexes 12.2.3.2.1 Basic mechanism Solvents can also interfere in the propagation step via the formation of radical-solvent complexes. When complexation occurs, the complexed radicals are more stable than their corresponding uncomplexed-radicals, as it is this stabilization that drives the complexation reaction. Thus, in general, one might expect complexed radicals to propagate more slowly than their corresponding free-radicals, if indeed they propagate at all. However, in the special case that one of the comonomers is the complexing agent, the propagation rate of the complexed radical may instead be enhanced, if propagation through the complex

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offers an alternative less-energetic reaction pathway. In any case, the complexed radicals would be expected to propagate at a rate different to their corresponding free-radicals, and thus the formation of radical-solvent complexes would affect the copolymerization propagation kinetics. 12.2.3.2.2 Copolymerization model A terminal radical-complex model for copolymerization was formulated by Kamachi.70 He proposed that a complex is formed between the propagating radical chain and the solvent (which may be the monomer) and that this complexed radical has a different propagation rate constant to the equivalent uncomplexed radical. Under these conditions there are eight different propagation reactions in a binary copolymerization, assuming that the terminal unit is the only unit of the chain affecting the radical reactivity. These are as follows.

RMi + Mj

RMi S + Mj

kij

kcij

RMiMj or RMiMj S where: i,j = 1 or 2

RMiMj or RMiMj S where: i,j = 1 or 2

There are also two equilibrium reactions for the formation of the complex:

RMi + S

Ki

RMi S where: i,j = 1 or 2

Applying the quasi-steady-state and long-chain assumptions to the above reactions, Kamachi derived expressions for r i and k ii , which are used in place of ri and kii in the terminal model equations for composition and kp: 1 + s ci K i [ C i ] 1 + s ci K i [ C i ] - and r i = r i ------------------------------------------------k ii = k ii ------------------------------1 + Ki [ Ci ] 1 + ( r i ⁄ r ci ) s ci K i [ C i ] where: ri = kii/kij; r ic = kcii/kcij; s ci = kcii/kii; i, j =1or 2 and i ≠ j

Variants of this model may be derived by assuming an alternative basis model (such as the implicit or explicit penultimate models) or by making further assumptions as to nature of the complexation reaction or the behavior of the complexed radical. For instance, in the special case that the complexed radicals do not propagate (that is, s ci = 0 for all i), the reactivity ratios are not affected (that is, r i = ri for all i) and the complex formation serves only removal of radicals (and monomer, if monomer is the complexing agent) from the reaction, resulting in a solvent effect that is analogous to a Bootstrap effect (see Section 12.2.3.4). 12.2.3.2.3 Experimental evidence There is certainly strong experimental evidence for the existence of radical-solvent complexes. For instance, Russell78-80 and co-workers collected experimental evidence for radical-complex formation in studies of the photochlorination of 2,3-dimethylbutane in various solvents. In this work, different products were obtained in aliphatic and aromatic

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12.2 Solvent effects on free radical polymerization

solvents, and this was attributed to the formation of a π-complex between the Cl atom and the aromatic solvent. Complex formation was confirmed by flash photolysis.81-84 Complex formation was also proposed to explain experimental results for the addition of trichloromethane radical to 3-phenylpropene and to 4-phenyl-1-butene85 and for hydrogen abstraction of the t-butoxy radical from 2,3-dimethylbutane.86 Complexes between nitroxide radicals and a large number of aromatic solvents have been detected.87-90 Evidence for complexes between polymer radicals and solvent molecules was collected by Hatada et al.,58,91 in an analysis of initiator fragments from the polymerization of MMA-d with AIBN and BPO initiators. They discovered that the ratio of disproportionation is combination depended on the solvent, and interpreted this as evidence for the formation of a polymer radical-solvent complex that suppresses the disproportionation reaction. There is also experimental evidence for the influence of radical-solvent complexes in small radical addition reactions. For instance, Busfield and co-workers92-94 used radicalsolvent to explain solvent effects in reactions involving small radicals, such as t-butoxyl radicals towards various electron donor-electron acceptor monomer pairs. The observed solvent effects were interpreted in terms of complex formation between the t-butoxyl radical and the electron-acceptor monomer, possibly via a sharing of the lone pair on the tbutoxyl oxygen with the π-system of the acceptor monomer. Several workers have invoked frontier orbital theory to rationalize such solvent effects in terms of radical-solvent complex formation, and thus provide a theoretical base.70, 95 Many workers have suggested radical-solvent complexes as an explanation for the influence of aromatic compounds on the homopolymerization of vinyl monomers. For instance, Mayo96 found that bromobenzene acts as a chain transfer agent in the polymerization of STY but is not incorporated into the polymer. He concluded that a complex is formed between the solvent molecule and either the propagating polystyryl radical or a proton derived from it. The influence of halobenzenes on the rate of polymerization of MMA was detected by Burnett et al.19,97,98 They proposed that the efficiency of a number of different initiators increased in various halogenated aromatic solvents and, since enhanced initiator or solvent incorporation into the polymer was not observed, they concluded that initiator-solvent-monomer complex participation affected the initiator efficiency. Henrici-Olive and Olive100-104 suggested that this mechanism was inadequate when the degree of polymerization was taken into account and they proposed instead a charge transfer complex between the polymer radical and aromatic solvent. The polymer radical can form a complex with either the monomer or solvent molecule, but only the former can propagate. Bamford and Brumby,16 and later Burnett et al.,105,106 interpreted their solvent-effects data for kp in terms of this donor-acceptor complex formation between aromatic solvents and propagating radicals. Radical-solvent complexes are expected to be favored in systems containing unstable radical intermediates (such as vinyl acetate) where complexation may lead to stabilization. In this regard, Kamachi et al.31 have noted that solvent effects on vinyl acetate homopolymerization result in a reduced kp. Kamachi et al.107 also measured the absolute rate constants of vinyl benzoate in various aromatic solvents and found that kp increased in the

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order: benzonitrile < ethyl benzoate < anisole < chlorobenzene < benzene < fluorobenzene < ethyl acetate They argued that this trend could not be explained by copolymerization through the solvent or transfer to the solvent because there was no correlation with the solvent relative permittivity or polarity, or with the rate constants for transfer to solvent. However, there was a correlation with the calculated delocalization stabilization energy for complexes between the radical and the solvent, which suggested that the propagating radical was stabilized by the solvent or monomer, but the solvent did not actually participate in the reaction. As noted in the introduction to this section, radical-solvent complexes may enhance the propagation rate if propagation through the complex offers an alternative, less-energetic pathway for propagation. An example of this behavior is found in the homopolymerization of acrylamide. The homopropagation rate coefficient for this monomer shows a negative temperature dependence, which has been explained in terms of radical-complex formation. Pascal et al.29,108 suggested that propagation proceeds via a complex that enhances the propagation rate, and this complex dissociates as temperature increases, thus explaining the normal temperature dependence of the propagation rate at high temperatures. This interpretation was supported by the observation that acrylamide behaves normally in the presence of reagents such as propionamide, which would be expected to inhibit complex formation. Given the experimental evidence for the existence of radical-solvent complexes and their influence on free-radical addition reactions such as homopropagation, it is likely that radical-solvent complexes will affect the copolymerization kinetics for certain copolymerization systems, and indeed many workers have invoked the radical-complex model in order to explain solvent effects in copolymerization. For instance, Heublein and Heublein109 have invoked a radical complex model in combination with a partitioning idea (see Section 12.2.3.4) to explain solvent effects on the copolymerization of vinyl acetate with acrylic acid. More recently, O'Driscoll and Monteiro110 suggested that the effect of benzyl alcohol on the copolymerization of STY-MMA was best described by an RC-type model. This was supported by pulsed-laser studies20 on the homopropagation reactions where Ea values were found to be increased slightly by the presence of benzyl alcohol. Czerwinski (see for example reference111 and references cited therein) has also published a variant of the RC model and has applied his model to a range of copolymerization experimental data. In conclusion, there is a strong experimental evidence for the importance of radical-solvent complexes in a number of specific copolymerization systems, especially when there is a large disparity in the relative stabilities of the different propagating radicals. 12.2.3.3 Monomer-solvent complexes 12.2.3.3.1 Introduction A solvent may also interfere in the propagation step via complexation with the monomer. As was the case with radical-solvent complexes, complexed monomer might be expected to propagate at a different rate to free monomer, since complexation might stabilize the monomer, alter its steric properties and/or provide an alternative pathway for propagation.

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12.2 Solvent effects on free radical polymerization

In examining the effect of such complexation on copolymerization kinetics, there are a number of different mechanisms to consider. In the case that the complex is formed between the comonomers, there are three alternatives: (1) the monomer-monomer complex propagates as a single unit, competing with the propagation of free monomer; (2) the monomer-monomer complex propagates as a single unit, competing with the propagation of free monomer, but the complex dissociates during the propagation step and only one of the monomers is incorporated into the growing polymer radical; (3) the monomer-monomer complex does not propagate, and complexation serves only to alter the free monomer concentrations. In the case that the complex is formed between one of the monomers and an added solvent, there are two further mechanisms to consider: (4) the complexed monomer propagates, but at a different rate to the free monomer; (5) the complexed monomer does not propagate. Models based on mechanisms (1) and (2) are known as the monomermonomer complex participation (MCP) and dissociation (MCD) models, respectively. Mechanisms (3) and (5) would result in a solvent effect analogous to a Bootstrap effect, and will be discussed in Section 12.2.3.4. In this section, we review the MCP and MCD models, and conclude with a brief discussion of specific monomer-solvent interactions. 12.2.3.3.2 Monomer-monomer complex participation model The use of monomer-monomer charge transfer complexes to explain deviations from the terminal model was first suggested by Bartlet and Nozaki,112 later developed by Seiner and Litt,113 and refined by Cais et al.114 It was proposed that two monomers can form a 1:1 donor complex and add to the propagating chain as a single unit in either direction. The complex would be more reactive because it would have a higher polarizability due to its larger π-electron system that can interact more readily with the incoming radical. The complex would also have a higher pre-exponential factor, as a successful attack may be achieved over a wider solid angle.113 The heavier mass of the complex would also serve to increase the pre-exponential factor. In addition to the four terminal model reactions, four complex addition reactions and an equilibrium constant are required to describe the system.

The composition and propagation rate can be expressed in terms of the following parameters.46 f 1 ° ( A 2 B 1 ) r 1 f 1 ° + (A 1 C 2 ) f 2 ° F1 - ------------------------------------------------------------------- = -----f 2 ° ( A 1 B 2 ) r 2 f 2 ° + (A 2 C 1 ) f 1 ° F2

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( A2 B1 ) r1 ( f2 ° ) + ( A1 B2 ) r2 ( f2 ° ) + ( A1 C2 + A2 C1 ) r1 f1 ° f2 ° k p = ----------------------------------------------------------------------------------------------------------------------------------------------( A 2 r 1 f 1 ° ⁄ k 11 ) + ( A 1 r 2 f 2 ° ⁄ k 22 ) where:

A1 = 1 + r1s1cQf1. and A2 = 1 + r2s2cQf2. B1 = 1 + s1c(1 + r1c-1)Qf2. and B2 = 1 + s2c(1 + r2c-1)Qf1. C1 = 1 + r1s1c(1 + r1c-1)Qf1. and C2 = 1 + r2s2c(1 + r2c-1)Qf2. 2Qfi. = {[Q(fj − fi) +1]2 +4Qfi}1/2 − [Q(fi − fj) + 1] and Q = k[M] fi is feed composition of Mi fi. = [Mi.]/[M] ri = kii/kij; ric = kiij/kiji; sic = kiij/kii where: i,j = 1 or 2 and i ≠ j

The applicability of the MCP model to strongly alternating copolymerization has been a long-standing point of contention. In essence, there are two opposing accounts of the strongly alternating behavior observed in copolymers of electron-donor-acceptor (EDA) monomer pairs. In the first account, this behavior has been attributed to the fact that the transition state is stabilized in cross-propagation reaction and destabilized in the homopropagation. Deviations from the terminal model are caused merely by penultimate unit effects. In the second account − the MCP model − the strongly alternating behavior is a result of propagation of a 1:1 comonomer complex which, as seen above, also leads to deviations from the terminal model. An intermediate mechanism, which will be discussed shortly, is the MCD model in which the complex dissociates during the propagation step. The main approach to discriminating between these models has been to compare their ability to describe the copolymerization data of various explicit systems, and to study the effect of added solvents on their behavior. Unfortunately, both approaches have led to inconclusive results. As an example, the system STY with maleic anhydride (MAH) has been perhaps the most widely studied EDA system and yet there is still uncertainty concerning the role of the EDA complex in its propagation mechanism. Early studies115,116 concluded that its behavior was best modelled by a penultimate model, despite the spectroscopic evidence for EDA complexes in this system. Later Tsuchida et al.117,118 fitted an MCP model, based on the evidence that the rate went through a maximum at 1:1 feed ratio in benzene or CCl4 but in strong donor solvents no such maximum occurred and instead the rate increased with the content of MAH in the feed. They argued that maximum in rate at 1:1 feed ratios was due to the fact that propagation occurred via the complex, which had a maximum concentration at this point. In strong donor solvents, the maximum rate moved to higher concentrations of MAH due to competition between the donor and STY for complexation with the MAH. However, a few years later, Dodgson and Ebdon119,120 conducted an extensive study of STY-MAH in various solvents and discounted the MCP model on the basis of an absence of a dilution effect with the inert solvent MEK. In an MCP model, a dilution effect would be expected due to the decrease in the relative concentration of the comonomer complex and the enhanced participation of the free monomer.121 Later, Farmer et al.122 reanalyzed this data and concluded that the composition data was consistent with both models and suggested sequence distribution may provide the answer. They also pointed out that there was a small dilution effect in MEK − greater than that predicted by

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12.2 Solvent effects on free radical polymerization

the penultimate model and less than that predicted by the MCP model. Hill et al.123 have suggested that interpretation of the effect of solvents is complicated by the fact that no solvent is truly inert, hence such results must be treated with caution. More recently Sanayei et al.124 have performed a pulsed-laser polymerization study on STY-MAH copolymerization in butanone and acetonitrile. They concluded that whilst the complex participation model described the copolymer composition it failed to predict the average kp data. Consequently the best description of this copolymerization was given by the penultimate unit model. There have been many other systems for which the MCP model has been proposed as an alternative to the penultimate unit model. For instance, Litt and Seiner used the MCP model to describe the composition of a number of systems, including MAH with 1-diphenylethylene, β-cyanacrolein with styrene,125 and vinyl acetate with dichlorotetrafluoroacetone and with hexafluoroacetone.113 An MCP model has also been suggested for the system STY-SO2.72,98,126-128 In this system, the composition changes with dilution or with solvent changes, strongly alternating behavior is observed across a range of feed ratios, and one of the comonomers (SO2) does not undergo homopolymerization. However, while the MCP model appears to be appropriate for some systems, in other strongly alternating copolymerizations it is clearly not appropriate. For instance, there are many strongly alternating copolymerizations for which there is no evidence of complex formation.69,72,121,129 Even when the complex formation is known to occur, results cannot always be explained by the MCP model. For instance, measurements of sequence distribution data revealed that, while both the MCP and penultimate model could provide an adequate description of the composition of STY with acrylonitrile (AN), only the penultimate model could account for the sequence distribution data for this system.130 As will be seen shortly, there is evidence that in some systems the heat of propagation would be sufficient to dissociate the EDA complex and hence it could not add to the monomer as unit. In this case, an MCD model would be more appropriate. Thus, it might be concluded that the MCP, MCD and the penultimate models are needed to describe the behavior of strongly alternating systems, and the selection of each model should be on a case-by-case basis. There have been many more systems for which the MCP model has been evaluated against the penultimate model on the basis of kinetic behavior. These studies have been extensively reviewed by Hill et al.123 and Cowie131 will therefore not be reviewed here. Instead, a few additional sources of evidence for the participation of the EDA complex will be highlighted. UV and NMR evidence for the existence of EDA complexes There is certainly a demonstrable existence of comonomer complexes in solutions of electron-donor-acceptor monomer pairs. These complexes can be detected, and their equilibrium constants measured, using UV or NMR spectroscopy. Techniques for this are described in detail in reviews of comonomer complexes by Cowie131 and Hill et al.123 The latter review123 also includes a listing of the equilibrium constants for the numerous EDA complexes that have been experimentally detected. The existence of comonomer complexes is not sufficient evidence for their participation in the propagation step of copolymerization, but the fact that they exist in solutions from which strongly alternating copolymers are produced suggests that they play some role in the mechanism. Further-

