Heat Capacity: Theory and Measurement 2020026266, 2020026267, 9781536181425, 9781536182057

Table of contents :
Contents
Preface
Chapter 1
The Equivalence of Heat Capacity and Entropy in Adiabatic Systems: Novel Precision Method to Determine the Heat Capacity of Gases by Means of Vapor Pressure
Abstract
Introduction
Thermodynamic Fundamentals on Heat Capacity
Irreversible Heat Capacity
Basic Principles to the Prediction of the Heat Capacity of Gases
Methods
Equivalence of Heat Capacity and Entropy
1. Working Systems
2. Nonworking Systems
Applications of the Heat Capacity- Entropy Equivalence
Heat Capacity Criterion to Equilibrium
Irreversible Heat Capacity as Boltzmann H Analogue. Temperature Dependence of H
Determination of the Heat Capacity of a Molecular Gas
Abridged Procedure. Heat Capacity-Pressure Correlation
Precision of the Method
Conclusion
References
Chapter 2
Molar Heat Capacity of Aqueous Blends of Monoethanolamine with Piperazine Using Micro-Reaction Calorimeter (µRC)
Abstract
Introduction
Experimental Section
Results and Discussion
Molar Heat Capacities of (MEA + H2O) System
Molar Heat Capacities of (PZ + H2O) System
Molar Heat Capacities of (MEA + PZ) System
Molar Heat Capacities of (MEA + PZ + H2O) System
Conclusion
References
Chapter 3
Studies of Thermal Analysis and Specific Heat Capacity for Quaternaryammonium Salts
Abstract
Introduction
Experimental Section
Materials
Methodology
General Procedure for Anion Metathesis Reaction
Thermal Analysis of Quaternary Ammonium Salts
Calculations of Specific Heat Capacity (Cp )
Results and Discussion
Conclusion
Acknowledgment
References
Chapter 4
The Excess Partial Molar Heat Capacity of Water Is a Measure of Its Structure in Binary Aqueous Solvent Mixtures
Abstract
Introduction
Data
References
Bibliography
Related Nova Publications
Bi-Linear Model of Correlation between Heat Capacity and Volume Thermal Expansivity of Solids as a Novel Tool for Evaluation the Reliable Numerical Data for Purposes of Chemical Thermodynamics: Application to Rare Gas Solids
Head of the Department of Higher Mathematics, Ural State Pedagogical University, Yekaterinburg, Russia
Heat Capacity of Rare-Earth Aluminum Garnets and Peculiarities of Transport Characteristics of Phonons Caused by the Schottky Anomalies at Low Temperatures*
A Bi-Linear Model of the Correlation between Heat Capacity and Volume Thermal Expansivity of Refractories as a Novel Tool for the Evaluation of the Reliable Numerical Data for Chemical and Physical Thermodynamics Part I. Grounds and Modelling*
Head of the Department of Higher Mathematics, Ural State Pedagogical University, Yekaterinburg, Russia
A Bi-Linear Model of the Correlation between Heat Capacity and Volume Thermal Expansivity of Refractories as a Novel Tool for the Evaluation of the Reliable Numerical Data for Chemical and Physical Thermodynamics.
Part II. Application to Periclase and Corundum*
Unfolding Thermodynamics of Nucleic Acids: Determining Heat Capacity Effects Using Differential Scanning Calorimetry (DSC) *
The Phase Composition, Grain Structure, Dielectric Spectra and the Heat Capacity of Bi1–xGdxFeO3 Solid Solutions*
A Study of the Heat Capacity of Ribonuclease A – Water Mixtures*
Kazan Federal University, A.M. Butlerov Chemical Institute, Kazan, Russia,
Index
Blank Page

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CHEMISTRY RESEARCH AND APPLICATIONS

HEAT CAPACITY THEORY AND MEASUREMENT

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CHEMISTRY RESEARCH AND APPLICATIONS Additional books and e-books in this series can be found on Nova’s website under the Series tab.

CHEMISTRY RESEARCH AND APPLICATIONS

HEAT CAPACITY THEORY AND MEASUREMENT

SØREN A. DAM EDITOR

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Library of Congress Cataloging-in-Publication Data Names: Dam, Søren A., editor. Title: Heat capacity : theory and measurement / Søren A. Dam. Description: New York : Nova Science Publishers, [2020] | Series: Chemistry research and applications | Includes bibliographical references and index. | Identifiers: LCCN 2020026266 (print) | LCCN 2020026267 (ebook) | ISBN 9781536181425 (paperback) | ISBN 9781536182057 (adobe pdf) Subjects: LCSH: Thermodynamics. | Second law of thermodynamics. Classification: LCC QC311.2 .H43 2020 (print) | LCC QC311.2 (ebook) | DDC 536/.71--dc23 LC record available at https://lccn.loc.gov/2020026266 LC ebook record available at https://lccn.loc.gov/2020026267

Published by Nova Science Publishers, Inc. † New York

CONTENTS Preface Chapter 1

Chapter 2

Chapter 3

vii The Equivalence of Heat Capacity and Entropy in Adiabatic Systems: Novel Precision Method to Determine the Heat Capacity of Gases by Means of Vapor Pressure Francisco Ros Molar Heat Capacity of Aqueous Blends of Monoethanolamine with Piperazine Using Micro-Reaction Calorimeter (µRC) Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang, Nabil El Hadri and Mohammad R. M. Abu-Zahra Studies of Thermal Analysis and Specific Heat Capacity for Quaternaryammonium Salts Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas, Dilip G. Hundiwale and Kesharsingh J. Patil

1

27

53

vi Chapter 4

Contents The Excess Partial Molar Heat Capacity of Water Is a Measure of Its Structure in Binary Aqueous Solvent Mixtures Yizhak Marcus

Bibliography

75 81

Related Nova Publications

153

Index

163

PREFACE In Heat Capacity: Theory and Measurement, the incidence of the second law of thermodynamics on heat capacity is examined with respect to heat flux taking place in a thermodynamically irreversible manner, as well as with respect to irreversible heat capacity (CIR = QIR/ T). In another study, the heat capacities of aqueous mixtures of monoethanolamine with piperazine were measured from (303.15 to 353.15) K with a micro-reaction calorimeter (µRC) at an interval of 5 K. The authors discuss how heat capacity is a significant thermodynamic quality because of its intrinsic significance and its connection with other thermodynamic properties like enthalpy, entropy and Gibbs energy. The closing study explores ho the excess partial molar heat capacity of the water in binary aqueous-solvent mixtures (W + S), CPWE, provides insight into water structure enhancement, if present. Chapter 1 - Thermodynamic fundamentals on heat capacity are looked over. Heat capacity is not an intrinsic property of a material as depends on the conditions of heat transfer. The incidence of second law of thermodynamics on heat capacity is examined with respect to heat flux taking place in a thermodynamically irreversible manner and with respect to irreversible heat capacity (CIR = QIR/T). In an adiabatic system in evolution the momentary entropy coincides with the heat capacity. Equations connected with this equivalence are derived, mainly the relation between

viii

Søren A. Dam

entropy and temperature for an adiabatic process. As an application of the equivalence, it is shown that irreversible heat capacity is alike to maximal entropy as an indicator of attainment of thermodynamic equilibrium. It substantiates the merely logical notion that thermodynamic equilibrium is reached when growing entropy is maximal. It is shown that irreversible heat capacity is an analogue of statistical magnitude Boltzmann H. The lacking connection of H with temperature is presented. Theoretical principles on the prediction of heat capacity of gases are examined. A novel method to determine with precision the heat capacity of vapors of molecular solids is described. The method at the start rests on the experimental vapor pressure and heat capacity of the solid. Thermophysical analysis in the method allows for obtaining an exact value for the heat capacity of a vapor at a determinate temperature of sublimation. In the method, all feasible heat capacities as functions of temperature are tested and the correct one is obtained with high accuracy for a temperature interval around the sublimation temperature. The analytical method ultimately correlates the pressure of a gas with the gas heat capacity by means of the gas vibrational entropy. Heat capacity is obtained by the method from genuine experimental data, without mixing with foreign techniques, with simple data handling and with an extreme precision. Chapter 2 - Heat capacities of aqueous mixtures of monoethanolamine (MEA) with Piperazine (PZ) were measured from (303.15 to 353.15) K with a micro-reaction calorimeter (µRC) at an interval of 5 K. The heat capacities (Cp /Jmol-1K-1) of PZ, MEA, MEA + H2O, PZ + H2O, MEA + PZ and MEA + PZ + H2O were studied. Various concentrations of these binary and ternary systems were studied. An excess molar heat capacity (CpE/Jmol1K-1) expression using the Redlich-Kister equation for the composition dependence is used to represent the measured Cp of aqueous amine blends. The average absolute percentage deviation (AAD %) for the calculation of the excess molar heat capacities are less than 3% for both binary and ternary systems. The molar heat capacities of blends and binary mixtures could be predicted with an accuracy of less than 1% using the coefficients and correlations reported in this work. The excess heat capacities of mixtures having MEA with PZ were found to be less than mixtures having MEA with

Preface

ix

other amines (e.g., 2-Piperidine ethanol (2-PE), Methyldiethanolamine (MDEA) and 1-amino-2-methyl-1-propanol (AMP)). Chapter 3 - Heat capacity is a substantial thermodynamic quantity because of its intrinsic significance and its connection with other thermodynamic properties like enthalpy, entropy and Gibbs energy. The measurement of heat capacity is an important application of differential scanning calorimetry, where results obtained with acceptable uncertainty and often with a negligible difficulty. In this contribution the authors report thermo-gravimetric analysis (TGA) and differential scanning calorimetry (DSC) profiles of tetraethyl, tetrapropyl, tetrabutyl, hexadecyltrimethylammonium bromide, tetrafluoroborate and hexafluorophosphate salts for a temperature range of 30 to 500oC (303-573 K). Furthermore, the exploration of heat flow data towards the calculations of specific heat capacity (Cp) at different temperatures has been accomplished by developing a simple mathematical operation. In addition to that, a suitable mechanism of thermal decomposition of the studied quaternary ammonium salts in the form of generation of PF5 and alkylhalide species with removal of trialkylamine for hexafluorophosphate salts has been proposed. Chapter 4 - The excess partial molar heat capacity of the water in binary aqueous-solvent mixtures (W + S), CPWE, provides insight into the water structure enhancement, if present. A cubic representation of CPE of binary aqueous-solvent mixtures CpE = b0 + b1xS + b2xS2 + b3xS3 is valid for waterrich mixtures, xS ≤ 0.3, hence also CPWE = –b2xS2 – 2b3xS3 is readily obtained. Values of CPWE(xS) were obtained for many aqueous co-solvent mixtures from literature data beyond those dealt with in the author’s previous publication. Typical values of the maximal CPWE are 10 to 20 J K-1 mol-1 or 24 to 48% of the difference ΔCPl-ig = CP(liq) – CP(id.gas), which for water at 25°C is 42 J K-1 mol-1. However, energy input into the water entails not only ordering of the water, but also input into vibrational modes. Therefore, only a fraction of the heat capacity of ideal gas water needs to be subtracted from CPWE in order that only structure (order) enhancement is reckoned. Empirically, a fraction of 0.3 appears to be satisfactory. A mixture model for water structure in terms of compact and bulky hydrogen bonded domains allows structure enhancement to be interpreted as transfer of molecules

x

Søren A. Dam

between them. Strong, small hydrogen bonding solutes do not enhance the structure, fitting well into it. Solutes with many methyl groups, though miscible with water, do enhance its structure.

In: Heat Capacity Editor: Søren A. Dam

ISBN: 978-1-53618-142-5 © 2020 Nova Science Publishers, Inc.

Chapter 1

THE EQUIVALENCE OF HEAT CAPACITY AND ENTROPY IN ADIABATIC SYSTEMS: NOVEL PRECISION METHOD TO DETERMINE THE HEAT CAPACITY OF GASES BY MEANS OF VAPOR PRESSURE Francisco Ros* Instituto de Química Médica, CSIC, Madrid, Spain

ABSTRACT Thermodynamic fundamentals on heat capacity are looked over. Heat capacity is not an intrinsic property of a material as depends on the conditions of heat transfer. The incidence of second law of thermodynamics on heat capacity is examined with respect to heat flux taking place in a thermodynamically irreversible manner and with respect to irreversible heat capacity (CIR = QIR/T). In an adiabatic system in evolution the momentary entropy coincides with the heat capacity. *

Corresponding Author’s Email: [email protected].

2

Francisco Ros Equations connected with this equivalence are derived, mainly the relation between entropy and temperature for an adiabatic process. As an application of the equivalence, it is shown that irreversible heat capacity is alike to maximal entropy as an indicator of attainment of thermodynamic equilibrium. It substantiates the merely logical notion that thermodynamic equilibrium is reached when growing entropy is maximal. It is shown that irreversible heat capacity is an analogue of statistical magnitude Boltzmann H. The lacking connection of H with temperature is presented. Theoretical principles on the prediction of heat capacity of gases are examined. A novel method to determine with precision the heat capacity of vapors of molecular solids is described. The method at the start rests on the experimental vapor pressure and heat capacity of the solid. Thermophysical analysis in the method allows for obtaining an exact value for the heat capacity of a vapor at a determinate temperature of sublimation. In the method, all feasible heat capacities as functions of temperature are tested and the correct one is obtained with high accuracy for a temperature interval around the sublimation temperature. The analytical method ultimately correlates the pressure of a gas with the gas heat capacity by means of the gas vibrational entropy. Heat capacity is obtained by the method from genuine experimental data, without mixing with foreign techniques, with simple data handling and with an extreme precision.

Keywords: irreversibility thermodynamics, irreversible heat capacity, heat capacity-entropy equivalence, heat capacity equilibrium criterion, maximal entropy, Boltzmann H-irreversible heat capacity analogy, Boltzmann H-temperature dependence, gas heat capacity, gas vibrational entropy, thermophysical analysis, pressure-heat capacity relationship

INTRODUCTION Thermodynamic Fundamentals on Heat Capacity Heat capacity refers to the rate of amount of heat absorbed by a body in relation to the change of temperature undergone by the body (equation 1). Heat is the form of transient energy that ultimately relates to measurable work. Heat and work are interconnected with the change in internal energy of the body according to first law of thermodynamics (equation 2). In turn,

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems

3

internal energy is the total content of energy of the body, but is not directly measurable. 𝑄

𝐶 = ∆𝑇

(1)

𝑄 − 𝑊 = ∆ 𝑈 = 𝑈2 − 𝑈1

(2)

Internal energy is a property of the actual state of the body, i.e., magnitude U is a “function of state” in agreement with the equation of state for the body [f(U, V, T) = 0]. Heat and work are not so as depend on the eventual path undertaken by the body to achieve a specific transformation having fixed starting and end states. The eventual amounts of heat and work in the transformation are regulated in conformity with equation 2. As heat is not a function of state, heat capacity is dependent on the particular conditions of the transfer of heat. Heat capacity cannot be specified by the equation of state of the body, in contrast with internal energy. Punctual heat capacity is defined in a precise manner by equation 3, in which differential dQ still carries on the character of being dependent on the conditions of evolution or measurement. Thus finite quantity C is not an intrinsic property or a function of state of a material. Differential dQ can further be expressed in terms of entropy and temperature as shown in the equation and according to second law.1 𝑑𝑄

𝐶 = 𝑑𝑇 =

𝑇𝑑𝑆 𝑑𝑇

(3)

The conditional nature of heat capacity is illustrated in Figure 1, which depicts in a T-S diagram two different paths for the same transformation (path A and B). The respective heats involved are the areas under the respective lines and as the integrals of differential TdS. The lateral diagram traces the respective heats taken on during the course of the processes and 1

The definition of heat capacity is general, regardless of the composition of a system. In mixtures or in anisotropic materials “partial” heat capacities may be ascribed to components or particular directions.

4

Francisco Ros

as functions of the temperature. The slopes (derivatives) of the lines represent the heat capacities for the two processes, and are different even though correspond to the same transformation having the same initial and final states. Thus heat capacity is not an intrinsic property of matter, unlike for example density and similarly to heat that is a form of energy external and not intrinsic to a material. T B QA, B

A QA

CB = dQB/dT CA = dQA/dT

B

T

QB

S

Figure 1. Dependence of heat capacity (C) on thermic path (T-S).

Beyond the normal external heat the so-called “internal heat” [1] (with a corresponding “internal” heat capacity) is a valid and useful concept to deal with processes in thermally isolated systems (i.e., adiabatic systems, Q = 0), wherein no external heat has to do, and normal heat capacity makes in turn no sense. Such internal heat (QI) ensues the natural development of entropy in the irreversible processes of adiabatic systems, i.e., TdS  dQI (dQ = 0). The concept will be used in the chapter in connection with heat capacity in adiabatic systems. Concerning heat capacity under specific thermodynamic conditions, heat capacity at constant volume is of much theoretical relevance as directly refers to the content of energy in a material, i.e., CV = dU/dT, and in addition is a factor in the transmission of heat in materials [2]. Heat capacity at constant pressure, Cp = dH/dT (enthalpy Hp = Q), allows for converting

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems

5

heats of change of state, of polymorphic transformations or of chemical reactions to different temperatures [2, 3]. Heat capacity is immediately measurable as a quantity, unlike closely related entropy, i.e., C = Q/T vs. “incremental” S = CT/T. Absolute entropies or entropy changes for transformations can be evaluated at different temperatures through the heat capacity by integration [1]. Beyond these features and a dimensional sameness (energy per temperature for both heat capacity and entropy), an essential relationship between heat capacity and entropy is not apparent. It will be shown in the chapter by means of a theoretical deduction that heat capacity is coincident with entropy in thermally isolated systems. The equivalence will be derived for both adiabatic systems performing and not performing work. Many spontaneous processes, such as the expansion of gases or relaxation processes, belong to the category of adiabatic transformations.

Irreversible Heat Capacity Irreversible heat capacity relates to heat that is transferred in a thermodynamically irreversible manner, i.e., CIR = QIR/T. Irreversible heat is absorbed or emitted by a body in such a way that the attendant changes in the body do not conform the equation of state but for the initial and final states. In other words, the path undertaken during the irreversible heat transfer is not a reversible path, i.e., not a succession of equilibrium states conforming the equation of state. Irreversible heat cannot be greater than the respective reversible heat according to Clausius inequality in second principle [1, 2] (Figure 2). In an irreversible absorption of heat, the amount of heat absorbed is limited by the initial low temperature of the body. Similarly, in an irreversible emission the amount of heat is limited by the initial low temperature of the exterior.

6

Francisco Ros

Figure 2. Reversible and irreversible heats and heat capacities (CIR = QIR/T).

In the diagram to the right in Figure 2, irreversible heat capacity is figured on the thick line to irreversible heat at the initial temperature. Thus, the value of QIR is permanent for the whole heat absorption, whereas reversible heat (QR) steadily augments during the absorption. Like irreversible heat, irreversible heat capacity is predetermined by initial temperature T1. A large jump or a fast output favors irreversibility, however depending on the nature of materials. Thermodynamic reversibility is an ideal concept as such reversible processes require infinitesimally small (differential d) and infinitely slow changes. In spite of this, many processes adhere well to reversibility in practice. The common notion that an adiabatic system reaches equilibrium when the entropy actually developed is maximal [2, 4] is an unsubstantiated notion. It is no more than a logical notion. It will be shown in the chapter that irreversible heat capacity allows for an insight to such a crude notion and provides a criterion to equilibrium. Reversible heat capacity is not useful for this purpose as operates without a distinction at any point of the process (CR = dQ/dT). Magnitude Boltzmann H of statistical mechanics [2] has to do with relaxation processes and departure from equilibrium. As connected with the role of irreversible heat capacity in the equilibrium, it will be shown that irreversible heat capacity works analogously to Boltzmann H in the attainment of equilibrium. Statistical Boltzmann H is a magnitude of

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems

7

nonequilibrium, like thermodynamical irreversible heat capacity, and the connection with each other will be shown. In addition, the relationship of H to temperature, which is lacking in a fundamental treatment using statistical mechanics, will be derived.