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more, the ability to measure their strengths and quantify the effects of solvents on their observed equilibrium constants without performing kinetic experiments may provide the key to establishing their role in the propagation mechanism. Since the alternative models for copolymerization include (or in some cases omit) the equilibrium constant for these complexes in different ways; if the equilibrium constant was to be measured separately and not treated as an adjustable parameter in the kinetic analysis, more sensitive model discrimination would be possible. To date, such an analysis does not appear to have been performed but it should be included in subsequent kinetic analyses of these explicit systems. Temperature effects The study of the temperature dependence of copolymerization behavior may also provide evidence for the role of comonomer complexes. As was seen previously in the study of acrylamide, complexes dissociate at high temperatures and hence, if the complex is involved in controlling an aspect of the polymerization behavior, a change in this behavior should be observed at the temperature corresponding to the complete dissociation of the complex. Such evidence has been obtained by Seymour and Garner132,133 for the copolymerization of MAH with a variety of vinyl monomers, including STY, VA, AN, and αMSTY. They observed that the copolymers undergo a change from strongly alternating to random at high temperatures, and these temperatures are also the temperatures at which the concentration of the EDA complex becomes vanishingly small. It is true that, since reactivity ratios have an enthalpy component, they approach unity as temperature increases. Hence, most models predict that the tendency of copolymers to form a random microstructure increases as temperature increased. Indeed, more recent work by Klumperman134 has shown that for STY-MAH copolymerization, the reactivity ratios do follow an Arrhenius type of temperature dependence. However, further work is required to verify this for the other copolymerizations listed above. Based upon the existing copolymerization data, it appears that for many systems there are sudden transition temperatures that correspond to the dissociation of the complex, which does suggest that the complex is in some way responsible for the alternating behavior.132,134 Stereochemical evidence for the participation of the complex Stereochemical data may provide evidence for the participation of the EDA complex. The EDA complex will prefer a certain geometry − that conformation in which there is maximum overlap between the highest occupied molecular orbital (HOMO) of the donor and the lowest unoccupied molecular orbital (LUMO) of the acceptor.135 If the complex adds to the propagating polymer chain as a unit, then this stereochemistry would be preserved in the polymer chain. If however, only free monomer addition occurs, then the stereochemistry of the chain should be completely random (assuming of course that there are no penultimate unit effects operating). Hence, it is possible to test for the participation of the monomer complexes in the addition reaction by examination of the stereochemistry of the resulting polymer. Such stereochemical evidence has been collected by a number of workers. For instance, Iwatsuki and Yamashita136 observed an unusually high percentage of cis units in MAH/butadiene copolymers. Olson and Butler137 studied the EDA system N-phenylma-

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12.2 Solvent effects on free radical polymerization

leimide (NPM)/2-chloroethyl vinyl ether (CEVE) and found that the stereochemistry at succinimide units in NPM-CEVE copolymers is predominantly cis, and random elsewhere. Furthermore, they noted that the proportion of cis units was correlated with those variables with which the concentration of the EDA complex was also correlated. In these examples, the cis geometry is that which is most stable for the complex. However, Rätzsch and Steinert138 have argued that this preference for cis geometry may also be explained by propagation occurring via a complex between the reacting free monomer and the chain end, as in an RC model. Thus this evidence should be used in conjunction with other evidence for model discrimination. Further stereochemical evidence for the MCP model has been obtained by Butler et al.139 They predicted that the usual preference for head-tail addition in free-radical polymerization would be overcome if propagation occurred via the EDA complex, and its favored geometry was a head-head conformation. They noted that for most EDA pairs head-tail geometry was favored and hence the predominance of head-tail linkages in these copolymers could not discriminate between free monomer addition and complex participation. To solve this problem, they designed and synthesized two monomer pairs for which a head-head conformation would be expected in their EDA complexes. These were the systems dimethyl cyanoethylene dicarboxylate (DMCE) with CEVE, and dimethyl cyanoethylene dicarboxylate (DMCE) with CEVE. They then showed that there were significant head-head linkages in the resulting copolymer and the proportion of these linkages was correlated with same types of variables that had previously affected the cis content of NPM/CEVE copolymers − that is, those variables which affected the concentration of the EDA complex. Thus they concluded that there was strong stereochemical evidence for the participation of the EDA complex in the propagation step. ESR evidence for the participation of the complex ESR studies have also been suggested as a means for providing information about the participation of the EDA complex. Since the addition of the complex is likely to occur more readily in one direction, if propagation occurs as the repeated addition of the complex then the propagating radical should be predominantly of one type. However, if free monomer addition predominantly occurs, both types of radicals are likely to be present at any time. Thus ESR can be used to distinguish between the two mechanisms. This approach was used by Smirnov et al.140 to show that, in the system phenyl vinyl ether/ MAH, the alternating addition of the free monomer predominates, but the participation of EDA complexes is important for the system butyl vinyl ether/MAH. They argued that the difference in the behavior of the two EDA systems was a result of the different strengths of their EDA complexes. In another study, Golubev et al.,141 used ESR to show that for dimethylbutadiene/MAH the cross-propagation of the free monomers dominated. However, Barton et al.142 has questioned the assignments of ESR signals in the previous studies and suggested that the ESR evidence was inconclusive. Furthermore, the predominance of one type of ESR signal may also be explained without invoking the MCP model. Assuming that cross-propagation is the dominant reaction, and that one of the radicals is much less stable than the other, it might reasonably be expected that the less stable radical would undergo fast cross-propagation into the more stable radical, resulting in an

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ESR signal dominated by the more stable radical. Hence it appears that ESR is not able to discriminate between this and the MCP mechanism. 12.2.3.3.3 Monomer-monomer complex dissociation model Tsuchida and Tomono117 suggested that the monomer-monomer complex described in the MCP model may dissociate upon addition to the chain, with only one unit adding. The concept was developed by Karad and Schneider143 who argued that the dissociation of the complex is likely since its heat of formation is typically less than the heat of propagation. As an example, they measured the heat of formation for a STY/fumaronitrile complex, and found that it was only 1.6 kcal/mol, significantly less than the heat of propagation (1520 kcal/mol). Under a complex-dissociation mechanism, the role of the complex is merely to modify the reactivity of the reactant monomers. A model based on the complex-dissociation mechanism was first formulated by Karad and Schneider143 and generalized by Hill et al.144 Again, eight rate constants and two equilibrium constants are required to describe the system.

RMi + Mj RMi + MjC Ki Mi + C

kij kiic

RMiMj where: i,j = 1 or 2 RMiMi where i,j = 1 or 2

MiC where: i,j = 1 or 2

As for the previous models, expressions for kp and composition can be derived in terms of these parameters by first calculating k ii and r i and then using them in place of kii and ri in the terminal model equations. The relevant formulas are: 1 + s ic K i [ C i ] 1 + s ic K i [ C i ] - and r i = r i ------------------------------------------------k ii = k ii ------------------------------1 + Ki [ Ci ] 1 + ( r i ⁄ r ci ) s ic K i [ C i ] where: ri =kii/kij; ric = kiic/kijc; sic = kiic/kii; i,j = 1 or 2 and i ≠ j

Efforts to compare this model with the MCP model have been hindered by the fact that similar composition curves for a given system are predicted by both models. Hill et al.144 showed that the composition data of Dodgson and Ebdon120 for STY/MAH at 60°C could be equally well described by the MCP, MCD or penultimate unit models. They suggested that sequence distribution would be a more sensitive tool for discriminating between these models. One study which lends some support to this model over the MCP model for describing this system was published by Rätzsch and Steinert.138 Using Giese’s145 “mercury method” to study the addition of monomers to primary radicals, they found that in mixtures of MAH and STY, only reaction products from the addition of free monomers, and not the EDA complex, to primary cyclohexyl radicals were found. Thus they concluded that the STY/MAH complex in the monomer solution is disrupted during the propagation step. It is likely that both the MCP and MCD mechanisms are valid and their validity in a specific system will depend on the relative strength of the EDA complex concerned. The MCD model may be useful for accounting for those systems, in which EDA complexes are known to be present but the MCP model has been shown not to hold.

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12.2 Solvent effects on free radical polymerization

12.2.3.3.4 Specific solvent effects Several monomers are particularly susceptible to strong solvent effects via specific interactions such as hydrogen bonding, ionic strength, and pH. The kinetic consequences of these specific interactions will vary from system to system. In some cases the radical and/ or monomer reactivity will be altered and in other cases a Bootstrap effect will be evident. It is worth noting that monomers which are susceptible to strong medium effects will not have reliable Q-e values, a good example of this is 2-hydroxyethyl methacrylate (HEMA) where there is a large variation in reported values. The reactivity ratios of HEMA with STY have been reported to be strongly dependent on the medium,146 similarly the copolymerization of HEMA with lauryl methacrylate is solvent sensitive;147 behavior which has been attributed to non-ideal solution thermodynamics (cf Semchikov's work in Section 12.2.3.4). Chapiro148 has published extensively on the formation of molecular associates in copolymerization involving polar monomers. Other common monomers which show strong solvent effects are N-vinyl-2-pyrrolidone, (meth)acrylic acids and vinyl pyridines. 12.2.3.4 Bootstrap model 12.2.3.4.1 Basic mechanism In the Bootstrap model, solvent effects on kp are attributed to solvent partitioning and the resulting difference between bulk and local monomer concentrations. In this way, a solvent could affect the measured kp without changing the reactivity of the propagation step. Bootstrap effects may arise from a number of different causes. As noted previously, when radical-solvent and monomer-solvent complexes form and the complexes do not propagate, the effect of complexation is to alter the effective radical or monomer concentrations, thereby causing a Bootstrap effect. Alternatively, a Bootstrap effect may arise from some bulk preferential sorption of one of the comonomers around the growing (and dead) polymer chains. This might be expected to occur if one of monomers is a poor solvent for its resulting polymer. A Bootstrap effect may also arise from a more localized preferential sorption, in which one of the monomers preferentially solvates the active chain-end, rather than the entire polymer chain. In all cases, the result is the same: the effective free monomer and/or radical concentrations differ from those calculated from the monomer feed ratios, leading to a discrepancy between the predicted and actual propagation rates. 12.2.3.4.2 Copolymerization model Copolymerization models based upon a Bootstrap effect were first proposed by Harwood38 and Semchikov149 (see references cited therein). Harwood suggested that the terminal model could be extended by the incorporation of an additional equilibrium constant relating the effective and “bulk” monomer feed ratios. Different versions of this socalled Bootstrap model may be derived depending upon the baseline model assumed (such as the terminal model or the implicit or explicit penultimate models) and the form of equilibrium expression used to represent the Bootstrap effect. In the simplest case, it is assumed that the magnitude of the Bootstrap effect is independent of the comonomer feed ratios. Hence in a bulk copolymerization, the monomer partitioning may be represented by the following equilibrium expression:

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f 1bulk f1 ---- = K -----------f 2bulk f2 The equilibrium constant K may be considered as a measure of the Bootstrap effect. Using this expression to eliminate the effective monomer fractions (f1 and f2) from the terminal model equations, replacing them with the measurable “bulk” fractions (f1bulk and f2bulk), the following equations for composition76 and kp150 may be derived. Kf 1bulk r 1 Kf 1bulk + f 2bulk F1 ----- = ---------------- ----------------------------------------F2 f 2bulk r 2 f 2bulk + Kf 1bulk 2 2

2

r 1 K f 1bulk + 2Kf 1bulk f 2bulk + r 2 f 2bulk 1 k p = ------------------------------------- ----------------------------------------------------------------------------------------Kf 1bulk + f 2bulk r 1 Kf 1bulk ⁄ k 11 + r 2 f 2bulk ⁄ k 22 Examining the composition and kp equations above, it is seen that the Bootstrap effect K is always aliased with one of the monomer feed ratios (that is, both equations may be expressed in terms of Kf1 and f2). It is also seen that once Kf1 is taken as a single variable, the composition equation has the same functional form as the terminal model composition equation, but the kp equation does not. Hence it may be seen that, for this version of the Bootstrap effect, the effect is an implicit effect − causing deviation from the terminal model kp equation only. It may also be noted that, if K is allowed to vary as a function of the monomer feed ratios, the composition equation also will deviate from terminal model behavior − and an explicit effect will result. Hence it may be seen that it is possible to formulate an implicit Bootstrap model (that mimics the implicit penultimate model) but in order to do this, it must be assumed that the Bootstrap effect K is constant as a function of monomer feed ratios. It should be noted that the above equations are applicable to a bulk copolymerization. When modeling solution copolymerization under the same conditions, the equations may be used for predicting copolymer composition since it is only the relationship between bulk and local monomer feed ratios that determines the effect on the composition and microstructure of the resulting polymer. However, some additional information about the net partitioning of monomer and solvent between the bulk and local phases is required before kp can be modelled. It should be observed that in a low-conversion bulk copolymerization, knowledge of the monomer feed ratios automatically implies knowledge of the individual monomer concentrations since, as there are no other components in the system, the sum of the monomer fractions is unity. However, in a solution copolymerization, there is a third component − the solvent − and the monomer concentrations depend not only upon their feed ratio but also upon the solvent concentration. Modeling kp in a solution copolymerization could be achieved by rewriting the above equilibrium expression in terms of molar concentrations (rather than comonomer feed ratios), and including the solvent concentration in this expression. The Bootstrap model may also be extended by assuming an alternative model (such as the explicit penultimate model) as the baseline model, and also by allowing the Bootstrap effect to vary as a function of monomer feed ratios. Closed expressions for composi-

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tion and sequence distribution under some of these extended Bootstrap models may be found in papers by Klumperman and co-workers.76,77 12.2.3.4.3 Experimental evidence The Bootstrap model was introduced by Harwood,38 who studied three solvent sensitive copolymerizations (styrene/methacrylic acid, styrene/acrylic acid and styrene/acrylamide) and found that the copolymers of the same composition had the same sequence distribution irrespective of the solvent used. This meant that the conditional probabilities governing radical propagation were independent of the solvent. On this basis, he argued that composition and sequence distribution were deviating from their expected values because there was a difference between the monomer feed ratios in the vicinity of the active chain end, and those calculated on the basis of the bulk feed. In other words, the solvent was altering the rates of the individual propagation steps by affecting the reactant concentrations and not, as in the other solvent effects models, their reactivities. However, Fukuda et al.64 have argued that the NMR evidence provided by Harwood is not conclusive evidence for the Bootstrap model since Harwood’s observations could also be described by the variation of the reactivity ratios in such a way that their product (r1r2) remains constant. This has also been raised as an issue by Klumperman and O'Driscoll.76 They showed mathematically that a variation in the local comonomer ratio is not reflected in the monomer sequence distribution versus copolymer composition − this relationship being governed by the r1r2 product only. An alternative explanation for Harwood’s experimental data may be the stabilization or destabilization of the radicals by the solvent, an interpretation that would be analogous to the MCD model. Simple energy stabilization considerations, as used by Fukuda et al.151 to derive the penultimate unit effect, also suggest the constancy of r1r2. Prior to Harwood's work, the existence of a Bootstrap effect in copolymerization was considered but rejected after the failure of efforts to correlate polymer-solvent interaction parameters with observed solvent effects. Kamachi,70 for instance, estimated the interaction between polymer and solvent by calculating the difference between their solubility parameters. He found that while there was some correlation between polymer-solvent interaction parameters and observed solvent effects for methyl methacrylate, for vinyl acetate there was none. However, it should be noted that evidence for radical-solvent complexes in vinyl acetate systems is fairly strong (see Section 12.2.3), so a rejection of a generalized Bootstrap model on the basis of evidence from vinyl acetate polymerization is perhaps unwise. Kratochvil et al.152 investigated the possible influence of preferential solvation in copolymerizations and concluded that for systems with weak non-specific interactions, such as STY-MMA, the effect of preferential solvation on kinetics was probably comparable to the experimental error in determining the rate of polymerization (±5%). Later, Maxwell et al.153 also concluded that the origin of the Bootstrap effect was not likely to be bulk monomer-polymer thermodynamics since, for a variety of monomers, Flory-Huggins theory predicts that the monomer ratios in the monomer-polymer phase would be equal to that in the bulk phase.154 Nevertheless, there are many copolymerization systems for which there is strong evidence for preferential solvation, in particular, polymer solutions exhibiting cosolvency or

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where one of the solvents is a non-solvent for the polymer. Preferential adsorption and desorption are manifest where the polymer adjusts its environment towards maximum solvation. With this knowledge, it may be expected that Bootstrap effects based on preferential solvation will be strongest where one of the monomers (or solvents) is a poor or nonsolvent for the polymer (such as copolymerization of acrylonitrile or N-vinyl carbazole). Indeed, early experimental evidence for a partitioning mechanism in copolymerization was provided by Ledwith et al.155 for the copolymerization of N-vinyl carbazole with MMA in the presence of a range of solvents. Direct evidence for preferential solvation was obtained by Semchikov et al.,156 who suggested that it could be detected by calculating, from measurements of the solution thermodynamics, the total and excess thermodynamic functions of mixing. Six monomer pairs were selected: Vac-NVP, AN-STY, STY-MA, Vac-STY, STY-BMA and MMA-STY. The first four of these monomer pairs were known to deviate from the terminal model composition equation, while the latter two were not. They found that these first four copolymerizations had positive ΔGE values over the temperature range measured, and thus also formed non-ideal polymer solutions (that is, they deviated from Raoult’s law). Furthermore, the extent of deviation from the terminal model composition equation could be correlated with the size of the ΔGE value, as calculated from the area between the two most different composition curves obtained for the same monomer pair under differing reaction conditions (for example, initiator concentration; or type and concentration of transfer agent). For STY-MMA they obtained negative ΔGE values over the temperature range considered, but for STY-BMA negative values were obtained only at 318 and 343K, and not 298K. They argued that the negative ΔGE values for STY-MMA confirmed the absence of preferential solvation in this system, and hence its adherence to the terminal model composition equation. For STY-BMA they suggested that non-classical behavior might be expected at low temperatures. This they confirmed by polymerizing STY-BMA at 303K and demonstrating a change in reactivity ratios of STY-BMA with the addition of a transfer agent. Based upon the above studies, it may be concluded that there is strong evidence to suggest that Bootstrap effects arising from preferential solvation of the polymer chain operate in many copolymerization systems, although the effect is by no means general and is not likely to be significant in systems such as STY-MMA. However, this does not necessarily discount a Bootstrap effect in such systems. As noted above, a Bootstrap effect may arise from a number of different phenomena, of which preferential solvation is but one example. Other causes of a Bootstrap effect include preferential solvation of the chain end, rather than the entire polymer chain,157 or the formation of non-reactive radical-solvent or monomer-solvent complexes. In fact, the Bootstrap model has been successfully adopted in systems, such as solution copolymerization of STY-MMA, for which bulk preferential solvation of the polymer chain is unlikely. For instance, both Davis157 and Klumperman and O'Driscoll76 adopted the terminal Bootstrap model in a reanalysis of the microstructure data of San Roman et al.158 for the effects of benzene, chlorobenzene and benzonitrile on the copolymerization of MMA-STY.

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Versions of the Bootstrap model have also been fitted to systems in which monomermonomer complexes are known to be present, demonstrating that the Bootstrap model may provide an alternative to the MCP and MCD models in these systems. For instance, Klumperman and co-workers have successfully fitted versions of the penultimate Bootstrap model to the systems styrene with maleic anhydride in butanone and toluene,76 and styrene with acrylonitrile in various solvents.77 This latter work confirmed the earlier observations of Hill et al.159 for the behavior of styrene with acrylonitrile in bulk, acetonitrile and toluene. They had concluded that, based on sequence distribution data, penultimate unit effects were operating but, in addition, a Bootstrap effect was evident in the coexistent curves obtained when triad distribution was plotted against copolymer composition for each system. In the copolymerization of styrene with acrylonitrile Klumperman et al.77 a variable Bootstrap effect was required to model the data. Given the strong polarity effects expected in this system (see Section 12.2.2), part of this variation may in fact be caused by the variation of the solvent polarity and its effect on the reactivity ratios. In any case, as this work indicates, it may be necessary to simultaneously consider a number of different influences (such as, for instance, penultimate unit effects, Bootstrap effects, and polarity effects) in order to model some copolymerization systems.

12.2.4 CONCLUDING REMARKS Solvents affect free-radical polymerization reactions in a number of different ways. Solvent can influence any of the elementary steps in the chain reaction process either chemically or physically. Some of these solvent effects are substantial, for instance, the influence of solvents on the gel effect and on the polymerization of acidic or basic monomers. Solvents can be used chain transfer agents, and as tools for controlling the stereochemistry of the resulting polymer. In the specific case of copolymerization, solvents can influence transfer and propagation reactions via a number of different mechanisms, thus providing opportunities to manipulate the copolymer composition and sequence distribution. 12.2.5 ACKNOWLEDGEMENTS We gratefully acknowledge the contributions of Professor Tom Davis to the original edition of this Chapter, and also the publishers Marcel Dekker for allowing us to reproduce sections of an earlier review, “A Mechanistic Perspective on Solvent Effects in Free Radical Polymerization”.160 REFERENCES 1 2 3 4 5 6 7 8 9

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12.2 Solvent effects on free radical polymerization

160 Coote, M. L., Davis, T. P., Klumperman, B. and Monteiro, M. J., J.M.S.-Rev. Macromol. Chem. Phys., 1998, C38, 567.

Index

851

Index Symbols “hard” acid 519 “hard” base 519 “optical” basicity 554 “soft” base 519 “stick” model 23 Numerics H NMR spectrum 666 2,6-p-toluidinonaphthalene sulfonate 187 2.4-toluene diisocyanate 330 2-propanol-water mixture 493, 501 31 P-NMR 816 9,10-diphenylanthracene 705 1

A ab initio computer-aided methodology 700 molecular orbital method 50 potential 50 abnormal sorption 316 absolute energy minimum 30 refractive index 59 vapor pressure 205 apparatus 203 measurement 202 absorption 511 band 637-638, 704, 715 line width 709 intensity 705 kinetics 355 maximum 771, 774, 776 solvent 267 spectrum 699, 712, 760 absorptive solvatochromism 657 abstraction reaction 828 acceptor 301, 526, 767, 809 component 151 number 81, 88, 513, 514, 767-768, 770-771, 774, 809, 811, 814-816 parameter 149, 768 solvent 627, 779

accessible surface 29 accuracy 277 acetaldehyde 43 acetic acid 2, 12, 523, 751 dimerization constant 443 acetone 80, 692, 705, 751 -water system 496 acetonitrile 2, 80, 190, 827 -water mixture 501 ACGIH 69 acid 81 decomposition temperature 534 interaction constant 512 scale in solution 35 solvatochromic behavior 639 -acid titration 676 -base 13, 35 adduct formation 514 concept 519, 765 consideration 816 definition 519, 523 dissociation 530, 534-535 enthalpy 512 equilibrium 13, 35, 516, 522, 532, 675 indicator 553 interaction 422-423, 511-513, 515-516, 522, 524, 570, 620, 737, 744 pair 545, 547 definition 521 processes 518 properties 665, 667, 741 range 531 reaction 538, 544, 553, 559, 767 self-dissociation 530 acidic character 665 function 422 melt 541 nature 21 properties 523, 525 region 543

852 acidity 543, 760 constant 675 empirical scale 537 estimation 549 function 541 parameter 675 probe 622, 638 scale 13, 35, 530, 542, 543, 562, 817 upper limit 534-536 -basicity scale 35 acoustic cavitation 396 dissipation 387, 394 wave admittance analysis 360, 362 propagation 379 acrylic membrane 752 activated complex 1 activation energy 33, 40, 43, 172-173, 360, 363, 436, 558, 802, 805, 824, 826 entropy 779 activity coefficient 36, 198, 211, 214, 220-221, 244, 245, 252, 255, 262, 264-266, 454, 485-486, 516, 523, 623 model 198 gradient 234 acylation process 421 acylonium cation 421 additivity rule 761 adduct formation 446 enthalpy 447 adhesion 357 adsorbed molecule 371 volatile molecules 371 adsorption chromatography 84, 88 aerosolization 376 affinity 12 scale 88 aggregate 745, 754 formation 746 morphology 745 aggregation 5, 480, 511, 744, 747 enthalpy 234 phenomenon 234

Index prevention 748 state 748 suppressing additive 748 tuning 748 air to solvent ratio 66 airflow 374 air-solvent interface 493 alcohol 60, 82 alcohol vapor pressure 61 alcoholysis 82 Alder 48 alkahest 11 alkali metal halide melt 562 alkoxylation 95 alkyl chain length 22 side chain 700 aluminum stearate 749 alundum 538 amide 302 amine 423 aminoacid 30, 32-33 ammonia 82 ammonolysis 82 amorphous domain 371 phase 372 polymer 162, 290-291 structure 369 volume fraction 372 amphiphile 746 amphiprotic 673 amphoterism 421-423 anaerobic fermentation 96 analytical equation 265 aniline point 74, 84 anion 809 composition 549 size 816 solvation 457, 458 -acceptor 422 -cation interaction 701 -donor 422 anionic solute 16 anisochoric swelling pressure 243 anisotropy decay 183 antimony bromide 525

Index antiparallel orientation 16 antistatic compound 761 antisynergism 155-156 Antoine equation 61-62, 85 apolar 80 molecule 67 non-HBD solvent 88 solvent 768 aprotic 38, 80 acid 422 solvent 81, 302, 430, 528, 759, 778, 798 Aristotle 1 aromatic hydrocarbon 72, 161 polyamide 752 solvent 826 Arrhenius 12 definition 524 parameter 826 plot 804 associate formation 422 associated solvents 427 association 35, 56 constant 420, 463 degree 418 number 744, 747 process 464, 477 asymmetric membrane 751 atactic polypropylene 294 polystyrene 162 athermal binary polymer solution 245 polymer solution 245 solution 246 athermic process 158 atmospheric lifetime 72 pollution 77 atom intermolecular radius 301 transfer radical polymerization 823 van der Waals volume 300 volume increment 300 atomic force microscopy 514 image 478

853 number 526 atomistic molecular dynamics 186 simulation 167 atmospheric distillation 91 attraction energy 19, 299 attractive interaction 16, 748 parameter 261 perturbation term 257 autodissociation ability 528 autoignition temperature 66, 86 autoionization 30, 32 autoprotolysis 438 constant 437-438 aviation industry 67 Avogadro's number 56 axial rotamer 445 azeotrope 76, 94 azeotropic distillation 94 mixture 63 B back-biting reaction 827 bacteria 86 Baldwin’s extrapolation 797 barbituric acid derivative 490 Barker-Henderson approach 784 barrier 357 height 16 properties 749 base interaction constant 512 properties 81 strength 563 basic capacity 466 properties 523, 526 basicity 540, 760, 790 effect 636 indicator 620 parameter 636 probe 622 scale 13, 35, 778, 817 upper limit 542, 551 bathochromic band shift 3

854 effect 699 shift 3, 82, 629, 637, 645, 657, 659-660, 712-713 solvatochromism 657 Beer’s law 375 Beerbower 143 benzene 2, 94, 445, 754 benzoid structure 713 benzonitrile 824 benzyl alcohol 824 Berthelot 2, 12 betaine dye 87 biaxial extension 317 stretching 349 bimolecular association 497 rate constant 37 reaction 37 binary interaction parameters 264 liquid 328 system 426, 430, 434, 436 without interaction 436 mixed solvent 435, 437, 446, 468, 508 system 434 mixture 188, 322, 326, 423, 480, 508 organic solvent 482 polymer solution 197, 219, 232, 248-249, 251, 259, 265-266 solvent 319, 325, 417, 420-421, 423, 425, 428-429, 433, 439, 451, 462 composition 324 ion product 437 mixture 190, 466, 481 conductivity 429 system 435 binding energy 513 binodal 164-165, 239 curve 196, 240-241 bioavailability 665 biochemistry 84 biodegradability 86 biodegradation half-life 86 rate 86

Index biodiesel 267 biological macromolecules 167 oxygen demand 72, 86 process 14 water 172, 175 biomacromolecule 14 biomass-derived solvent 3 biomolecular interactions 701 surface 173 biomolecule 16, 175 biosensing 701 biphenyl 491 birefringence 183 Birge model 714 Blanks-Prausnitz approach 154, 156 block copolymer 741 length 745 blow molding 749 blue band shift 82 shift 691, 693, 700, 708, 713 Boerhaave 12 Bohr radius 715 boiling 379 point 21, 56, 58, 62-63, 70, 83, 222, 798-799 measurement 56 process 398 temperature 20, 76, 216 Boltzmann factor 26 bond element 151 length 300-301, 807 rupture 37 strength 376 bonded atoms 692 Bondi's approach 160 bonding mode 791 Bootstrap effect 827, 830, 832, 836, 842, 845 model 842-844 borax 572 Born equation 805, 807 excess free energy 805

Index model 805, 809 radius 806-808 Bottcher's relation 148 bound water 173, 175 boundary conditions 263 liquid concentration 310 swell ratio 309 Boyle 12 Br 524 branched alcohol 60 Brannon-Peppas equation 369 breakthrough time 361 breastfeeding 85 bridging oxygen 190 water molecule 190 Bristow-Watson method 280 relationship 336 broadband pump-probe spectroscopy 188 upconversion 178 bromide ion acceptor 525 bromobenzene 824 Brønsted behavior 79 equation 623 –Lowry acid 516 acid-base pair 534 acidity/basicity 81 definition 524 Brooker’s merocyjanine 712 bubble dynamics 379, 391 formation 375 growth 384 nucleation 407 Buckingham's formula 705 Budo form 168, 169 bulk solvation 168 solvent mixture 488 water 172, 175 buoyancy 242

855 butadiene 703 diol 330 -nitrile rubber 319 butanol 95, 96 butyl acetate 62 C calorific value 86 calorimeter 277-278 calorimetric measurement 81, 763 method 278 cancellation approximation 498, 500 condition 499 cancer 85 canonical partition function 247 capacity factor 502 capillary effect 406 zone electrophoresis 666 carbocation 42 carbochlorination 567 carbohalogenation 537, 568 carbon black 568 dioxide 38, 67 monoxide 70 tetrachloride 754, 790 carbonate ion 557 carbonyl absorption 346 frequency 369, 755 shift 755 group 362 stretching 369 frequency 513, 516 carcinogen 71, 85, 99 carcinogenesis 85 carcinogenic 71 Carnahan-Starling equation 258 hard-sphere monomer fluid 261 term 258, 260 carnallite 594 carotene 701, 704 carotenoid 479 Car-Parrinello approach 30

856 Casimir force 481 potential 480 casting 750 catalyst 3 deactivation 91 catalytic chain transfer 828 reaction 828 cracking 91, 94-95 effect 43, 66 hydrocracking 91 reaction 2 reforming 91, 92 cathetometer 207, 209-210, 242, 279, 364 cation 542, 809 acidity 570 donor 521 polarizing action 583 radius 522 solvation 772 cationic solute 16 cavitation contribution 29 energy 15 free energy 23 term 29 cavity 27, 703 compression 393 formation 783, 795 energy 782, 784 growth rate 398 radius 808 surface 23 area 506 -based model 794-795 cell volume 250-251 cell's genetic material 85 cellular metabolic process 85 cellulose 160, 750 acetate butyrate 154 fiber 479 membrane 227 molecular dissolution 480 center of inversion 708 central atom 521

Index centrifugal force 234 homogenizer 239 centrifuge 239 centrosymmetric molecule 708 chain 747 architecture 823 branching 263 conformation 83, 794 conformational movement 38 end 823 expansion 739 flexibility 161, 367 length 159, 258 mobility 759 reference system 261 scission 759 segment 365, 758 separation 162 transfer 828 coefficient 828 -bonding contribution 259 -chain aggregation 754 -of-rotators equation 258 Chako's formula 703 change of entropy 144 charge 171, 542 balance 38 decay rate 68 delocalization 35 density 29 distribution 170, 691 transfer 21, 170, 628 complex 645, 834 configuration 831 stabilization 831 state 693 transition 87, 708 -fluctuation forces 17 charged species 80 Charnahan-Starling equation 798 chemical adduct 418 approach 766, 770 bond 354 constitution 79 dislocation 443