Basic Principles to the Prediction of the Heat Capacity of Gases In order to predict the heat capacity of a perfect molecular gas (consisting of mutually uninteracting molecules) it is necessary to know the molecular vibrational energy as function of the temperature. Molecular rotational and translational energies are immediate, i.e., 3RT/2 each. Heat capacity at constant volume results from the energy-temperature function by differentation (CV = dU/dT). The vibrations in a molecule can be described by the normal modes of vibration that are separable and are characterized by a distinctive individual frequency. Normal vibrations amount in number to 3n  6 in nonlinear molecules (n atoms). Heat capacity results by summation of the heat capacities for the individual vibrations. The energy-temperature function for a vibration is described by the quantic harmonic oscillator (Planck-Einstein oscillator) [2, 5], whose energy depends on the characteristic frequency of the vibration as well as of temperature. Anharmonicity for this oscillator is generally of no concern. It does not represent an essential improvement to the sufficient PlanckEinstein model. Indeed, the crucial point for prediction is an accurate knowledge of the vibrational frequency of the oscillator. Vibrational frequencies may be obtained spectroscopically, although it may require a sophisticated analysis in complex molecules having a large number of normal vibrations. The application of estimated frequencies from similar molecules generally results in outsize errors both in energy and heat capacity. The theoretical calculation of vibrational frequencies or, differently, vibrational force constants conveys rough approximations. Accuracy in predicting thermic molecular energy ultimately relies on correct vibrational frequencies.

8

Francisco Ros

In organic molecules, athermal quantic zero-point energy is the main component of vibrational energy on account of tight interatomic bonding in the molecule (strong vibrational force constants). Zero-point energy is proportional to the oscillation frequency, and the latter in turn determines together with temperature the remaining thermal vibrational energy. For the ester dealt with in the chapter, zero-point energy represents a 99% of the total vibrational energy at 20ºC [1]. A high accuracy is hence critical to vibrational frequencies in view of the little thermic vibrational energy that determines the heat capacity. Besides, a high accuracy for frequencies is necessary in making balances of vibrational energy for chemical reactions, for example in predicting enthalpies of reaction (the vibrational energy is independent of the potential energy of chemical bonding). The vibrational energy for a reaction results by summation of the vibrational energies for the reaction components. By this summation the absolute error in energy is much exalted, which emphasizes the need of accuracy for vibrational frequencies. A number of methods exist to estimate the heat capacity of gases by summation of heat capacity contributions of atomic groups in the molecule [6-8]. Such contributions imply a more or less arbitrary partition of the molecule, yet rest on an empirical basis. In essence, it is alike to Neumann and Kopps law according to which the heat capacity of a polyatomic solid is the sum of the heat capacities for the different constituent atoms [2]. In the chapter, a novel method to determine the heat capacity of gases is described which relies upon experimental data and eludes the bothersome use of vibrational frequencies as well as the artificial partition of the molecule. Thus, the method rests on the experimental vapor pressure and derived heat of vaporization for a solid, and on the experimental heat capacity of the solid. The absolute entropy of the gas phase (obtained from the heat capacity of the solid and the heat of vaporization [1]) is used as relates to the vapor pressure by the gas translational entropy. The analytical method in essence correlates the pressure of a gas with the gas heat capacity by agency of only the gas vibrational entropy. The method is sketched in Figure 3. A high accuracy to the heat capacity is achieved by this method.

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems

9

material

heat of passing to gas state (DH)

vapor pressure

experimental entropy of passing to gas state (DS)

balance of entropy (checkout): ST = DS - SR - SV - S(material) variation of vibrational entropy (SV) with temperature depends on heat capacity experimental translational entropy of gas molecule (ST)

trial heat capacity is tested to check out ST to experimental value ST

heat capacity of gas

Figure 3. New general method for determining the heat capacity of gases.

METHODS Equivalence of Heat Capacity and Entropy The mathematical deduction consists of multiple steps including the use of assisting thermodynamic functions and simple operations of differential calculus. Three of the steps are of physical significance. Both adiabatic systems performing and not performing work are analyzed. Work will be set forth as mechanical work for chemical systems (dW = pdV), yet the reasoning and equations are general, holding for work of elongation or polarization, electrical work, and the like (dW = YdX).

10

Francisco Ros

1. Working Systems First law of thermodynamics (dU = dQ  dW) is expressed by equation 4 (adiabatic system, dQ = 0). Entropy increases as the process is taken to be irreversible (dS > 0) in conformity with a natural process. The use of differentials rather than finite increments is compatible with the irreversibility since a reversible path that simulates the irreversible path is adopted. The increase in entropy is directed to internal heat (TdS = dQI), as pointed out in Introduction. Now this internal heat can only be produced in the system at the expense of internal energy as this is the only energetic reservoir of the thermally isolated system. Hence dQI = dU, which results in equation 5 (TdS = pdV) by substitution at 4. 𝑑𝑈 = −𝑝𝑑𝑉

(4)

𝑑𝑆 𝑑𝑉

(5)

=

𝑝 𝑇

The assisting thermodynamic function corresponding to the system is equation 6. It relates to general assisting internal-energy function U = TS  pV. This is applicable regarding general differential equation dU = TdS  pdV, and is here set at zero (equation 6) for consistency with present particular differential equation 5 (TdS  pdV = 0). As an assisting function as it is, equation 6 lacks physical meaning, but correlates the thermodynamical variables in a mathematically operative manner. It is conditional on and auxiliary to prior 5. Differentiation of equation 6 and use of equality 5 gives 7 (SdT  Vdp = 0). 𝑇𝑆 − 𝑝𝑉 = 0

(6)

𝑑𝑝 𝑑𝑇

(7)

=

𝑆 𝑉

The assisting enthalpy function for the system (equation 8, analogous to general enthalpy H = U + pV) gives equation 9 by differentiation followed by use of equality 5. Differential dH in equation 9 is an exact differential in

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 11 differential calculus terms and their coefficients can therefore be expressed as partial derivatives by (V/S)T = (T/p)V (a Maxwell equation [2]). As to the adiabatic system being considered the use of partial derivatives can be left out because real external heat does not play a role in first law as applied to the system (dU = dQ  dW with dQ = 0). It implies that the system is physically deprived of one degree of freedom in the frame of thermodynamic variables. The degrees of freedom (number of independent variables), which are normally two according to the equation of state [f(p, V, T) = 0], are thus reduced to one in an adiabatic system, and simple derivatives can therefore be used. Thus, the applicable Maxwell equation to the system is 10. Elimination of dp/dT from 7 and 10 provides crucial equation 11. 𝐻 = 𝑝𝑉

(8)

𝑑𝐻 = 𝑉𝑑𝑝 + 𝑇𝑑𝑆

(9)

𝑑𝑆 𝑑𝑉

=

𝑑𝑝 𝑑𝑇

(10)

𝑑𝑆 𝑆

=

𝑑𝑉 𝑉

(11)

The deduction is again carried out from equation 5 as modified to 12 (TdS + Vdp =0). In this, term pdV has been exchanged by Vdp, which is a valid operation as the resultant equation is actually dH = 0 (see 9). Moreover, this exchange with an inversion of sign renders in the end the proper qualitative correlations between variables for the working adiabatic system. Equation 12 and Maxwell equation 10 give 13 by elimination of dS/dp. 𝑑𝑆 𝑑𝑝

= −𝑇

𝑉

𝑑𝑉 𝑉

=−

𝑑𝑇 𝑇

(12) (13)

Finally, elimination of dV/V from equation 11 in the first deduction and equation 13 in the second one yields the entropy-temperature relationship

12

Francisco Ros

for the system (TdS = SdT, equation 14), whereby the coincidence of heat capacity and entropy in absolute value arises. 𝑆 = −𝑇

𝑑𝑆 𝑑𝑇

=−

𝑑𝑄I 𝑑𝑇

= −𝐶

(14)

Heat capacity at constant volume (CV) is always positive [4] because in the absence of interferring work a gain of heat can only rise the temperature of a system, and heat capacity at constant pressure (Cp) is likewise positive [4]. However, these correspondences to sign do not preclude the negative value of heat capacity in the specific case of an adiabatic system, as manifested by equation 14 (S > 0) and in the following manner. In a working adiabatic system a lowering of the temperature will occur when the process is irreversible, as in a spontaneous expansion of a thermally isolated gas. It is in conformity with equation 14, dS > 0 then dT < 0. The decrease in temperature in the isolated system occurs despite the positive production of heat, and heat capacity is negative. The heat capacity functions as internal heat capacity. It will be shown in the following subsection that internal heat capacity is however positive in the case of a nonworking adiabatic system. Volume-pressure relationship dV/V = dp/p ensues equations above, and pressure decreases in the working adiabatic system as volume increases.

2. Nonworking Systems The starting equation is 15 as expression of first law of thermodynamics for the system. “Internal volume” (VI) [1] like internal heat (dQI = TdS) is necessary to handle first law in the thermally isolated system at constant volume, i.e., dQ = dW = 0, also dU = 0. Internal volume correlates with “internal work”, i.e., dWI = pdVI. 𝑇𝑑𝑆 − 𝑝𝑑𝑉I = 0

(15)

The pertinent assisting functions are equation 16 and 17. These with 15 provide crucial 18 by the same methodology as in the preceding subsection (Maxwell equation dS/dVI = dp/dT).