Index equilibria 496 equilibrium 1, 12-13, 34-35, 419, 423, 439, 461, 475 form 441 interaction 57, 417, 430, 432 permittivity 430 ionization mass spectrometry 14 kinetics 499-500 network 336, 341, 354 density 339, 344 parameter 342 oxygen demand 72 potential 166, 197, 199, 219, 241, 243, 245, 256, 305, 307-308, 365-366, 468-469 difference 218 of mixing 133 reaction 1, 34, 36-37, 39, 79, 82-83, 445 design 47 order 35 rate 36-37, 87, 499 reactivity 2, 665 reference reaction 82 resistance 357 shift 514, 645, 649, 666, 699, 816 structure 87, 158, 265, 336, 343 technology 518 transformation 1, 11 chloride ion donor 522 chlorinated paraffin 344 chloroaluminate melt 522 chlorofluorocarbons 86 chloroform 754 choline chloride 189 chromatographic separation 2 chromophore 3, 180, 185, 189, 627, 659, 715 chromophoric compound 692-693 solute 691, 696 chronic toxicity 85 Claisen 2, 13 classic solvosystem concept 526-527, 529 classical dispersion theory 703 clathrate cage model 794, 796, 798 water cage 797 Clausing parameter 279

857 Clausius -Clapeyron equation 61, 85, 278 -Mosotti relation 703 clinical diagnostics 701 Cloizeaux law 309, 317 Clostridia 95 Clostridium beijerinckii 96 cloud point 165, 232, 238, 751 curve 237-239 Cluff-Gladding method 338-339 cluster size 791 coagulation bath 751 coating 76, 750 electrochemical deposition 518 morphology 515 cobaloxime 828 coherent Raman scattering 184 cohesion energy 137, 142, 145, 148, 298, 300 computation 300 cohesive energy 135, 143-145 density 135, 146, 768 parameter 700 enthalpy 288 interaction 22 migration 762 pressure 72, 768 coil transition 746 coiled conformation 754 collapse rate 390 collision 14 color reflection 481 column dead volume 502 combinatorial contribution 245, 247 entropy of mixing 245 combustible liquid 86 combustion 12, 67, 85-86 chamber 66 commercial availability 79 common acidity scale 539 monomer 824 compatibility 11, 156, 159, 162-163 compatibilizer 749 compatible system 742 compensative effect 475

858 complex anion 519, 521, 526-527 formation 471, 500 complexation 569, 832 process 472 complexometric titration 575 compressibility 20, 257, 781 behavior 257 factor 278 compressible material 383 compression 349 modulus 344 computational calculation 27 computer simulation 23-24 -aided molecular design 700 concentration 1, 741 gradient 234 condensation 204 product 760 reaction 35 condensed medium 691, 698 phase 37, 278, 781 conductive solution 430 conductivity 420 specific 435 conductometric titration 675 configuration 26 energy 159 configurational entropy of mixing 158 confined medium 179 water 167, 172 conformal structure 761 conformation 31, 33, 35, 233 change 700-701 conformational change 189, 636-637, 711, 714, 718 enthalpy 289 conformer 31, 418, 444 electrostatic component 445 equilibrium 418, 443 constants 444 ratio 418 stability 445 transformation constant 445

Index conformic equilibrium 418 conjugated acid solvation 536 -base pair 530 base 530 structure 66 conservation law 392 principle 25 constant partial pressure 542 pressure enthalpy 137 constituent ion 518 constitutive equation 305 contact angle advancing 512 measurement 511 interaction parameter 160 surface 29 continuum model 23, 27-30, 33, 167 reaction field model 715 contraction 429 controlled solvation 439 convection drying 374 regime 411 convective flow 477 time derivative 384 conversion process 94 cooling rate 752 coordination number 151, 808 sphere 454 composition 471 -chemical approach 767 copolymer composition 830 copolymerization propagation kinetics 830 solvent effect 835 core size 745 corn protein 742 correlation analysis 82, 88

Index corrosion 357, 519 protection 761 co-solvency criterion 322 cosolvent 374, 487, 492, 502, 507 identity 491 Cottrell pump 216 counterion 778 covalent bond 81 bonding 259 bromide 525 chain-bonding 261 component 441, 460, 464 constituent 475 halides 527 interaction 513 Cox equation 61 craze formation 757 cresol 95 critical behavior 239 concentration 740 opalescence 238 point 163, 239, 241, 480-481 shear rate 740 temperature 165 crosslink 336, 363, 759 density 162, 367 crosslinked elastomer 5, 164, 281, 283, 305, 319, 322, 324, 326, 349, 356 solubility parameters 284 polymer 241, 330, 354 polyurethane 366 crosslinking 158, 746 agent 330 point 343, 347 cross-propagation reaction 837 crude oil 91 distillation 93 process 91 cryoscopic measurement 236 method 236 cryoscopy 195-196, 236 crystal energy 486

859 growth 580 lattice 1 energy 486, 496 size 579, 594 base frequency 211 crystalline domain 371 phase 372 polymer 162-163 solvent 366 structure 477, 755 volume fraction 371 crystallinity 5, 363, 372, 749, 754, 760 degree 373 crystallite 479 crystallization 369, 513, 749, 754-755, 757 front 568 process 369, 580, 755 curing 347 rate 375 time 362 curvature correction factor 488, 506 cybotactic cavity 621 region 508, 619, 621 cyclodextrin cavity 186 cyclohexadiene 703 cyclopentadiene 703 cyclopentanone 705 cylindrical aggregate 746 D Dalton law 388 dead time 502 Deborah number 358 Debye form 168 Debye type 175 -Hückel equation 523 decalin 754 decaying memory principle 380 deep eutectic solvent 6, 22, 189 Dee-Walsh equation of state 251 definition 87 deformable quasi-lattice 159 deformation 306, 342, 382 history 380, 383

860 degenerate Hansen’s spheres 155 degree of freedom 247, 249 saturation 267 dehydration 95 dehydrocyclization 92 dehydrogenation 92 delocalization stabilization energy 835 demixing 240, 259 equilibrium 232 region 255, 264 dendritic polymer 263 dense packing 748 density 20, 23, 341, 417, 425, 428, 792, 803 deviation 434 -functional theory calculations 701 dental adhesive 376 deoxyribonucleic acid 188 depolarization factor 704 deposition process 477 deprotonation grade 816 dermal 70 desalting 91 desmotropic constant 2 desolvated adduct 451 desolvation contribution 477 energy 477 consumption 477 desorption 364 method 205 deswelling 370 concentration 242 process 367 determinant 87 deterministic optimization 700 deuterated xylene 234 dextran 222, 231 dialkyl sulfide 96 dialysis 746 diaxial conformer 445 dichloroethane 774, 809 dichloromethane 751 dichroism 183 dielcometry 443 dielectric analysis 376

Index approach 766, 770-771 constant 20, 28, 33, 38, 40, 67-68, 83, 168, 526, 761, 766-767, 772-773, 789, 799 continuum 168, 619, 766, 801 model 167 effect 35 measurement 770 medium 27-28, 703 permittivity 426 relaxation 172, 176, 795 saturation 805 model 766 Diels-Alder reaction 700 diethyl ether 3, 62, 85 malonate 824 phthalate 824 differential ebulliometer 215 enthalpy 243 manometer 205 refractometer 203, 205 solvation 83 vapor pressure measurement 204-205 apparatus 204-205 differentiating solvent 464 diffraction experiment 15 diffusion 36, 37, 53, 161, 189, 305, 351, 357-358, 363, 579, 797 boundary 370 coefficient 49, 211, 224, 225, 234, 266, 307, 310, 312, 314-316, 353, 355-356, 362-363, 372, 375-376, 398 data 226 Deborah number 358 distance 367, 368, 370 elastic 358 equation 307, 308 equilibrium 234 flux 307 force 305 free-volume theory 358 gradient 358 kinetics 305, 311, 314, 350 parameter 162

Index process 358 rate 362, 363, 370-371, 373, 824 theory 359 time 358 transport 401 wave 312 -controlled rate 37 -limited value 37 diffusive orientation 184 diffusivity 360 digital camera 364 dilation 364 diluent 134 dilute concentration region 223 polymer solution 224, 230 solution 202, 263 diluted polymer solution 327 solution 327 diluting capability 84 dilution activity coefficient 267 effect 827 ratio 74, 134 dimer concentration 443 form 443 dimerization 95 constant 443 dimethyl formamide 81, 481, 790, 827 sulfoxide 2, 80-81, 302 Dimroth-Reichardt betaine 495 parameter 492 value 485 dinonyl phthalate 824 dioxane 481 diphenyl ether 3 diphenylhydantoin 490 diphenylmethane diisocyanate 347 dipolar 80 aprotic solvent 80, 88 atom 18 correlation length 807 interaction 786

861 molecular moment 30 molecule 37, 80, 700, 713 solvation energy 700 moment 17, 20, 33, 38 vector 17 response 784 solvation mechanism 790 transition 37 dipolarity 80, 88, 699, 759 parameter 657 dipole 171 approximation 709 density 768 induction 143 interaction 784 moment 16-17, 68, 83, 147, 154, 168, 175, 418-419, 431, 444-445, 503, 621-622, 636, 645, 660, 692-693, 701, 712-713, 715, 717-718, 773, 786-787, 799 change 621 direction 628 modulus 621, 627 orientation 67, 143, 798 reorientation 804 -dipole force 620, 781 interaction 16, 137, 249, 301, 443-444, 454 diprotic acid 683 Dirac’s delta function 381 direct potentiometric titration 576 pressure measurement 209 discontinuum 83 dispersion 37, 73, 783 component 513 contribution 515 effect 713 energy 27 force 17, 506 of interaction 136 interaction 3, 17, 83, 85, 144, 784, 791 term 260 -repulsion energy 15 dispersive coupling 786 force 789 interaction 143, 299, 701

862 solvation energy 784 disproportionation 669 dissipative factor 391 dissociation 35, 536, 593 constant 81, 551, 579, 588, 592, 596, 665, 682 degree 537 energy 668 parameter 676 reaction 783 dissolution 12, 133, 137, 161, 794 process 30, 158 temperature 288 dissolved polymer 83 water 84 distance 18 between crosslinks 365 distillation unit 92 disulfide bond 742 domain structure 342, 354 donocity 761 donor 301, 459, 767, 809 component 151 number 81, 88, 458, 513-514, 620, 668, 767, 773-774, 809, 811, 813-816 parameter 149 solvent 771 strength 774, 816 scale 818 substance 439 -acceptor approach 809 bond 420 chromophore 709 concept 767 interaction 519, 521, 544, 620 molecule 708 process 521-522 properties 439 reaction 520, 529 dopant 519 Doppler broadening 696 double bond 692 addition 162 calorimeter 278 lattice model 265

Index Drago's equation 513 driving force 363 droplet diffusion coefficient 748 drug delivery 185 system 369 permeation 267 thermodynamic activity 267 drying 357-358, 370 kinetics 511 oil 95 process 370-371 rate 372 time 372-373, 376, 480 dryness point 371 dualistic model 149 dye absorption band 624 dynamic equilibrium 367 light scattering 234, 362, 744 E early-time solvation dynamics 191 ebulliometer 208, 215 ebulliometric constant 221 equipment 209 measurement 221 method 279 ebulliometry 195-196, 201, 208, 215 effective conjugation length 700 mobility 666 molecular volume 748 network density 354 permeation 267 efficiency factor 823 eigenstate 707 Einstein's equation 738 elastic deformation 241 diffusion process 358 free energy 365 network 325 deformation 196 neutron scattering 233 polymer 161

Index elastically active chain 162, 336 elasticity equilibrium modulus 339 potential 162 theory 308 elastomer 315, 323 structure 341 swelling 311 kinetics 316 elastomeric polymer network 349, 350 electric charge 37 conductivity 67, 429, 525, 761 activation energy 436 coefficient 436 dichroism 628 field 67, 80, 176, 713, 805 strength 67 moment 705 potential 171 electrochemical process 518 electrodynamic forces 17 electrografting 761 electroluminescent performance 480 electrolysis 593-594 electrolyte strength 464-465 electrolytic dissociation 420 electromotive force measurement 438 electron acceptor 369, 622 bombardment 14 cloud 80, 693, 713 density 812 contour 808 diffraction studies 50 distribution 692 pair 73, 81, 521, 659 acceptor 521 transfer 167 -deficient atom 369 electronegative atom 82 element 20 electronegativity 519, 692, 789 electroneutral molecule 16

863 electronic absorption band 708 spectra 495 charge 693 circuit 211 cloud 17 delocalization 659, 660 description 27 distortion 15 excitation 621, 627-628, 637 industry 67 molecular cloud 18 polarizability 80, 83, 768 polarization 803 spectra 691 Stark spectroscopy 701 state 701 structure 692 transfer 13 transition 495, 626, 636-637, 641, 644-645, 659-660, 703, 803 energy 87 electron -pair acceptor 81 donor 81 -transfer process 17 reaction barrier 16 electrophilic ability 767 monomer pair 832 electropolymerization 761 electrospun fiber 69 electrostatic charge 69 component 441, 447, 469 constituent 475 contribution 15, 27, 713 energy 15 factor 68 forces 16, 82 hazard 68, 69 interaction 15-16, 35, 43, 82, 189, 441-442, 485, 513, 544 energy 437

864 model 444 potential 28, 480 surface 636 repulsion 187 saturation 619 solvation 693 stabilization 36 electrostatics 16 electrostriction 805, 808 elimination 82 ellipsoidal cavity 703, 705 elliptical polarization 183 elongation 755 eluting power 88 elution on a plateau 214 mode 221 emission 480 emissive solvatochromism 657 emitted fluorescence 178 empirical acidity scale 558-559, 562 model 27 parameter 2 solvent parameter 777 enantioselective reduction 96 end-chain propagation 827-828 endothermic 1 effect 477 energetic barrier 37 contact point 245 interactions 245 energy barrier 32 conservation law 383 contribution 15, 27 decomposition 21 difference 40 expenditure 162 gap 176, 712 difference 717 gradient method 50 of cavity formation 496 of interactions 137 of mixing 136 of vaporization 246 partition 15

Index storage mechanism 792 term 360 transition 715 engineered morphological structure 744 enol constant 2 form 419 enolization 43 capability 2 power 2 entangled chains 373 entanglement 740 enthalpic terms 779 enthalpy 62, 158, 474, 514, 565, 790, 793, 797 change 57 contribution 165 energy 159 of mixing 149, 158, 160, 321 of relaxation 289 of vapor formation 278 of vaporization 217, 222 entropic contribution 202 effect 794 parameter 250-251 entropy 36, 158, 165, 243, 790, 793-794, 797, 804 change 137, 250 of mixing 161 component 323, 336 contribution 165 deficit 798 of mixing 158, 497 term 779 -enthalpy compensation 796 environment ecology 518 polarity 707 environmental characteristics 99 fate 89 pollution 749 eosin 188 EPA 71 equation 280 of state 198, 218, 244, 247-248, 250, 256-257, 259-260, 264, 266, 379

Index equidensity surface 28 equilibrium 36 cell 208, 223 chemical process 441 composition 488 concentration 345, 543 constant 2, 88, 172, 267, 417, 421, 430, 438, 441-445, 447-449, 452, 461, 467, 469-470, 473, 485, 508, 523, 531, 538, 561, 565, 765 angle 512 fraction 327, 328 parameters 39, 543 process 468, 473 scheme 418 shift 558 solubility 486, 489, 505 solvent absorption 209, 211, 224 state 222 swelling 154, 162, 164, 242, 281, 283-284, 319-321, 323-326, 330, 336, 339-342, 345, 347, 349, 354, 356, 368 data 333 degree 350 ratio 317 state 309 temperature 204, 256 time 205, 209 correlated function 171 equimolar solvate 453 equimolecular composition 434 equipment design 277 wall 64 equipotential surface 28 equivalence point 558, 563 equivolume mixture 427 permittivity 427 ESR 2, 758, 840 essential state model 709 ester side chain 827 esterification 2, 12, 95 ET(30) 88, 771, 786 scale 624 value 87-88 etching 518 ethanol 2, 12, 96 etherification reaction 421

865 ethyl acetate 96 lactate 3 ethylene glycol 22, 95 -propylene rubber 319 eutectic liquid 188 evaporation 85, 750 enthalpy 277-278, 280 loss 478 number 85, 89 process 374, 376 rate 58, 62, 85, 374-376, 478 time 751-753 excess energy model 262 enthalpy 247 entropy 246-247, 799 Gibbs free energy 265 scattering 229 thermodynamic properties 247, 251 volume 247, 266 effect 245 of mixing 246 excessive molar volume 434 exchange equilibria 508 interaction 421, 470 mechanism 421 process 467 reaction 508 repulsion 18 exciplex 802, 804 excitation 701, 712 excitation energy 691, 693 frequency 179 pulse 711 excited molecule 712 solute 712, 787 state 176-177, 180, 660, 691-693, 696-697, 701, 712, 759, 787 exothermic 1 enthalpy 513 expansibility 795 expenditure of energy 161

866 experimental isotherm 431 explosive limits 86, 89 exponential potential 19 exposure time 361 external degree of freedom parameter 254 extract 84 extraction 2, 59 conditions 479 yield 479 extractive distillation 94 extrathermodynamic correlation 485 extreme swelling 319, 322-324 F fabrication speed 480 fatty acid ester 3 Fedors' method 481 supposition 300 feedstock 91, 95 femtosecond laser 177 transient absorption technique 181 fertility 71, 85 fiber 750 fibrilar crystalline structure 756 Fick’s law 363 Fickian diffusion 367 kinetics 358 field 171 gradient 171 strength 80 filler 363 film thickness 361, 375-376 -forming process 479-480 finite strain 349 fitting parameter 249 flame ionization detector 212 propagation 64 flammability limit 63-64, 86 flammable liquid 86 flash point 64, 76, 86, 89, 96 determination 64 estimation 63 flexible chain 161

Index Flory's equation 292, 309 of state 254, 257 free-volume equation of state 257 interaction parameter 515-516 model 249-250, 258 theory 308, 317, 327 -Huggings’ law 402 approach 231, 246 combinatorial entropy 255 term 255 constant 402 derivation 245 equation 158, 389 expression 245 interaction function 246 parameter 199, 308 mixture 244 model 265, 267 parameter 144, 322, 349-350, 352, 356 relation 242 theory 165, 199, 202 -Orwoll-Vrij model 248, 255 -Rehner equation 162, 322-323, 336, 338, 342, 350, 355 theory 326 flowing afterglow 14 fluctuating dipole 18 fluctuation density 172 -dissipation response 171 fluid diffusion 349 equation-of-state 266 fluorescence 696 detection 181 emission 646 intensity 178, 747 lifetime 705 properties 177 quantum efficiency 711 recovery after bleaching 362 signal 711

Index spectrum 177 shift 168 upconversion 186, 188-189 method 177 fluorescent chromophore 711 excited state 697 probe 625 fluorinated container 749 fluorination process 525 fluorine 749 fluorous biphase 823 biphasic catalysis reaction 3 flux 518, 572 formaldehyde dialkylacetals 3 formamide 190 formation constant 471-472 fossil fuels 96 Fourier transform infrared 360, 511, 754, 795 fractionation 744 fragmentation reaction 82 Franck-Condon principle 495, 787 state 697, 699, 787 Franklin's concept 523 definition 528 solvosystem concept 525, 529 free activation energy 439 energy 34, 161, 167, 172, 291, 441, 443, 462, 797, 801 change 464, 497 difference 173 linearity 439 of activation 500 of association 462 of complex formation 496 of desorption 515 of mixing 136, 327, 365 of solution 485, 486, 490 of transfer 776 surface 802 transfer 455 induction decay of coherence 184 ions 461

867 radical 37 polymerization 823, 828, 830 propagation reaction 826 rotation 636 space 22 tautomeric form 419 volume 55, 159, 164, 247, 370, 761, 781, 795, 803 coefficient 358 contribution 254-255 control 370 correlation 359 dissimilarity 247, 255 effect 247 expression 255 model 244 term 359 theory 266, 362, 374 water 172, 174 Freed-Flory-Huggins equation 265 freeze resistance 96 freezing point 84 depression 67 frequency dielectric constant 169 friction coefficient 761 frozen non-equilibrium state 204 fugacity 219 coefficient 197, 244, 256 functional flexibility 490 G gas bubble dynamics 393 chromatograph 214 kinetic theory 14 phase 14, 17, 30-31, 34-35, 37, 168 tank 749 -expanded liquid 3 -liquid chromatography 324 partition coefficient 89 gate pulse 178 Gee's equation 154 gel 3, 365, 370, 754 phase 366 structure 754 gelation 754 behavior 754

868 mechanism 754 time 742 general acidity scale 541 solvent effect scale 656 generalized scale of acidity 534 solvosystem concept 533 genome 85 geometrical distortion 33 geometry 826 Gibbs' energy of mixing 158, 164 of solvation 649 equation 136 free energy 440, 544, 763 of mixing 196, 199, 229, 231, 240-241 of swelling 242 residual 199 solvation energy 440 -Dugem-Margulis equation 204, 468 Ginzburg-Landau theory 188 glass corrosion 559 transition enthalpy 289 jump 291 region 213 temperature 188, 213, 224-225, 285, 358-359, 369-370, 761 glassy microdomain 371 polymer 161 state 372 global fitting 178 warming potential 72 gloss 761 glove 357 glycerol 3, 22, 507, 660-661 -water mixture 493 glycidyl methacrylate 38 glycine 31-32, 34 solution 30

Index graphene 481 electrostatic repulsion 481 oxide dispersion 481-482 reflectance spectra 481 graphic display 28-29 graphite exfoliation 481 gravimetric sorption 201 measurement 211, 224 gravitational force 15 green solvent 96 technology 518 ground electronic state 176 state 691-692, 696, 712-713 energy 693, 712 group-contribution lattice 266 method 265 grown crystal 519 Guoy-Chapman layer 187 Gutmann’ acceptor number 644 gyration radius 480, 738-739, 744, 747 H halide melt 573 hydrolysis 536 halobenzene 824 halogenated hydrocarbon 63 solvent 773 halogenation 95 Hammett 2 equation 623 function 539, 546 reaction constant 623 Hammond-Stokes plot 53 relation 49 Hansch-Leo constant 84 Hansen’s 5 approach 144-145, 148, 165, 301 scale 73 solubility parameters 149, 267, 751 volume 154 /Flory-Huggins model 267

Index hard chain molecule 261 domain 336, 338, 341, 347 rupture 346 segment 343 domain 354 sphere 780 potential 18, 25, 48 reference chain 261 repulsion 19 hardcore repulsion 18 volume 198 harmonic frequencies 28 haze 62 head-head conformation 840 gas chromatography 201, 214, 225, 267 head-tail geometry 840 heat absorption 161 capacity 289, 790, 792-793, 796 conductivity 383 dissipation 387 flow 375 flux 387 loss 278 movement energy 477 of combustion 67 of mixing 136, 149, 159 of reaction 67 of vaporization 61, 62, 67 supply rate 62 transfer 366, 392, 406 coefficient 404, 407, 409 heating surface 399 helical conformation 754 form 754 Helmholtz energy of mixing 265 free energy 512 Henderson-Hasselbalch function 682 Henry's constant 76, 221, 225-226, 255, 262, 264 law 75, 195, 364, 467, 544 heteroassociate 419

869 heterogeneous two-phase system 365 heterolytic breakdown 528 dissociation 527 heteromolecular adduct 423, 445 associate 418, 430, 434 formation 448 ionization 420 association 419-420, 432, 434, 445, 447, 449, 451, 454, 460, 469, 471 constant 432, 467 process 437, 447, 451, 467 interaction 431 hexagonal ring 659 hexamethylphosphoric triamide 3 hexane 160, 324 concentration 752 high-pressure mass spectrometry 14 liquid chromatography 502 Hildebrand 5 and Scatchard equation 136 hypothesis 55, 365 solvent activity 76 model 73 solubility parameter 72-73, 83, 769 theory 52, 136, 158 Hills notation 74 hindered translational motion 184 Hodge-Sterner table 70 hole 358 free volume 359 size 358 theory 55, 251 homomolecular association 417, 420, 442-443, 469-470 constant 418 process 431, 442 homomorph 622, 627, 637 concept 148 homopolymerization reaction 824 homopropagation 826 rate 824 coefficient 835 reaction 824, 831

870 Hook's law 207 horsepower 59 Huggins’ equation 280 interaction parameter 158 parameter 149 Hughes 13 -Ingold rule 13 theory 779 human disease 748 sense of smell 70 humidity 62 Huyskens-Haulait-Pirson approach 135 hybrid arrangement 27 hybridization 659, 789 hydration 22, 175, 793 free energy 805 shell 33, 172-173, 175-176 hydrocarbon 82, 148 chain 186, 759 hydrochlorofluorocarbons 86 hydrocracking 92 hydrodealkylation 95 hydrodynamic cavitation 398 interaction 385 resistance 408 hydrogel 368, 369 swelling 369 hydrogen acids 421 atom 823 bond 20, 21, 31, 37, 144, 301, 362, 693, 713, 737 accepting ability 812 acceptor 81-82, 699 basicity 22, 636 contribution 146 coupling 172 donor 22, 81-83, 699 donor site 22 formation 761 formation enthalpy 151 interaction 21, 48, 144, 787 potential 144

Index rupture 163 shift 701 bonding 79, 82-83, 143, 144, 172-173, 259, 266, 362, 507, 620, 649, 693, 699, 712, 768, 790, 827 density 22 energy 143 environment 22 interaction 73 network 186 number 143 solvent 760 bridges 43 protagonism 20 hydrolysis 82, 536, 566, 567 constant 592 hydronium ion 668 hydroperoxide formation 758 hydrophobic 793 behavior 795 effect 22, 489, 794 interaction 15, 22, 82, 487 solute 794 surface 185 hydrophobicity 84, 796, 798 parameter 491 hydroxyl group 42, 57, 66, 75 radical 72 hygroscopic solvent 84 hygroscopicity 84 hygroscopy 84 hypernetted chain integral equation 50 hyperpolarizability 709, 715 hypsochromic sensitivity 644 shift 3, 82, 625, 644, 645, 712 solvatochromism 657 hypsochromism 624 I iceberg model 22 ideal entropy 137 of mixing 136, 159 gas limit 248, 257 mixing 266 solution 453

Index ignition energy 65, 66 source 63, 65 immiscible solvents 84 immobilized enzyme system 369 impurities 565 incident radiation 375 incompressibility condition 307 incompressible media 307 indane 480 indazole 659 indicator 553 electrode 582 calibration 563 induced dipole moment 80 dipole-induced dipole interaction 18 induction 17 interaction 143 interactions 148 inductive measurement 242 industrial coating 67 process control 744 inert 81 gas 64, 75 infinite dilute case 214 dilution 212, 267 activity coefficient 211, 267 infinitely dilute solution 49 infrared 2 absorption spectroscopy 190 spectrum 182 optics 518 pump-probe spectroscopy 190 Ingold 13 inhalation 70 inhomogeneity 64 initial state 13 initiation process 823 reaction 823 initiator decomposition rate 823 efficiency 834

871 injector block 214 inkjet 477 inner coordination sphere 791 instability 748 instrument response function 177 interacting components 433 mixed solvent 435 solvent 701 solvent molecule 83 interaction 164, 265, 432 energy 15, 148, 158, 506 of links 161 enthalpy 135 function 200 mechanism 511, 779 parameter 164, 199, 250-251, 322-323, 326, 330 potential 16, 19, 698 strength 701 term 742 interatomic distance 50 interaction 50 spacing 18 interchange energy 246 interface boundary 580 energy 579 morphology 511 motion 387 interfacial structure 701 tension 506-507, 745 water 172, 186-187 intermediate 421 state 444 intermolecular 20 association 748 attraction 258, 298 attractive force 783 bond 365 bonding configuration 791 complex 742 distance 16, 17, 19 energy 248 force 1, 15, 20, 698, 817

872 hydrogen bonds 80 interaction 21, 49, 80, 136-137, 194, 302, 417, 691, 780 energy 298 theory 15 mechanism 32, 42, 43 potential 261, 780 energy 257 function 50 process 43 proton transfer 32 repulsion 782 segment-segment interactions 264 vibrational mode 184 spectrum 186 internal energy 136 of mixing 137 intersolute effect 486, 497 interstellar medium 30 intramolecular 20 bonding 21 charge-transfer 3 hydrodynamic interaction 739 hydrogen bond 645 interaction 82 mechanism 32-33 motion 170 nuclear relaxation 697 polymer 83 process 32 proton transfer 32 relaxation 179 intrinsic viscosity 738, 741-742 inverse gas chromatography 196, 512 gas-liquid chromatography 195, 201, 211 apparatus 212 inversion process 750 inverted solvatochromism 657 ion 36-37, 81 associate concentration 435 association 461, 464, 466 constant 461 process 461-462, 465, 467 chromatography 666 concentration 465

Index product 461 cyclotron resonance 14 dipole interactions 699 dissociation process 461 formation 420 kinetic energy 14 pairing 790 radius 549 -dipole interaction 454, 459 ionic associate 420 concentration 461 association 420, 475 constant 457, 476 process 476 concentration 463 couple 419 dissociation 420 equilibrium 461 hydration 805 interaction 816 liquid 3, 22, 167, 188, 480, 707, 777, 809-810, 813-816 high-temperature 518 polarity 817 room-temperature 518 media 527 melt 518, 528, 533, 541, 554, 569 pair 477 formation 477 barrier 477 radius 542, 805, 807 solvation 805 solvent 518, 528, 534, 536, 538, 542 composition 538 high-temperature 526 impurities 518 strength 36, 472 structure 31 substance dissolution 17 transition state 779 ionization 14, 43, 668, 826 constant 420, 438, 467 potential 784 ionized complex 419 species 738

Index ionizing solvent 623 ionophore 466 irradiation flux 585 isobaric expansibility 781 isochemical potential 197 isochore equation 445 isochoric conditions 206, 782 swelling 243 isodielectric mixture 459 solution 464 universal solvent 449 values 473 isohydric method 676 isokinetic relationship 768 isolated molecule 30 isomerization 13, 35, 41, 43, 91-92 equilibrium 444 reaction 418 isoparaffins 91 isopiestic isothermal distillation 218 measurement 206, 231 method 265 sorption 264 balance 215 sorption measurement 207 technique 224 /desorption 201, 205 technique 206 vapor pressure/sorption measurement 218, 226 sorption 214, 225 apparatus 208-210, 211 isoplethal diagram 239 isopolar 37 isorefractive phase 238 isotactic 754 polystyrene 162 isotherm 207 calculation 427 shape 434 isothermal compressibility 160, 781, 790 conditions 206

873 distillation 201, 206 saturation 575, 578-579 method 570, 572, 588 isotropic 173 exchange 526 IUPAC systematic nomenclature 74 J Jackob's number 402-403 Jaumann's derivative 383 Jouyban-Acree model 508 jumping unit 358 K Kamachi expressions 833 Kamlet-Taft parameter 816-817 solvatochromic parameters 699 solvent parameter 812 Kauri butanol number 73-74, 84, 133 keto-enol equilibrium 419 isomerization 43 tautomerism 2, 13, 42 transformation 419 ketonic form 42 kinetic control 39 curve 350, 356 method 535 swelling curve 315 Kirkwood correlation 798 factor 789 function 766 -Riseman-Zimm model 385 Knauer membrane osmometer 227 knot 746 Knudsen method 279 Henry, Cox equation 85 Kohlemann-Noll theory 383 Kosower 3 scale 625 Kratky camera 232 L laminar thickness 749

874 Langmuir method 279 sorption 364 Laplace transform 176 Laporte's rule 708, 716 laser central frequency 184 flashing rate 827 pulse width 178 latent heat of vaporization 20, 277-278 lattice fluid equation 250 model 244, 251, 256 theory 250 size 250 theory 200 -hole theory 250-251 law of definite proportions 12 Le Chatelier's law 65 principle 522 Leffler-Grunwald delta operator 489 Legendre polynomial 684 Lennard-Jones disk 797 energy 784 potential 19, 20, 48, 50 783 lethal dose, LC50, LD50 70, 85 leveling effect 464 Lewis acid 422, 525-526, 668, 775, 823, 827 parameter 511 reference 81 /base behavior 79 acidity 81, 88 /basicity 81 base 81, 521-522, 775 parameter 511 basicity 88 scale 81 definition 522, 524 number 403 liate activities 437 ion 437-438