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 13 𝑇𝑆 − 𝑝𝑉I = 0

(16)

𝐻 = 𝑝𝑉I

(17)

𝑑𝑆 𝑆

(18)

=

𝑑𝑉I 𝑉I

Next, differential VIdp is introduced as a substitute for differential work pdVI [2] in starting equation 15 giving 19 (TdS  VIdp = 0). This in turn provides equation 20 by means of Maxwell equation. 𝑑𝑆 𝑑𝑝 𝑑𝑉I 𝑉I

= =

𝑉I 𝑇

(19)

𝑑𝑇 𝑇

(20)

Finally, elimination of internal-volume terms from equation 18 and 20 provides the entropy-temperature relationship that affords the coincidence of entropy with heat capacity for the nonworking adiabatic system (equation 21). The heat capacity has a positive value like internal heat and the change in temperature (dS > 0 then dT > 0). 𝑆=𝑇

𝑑𝑆 𝑑𝑇

=

𝑑𝑄I 𝑑𝑇

=𝐶

(21)

Entropy and temperature grow up in an irreversible process of a thermodynamically isolated system (both adiabatic and at constant volume), what is in constrast with the irreversible process of a system no more than thermally isolated, as discussed in the preceding subsection. Pressure increases with temperature in the thermodynamically isolated system as manifested by pressure-temperature relationship dp/p = dT/T, resulting by equalization of above equations. The latter p-T equation also holds for the working adiabatic system.

14

Francisco Ros

Applications of the Heat Capacity- Entropy Equivalence Heat Capacity Criterion to Equilibrium The relation of temperature to entropy in a working adiabatic system is linear with a negative slope as results from equation 14 and is represented in Figure 4. The irreversible heat capacity for the transformation is expressed by equation 22 with reference to the figure. This equation is in conformity with what was indicated in Introduction concerning irreversible heat, namely here irreversible internal heat QI. The reference temperature to evaluate QI is thus the low final temperature for the transformation. Heat capacity CIR has then a negative value as T2 < T1 [cot  cot(  ) < 0)], in conformity with what has been above shown concerning the sign of heat capacity for a working adiabatic system. 𝑄

𝑆 −𝑆

𝐶IR = ∆𝑇I = 𝑇2 𝑇2 −𝑇1 = 𝑇2 cot𝜙 2

1

(22)

Trigonometric cot can alternatively be expressed in terms of the final temperature and the corresponding triangle base by cot = (a  S2)/T2, in which a is the intercept of prolongated line T-S at S axis. From this equality and 22, expression 23 for S2 results. 𝑆2 = 𝐶IR + 𝑎

(23)

Now the final, equilibrium point of the irreversible transformation can of course be taken as a punctual reversible stage for which infinitesimal differentials rather than the finite increments can be used. Consequently, the above discussed equivalence of heat capacity and entropy (S = C) applies to the equilibrium point. To fulfill this equilibrium condition, quantity a in equation 23 is to take value 2S2 so that S2 be equal to CIR, as appropriate to the equilibrium (S2 = CIR). This equality can be achieved in two ways in reference to Figure 4. First, a translation of T axis by distance 2S2  a so that a in equation 23 becomes 2S2. By this geometrical operation the value of S2 becomes greater, which is congruent with the actual growth of entropy in

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 15 approaching equilibrium. On the contrary, heat capacity CIR is not altered by this operation as neither T2 nor  are altered (equation 22).

Figure 4. Shifts of entropy and irreversible heat capacity to reach equilibrium [working adiabatic system, CIR(equil.) = T2(S2  S1)/(T2  T 1)].

Alternatively, line T-S is rotated around final point (T2,S2) so that the intercept of the prolongated, rotated line on S axis lies at the previously translated origin. Distance S1-S2 is kept constant in the rotation. Upon the rotation, quantity a anew becomes 2S2, fulfilling the condition of equilibrium (S2 = CIR). In this operation, entropy S2 remains unaltered while CIR decreases since the denominator of equation 22 increases by the lowering of T1 to T 1.

Figure 5. Shift of irreversible heat capacity to reach equilibrium [nonworking adiabatic system, CIR(equil.) = T1(S2  S1)/(T 2  T1)].

16

Francisco Ros

In conclusion and considering both operations, equilibrium is attained when growing irreversible entropy encounters decreasing irreversible heat capacity at the equilibrium point. The deduction can be carried out in the same manner manner for an adiabatic system not performing work (positive T-S slope, S = C at equilibrium) and with the same conclusion. For this case of a nonworking adiabatic system, Figure 5 shows the rotation so as to annul distance a at equilibrium as it is required by pertinent equation 24. The rotation again conveys a decrease in irreversible heat capacity now as a positive quantity. 𝑆1 = 𝐶IR − 𝑎

(24)

Irreversible heat capacity thus substanciates the condition of equilibrium for adiabatic processes, serving as an indicator to an enigmatic maximal entropy and as a criterion of equilibrium.2

Irreversible Heat Capacity as Boltzmann H Analogue. Temperature Dependence of H The path followed by irreversible heat capacity in approaching equilibrium is not the same as for reversible heat capacity. For a nonworking adiabatic system, the former path is given by CIR = T1cot(T 2) in reference to Figure 5, whereby (T 2) is a decreasing variable function of progressive T 2. On the other hand, the reversible heat capacity is given by C = Tcot where  is constant. Irreversible CIR decreases in approaching equilibrium while reversible C contrariwise increases. This decrease of CIR in approaching equilibrium is alike to that of statistical magnitude Boltzmann H at the same stage.

2

For an irreversible adiabatic free expansion, where the system would be perfectly thermally isolated and no opposing external force would exist at all (p = 0), entropy would ideally increase without limitation and equilibrium would not be reached. This process is necessarily irreversible on account of the inexistance of a compensating external force, and being an irreversible process the entropy unavoidably increases. In a sense, this system is like a nonworking adiabatic system despite the change in volume in the former: internal energy remains constant on account of the actual absence of work in the adiabatic free expansion, and equally to the thermodynamically isolated system.

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 17 For the present objective, Boltzmann H theorem [2] can be expressed by equation 25 (kB Boltzmann constant), with time derivative dH/d < 0. Magnitude H (H = NilnNi) decreases in approaching equilibrium (as CIR does), while entropy increases as usual (kBdH/d = dS/d < 0). 𝑘B 𝐻 = −𝑆 + const

(25)

The constant at the right hand side of equation 25 can be expressed as const = S0 + kBlnPº, in which S0 is a reference statistical entropy and Pº is an anchoring probability (Pº = NN). In a thermodynamic analogy, such constant can be expressed by initial entropy S1 plus a constant b, which results in equation 26. Constant b is similar to intercept a in Figure 5. In order to ensure a positive value for H in equation 26 (as H is positive) quantity b must be positive, like a in Figure 5 and like original term kBlnPº. Equation 26 connects magnitude H with the overtaking of entropy, i.e., S1  S, to reach equilibrium. This feature is not revealed by the statistical formulation (equation 25). 𝑘B 𝐻 = 𝑆1 − 𝑆 + 𝑏

(26)

Now taking into account equality 24 (S1 = CIR  a), equation 26 converts into 27 (c = b  a). This equation stands for a quantitative connection of irreversible heat capacity with magnitude Boltzmann H, beyond the above appraisal of a common decrease of both magnitudes in approaching equilibrium. Since irreversible heat capacity equals entropy at equilibrium, quantity c relates to H at equilibrium. 𝑘B 𝐻 = 𝐶IR − 𝑆 + 𝑐

(27)

The connection of magnitude H with temperature is afforded by equation 28. This follows equation 26 considering the entropy-temperature relation for the system, i.e., S = TdS/dT = Tcot (equation 21 and Figure 5).

18

Francisco Ros 𝐻=

cot𝜙 (𝑇1 𝑘B

𝑏

− 𝑇) + 𝑘

B

(28)

The dependence of H on temperature is of opposite direction to the change in the temperature. Thus, temperature increases in the nonworking adiabatic process as it has been above shown, while H decreases according to the first term at the right hand side of equation 28, i.e., dH/dT = cotT1/kB < 0. This correlation of H with temperature is fully congruent with the statistical nature of the former (dH/d < 0).

Determination of the Heat Capacity of a Molecular Gas The heat capacity of the ester shown in Figure 6 was determined in the gas state by the method sketched in Figure 3. The molecule contains a chiral atom giving rise to two optical isomers, but it does not affect the determination of heat capacity that concerns the perfect gas state of the ester (chirality does not affect thermic status of an isolated molecule). At temperatures below 90ºC the ester exists as a solid and sublimes to the gas state with an experimentally perceivable vapor pressure.

Figure 6. Ester.

The vapor pressure and the attendant enthalpy and entropy of sublimation were previously measured experimentally [1], and so it was the heat capacity of the ester in the solid state which was also needed. The absolute entropy of the solid, also needed, was previously determined with high accuracy by a related method [1], having been determined by the heat capacity of the solid.