Index libration motion 178, 189 librational motion 184 lifetime 759 Lifshitz-van der Waals interaction 511 ligand 521, 807 light absorption 88, 480, 703 angular frequency 715 excitation regime 707 pulse 183 scattering 229, 232 velocity 59 -absorbing solute 82 -emitting diode 480 efficiency 480 like dissolves alike 789 limiting activity coefficient 225 solvent activity 264 line width parameter 710 linear correlation 61, 88 free-energy relationships 5 polymer 161 regression analysis 88 lionium ion 437-438 lipase 479 lipophilic hydrocarbon-like group 82 lipophilicity 665 Lippert-Mataga 701 liquid absorption 306 compressibility 379 crystal 187 distribution 308-309 phase 1, 36, 76, 198, 244, 320 composition 323, 325 state 14 theories 780 transport 752 waste 518 with memory 383 /liquid phase-transfer 2 -liquid demixing 224, 247 behavior 231

Index equilibrium 237 data 267 extraction 94 lithium cobaltate 536 London's forces 17 lone electron pair 645 long range effect 24 longitudinal stress 308, 310 stretch 306-307 Lorentz local field theory 713 -Berthelot rule 50 -Lorenz correction 703 Lorentzian 715 lower critical solution temperature 163-164, 398 flammability limit 65 luminescence 568, 586 Lux acid 521 -base equilibrium 528 reaction 546 base 553, 594 -Flood acid 555 -base dissociation 537 equilibrium 544 interaction 534 process 532, 555 acidity 553, 556 base 556 definition 521-522, 527 indicator 544 lysozyme protein 188 M macromolecular chain 385 function 16 macromolecule 198 macroscopic continuum 83 macrostructure 752 magnetic suspension balance 266 Marangoni flow 477-478 Marcus electron transfer theory 16

875 Mark-Houwink relationship 386 martensite 410 Martin equation 386 mass action law 523, 526 calorimeter 278 conservation law 382 fraction 424 transfer mechanism 38, 305 transport 364 uptake 369 mater conservation law 307 material deformation 305 design 47 extension 309 stability 758 volume 306 mathematical model 349 modeling 666 maximum permissible concentration 69 Maxwell's liquid 384 model 383 Mayo-Lewis model 830 mean dipole moment 443 field potential 799 polarizability 80 spherical approximation 807 -field theory 782 mechanical action 341 equilibrium 307 stress tensor 307 toughness 357 mechano-diffusion mode 305 medicinal chemistry 84 medium effect 486, 488, 506 polarizability 659 melt acidity 535, 580, 592, 595, 597 basicity 554 cation acidity 559 decomposition temperature 558

876 neutrality point 535 oxoacidity parameters 538 viscosity 742-743 melting 518 enthalpy 366 heat 163 point depression 292 can 195 temperature 20 membrane 227, 266, 357, 744, 750 asymmetry 228 lifetime 364 morphology 750 osmometer 226 osmometry 196, 216, 226, 231, 243 oxygen electrode 561 pore size 749 selectivity 750 surface 228 Menschutkin 2, 12 kinetics 647 reaction 37, 38, 647, 770, 779 menstruum universale 11 metal chloroaluminate 521 electronegativity 556 oxide precipitation 568 metastable condition 164, 165 metering 59 methacrylate polymer 827 methacrylic acid 22 methanol synthesis 43 -water system 496 methanolysis 470 methyl methacrylate 824 methylcarbazole 659 methylindole 659 methylpyrrole 659 methyltrioctylammonium chloride 22 Metropolis group 48 scheme 47 Meyer-Schuster reaction 41, 42, 43 micelle 3, 745 microbalance 209 detection 224

Index technique 207 microcalorimeters 278 microemulsion droplet 748 diameter 748 microfabrication 711 microfiltration 749 membrane 749 microorganism 86 microphase segregation 343, 346, 356 separation 336 microscopic description 23 environment 34 model 28, 714 order 36 microsegregation 341 microstructure 830 microwave power 376 -assisted drying 376 minimum energy 24 ignition energy 66 spark ignition energy 66 mixed solvate 454 solvent 215, 322, 417-422, 424, 430, 433, 439, 453-454, 456, 458, 460, 463, 466, 470, 475-476, 489, 495, 503-504 composition 423, 456 effect 441 physical properties 423 system 503, 505 mixer 59 mixing ratio 190, 477 rule 248, 250, 256, 258-259, 481 mobility 373, 760 mode coupling 188 model approximation 196 prediction 265 process 485 moisture-free environment 84 molality 265 molar attraction constants 298

Index cohesive energy 135 conductivity calculation 435 enthalpy of evaporation 85 extinction coefficient 713 fraction 158, 424, 425, 434, 456 latent heat of vaporization 298 polarization 425 ratio 341 NCO/OH 347 structural unit 291 transition energy 508 volume 68, 135, 264, 277-278, 284, 299, 349, 356, 365, 425, 428-429, 434, 746 deviation 435 equation 435 -fractional composition 428 mold 749 mole fraction 516 molecular absorption 696 aggregation 746 association 76 cavity 28 complex 755-756 design 22, 47 diameter 56, 137 dipole moments 701 dynamic simulation 24 dynamics 23, 26, 34, 47 simulation 190, 701 ensemble 48 design 47, 48, 49, 50 formula 74 hydrodynamics theory 186 interaction 55, 135 level 16 mass 60, 61, 74, 144, 158, 161 between crosslinks 366 mechanism 40 model 167, 754, 780 movement 17 nonsphericity 799 orbital calculation 48, 50 method 38 probe 622, 699 reorientation 176

877 rotation 16 separation 137 shape 649 sieves 75 simulation 23, 48, 49, 265 molecular size 36, 244, 649, 795 solvent 518 structure 161, 755, 757 surface 28-29 area 55, 500 model 29 symmetry 67 theory 782 volume 55, 363, 366 weight 58, 60, 62, 361-362, 372-373, 480, 516, 738, 740, 760 distribution 760 -scale curvature effect 506 molecule symmetry 709 molten oxygenless medium 528 polymer 247 salt 518, 519, 544, 553, 565, 570 silicate 559 sulfate mixture 535 momentary dipole 17 moment-moment correlation function 175-176 monoacidic base 532 monomer complex 839 concentration 827 devolatilization 264 electronic energy 50 formation 443 -dimer equilibrium 442 -monomer charge transfer complex 836 -solvent complex 835 mono-phase reaction 3 monoprotic acid 665 Monte Carlo 701 method 26 model 23 modeling 257 simulation 47, 264, 797 morphological engineering 748 feature 745

878 morphology 62, 480, 744 motion equations 47 multi-dimensional approach 142 multilayer coating 376 multiparameter correlation equation 82, 88 multipolar interaction 189 multishell continuum model 186 multivariate statistical method 88 mutagen 85, 99 mutagenesis 85 mutagenic 71 mutagenicity list 71 mutation 85 mutual diffusion 358 coefficient 359-360 dissolution 280 solubility 135-136 Myers-Scott function 684 N N,N'-dimethylpropyleneurea 3 N,N-dimethylformamide 69 nanocavity 186 nanofiber 746 nanosphere 745-746 nanostructure 744 nano-structured elastomer 343 naphthalene 504, 824 natural broadening 696 negative enthalpy 88 free energy 145 partial charge 692 solvatochromic shift 691, 693 neoteric solvent 3 net heat of combustion 86 network density 330, 333, 338-340 knot 162 parameter 339, 354 neutral configuration 31 point 532 solution 531 neutrality condition 438 point 532-533, 535

Index neutron diffraction 754, 806 scattering 233 Newton 47 flow law 379 Newton-Euler equation 47 Newtonian viscosity 738 Newtonian viscosity 408 NIOSH 69 nitrate melt 535 nitration 422 nitric acid 422 nitrile rubber 361 nitrobenzene 693 nitrogen pentoxide 535 nitro-isonitroso tautomerism 2 nitromethane 775, 790, 809 nitronium cation 535 nitroxide mediated polymerization 823 radical 834 N-methyl formamide 190 N-methyl pyrrolidone 824 N-methyl-2-pyrrolidone 481 nonaqueous solvent chemistry 516 noncovalent molecular complex 496 nondestructive imaging 711 non-electrolyte solution 133 non-equilibrium response 171 swelling 349 non-interacting components 425, 427-428 non-ionizing solvent 81 non-ionogenic ionic associate 420 nonlinear theory 305 nonpolar 2, 80, 796 nonpolar aprotic solvent 302 cavity 185 excited state 701 polymer solution 254 relaxation 188 solute 713 solvation 779 solvent 82, 167, 191, 692 substrate 73 surface area 492, 506

Index non-random two-liquid activity coefficient model 267 model 265 non-redox system 668 nonspecific dispersion 82 nonsphericity effect 799 normalized scale 699 Norrish type II 759 NTP 71 nuclear configuration 17 distortion 15 force 15 magnetic resonance 2, 13, 360, 443, 649, 699, 763, 795, 811-812, 844 chemical shift 81 probe 812 pulsed-gradient spin-echo 360 shift 766, 812 spectra 82 wastes 518 nucleate boiling 404, 407 nucleation frequency 404 nucleic acids 16, 21 nucleophile 82 nucleophilic ability 767 attack 42-43 monomer pair 832 numerical integration 47 N-vinyl-2-pyrrolidone 826 O Occam's razor 49 octane 160 octanol/water partition coefficient 84, 491-492 octupolar 789 odor detection 70 threshold 76 offending substance 70 OH spectral diffusion 183 stretching region 182 Oldroyd equation 382 oligobutadiene diol 319 isoprene diol 330

879 oligomer 216, 343 solution 224 one-dimensional solubility parameter 161, 280 one-photon absorption 707 schematic illustration 712 spectra solvent effect 712 Onsager 701 cavity field 713 model 700 theory 713 -Böttcher theory 705 Ooshika-Lippert-Mataga equation 170 optical clarity 357 dielectric constant 768 image 478 Kerr effect 183, 185 spectroscopy 190 micrograph 755 properties 369 single crystal 519 oral 70 orbital energy 770 theory 834 organic base 369 cation 189 solar cell 480 organism 85 orientation 16-17, 754 interaction 143 of bound water 172 orientational correlation 797 function 169 relaxation 697 oriented dipole 712 orthorhombic 755 oscillating component 183 oscillator probe 184 strength 696, 703, 710, 713, 715, 717-718 OSHA 69, 71 osmometer 227 osmometry 195, 201

880 osmotic balance 38 coefficient 265 equilibrium 241 pressure 12, 229, 233, 367 second virial coefficient 229 virial coefficient 195 expansion 230 Ostvald-Freundlich equation 578 outer electron shell 519 overlayer thickness 514 oversaturation 580 overspray loss 67 oxidant 518 oxidation 95 degree 521 oxide acidity 558 ion 527, 557 adduct 536 concentration 537 donor 536 equilibrium constant 536 exchange 575 powder calcination 579 oxidizer 63-64 oxoacidic acid-base pair 534 properties 544-545 oxoacidity 522, 534, 537, 543 function 541 scale 550, 552 oxoanion 535-536 oxobasicity index 540-541, 544-546, 548-549, 551-552, 564 oxochloride 574 oxygen concentration 64, 66 electrode 556 electrode reversibility 559 impurities 568 index 523, 555 oxygen-less melt 527, 534, 536-537 ozone depleting potential 72, 86 P π bonding network 827

Index packaging 59, 357 material 357 packing density 367 fraction 261, 780 Padé approximation 784 paint components 701 paint industry 74 pairwise interaction energy 265 Papirer's equation 512 Paracelsus 11 paraffins 91 parison 749 particle scattering factor 230 partition coefficient 22, 495 constant 84 energy scheme 23 function 251 scheme 15 partitioning 2 Patterson equation 159 Pauling crystal radius 805 π-complexation 826 peak wavelength 482 Pearson’s classification 519 Peclet number 387 Peiffer expression 147 penetration depth 312 Peng-Robinson equation 262 pentagonal ring 659 Percus-Yevick relation 50 perfect gas 30 perfluorinated hydrocarbon 3 perfluorohexane 3, 267 perichromism 3 periodic boundary conditions 24 periodical loading 343 permanent dipole 148 moment 80, 142 dipolar moment 15 permeability 5, 749 coefficient 364 permeation 363-364 flux 750

Index permittivity 417-418, 420, 425, 429-430, 441, 442-443, 445, 461, 464, 473, 475, 477 absolute temperature coefficient 427 change 437, 460 effect 454 function 426 temperature coefficient 427 peroxide 758-759 formation 758 persistence length 480 perturbation 170 approach 795 expansion 803 theory 709, 715 perturbed-hard-chain theory 257 perturbing potential 260 pervaporation flux 752 membrane 749 parameter 753 transport parameters 752 perylene diimide drop 478 petrochemical industry 91 petroleum industry products 92 Pfizer 3 pH 76, 368, 369, 500, 516, 742, 826 measurement 516 pharmaceutical 3, 6, 84 compound 266, 486 pharmacokinetic properties 665 phase boundary 365, 579 diagram 163-164 equilibria 48 equilibrium calculation 261 separation 159, 398 process 750 temperature 480 transition 398, 701 volume ratio 239 -transfer process 35 phenomenological 485 approach 817 model 492 theory 495, 499, 502 thermodynamics 200-201, 228

881 phosphorescence 696 rate constant 760 phosphorus oxochloride 524 photochemical ozone creating potential 86 photocleavage 759 photodynamic therapy 711 photoexcitation 170, 176, 191, 660 photolysis 759 photon echo 183, 188 spectroscopy 181, 188 photooxidative process 758 photoresist 759 photosensitizer 759 action 759 photostabilizer 760 photovoltaics 480 physical approach 780 meaning 135 network 336, 338, 340-343, 346-347, 354 density 340, 344, 347 process 2 properties 79 piezoelectric detection 224 detector 207 method 211 quartz crystal 210 sensor 223 sorption 201 detector 207, 210 technique 224 Piola stress tensor 307 Planck constant 716 plastic container 749 plasticizer 38, 319, 354, 363 sorption 347 plasticizing action 759 effect 761 polar 13, 137, 765, 796 contribution 147 environment 715 force 266 group 161 head 186 headgroup 187

882 hydrogen-bonded solvent 692 interaction 143, 828 interactions 144 liquid 143 medium 16, 30, 167 molecule 148 non-hydrogen bonded solvent 692 organic solvent 480 solute 168 solvation 167, 779 dynamics 167 solvent 83, 148, 167-168, 176, 187-188, 693, 713, 737, 779, 823, 831 species 36 substance 17, 299 system 507 polarity 160-161, 336, 340, 343, 347, 445, 471, 492, 495, 668, 692, 758, 760, 790, 828 definition 80 effect 260, 830 index 439 scale 627, 629, 768, 786, 816-817 polarizability 17, 80, 88, 168, 181, 189, 503, 699, 705, 759, 783, 799 behavior 660 correction parameter 699 term 650, 700, 768-769 effect 168 volume 80 polarizable continuum model 38 polarization 37, 67, 519 energy 15 interaction 17 polarizing action 577 polaron 801 polar-polarizable spheres 781 poly(acrylic acid) 744 poly(α-methylstyrene) 229 poly(ethylene glycol) 222, 236, 255 poly(ethylene oxide) 22, 234, 742, 755 crystal structure 756 poly(lactic acid) 86 poly(N-vinyl caprolactam) 265 poly(propylene oxide) 742 polyacrylates 285 polyacrylonitrile 161, 750

Index polyamide 515, 749, 750 polyaniline 761 polybutadiene 160 nitrile rubber 283 urethane 316, 319, 340 elastomer 155 polycarbonate 260, 750, 755 crystallinity 756 polychloroprene 161 polydiethylene glycol adipate 330 polydimethylsiloxane 233, 255, 761-762 polydisperse polymer 231, 233-234, 239, 240 polydispersity 228 polyester urethane 283, 319 polyether urethane 281 polyetheretherketone 369, 755 polyetherimide 750 polyetherimide membranes 751 polyethersulfone 750 polyethylene 86, 162-163, 749, 758 crystal 749 fluorination 749 thermolysis 760 wax 760 polyethylmethacrylate 135 polyfluorene 479-480 crystallinity 480 polyimide 145, 154, 747, 750, 759 polyisobutylene 285, 739 polyisobutylmethacrylate 135 polyisoprene 160 polymer blend 232, 250 brush 744-745 chain 161, 200, 761, 823, 827 coil 83, 827 concentration 204, 218, 745, 752 crystallinity 363 density 300 dissolution 160 equation of state 197 equilibrium swelling 280 gel 349, 740 jumping unit 359 matrix 349 molecular weight distribution 823 molecule dynamics 233

Index morphology 757 network 162, 349, 354 swelling 356 permeability 749 polydisperse character 201 processing 742 reinforcement 757 segment 55, 158, 233, 248, 366 segmental relaxation 367 solubility parameter 280, 282, 285 solution 194, 197, 204, 209, 221, 234, 246, 252, 263, 280 dilute 194 equation of state 247 liquid-liquid demixing 196 thermodynamic data 215 model 198 properties 221 thermodynamics 198, 244 vapor pressure 202 vapor-liquid equilibrium 196 virial coefficient 235 stability 755 structure 133 superstructure 151 surface tension 152 swelling 283 volume fraction 162 /solvent interactions 83 polymeric membrane 364 solution 395 polymerization degree 200 reaction control 823 yield 760 polymerizing medium 828 polymers solubility parameters calculation 298 polymer-solvent interaction 159 system 234 polymethacrylates 285 polymethylmethacrylate 135, 161, 361-362, 369, 514-515, 741 aggregation 516 polymorph 791

883 polyolefin 750 polyoxybutylene glycol 330 polyoxypropylene triol 330 polyphenylene 739 polyphenyleneoxide 750 polypropylene fluorination 749 polyprotic acid 665, 675 polypyrrole 514, 515 polypyrrole oxidation kinetics 38 polysilane foams 752 polystyrene 161-163, 213, 218, 231, 233-234, 236, 285, 360, 362, 744, 754, 762 stress-strain behavior 755 waste 760 polysulfone 750-751 polytetramethylene oxide 343 polytherm 473, 475 data 438 polythiophene 754 polyurethane 162, 330, 336, 340, 353-354, 375, 749 urea 354 -solvent system 337 polyvinylacetate 233, 236, 266 polyvinylalcohol 160, 236, 372-373 polyvinylchloride 161, 163-164, 746-747, 754 polyvinylmethylether 233 polyvinylpyrrolidone 187 polyvinylidenefluoride 749, 750 pore size 750 porous membrane 749 positive solvatochromic shift 691 potassium nitrate 532 potential barrier 43 potential energy 16, 83, 86, 135, 365, 788 surface 38, 39 function 48 potentiometric cell 549 method 555 titration 534, 551, 556, 558, 563, 572, 578, 581, 595, 675 method 572 power conversion efficiency 480 swelling mode 314

884 Poynting correction 219 precipitated oxide 570 precipitation 62, 549 value 751 prediction 322, 327 method 49 pre-exponential factor 824, 826 preferential solvation 508, 649, 830, 845 parameter 508 sorption 327-328 preliminary strain 348 swelling 152 pressure 158, 164, 797 measuring device 203 Prigogine's 251 approximation 247 cell model 249 model 249 theory 159 -Flory-Patterson equation 251 of state 251 model 257 theory 247, 249, 256 primary radical 823 principal component analysis 88 probe beam 183 charge transfer 622 homomorph 621 molecule 82, 167, 176 orientation change 621 polar character 622 solute 167 sphere 29 -homomorph couple 638 process condition 518 entropy 474 free energy 447, 462 kinetics 360 parameters 417 rate 417, 518 processing regime 751 product distribution 1

Index propagating radical 827-828 propagation 826-827 kinetics 830 rate 824, 829, 835 coefficient 826, 827 reaction polarity effect 831 step 826, 829-830, 832, 840, 842 protective layer 749 protein 16, 21-22, 188, 701, 748 protic 38 acid 457 acidity 531, 539, 553 ionic liquid 701 solvent 81, 88, 769, 773 protogenic 673 solvent 81 protolysis equilibrium 437 protolytic acid-base equilibria 533 solvent 539 proton 22, 80 accepting/donating 81 acceptor 21, 151, 338-339, 347 acidity 524 affinity 418, 423 coordination vacancies 460 donor 21, 151 function 423 migration 31 permittivity 458 primary medium effect 539 resolvation 459-460 process 457, 460 selective solvation 457 solvation energy 457 transfer 167, 420, 422, 668 reaction 81 protonation 42, 508 protonic transfer 32-34 protophilic 673 Proust 12 pulse photon-echo spectroscopy 180 response function 170 -induced critical scattering 232 pulsed laser polymerization 827

Index ruby laser 710 pure liquid 63 solvent 222 scale 621 vapor pressure 207 purification 533, 537, 568, 585 purity 56, 79 pyridine 828 pyrimidine base 188 pyrohydrolysis 542, 543 pyrolysis 95 pyronitrate ion 557 pyrophosphate ion acidity 564 pyrrole 622 Q quadrupolar 789 strength 789 quadrupole moment 788 magnitude 171 quantitative structure/activity relationship 84 quantum chemical calculation 460, 718 chemistry 47 dots 481 mechanical calculation 700-701, 783 equation 28 nature 18 mechanics 27, 28, 30, 32 methodology 701 oscillator 784 treatment 27, 30 yield 759 quasi-equilibrium state 535 quasi-static boundary value 168 quaternization 2 quinonoid structure 713 R rabbit 70 radial distribution function 806 radiant energy 374-375 absorption 375 radiation quantum theory 707 wavelength 759

885 radiative rate constant 703, 705 radical 760, 823, 826-827 lifetime 758, 824 polymerization 826 stabilization 826 -radical termination 824, 829 Raman cross-section 184 spectroscopy 701, 816 random dense state 791 mixing 248, 250-252 network model 797 Raoult's law 202, 244, 648, 845 rat 70 rate coefficient 827-828 constant 36-37, 83, 169, 417, 765 limiting step 42 of drying 371 -limiting step 42 -of-strain tensor 379 Raul's law 389, 398, 402 Rayleigh factor 230 ratio 744 scattering 801 time 387 reactant 1, 36 complex 40 reacting solute 82 reaction catalyst 1 field 168 function 768 heat 278 mechanism 23 model 39 parameters 700 partner 1 path 31, 39, 42 products 3 rate 1, 12-13, 23, 35, 37-38, 42, 88, 700, 779 constant 38 solvent 267 effect 700 temperature 1

886 vessel 1 yield 1, 417 reactivity 36-37, 83, 758, 760 real free-volume relation 255 rearrangement reaction 419 receding contact angle 512 recovery 479 recrystallization 2, 579 red shift 82, 691, 707, 713 redistribution 176 Redlich -Kister function 684 -Kwong equation of state 259 reduced density 261 reduction entropy 778 reference concentration 218 configuration 349 melt 540 solvent 62, 502 state 245 reflection color 482 spectrum 482 refraction absolute angle 59 index 147, 713 refractive angle 59 index 23, 82, 147, 205, 235, 703-704, 709, 713, 768, 789 change 238 gradient 234 Reichardt's dye 712, 718 parameter 438 reinforcing filler 343 relative 13 acidity index 539 activity 473 basicity of solution 540 energy order 40 humidity 374 nuisance factor 70 orientation 16 permittivity 16, 23, 28, 33, 80, 82-83, 168, 229, 526 correlation 832

Index rate constant 37 scale 13 solubility 489 viscosity 738 relaxation 178, 186 process 175, 177 rate 368 time 69, 358, 381, 384-385 -controlled diffusion 367 reorganization energy 16 replication 85 reproducibility 477 reproduction 85 reproductively toxic 71 reprotoxic chemical 85 reprotoxicity 85 reptation 362 repulsion 37, 82 energy 19, 27 potential 19 repulsive electrostatic potential 480 repulsive force 18, 780-781 residual activity coefficient 253-254 chemical potential 244 term 246 contribution 245 function 246 molecules 371 part 246 solvent 370-371, 376 activity 248-249, 251, 255 residue 85 resistivity 68 resolvating agent 458 resolvation 449, 451, 452 constant 453-454, 456-457, 460, 467 free energy 459 process 447, 452, 457, 459-460, 471 enthalpy 459 resonance factor 760 restacking 481 restricted angular motion 191 restructuring 777 retardation time 382 retention time 212, 502

Index volume 502, 512 reverse micelle 186 osmosis membrane 227 titration 561 reversed phase liquid chromatography 666 reversible addition fragmentation chain transfer 823 Reynolds number 390, 395 rheological behavior 379 equation 379 properties 737, 755 Rider's approach 153, 155 model 144 rigid aromatic structure 628 chain 161 interlocking spheres 28 sphere 18, 29 ring alignment 754 risk assessment 64 rod-like structure 745 Rohsenow correlation 406 rotamer 627 energy 444-445 rotating ebulliometer 216 rotation 31 rotational degree of freedom 258 diffusion constant 169, 173 energy level 696 frequency 189 motion 258 pendulum 364 rotator 259 Rouse law 393 theory 384-385 RTECS number 75 rubber 161, 164, 319, 330 elasticity 196 membrane 361 natural 361 rubbery state 371 rubredoxin protein 188

887 S Saint-Gilles 12 salicylic stabilizer 760 sample swelling 352 Sanchez-Lacombe lattice-fluid model 251 theory 256 saturation detection 576 saturator 214 temperature 225 scaled particle theory 795 Scatchard equation 299 -Hildebrand theory 246 scattering intensity 231, 233 methods 196 theory 231 Schlieren photography 234 Scholte's extension 705 scintillation material 519 single crystal 568, 585 scintillators 518 Scriven number 401, 403 seawater 267 second osmotic virial coefficient 236 virial coefficient 219, 223, 228, 231-233, 264, 480, 744 region 244 sedimentation coefficient 234 equilibrium 196, 236, 243 threshold 285 velocity 234 segment fraction 248 number 251 size 250 segmented heterogeneous elastomer 347 polyurethane 343, 347 urea 343 selective solvation 5, 452 selectivity 750

888 self -diffusion 358 coefficient 51, 358, 360, 362 -dissociation degree 528 process 522 -ionization degree 524 process 523-524 semiconductor 477 semicrystalline polymer 371 semipermeable membrane 216 separation factor 752 layer 750 process 749 sequential addition method 592 shape fluctuations 176 shear modulus 352, 367 rate 738-739 stress 738 thinning behavior 742 shielding effect 827 short distance interactions 30 Shreder's equation 582, 586 solubility 574 shrinkage 62 side chain 816 length 815 silica gel 75 nanoparticles 748 silicon dioxide 565 Simha-Somcynsky equation of state 251 similia similibus solvuntur 11, 789 simulation 26 method 27 single crystal 568 temperature ebulliometer 216 singlet oxygen 650, 759-760 lifetime 759 quantum yield 759 singular spectral behavior 660 size parameter 250 skewness parameter 685

Index skin formation 376 layer thickness 753 skin thickness 751 small angle neutron scattering 195 X-ray scattering 195, 232 molecule 198 Small's method 298 snapshot 33-34 Snell's law 59 Snyder value 89 Soave-Redlich-Kwong equation of state 262 sodium metaphosphate 572 nitrate 528 soft energetic barrier 33 repulsion 19 segment 343, 347 solar cell performance 480 solid state 14, 36 surface 511 /solid reaction 1 -liquid equilibrium 198 solitary electron 20 solubility 21, 72, 277, 744, 795, 797 area 154-155 calculation 151, 300 criterion 151, 159, 164 data 266, 503, 549, 781 effect of pressure 164 estimation 569 limits 146 model 73 parameter 38, 73, 75, 133, 135, 137, 142, 145, 152, 277, 280, 302, 319, 321, 336, 481, 549, 751 approach 263 concept 5, 246, 336 polar component 148 prediction 151, 288 system 153 theory 164 prediction 151

Index product 577 sphere 145 radius 145 system variables 158 temperature effect 163 thermodynamic principles 164 volume 145, 154 radius 155 solubilizing power 74 solute 27, 55, 79-80, 89, 777 activity 486 cavity 27, 29, 506 dipole moment 168 energy change 15 equilibrium solubility 485 geometry 28 hydrophobicity 84 interaction energy 486 ion 17 molecular volume 738 molecule 696 nonpolar surface area 502, 506 partition coefficient 491 polarity 506-507 polarizability 168 polarization 15 quadrupole 171 solubility 503 solvent-accessible surface area 491 surface area 506 volume space 73 -solute interaction 267, 486-487, 495-496, 505, 713 -solvation shell 493 -solvent interaction 13-15, 23, 30, 34, 37, 39, 49, 79, 82, 487, 620, 767 system 167 solution 1, 17, 34, 84 free energy 489 lattice 159 phase 486-487, 500 statistical theories 159 solvate composition 419, 456 ionization 419 shell 453-456

889 composition 453-454, 456 -active component 450-452, 459, 463, 466, 473 solvated conjugate 530 proton 457 solvate-inert component 418, 450, 454, 463 solvating ability 437, 439, 668 agent 457 complex 508 effect 621 power 790 solvation 22, 36, 73, 82, 439, 442, 454, 470, 645, 668, 691, 768, 772, 776-778, 796, 827 ability 439 capability 80, 82, 87 chemical potential 784 component 188 constant 489, 492, 498, 502-503, 505 correlation function 170, 181, 186 dynamics 167-168, 176-177, 186-188, 191 effect 16, 486-487, 489, 495, 502-503, 505, 796 energy 35, 441, 444, 450, 460, 463, 488, 691-693, 697, 700, 769, 784 equilibrium 454 constant 487 exchange constant 505 free energy 27-28, 171, 784, 809 frequency 189 interaction 462 mechanism 768 model 648 parameter 494 power 80 process 452 relaxation 188-189 shell 22, 175, 487-488, 492, 505, 508, 766, 803, 805, 816 sphere 621 theory 785 solvational interaction modeling 698 solvation-inert component 441 solvative form 452 surrounding 447

890 solvatochromic absorption band 87, 716 analysis 645 approach 812 behavior 644, 770 chromophore 87 dye 3, 626, 701, 763, 809 effect 638, 696, 699, 707 equation 659, 700 indicator 645, 773, 811-815 method 639 molecule 712 parameter 660, 699 paranitroaniline 712 polarity parameter 492 probe 508 properties 508 red shift 693 shift 691-693, 697-698, 701, 766 spectral shift 691 solvatochromism 3, 82, 626, 629, 636, 645, 647, 649-650, 707, 714, 765, 767, 776, 786, 788, 818 inversion 656 negative 3, 714-715, 718 positive 3, 714, 717 solvency 83 solvent absorbance 86 acceptor number 778 strength 774 acidic/basic 81 acidity 637, 644-645, 660, 700 scale 638, 640 activity 158, 162, 194, 196, 202, 205-206, 214, 217-218, 222, 224, 228, 232, 234, 239-241, 243-245, 247-249, 255-256, 259, 261, 263, 265 266 coefficient 75, 199, 213 data 246 estimation 265 isotherm 195 measurement 217 value 223 admixture 536 affinity 369 amphiprotic 81

Index application 87 aprotic 528, 533 aromatic 134 atmospheric half-life 77 autoignition temperature 65-66 basicity 622, 636-637, 641, 660, 700 scale 636, 767 behavior 17, 359 biodegradation 72 half-life 77 boiling point 56-58, 63 box 621 cage 36-37, 824 calorific value 67 catalytic effect 41 cavity 492, 495 chain transfer agent 834 characteristics 133 characterization 699 charge distribution 29 chemical potential 55, 158, 206, 230, 349, 359, 365 properties 55 reactions 765 structure 57 classification 79, 87 scheme 88 cohesive energy density parameter 700 combination 750 combustible 86 combustion 67 heat 66 composition 455, 469, 472, 486, 488, 497, 500, 503, 508, 666 concentration 76, 84, 206, 241, 264, 358, 480 range 224 condensation 209 consumption 751 continuum model 15, 35 coordination properties 769 corrosion 210 crystallization 370 database 55 definitions 79 density fluctuation 481 design 47, 700 dielectric