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 19 The base equation for the procedure is 29 referring to the entropy of sublimation as itemized regarding the motional components (translational, rotational and vibrational) for the entropy of the gas. The entropy of the solid [S(s)] is only vibrational, the entropy of cohesive potential energy between molecules being null [1]. ∆𝑆 = 𝑆T + 𝑆R + 𝑆V − 𝑆(s)

(29)

The variation of the entropy of sublimation around the considered experimental temperature of sublimation for the solid [78.6ºC (351.8ºK)] was analyzed. It is expressed by equation 30 as a function of the temperature [1]. In the equation, the heat capacities of the gas and the solid refer to constant pressure consistently with the enthalpy of sublimation (equal to the heat of sublimation at constant pressure). ∆𝑆 =

∆𝐻(351.8°K) 𝑇

+

1 𝑇 [𝐶(g) ∫ 𝑇 351.8

− 𝐶(s)] 𝑑𝑇

(30)

The heat capacity of the gas is the unknown in equation 30. The essence of the method consists of testing trial C(g) so that the S obtained with 30 yields the correct experimental translational entropy (ST) in being put in precedent equation 29. The experimental ST for the checkout derives in an exact manner from the experimental vapor pressure, and is known [1]. It derives from the vapor pressure by means of exact Sackur-Tetrode formula that correlates the translational entropy of a perfect gas with the gas pressure (equation 31 [2]). 𝑆T = 𝑅ln

𝑅𝑇 2𝜋𝑚𝑘B 𝑇 3/2 ( ) 𝑁A 𝑝 ℎ2

5 2

+ 𝑅

(31)

The supplementary rotational and vibrational entropies of the gas for equation 29 are accurately known data [1]. The rotational entropy can however be omitted in the procedure for simplification with no loss of accuracy, and the checkout equation is then 32. Equation 33 is the applicable test equation corresponding to checkout 32. In 33, term 351.8SR(351.8ºK)/T

20

Francisco Ros

has been subtracted to counterpoise mathematically and in the thermodynamically right manner the omission of rotational heat capacity (3R/2). Equation 33 is mathematically and thermodynamically entirely correct with respect to 30. ∆𝑆 † = 𝑆T + 𝑆V − 𝑆(s) ∆𝑆 † =

(32)

∆𝐻(351.8°K)−351.8𝑆R (351.8°K) 𝑇

+

1 𝑇 [𝐶(g) ∫ 𝑇 351.8

3 2

− 𝐶(s) − 𝑅] 𝑑𝑇 (33)

As a starting trial C(g), it was chosen the approximate heat capacity of the gaseous ester as estimated by Rihani-Doraiswamy method (equation 34, in J ºK-1 mol-1) [8]. To obtain a set of trial C(g)'s, equation 34 was varied by multiplying by variable factor f 1.01-1.18, which was a sufficient range. A sample assay for f = 1.08 is shown in Table 1. The temperature range is a limited interval of 15ºC around the experimental sublimation temperature (351.8ºK). Values SV, S(s) and ST(experimental) were taken from the literature as above indicated. 𝐶(g) = −0.001𝑇 2 + 1.741𝑇 − 26.9

(34)

Table 1. Sample assay. Entropies in J ºK1 mol1 Temperature (ºK) 344.3 347.3 350.3 353.3 356.3 359.3

∆𝑆 † 207.69 204.87 202.08 199.29 196.53 193.78

SV

S(s)

222.40 226.61 230.80 235.14 239.36 243.78

326.00 331.45 337.03 342.62 348.05 353.60

ST (predicted) 311.29 309.71 308.31 306.77 305.22 303.60

ST (experimental) 314.56 311.67 308.82 306.02 303.27 300.57

The data in the table refer to a single trial C(g) as a function of temperature. For appraising such single heat capacity, the set of predicted ST values in the table was compared with the set of experimental ST values with

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 21 regard to the middle temperature for the temperature interval as the only experimental temperature of sublimation available (351.8ºK). The linear regressions for the two sets [ST(pred.) = 0.50914T + 486.60, ST(exp.) = 0.93286T + 635.66] were thus compared at that specific temperature, giving a discrepancy of 0.0015% between the ST(pred.) and ST(exp.) values (351.8ºK). This small discrepancy permitted however an appraisal since was discernible from discrepancies for other trial C(g)'s. Thus, Figure 7 shows a survey of the test for the set of trial heat capacities, wherein the discrepancy between ST(pred.) and ST(exp.) has been converted into an equivalent discrepancy in terms of realistic vapor pressures. An absolute minimum of error is found at the f value of 1.09 [C(g) = 1.09  103T2 + 1.898T  29.32], for which the error is practically zero.

Figure 7. Survey of the test [f multipying factor to starting C(g)].

Abridged Procedure. Heat Capacity-Pressure Correlation The entropy of the solid was next omitted in the equations of the test, similarly and in addition to the omission of rotational entropy of the gas, what resulted in checkout equation 35 and test equation 36. The omission of the heat capacity for the solid is exactly counterbalanced by introduction of

22

Francisco Ros

term 351.8SV(351.8ºK) in 36. In this manner, the heat capacity of the gas phase can be found out with no loss of exactness getting rid of the solid phase, as well as of the rotational motion in the gas phase. Carrying out the full test with the abridged equations, the optimal C(g) was not significantly displaced, lying at f 1.08 versus 1.09 for the standard test. This small difference is possibly consequence of a slight drift of SV and S(s) values from correct values with temperature, the values being in fact anchored at just 351.8ºK. ∆𝑆 †† = 𝑆T + 𝑆V ∆𝑆 †† =

(35)

351.8[𝑆T (351.8°K)+𝑆V (351.8°K)] 𝑇

+

1 𝑇 [𝐶(g) ∫ 𝑇 351.8

3

− 2 𝑅] 𝑑𝑇

(36)

A direct correlation between the translational entropy of the vapor (ST) and the heat capacity [C(g)] ensues equation 35 and 36 taking into account the relationship of SV to C(g) as given by equation 37 (CV = CV  2(3R/2), CV = Cp  R). Substitution of this equation in 35 followed by equalization to 36 results in the correlation between ST and C(g) (equation 38). In this equation, C(g) is a function of temperature and is incorporated into integrals. Equation 38 is thermodynamically exact on condition that exact Planck's equation for changes of states [1, 4] in the form that was used for base equation 30, namely as dH = [C(g)  C(s)]dT, is also exact. This shortened expression of Planck's equation is actually an approximation, but is valid for low vapor pressures as it is the present case. 𝑇

𝑆V = ∫351.8

𝐶(g)−4𝑅 𝑑𝑇 𝑇

351.8[𝑆T (351.8°K)+𝑆V (351.8°K)] 𝑇 𝑇 𝐶(g)−4𝑅 ∫351.8 𝑇 𝑑𝑇

𝑆T =

(37) +

1 𝑇 [𝐶(g) ∫ 𝑇 351.8

3 2

− 𝑅] 𝑑𝑇 − (38)

Then a correlation between vapor pressure and heat capacity for the vapor follows considering the relationship between translational entropy and

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 23 vapor pressure by Sackur-Tetrode formula (equation 31). The resulting general correlation for pressure and heat capacity of a gas is given by equation 39, valid for a perfect molecular gas. Constant A and B embody a reference temperature T0 (e.g., 351.8ºK), the molecular mass for the gas, and the translational and vibrational entropies of the gas at T0. For a wide T-T0 interval these constants will become variable parameters consistently with the basis of the equation. ln𝑝 = A −

B 3 1 − ln𝑇 − 𝑇 2 𝑅𝑇

𝑇

𝐶𝑝 (g)𝑑𝑇 + 𝑇0

1 𝑅

𝑇

𝐶𝑝 (g) 𝑑𝑇 𝑇 𝑇0

(39)

Although it can actually be generalized to a lonely gas, equation 39 originally refers to a vapor in equilibrium with a solid phase, what sets a condition on the equation. Thus, beyond the perfection required to the gas by Sackur-Tetrode formula, a low pressure is further required in order to eliminate the incidence of the gas-solid equilibrium on the lonely gas. So, primordial Planck's equation for changes of state, above indicated, demands a low pressure be acting on the solid phase in contact with the vapor, but this effect is quite negligible at normal pressures. Hence equation 39 is an unmistakable relationship of the pressure of a gas to the heat capacity of the gas.

Precision of the Method The set of C(g)'s as functions of temperature which was used to obtain the optimal C(g) is not complete as does not take into account all inclinations of a C(g) line. Consequently, the test is not enterely precise. On the other hand, the test is considered exact just for the middle temperature of the used temperature interval. This temperature stands for the temperature of sublimation to the only experimental value of entropy of sublimation that was available. This single value of entropy of sublimation was determined from a number of vapor pressure measurements in the temperature interval [1]. By this reason, C(g) values as obtained by the test at temperatures other than such middle temperature are not considered as exact, yet highly accurate.

24

Francisco Ros

Deflection of a C(g) line about the middle point of the line [so as to enlarge the scope of the trial C(g) set] represents a modification that is of second order with respect to the test. Thus, when a selected C(g) was deflected by a 30% in slope, the new C(g) value at the extreme of the temperature interval diverged by only 0.5%. In comparison, multiplication of the C(g) by f 1.1, a 10% modification in the way previously used in the test, represented a significative alteration of a 10% in the C(g) value at the interval extreme. The test was conducted using a set of trial C(g)'s deflected about the middle temperature, which were derived from the best C(g) that had been obtained in the above standard manner (Figure 7, f 1.09). The task was undertaken in order to find out a proper variation of the best C(g) with the temperature, in addition to completing the scope of the test. For the purpose, such starting C(g) was approximated as linear [C(g) = 1.129T + 106.5], as it practically is in the small 15ºK interval. Figure 8 shows the results obtained. An error of zero was found to the heat capacity disentangled in equation 40, which was taken as definitive and is strictly valid from 344 to 359ºK [C(g) in J ºK-1 mol-1).

Figure 8. Optimization of the test for the inclination of C(g) as function of temperature [C(g) = aT + b].

The Equivalence of Heat Capacity and Entropy in Adiabatic Systems 25 𝐶(g) = 1.302𝑇 + 45.56

(40)

The accuracy of the method relies on the original experimental heat of sublimation (wherefrom sublimation entropy derives, S = H/T), other inaccuracies having dropped out in the test. It is of the order of one percent (1-3%) including numerical handling. The error of the method mainly results from the measurement of vapor pressures by Knudsen effusion method [1, 5, 9] for determining the heat of sublimation (ca. 1% error for H). Table 2 shows selected values of heat capacity by equation 40. The value at 45ºC is an extrapolation outside the regular temperature range. The corresponding values by Rihani-Doriswamy method of estimation for the ester (equation 34) deviate from the values in the table by 7-8%, which is an exceedingly large deviation for heat capacity when accuracy is appreciated. Table 2. Selected values of heat capacity for the gaseous ester (at constant pressure, in cal ºC-1 mol-1) Temperature (ºC) 45 79 86

Cp 110 120 123

CONCLUSION It has been proven that in thermally isolated systems undergoing an irreversible transformation the heat capacity, as internal heat capacity, equals in absolute value the entropy of the system during the process. Distinctive irreversible heat capacity is an indicator of the achievement of thermodynamic equilibrium which is parallel to a vague reversible maximal entropy. It has been shown that the heat capacity of a gas can be determined from limited thermodynamic data, without artificial manipulation of the molecule, with a simple data handling and with high accuracy. A general

26

Francisco Ros

thermodynamic equation that correlates the pressure of a gas with the gas heat capacity has been derived.

REFERENCES [1]

[2]

[3]

[4] [5] [6] [7] [8]

[9]

Ros, Francisco. 2019. “Novel Determination of Potential Energy of Cohesion in Solids and Liquids: Time Efficiency of Potential Energy in Thermal Processes”. In Advances in Energy Research, edited by Acosta, Morena J., vol. 31, in press. New York: Novo Science Publishers. Aguilar Peris, José. 1970. Termodinámica y mecánica estadística. Valencia: Saber. [Thermodynamics and Statistical Mechanics. Valencia: Saber]. Roux, M. V., Jiménez, P., Vacas, A., Cano, F. H., Apreda-Rojas, M. C., and Ros, F. (2003). A Compact and Lipophilic Enantiomer Showing a Bilayer Crystal Structure  Free Energy of Spontaneous Resolution of the Racemic Compound into the Crystalline Enantiomers. European Journal of Organic Chemistry, 2003: 20842091. Denbigh, Kenneth. 1971. The Principles of Chemical Equilibrium. London: Cambridge University Press. Díaz Peña, M., and Roig Muntaner, A. 1984. Química Física. Madrid: Alhambra. [Physical Chemistry. Madrid: Alhambra]. Perry, R. H., and Chilton, C. H., eds. 1973. Chemical Engineering’s Handbook. New York: McGraw-Hill. Benson, Sydney W. 1982. The Foundations of Chemical Kinetics. Malabar: Krieger. Rihani, D. N., Doraiswamy, L. K. (1965). Estimation of Heat Capacity of Organic Compounds from Group Contributions. Industrial & Engineering Chemistry Fundamentals, 4:17-21. Colomina, M., Jiménez, P., Turrión, C. (1982). Vapour pressures and enthalpies of sublimation of naphtalene and benzoic acid. Journal of Chemical Thermodynamics, 14: 779-784.

In: Heat Capacity Editor: Søren A. Dam

ISBN: 978-1-53618-142-5 © 2020 Nova Science Publishers, Inc.

Chapter 2

MOLAR HEAT CAPACITY OF AQUEOUS BLENDS OF MONOETHANOLAMINE WITH PIPERAZINE USING MICRO-REACTION CALORIMETER (µRC) Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang, Nabil El Hadri and Mohammad R. M. Abu-Zahra* Department of Chemical Engineering, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates

ABSTRACT Heat capacities of aqueous mixtures of monoethanolamine (MEA) with Piperazine (PZ) were measured from (303.15 to 353.15) K with a micro-reaction calorimeter (µRC) at an interval of 5 K. The heat capacities (Cp /Jmol-1K-1) of PZ, MEA, MEA + H2O, PZ + H2O, MEA + PZ and MEA + PZ + H2O were studied. Various concentrations of these binary and *

Corresponding Author’s. Email: [email protected], Tel.: +97128109181.

28

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al. ternary systems were studied. An excess molar heat capacity (CpE/Jmol1K-1) expression using the Redlich-Kister equation for the composition dependence is used to represent the measured Cp of aqueous amine blends. The average absolute percentage deviation (AAD %) for the calculation of the excess molar heat capacities are less than 3% for both binary and ternary systems. The molar heat capacities of blends and binary mixtures could be predicted with an accuracy of less than 1% using the coefficients and correlations reported in this work. The excess heat capacities of mixtures having MEA with PZ were found to be less than mixtures having MEA with other amines (e.g., 2-Piperidine ethanol (2-PE), Methyldiethanolamine (MDEA) and 1-amino-2-methyl-1-propanol (AMP)).

Keywords: molar heat capacity, excess molar heat capacity, amines, blends

INTRODUCTION A feasible solution to decrease the emission of CO2 to the atmosphere is capturing them and storing them subsequently. Most matured technology to capture CO2 from industrial gases is the chemical absorption technology using a reactive solvent such as aqueous amines [1]. Screening of the solvent for the capture process is quite a complex process due to the varying characteristics such as reactivity, cyclic loading, temperature stability, stability towards oxygen and binding energy [2]. Piperazine activated aqueous alkanolamine solutions have such advantages and they have been extensively studied and proposed as a more efficient bulk removal solvent [3-4]. Adeosun et al. studied four PZ blends (MEA + PZ + H2O; DEA + PZ + H2O; AMP + PZ + H2O; MDEA + PZ + H2O) for their absorption capacity with absorption rate and suggested for further thermodynamic studies for the feasibility of such blends for post-combustion capture applications. CO2 absorption rate and solubility of PZ blend with MEA (MEA + PZ + H2O) were found to be superior and suggested to be a better solvent for CO2 capture application [5]. Adeosun et al. [4] reported that the absorption capacity of MEA + PZ + H2O blend is (0.69 to 0.75) molCO2/molamine and 1.68 mmolmol-1.s-1. In this work, the thermodynamic work of measuring

Molar Heat Capacity of Aqueous Blends …

29

heat capacity for the blend (MEA + PZ + H2O) was carried out to find their behavior in variation with concentrations and temperatures. Knowledge of heat capacities of liquids as a function of temperature gives some insight into their molecular structure and intermolecular interactions [6]. Molar heat capacities at various temperatures are required for the calculation of thermodynamic properties such as enthalpy (H), entropy (S) and Gibbs energy (G). These data are needed to design of absorbers, regenerators, condensers, heat exchangers and reboliers used in CO2 capture or gas plants [7]. The heat capacities of some of the pure alkanolamines have been reported in the literature [6,8-13]. Heat capacities of aqueous alkanolamine solutions (binary systems) are also available in the literature: MEA + H2O; [9] DEA +H2O;[9], DGA + H2O;[10] MDEA + H2O; [11] some physical solvents + water;[12] some alkanolamines + H2O; [13] and some cyclic amines + H2O [7]. The heat capacities of CO2-loaded for aqueous solutions of MEA, DEA, MDEA, aqueous MDEA + MEA, and MDEA + DEA were also studied at 298 K [14]. The blends of amines (ternary systems) were also available in the literature: MEA + MDEA + H2O; [15-16] MEA + AMP + H2O; [15,17] MEA + 2-PE + H2O; [18] DEA + AMP + H2O; [19] DEA + 2-PE + H2O; [20] AMP + Sulfolane + H2O; [21] PZ + Diethylenetriamine (DETA) + H2O;[22] PZ + 3-(methylamino)propylamine (MAPA) + H2O;[22] PZ + AMP + H2O;[23] and PZ + MDEA + H2O [3]. The heat capacity of MEA + PZ + H2O has not yet studied in the literature. It is the purpose of this study to determine experimentally the heat capacities of MEA + PZ + H2O by using a micro-reaction calorimeter (RC). An excess molar heat capacity expression, using the Redlich-Kister equation for the concentration dependence, was applied to represent the measured Cp data.

EXPERIMENTAL SECTION The purity and the details of the chemicals used in this work are presented in Table 1. The aqueous amine solutions were prepared using

30

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al.

distilled water on the basis of molar fraction. Accordingly, desired amounts of amine and water were weighed using an analytical balance (Cole-Parmer Symmetry) with the readability of 0.0001 g and then mixed well using a magnetic stirrer to obtain an aqueous amine solution with a designated molar fraction. The heat capacity was measured using a Micro Reaction Calorimeter provided by Thermal Hazard Technology (UK). Heat capacity was measured at temperature ranging from (303.15 to 353.15) K. The measurement of the heat capacity was achieved by making a “step-change” in the temperature of the cell in comparison to an empty vial. At each temperature, the heat was repeatedly measured 3 times with a step of ± 0.5 K. First, blank test was conducted with an empty vial. Then, approximate (0.5 to 1) g of sample was placed in the analysis vial and conducted test with the same condition used for the blank. The heat capacity was calculated by URC Analysis software provided Thermal Hazard Technology (UK) based on the equation (1),

𝐶𝑝 =

(Q-Qblank )

(1)

(m×∆T) Table 1. Sample Table

Chemical Name

Molecular Weight (g/mol) Monoethanolamine (MEA)* 61.08 Piperazine (PZ)* 86.14 * Samples were used without further purification.

Source Sigma-Aldrich Sigma-Aldrich

Chemical Formula C2H7NO C4H10N2

Purity (mass) ≥ 99% 99%

Where, Cp (Jg-1 K-1) is the heat capacity of sample, m is the mass of sample (g), ΔT is the temperature step (1 K) and Q (J) and Qblank (J) are the heat change of analysis cell with sample and without sample, respectively. The Cp unit (Jg-1 K-1) can be converted to (Jmol-1 K-1) by multiple with molecular weight of the sample. In order to evaluate the accuracy of this method, the heat capacity of water was measured at the same condition that would be used for the sample

Molar Heat Capacity of Aqueous Blends …

31

analysis and compared with the available reference data [24-25]. The accuracy of the Cp measurement was estimated to be ±2.5% on the basis of the measurement of the Cp of water (Table 2). The uncertainty of the Cp measurements was estimated to be  0.05 J. mol-1.K-1. Table 2. Heat capacities of pure H2O, MEA and PZ Cp/(J.mol-1.K-1) T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

Osborne et al., 193924

Liu et al., 199925

75.28 75.27 75.28 75.29 75.32 75.35 75.38 75.43 75.48 75.53 75.60

75.27 75.30 75.32 75.36 75.37 75.41 75.43 75.45 75.46 75.50 75.52

H2O 75.28 75.27 75.28 75.29 75.32 75.35 75.38 75.43 75.48 75.53 75.60

Current Work MEA PZ 168.4 176.0 170.4 177.6 171.0 179.8 171.7 181.6 172.7 183.9 174.0 186.0 175.3 187.9 177.0 190.5 178.9 192.5 180.1 194.8 181.3 197.0

Standard uncertainties u are u (T) = 0.01 K, Uc (Cp) = 0.05 Jmol-1K-1 (level of confidence = 0.95).