Index effect 703 properties 27 diffusion 62, 202, 360, 365, 374, 376 coefficient 55 diffusivity 360 dipolar aprotic 80 non-hydrogen-bond donor 88 dipolarity 700 dipole 783 moment 143 discrete molecule 31 distribution function 27 donor number 771 properties 758 drying 370 time 376 effect 11, 35, 40, 445, 459-460, 471, 489-490, 496, 501-503, 619, 622, 823, 826-828, 832, 834-835 modelling 23 phenomenological theory 485 electric conductivity 67 evaporation 362, 371, 376 rate 55, 57, 62 time 753 exchange model 508 excluding surface 29 expansibility 781 extraction 84, 91 first kind 530, 531 flammability limit 63-64 flammable 86 flash point 58, 63 free ions 67 freezing point 56, 58-59 depression 236 fugacity 196 fusion heat 67 general interactions 619 geometry 506 global effect 30 warming potential 77 good 83 heat of vaporization 56 heating 465

891 Hildebrand solubility parameter 56, 74 hydrogen bonding 82 hydrogen-bond accepting 81 acceptor power 143 donating 80-81, 88 hydrophylic 82 hydroxyl rate constant 77 hygroscopic 84 identification 74 ignition energy 65 risk 61 source 65 industrial use 59 inert 703 ingress 357 interaction 80, 737 parameter 336 with solute 82 ionic product 524 ionizing 523 power 622-623 jumping unit 359 Lewis basicity 767 macroscopic density 27 manufacture 91 medium 823 migration 357 minimum ignition energy 65 miscible 83 mixed 439 systems 485 mixture 1, 69, 155, 374, 417, 429, 477, 737, 748 flash point 63 solubility parameter 154 modeling 15 molar enthalpy 366 fraction 755 volume 56, 145, 280, 360, 747 molecular 518 design 47 dimension 364 size 481 weight 55, 59, 61, 68

892 -sized cavity 488 molecule 27, 30, 233, 248, 256, 691 distribution 15 geometry 360 size 766 movement 357, 766 time scale 358 mutagenic 85 nature 486 negative solvatochromism 82 neoteric 3 non-hydrogen-bond accepting 81 donating 81 non-interacting 737 nonpolar 17, 142, 703, 765 nontoxic 3 normal 80 occupational exposure indicators 69 odor threshold 58-59, 70 value 85 ozone depletion 72 potential 86 parameter 82, 87, 264, 700 partial pressure 262, 374 partition 77 partitioning 84 penetration 361 permeation 749 flux 364 permittivity 457, 466, 473 persistence 77 pharmaceutical system 485 physical properties 55 polarity 2, 3, 13, 38, 68, 79-80, 82, 87, 364, 460, 508, 619, 628, 642, 697, 699, 712, 717, 763, 808, 832, 846 function 647 parameter 82, 87, 716 scale 623 polarizability 619, 650, 700, 784 positive solvatochromism 82 power 133-134 probe 620 sphere 29 production methods 79

Index process 95 properties 74, 99, 133, 349 protogenic 81 protolytic 533 protophilic 81 purity 60, 217 quality 22, 366 reaction field 28 rate 619 reactivity 765 refractive index 59-60, 68 relative permittivity 67-68, 835 vapor density 60 relaxation 190, 696 removal rate 357 reorganization 803 energy 181, 778, 805 reorientation 701 replacement 751 reprotoxic 85 research 68 residence time 59 residual 199 residue 85, 357 rheological properties 737 role 12 scale 619-620, 622, 626, 767 second kind 530-531 selection 164, 454 self-association 49 self-diffusion coefficient. 359 self-ionizing 81 separation 749 shape 49 size 506 adsorption constant 77 solubility 226 parameters 138 solvatochromic parameters 700 sorption 357 species 82 specific effect 31 gravity 59 heat 58, 62

Index interactions 620 specification 85, 99 storage 57 strength 84 structure 779 structuring 795 supercritical 207 surface tension 62, 74 switchable 4 system design 153 thermal capacity 159-160 thermal conductivity 75 thermodynamic compatibility 330 quality 349, 352, 356 theta 83 toxic 3 toxicity 85 indicator 70 transfer effect 216 transport 749 phenomena 357 tunable 4 urban ozone formation 72 UV absorption maxima 77 vapor 59, 203, 208 concentration 86 condensation 210 temperature 56 density 61 fugacity coefficient 218 phase 206, 244 pressure 61-63, 204, 206, 264 sorption method 224 viscosity 57, 75 volatility 62, 85 volumetric expansion 160 welding 762 /polymer pair 224 -dependent process 82 -free reaction 4 -induced absorption band shift 714 shift 82, 620 -solute interaction 55, 700 -solvent interaction 23, 486, 488, 700

893 solvo -acid 530 -base 530 solvolysis 82, 500, 525, 530, 533-534, 538, 547, 779 rate 622-623 constant 623 solvolytic 43 mechanism 42-43 solvophobic effect 489, 503 interaction 82 solvosystem concept 524, 526-529 sonar impact 57 sorption 325-327, 347, 363-364 equilibrium 266 kinetics 354 profile 363 properties 343-344 -desorption hysteresis 224 sound field 387 wave 387 space shuttle 761 spatial network 354 specific conductivity 429 isotherm 436 heat 62 hydrogen-bond interaction 82 interaction 20, 27, 37, 137, 149, 161, 418, 824 resistance 67 solvation 443, 445, 447-448, 459, 466 effect 449 energy 417 viscosity 738 spectral absorption 87 analysis 346 broadening 696 diffusion 176, 182 excitation 696 intensity 758 line 691 broadening 696 shift 554 maximum 691

894 shift 176 magnitude 621 transition 696-697 spectroscopic excitation 691 measurement 699 parameter 143 speed of light 709, 715-716 spheres of solubility 73 spherical cavity 168, 704 gas bubble 390 micelle 745 molecule 159 solubility volume 145 solute 171 structure 186 spherulite 755 spinning 750 spinodal 164-165, 232 condition 231 curve 196, 231, 240-241 decomposition 746 spin-spin interaction 443, 467 spontaneous dissolution 161 Raman spectrum 184 Spriggs law 385 stability constant 430, 472, 473 stabilization 758 stainless steel cell 206 standard fugacity 198 solvent 532, 541 state chemical potential 197 fugacity 197, 218, 256 starlike 745 micelle 744 states theory 164 statistical associating fluid theory 259 mechanics 47 thermodynamic model 242 Staverman correction 256 relation 252 steady state diffusion 364

Index stepwise decomposition 536 solvent exchange model 508 stereochemistry 827, 839 stereocontrol 827 agent 827 stereocontrolled radical polymerization 823 steric repulsion 18 Stern layer 187, 719 thickness 187 Stockmayer fluid 803 Stockmayer-Casassa relation 228 stoichiometric coefficient 421, 446 equilibrium model 502 process 487 stoichiometry 556 Stokes shift 168, 179, 181, 187, 627, 646 analysis 788 -Einstein relation 49 storage system 59 tank 59, 75 strain 343, 347, 349 effect 344 strand 746 stress cracking 749 tensor 305, 379, 383 stretching 341 structural color reflection 481 structure 336 structured fluid 80 solvent 80, 82 styrene 824 submicrostructure 762 substitutes 99 substitution 82 sulfuric acid 422 sum frequency generation spectroscopy 701 sum-over-states method 709 superacidic solvent 526 supercooled liquid 188, 290, 507 supercritical condition 36

Index fluid 3, 43, 707, 823 superheated solution 398 supermolecular method 24 supermolecule 32 calculation 32 model 24, 30 supersaturation 267 supramolecular assemblies 167 structure 343 surface adsorption effect 207 surface area 491 area fraction 253, 256 coating 511 crazing 756 distribution 514 electrostatic potential 636 energy 579, 761 envelope 29 fraction 248 free energy 511 modifier 511 morphology 357 properties 758 roughness 514-515 smoothness 762 tension 23, 62, 75, 83, 147, 151-152, 285, 373-374, 388, 406, 488, 492-494, 503, 505-507, 513, 515, 745 coefficient 407 data 494 treatment 518 vibrational technique 701 -specific vibrational spectra 701 -to-volume parameter 249 surfactant 186 suspension polymerization 823 Svedberg equation 235 swell ratio 309 swelling 152, 155, 160-162, 308, 310, 322, 330, 343, 349, 355, 357-358, 364-366 curve 243, 323, 356 data 330, 345 degree 241-242, 280, 288, 350, 353, 367 equilibrium 196, 241, 243, 319, 365, 368 experiment 336, 350

895 general theory 365 kinetic curve 314, 315, 349, 352, 355 kinetics 305, 310, 349-350, 352, 367-368, 511 modes 317 pressure 243, 367 process 305, 310, 349, 365, 367-368 model 317 rate 368 ratio 159, 283 studies 366 swollen network 196, 365 polymer 328 polymer network 241 region 364 symmetric liquids 283 synchrotron technique 232 syndiotactic 754 syndiotacticity 827 synergism 155-156 syngas 43 synproportionation 669 synthetic polymer chemistry 823 solvent 95 system energy 32 variables 158 viscosity 432 T tautomeric equilibrium 2, 13, 418, 666 form 418-419 tautomerism 2, 35 Taylor convention 715 Teas’ approach 146 technological process 357 telechelic polyolefin 749 temperate climatic condition 57 temperature 16, 158, 161, 363, 374, 376, 429, 437, 442-443, 458, 473, 700-701, 747, 751, 755 change 473 correction 59 rise 534 superposition principle 395 -shift factor 385, 386 temporal interferogram 181

896 tensile strength 755 terminal functional group 343 terminology 418 ternary electrolyte 265 terpineol 96 tertiary amine 2 tetrachloromethane 3 tetrahedric coordination 21 tetrahydrofuran 758, 790 tetramethylsilane 699 theophylline 486 theoretical model 167, 172 oxygen demand 72 theory of regular solutions 136-137 solvation 170 therapeutic preparation 748 thermal annealing 480 capacity 277 conductivity 83 detector 212 cracking 91 decomposition 536 yield 760 degradation 757 energy 16, 792 expansion 247, 251 coefficient 389 motion 417, 696 movement 16, 161 stability 535, 567 thermistor 216 sensor 217 thermochromic coefficient 787 thermochromism 765, 768 thermodynamic absorption equilibrium 207 affinity 135, 356 analysis 475, 788 ansatz 196, 231 behavior 194 characteristics 473, 475 compatibility 319 consequences 159 control 39

Index cycle 242, 440, 497, 500 data 196, 234, 236, 249, 575 description 473 equation 196 equilibrium 202, 205, 215, 222, 256, 388, 699 absorption 195 behavior 212 conditions 196 data 257 excess properties 251 function 48 implication 16 interaction parameter 330, 389 limit 36 model 194, 243 parameter 145, 162, 349 perturbation theory 256-257 properties 24, 471 quality 350 stability condition 240 work of adhesion 511 thermodynamics chemical reaction 765 laws 278 perturbation theory 247 thermogravimetric analysis 554 thermohydrodynamics 383 thermolysis 760 thermostated equilibrium cell 204 thermostating 205 theta temperature 83 thickening 742 thickness 361 three-dimensional network 241 non-linear theory 349 threshold limit value 85 time resolution 177 time-correlated function 170 time-correlated single photon counting 177 time-resolved decay 177 time-resolved emission spectra 177 time-resolved IR-spectroscopy 183 time-temperature superposition principle 385 time-weighted average 85 TIPS potential 50 titanium oxide 593

Index titration 553 toluene 94, 218, 229, 330, 338, 355-356, 827 tomato waste 479 torque 59 molecular cohesion 768 solubility 588 surface area 506 toxicity 79, 89 transcription 85 transfer coefficient 828 enthalpy 366 reaction 828 transferable potential parameter 50 transformation free energy 445 transient absorption 189 transition cation 573 energy 620, 696, 713 frequency 180 metal 519 moment 696 rubbery-to-glassy state 371 state 13, 32-33, 37, 39-41, 43, 500-501, 623, 826, 830831 geometry 827 polarity 828 stability 40 structure 83 temperature 359 vector 40 transitional motion 184 translation 178 motion 186, 188-189 transport phenomena 362 transversal stretch 306 transverse mechanical loading 307 tribological properties 357 tributyl phosphate 344 trichlorofluoromethane 86 triclinic crystal 755 trigonal crystallite 754 trimethylolpropane 330 triprotic acid 682 troposphere 86 Trouton’s entropy 798

897 quotient 798 rule 56, 798 tryptophan 188 two-phase separation 3 two-photon absorption 707, 709-710, 716, 718 cross-section 709, 718-719 process 707, 709, 717 strength parameter 710 excited fluorescence 710 microscopy 711 solvatochromism 707 transition probability 715 two-state approximation 715 t model 709 U Uhlig's model 488 ultracentrifuge 195-196, 234, 239, 243 ultrafiltration 749 membrane 749 ultrasound wave 386 unborn child 85 undercooled state 57 UNIFAC concept 252, 255 method 253 model 252, 255, 262 prediction 267 table 254 -FV model 266 unified solvent polarity scale 620 uniform liquid 324 uniformity 477 unimolecular reaction 500, 502 unit activity 84 cell 755 unitary free energy 497 universal polarity scale 626 solvation effect 448 unperturbed Gaussian chain 739 unpolarized charge distribution 15 unswollen region 364 upconversion data 178

898 upconverted signal 178 upper critical solution temperature 163 flammability limit 63-64 UV cutoff 86 degradation 757 /Vis absorption band 3 /Vis/NIR 2 /Vis/NIR absorption band 82 -Vis absorption band 707 intensity 713 V vacuum electrostatic component 460, 464 relief vent 75 van der Waals 79, 544 attraction term 261 dispersion forces 21 energy parameter 265 equation 781 forces 15, 21, 80, 82-83 hard-core volume 255 perturbation 261 radius 300 surface 28 theory 262, 784 volume 300 van Helmont 12 van Laar's concept 246 van't Hoff's 12 characteristics 475 constituent 474 parameters 473 vapor concentration 64, 86 formation enthalpy 278 lift pump 216 phase 198, 204, 216 equilibrium 215 pressure 62-64, 83, 85, 202, 209, 215-217, 265, 280, 322, 389 difference 204 measurement 195, 201, 229, 241 pure solvent 204 sorption 214 measurement 223

Index /pressure measurement 241 temperature 64 transport 752 /air mixture 66 -liquid equilibrium 198, 265, 267 data 194, 213, 215 measurement 201, 215 -pressure measurement 196 osmometer 217 osmometry 195-196, 216, 222 vaporization energy 148 heat 73 molar enthalpy 769 veritable fraction 424 vertical transition 697, 787 vesicle 3, 745 vesicular aggregate 745 vibrational band 701 degree of freedom 247 echo experiment 182 peak shift 183 spectroscopy 187 energy level 696 frequency 182 lifetime 176 relaxation 179 spectra 691 vibronic coupling 716 effect 708, 715 vinyl acetate radical 826 virial coefficient 222, 228, 236 equation 219, 223, 228, 233 of state 218, 244 expansion 235 visbreaking 91 viscoelastic liquid 390 viscosity 58, 83, 322, 373-374, 417, 427-429, 738-739, 741, 744, 748, 760, 823, 828 influence 437 isotherm 432-434

Index relative temperature coefficient 428 viscous polymer 239 void volume 502 volatile liquid 86 organic compounds 85 volatility 536 volume change 137, 242, 369 compression 434 fraction 154, 307, 324-325, 328, 372-373, 424, 426, 781 space 73 -fractional additivity 427 volumetric absorption coefficient 375 swelling ratio 309 Vrentas-Duda free-volume theory 374 W wall boundary layer 407 warning system 70 water 11, 16, 20, 31, 63, 82, 699 activity 265 content 75 diffusion 361 dynamics 179 molecule 701 orientation 173 tetrahedral structure 21 -water interaction 82 waterborne coating 373-374 wave function 28, 696 number 770-771 wavelength 177 absorption 770 difference 638 Weissenberg effect 408 weld strength 762 wetting 151 angle 407 Wilke-Chang equation 49 Wilson activity coefficient model 266 equation 266 model 481 Wislicenus 2, 13

899 Wong-Sandler mixing rules 262 work of adhesion 512 rupture 151 X XPS 513-514 chemical shift 513 X-ray fluorescent spectroscopy 554 photoelectron spectroscopy 511 scattering 232-233 xylene 94, 213, 751 Y yield value 755 Z Zdanovskii's rule 267 zein 742 zeolite 187 Zimm's plot 231, 234, 744 diagram 232 zirconia 538 Z-value 87 zwitterionic form 30, 33 geometry 31 zwitterion 31, 33-34