RESULTS AND DISCUSSION Table 2 shows the experimental data of the heat capacities for pure H2O, MEA and PZ for temperatures from (303.15 to 353.15) K. The Cp value of water in Table 2 are compared with literature and used to validate the experimental results and accuracy of the micro calorimeter used in this work. Figure 1 expresses the comparisons between the results of this work and the literature values of both MEA and PZ [7, 24]. Comparing the values of the experimental results of MEA from this work with Rayer et al, showed a good agreement with only 0.4% absolute average deviations (AAD%). However, a deviation in the graph was noticed when the results of PZ from this work were compared with the extrapolated results of Chen and Li et al. and the ADD% of 1.2% was found. Chen and Li et al. [24] extrapolated the heat

32

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al.

capacity values of PZ from the experimental results of higher temperatures to the lower temperatures, whereas in this work the experimental values were obtained at the lower temperature range. This may be the reason for the deviation shown in the Figure 1. The obtained values of Cp of MEA and PZ are expressed as a function of temperature as follows:

CpMEA/(J∙mol−1 ∙ K-1 ) = 91.10+ 0.255 × (T/K)

(2)

CpPZ/(J∙mol−1 ∙ K-1 ) = 46.83+ 0.425 × (T/K)

(3)

205 200

Cp/(J.mol-1.K-1)

195 190 185 180 175 170 165 300

310

320

330

340

350

360

T/K

The values of Cp for binary systems MEA (1) + H2O (2), PZ (1) + H2O (2) and MEA (1) + PZ (2) were also measured, and will be discussed in the following sections, for temperatures from (303.15 to 353.15) K for the entire mole fraction ranges from 0 to 1. For PZ, the additional mole fraction ranges

Molar Heat Capacity of Aqueous Blends …

33

were chosen in the region where PZ is more soluble in water (xPZ < 0.2) to determine the behavior of heat capacity of solution compare with the region where PZ is less soluble in water (xPZ > 0.2). The excess molar heat capacity (CpE/Jmol-1K-1) for the aqueous mixture was calculated using the expression as given below: [17]

𝐶𝑝𝐸 = 𝐶𝑝 − ∑𝑖 𝑥𝑖 𝐶𝑝𝑖

(4)

where Cpi is the molar heat capacity of the pure component i (Jmol-1K-1), xi is the mole fraction of each component in the solution. The calculated values of CpE are also listed in Tables 3, 5 and 6.

Molar Heat Capacities of (MEA + H2O) System Table 3 lists the experimental results obtained for aqueous MEA system. Figure 2 shows the concentration dependency of the molar excess heat capacities at various temperatures for MEA + H2O. The molar heat capacity values for aqueous MEA system increased with temperature from (303.15 to 353.15) K. Also, as the concentration of MEA decreased from 0.2 to 0.8 mole fraction it’s molar heat capacity increased (see Table 3). The molar excess heat capacity increased steadily as the concentration of MEA increased until a maximum value was reached at around x1 = 0.45 and then the CpE values fell gradually to zero for all temperatures. The molar excess heat capacity values were correlated with a RedlichKister equation represented as follows: 𝐸 𝐶𝑝,12 /(J∙mol−1 ∙ K-1 ) = 𝑥1 𝑥2 ∑𝑛𝑖=1 𝐴𝑖 (𝑥1 − 𝑥2 )𝑖−1

(5)

34

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al. Table 3. Heat Capacities (Jmol-1K-1) of MEA (1) + H2O (2)

T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

x1 = 0.2

x1 = 0.4 CpE 0.8 1.2 1.6 1.9 2.2 2.4 2.9 3.3 3.5 3.8 4.3

Cp 94.7 95.5 96.0 96.5 97.0 97.5 98.3 99.0 99.7 100.3 101.0

Cp 114.4 115.7 116.5 117.3 118.1 119.3 120.5 121.4 123.0 124.0 125.0

x1 = 0.6 CpE 1.9 2.4 2.9 3.5 3.8 4.5 5.1 5.3 6.2 6.6 7.1

Cp 132.7 134.3 135.2 136.0 137.0 138.5 139.4 140.9 142.5 143.8 144.9

x1 = 0.8 CpE 1.5 1.9 2.5 2.9 3.2 3.9 4.1 4.5 5.0 5.5 5.9

CpE 0.1 0.4 0.6 0.9 1.2 1.5 1.7 1.9 2.3 2.5 2.8

Cp 149.9 151.8 152.5 153.3 154.4 155.8 157.0 158.6 160.5 161.7 163.0

Standard uncertainties u are u (T) = 0.01 K, u (x) = 0.0001, Uc (Cp) = 0.05 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4. 8

CpE/(J.mol-1.K-1)

6

4

2

0 0.0

0.2

0.4

0.6

xMEA

0.8

1.0

Molar Heat Capacity of Aqueous Blends …

35

Depending on the complexity of the binary systems, the number of terms (Ai) should be used to represent CpE. Ai depends on the temperature and correlated as a function:

𝐴𝑖 = 𝑎𝑖,0 + 𝑎𝑖,1 (𝑇/K) + 𝑎𝑖,2 (𝑇/K )2

(6)

The values of ai,0 and ai,1 for MEA + H2O system are reported in Table 4. The solid lines in Figure 2 were drawn using equation 5 for different temperatures and concentrations. AAD% calculated for CpE and Cp values for MEA+H2O were found to be 2.4% and 0.2%, respectively. Table 4. Parameters of Excess Molar Heat Capacity for Binary Systems Binary system MEA (1) + H2O (2) PZ (1) + H2O (2) MEA (1) + PZ (2)

i 1 2 3 1 2 3 1 2 3 4

ai,0 -113.68 22.59 -6.23  10-4 -174.36 -30.95 -350.62 -662.07 -35.67 -256.69 89.24

Parameters ai,1 0.40 -0.09 -4.36  10-2 0.40 -0.53 0.84 3.50 0.90 0.66 0.20

ai,2

-4.89  10-3 -1.66  10-3 -7.22E  10-4 -3.64  10-4

no. of data points 44

AAD% C pE Cp 2.4 0.2

44

1.4

0.1

44

1.7

0.1

Molar Heat Capacities of (PZ + H2O) System Table 5 shows the experimental data resulted in this work for the PZ+H2O system. Piperazine exist as a solid in room temperature and has a low solubility in water as the concentration exits certain ranges [26]. In order to account for this behavior, more concentration ranges were taken in lower mole fraction ranges (xPZ) between (0 to 0.2). Figure 3 shows the concentration dependency of the molar excess capacities at various temperatures for PZ + H2O. The molar excess heat capacity values increased

36

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al.

as temperature increases from (303.15 to 353.15) K through the entire range of the mole fractions. The molar excess heat capacity values were positive for 0 < xPZ < 0.4 and negative for 0.4 < xPZ < 1 mole fractions. The maximum molar excess heat capacity showed for diluted solution of PZ at xPZ = 0.2 and then the curve plummeted to a negative molar excess heat capacity. The minimum value for the CpE achieved at a concentrated solution of PZ around xPZ = 0.78. The molar excess heat capacity values were correlated with a Redlich-Kister relation as shown in equation 5. Using the same equation, the solid lines in Figure 3 were drawn for different temperatures and mole fractions. The coefficients required for the equation to predict are presented in Table 4. AAD% obtained for PZ + H2O system for CpE and Cp values were found to be 1.4% and 0.1%, respectively.

10

CpE/(J.mol-1.K-1)

0

-10

-20

-30

0.0

0.2

0.4

0.6

xPZ

0.8

1.0

Table 5. Heat Capacities (Jmol-1K-1) of PZ (1) + H2O (2) T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

x1 = 0.05 Cp CpE 82.30 2.0 82.70 2.3 83.20 2.7 83.70 3.1 84.20 3.5 84.70 3.8 85.20 4.2 85.70 4.5 86.20 4.9 86.80 5.3 87.30 5.6

x1 = 0.1 Cp 88.80 89.60 90.42 91.20 92.07 93.06 93.80 94.94 95.49 96.13 97.07

CpE 3.5 4.1 4.7 5.3 5.9 6.7 7.2 8.0 8.3 8.7 9.3

x1 = 0.15 Cp CpE 94.45 4.1 95.87 5.2 97.00 6.0 97.80 6.6 99.28 7.7 100.00 8.1 101.00 8.7 102.00 9.3 103.00 10.0 104.88 11.5 106.10 12.3

x1 = 0.2 Cp CpE 99.72 4.3 100.80 5.1 102.00 5.8 103.50 6.9 104.60 7.6 106.00 8.5 107.00 9.1 108.50 10.1 109.98 11.1 111.37 12.0 112.43 12.6

x1 = 0.4 Cp 111.00 112.20 113.70 115.00 116.70 118.20 119.60 121.35 122.80 124.40 126.00

C pE -4.6 -4.0 -3.4 -2.8 -2.1 -1.4 -0.8 -0.1 0.5 1.1 1.9

x1 = 0.6 Cp CpE 112.50 -23.2 114.00 -22.7 116.00 -22.0 118.00 -21.1 119.50 -21.0 120.00 -21.7 122.00 -20.9 124.00 -20.5 126.00 -19.7 128.00 -19.1 129.50 -18.9

x1 = 0.8 Cp CpE 123.00 -32.8 125.00 -32.2 127.00 -31.9 129.00 -31.3 130.50 -31.7 132.50 -31.3 134.50 -30.9 137.00 -30.5 139.00 -30.1 141.00 -30.0 143.00 -29.7

Standard uncertainties u are u (T) = 0.1 K, u (x) = 0.001, Uc (Cp) = 0.5 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4.

38

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al.

Molar Heat Capacities of (MEA + PZ) System Table 6 displays the results obtained for the blend of (MEA + PZ) system. Figure 4 shows the concentration dependency of the molar excess capacities at various temperatures for MEA+PZ system. The molar excess heat capacity values were negative for entire temperature ranges. It means that the contribution by the pure amines to the molar heat capacity (∑i xi Cpi) dominates the contribution by the blended amines (Cpblend ) in equation 4. Therefore, the mixing process increases the molar heat capacity values of individual amines. The values of molar excess heat capacity increased as temperatures increase and the maximum value achieved at a higher concentration of MEA. The curve decreased sharply at lower concentration of MEA and then rose gradually after it hit a minimum at around xMEA = 0.25 and xPZ = 0.75. The molar excess heat capacity values were correlated with a Redlich-Kister relation as shown in equation 5. The coefficients required to predict the CpE values are given in Table 4. AAD% obtained for MEA + PZ system for CpE and Cp values were found to be 1.7% and 0.1%, respectively. Table 6. Heat Capacities (Jmol-1K-1) of MEA (1) + PZ (2) T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

Cp 147.0 149.3 151.7 154.1 156.6 159.1 160.8 163.4 166.1 168.1 170.1

x1 = 0.2 CpE -27.5 -26.9 -26.4 -25.5 -25.1 -24.5 -24.5 -24.4 -23.6 -23.8 -23.8

Cp 155.4 158.5 160.5 162.2 164.3 166.3 168.2 170.8 173.0 175.7 178.0

x1 = 0.4 C pE -17.6 -16.3 -15.8 -15.4 -15.1 -14.9 -14.6 -14.3 -14.0 -13.2 -12.7

Cp 162.6 164.8 166.9 168.5 170.5 172.5 174.4 176.7 178.5 180.2 182.0

x1 = 0.6 CpE -8.9 -8.5 -7.6 -7.2 -6.7 -6.3 -6.0 -5.7 -5.8 -5.8 -5.6

x1 = 0.8 Cp CpE 167.2 -2.7 169.4 -2.5 170.7 -2.1 172.0 -1.7 173.5 -1.5 175.2 -1.2 176.8 -1.0 178.8 -0.9 180.7 -0.9 182.2 -0.9 183.6 -0.8

Standard uncertainties u are u (T) = 0.1 K, u (x) = 0.001, Uc (Cp) = 0.5 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4.

Molar Heat Capacity of Aqueous Blends …

39

Table 7. Heat Capacities (Jmol-1K-1) of MEA (1) + PZ (2) + H2O (3) for x3 = 0.8

T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

x1/x2 = 0.16/0.04 Cp 97.0 97.6 98.1 98.6 99.0 99.7 100.2 100.7 101.2 101.8 102.5

CpE 2.8 3.0 3.3 3.6 3.8 4.1 4.4 4.4 4.5 4.8 5.2

x1/x2 = 0.12/0.08 Cp 101.9 102.6 103.4 104.1 104.8 105.2 105.7 106.2 106.7 107.4 108.1

CpE 7.4 7.7 8.3 8.8 9.1 9.2 9.3 9.4 9.5 9.8 10.1

x1/x2 = 0.08/0.12 Cp 106.8 107.9 108.8 109.6 110.3 111.0 111.7 112.4 112.9 113.5 114.1

x1/x2 = 0.04/0.16

CpE 12.0 12.7 13.3 13.8 14.2 14.5 14.8 15.0 15.2 15.3 15.5

Cp 107.6 108.5 109.3 110.2 111.1 112.0 113.0 114.0 115.3 116.3 117.2

CpE 12.5 13.0 13.5 14.0 14.5 15.0 15.6 16.1 17.0 17.5 18.0

Standard uncertainties u are u (T) = 0.1 K, u (x) = 0.001, Uc (Cp) = 0.5 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4. 0

CpE/(J.mol-1.K-1)

-5

-10

-15

-20

-25

-30 0.0

0.2

0.4

0.6

xMEA

0.8

1.0

40

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al. 10

(a) 5

CpE/ (J.mol-1.K-1)

0 -5 -10 -15 -20 -25 -30 0.0

0.2

0.4

0.6

0.8

1.0

0.15

0.20

0.25

xMEA 10

(b)

CpE/ (J.mol-1.K-1)

8

6

4

2

0

-2 0.00

0.05

0.10

xPZ

Figure 5 shows the comparison of the molar excess heat capacity for different blended amines of binary mixtures available in literature. Figure 5 (a) shows the variation of CpE for MEA blend with 2-PE (cyclic amine) [18], AMP (hindered amine) [17], MDEA (tertiary amine) [16] and PZ (cyclic diamine). It can be observed that the lowest CpE was obtained for MEA + PZ blend. Figure 5 (b) gives the variation of CpE for PZ blend with H2O

Molar Heat Capacity of Aqueous Blends …

41

(Unreacting solvent with CO2), MDEA (slowly reacting amine with CO2) [28], AMP (moderately reacting amine with CO2) [23] and MEA (highly reacting amine with CO2). It can be concluded that the lowest CpE obtained for PZ blend with the highly reacting amine with CO2 (i.e., MEA).

Molar Heat Capacities of (MEA + PZ + H2O) System The heat capacity values of a ternary system MEA (1) + PZ (2) + H2O (3) were measured for temperatures ranging from (303.15 to 353.15) K by varying x3 from 0.2 to 0.8. The obtained results are given in Tables 7-10 along with CpE calculated using equation 4. Figures 6-9 illustrates the experimental results obtained from this work. For the ternary system, the compositional dependence of the excess molar heat capacity was correlated using Redlich-Kister equation as follows: 𝐸 𝐸 𝐸 𝐶𝑝𝐸 /J∙mol−1 ∙ K-1 = 𝐶𝑝,12 + 𝐶𝑝,13 + 𝐶𝑝,23 + 𝑥1 𝑥2 𝑥3 ∑𝑛𝑖=1 𝐵𝑖 (𝑥1 − 𝑥3 )𝑖−1 +

𝑥1 𝑥2 𝑥3 ∑𝑛𝑖=1 𝐶𝑖 (𝑥1 − 𝑥2 )𝑖−1

(7)

Table 8. Heat Capacities (Jmol-1K-1) of MEA (1) + PZ (2) + H2O (3) for x3 = 0.6 T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

x1/x2 = 0.32/0.08 Cp CpE 116.1 3.0 117.4 3.5 118.3 4.0 119.1 4.5 120.2 5.0 121.3 5.5 122.4 6.0 123.6 6.5 124.9 7.0 126.0 7.5 127.1 8.0

x1/x2 = 0.24/0.16 Cp CpE 121.9 8.2 123.1 8.6 124.2 9.2 124.8 9.3 126.1 10.0 127.5 10.8 128.3 11.0 129.3 11.1 130.3 11.3 131.4 11.7 132.2 11.8

x1/x2 = 0.16/0.24 Cp CpE 127.3 13.0 128.6 13.5 129.6 13.9 130.4 14.2 131.5 14.5 132.7 15.0 133.7 15.3 134.9 15.6 136.1 16.0 137.2 16.3 138.2 16.6

x1/x2 = 0.08/0.32 Cp C pE 125.9 11.0 127.1 11.5 128.4 12.0 129.5 12.5 131.0 13.1 132.3 13.7 133.9 14.5 135.4 15.0 136.2 15.0 137.1 15.0 138.4 15.5

Standard uncertainties u are u (T) = 0.1 K, u (x) = 0.001, Uc (Cp) = 0.5 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4.

42

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al.

Table 9. Heat Capacities (Jmol-1K-1) of MEA (1) + PZ (2) + H2O (3) for x3 = 0.4 T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

x1/x2 = 0.48/0.12 Cp CpE 133.4 1.3 134.5 1.2 134.9 1.2 135.4 1.1 136.1 1.0 136.8 0.8 137.6 0.8 138.6 0.6 139.5 0.4 140.3 0.3 141.0 0.1

x1/x2 = 0.36/0.24 Cp C pE 136.5 3.5 137.4 3.3 137.8 3.0 138.3 2.8 138.9 2.5 139.5 2.1 140.2 1.8 141.1 1.5 141.9 1.1 142.5 0.7 143.1 0.3

x1/x2 = 0.24/0.36 Cp CpE 142.4 8.5 143.4 8.4 144.1 8.2 144.7 8.0 145.5 7.8 146.4 7.5 147.1 7.3 148.2 7.0 149.0 6.6 150.1 6.5 150.7 6.0

x1/x2 = 0.12/0.48 Cp CpE 140.9 6.1 141.8 6.0 142.8 5.9 143.7 5.8 144.9 5.8 146.1 5.8 147.2 5.8 148.7 5.8 149.8 5.8 151.1 5.8 152.3 5.8

Standard uncertainties u are u (T) = 0.1 K, u (x) = 0.001, Uc (Cp) = 0.5 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4.

Table 10. Heat Capacities (Jmol-1K-1) of MEA (1) + PZ (2) + H2O (3) for x3 = 0.2 T/K 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

x1/x2 = 0.64/0.16 Cp CpE 150.8 -0.2 152.3 -0.2 153.0 -0.3 153.6 -0.4 154.5 -0.5 155.5 -0.7 156.4 -0.9 157.8 -1.1 159.0 -1.4 159.9 -1.7 160.7 -2.0

x1/x2 = 0.48/0.32 Cp CpE 153.8 1.6 155.0 1.3 155.7 1.0 156.3 0.7 157.1 0.3 158.0 -0.1 158.8 -0.5 160.0 -1.0 161.0 -1.6 161.8 -2.1 162.5 -2.7

x1/x2 = 0.32/0.48 Cp CpE 158.6 5.2 159.9 5.0 161.0 4.9 162.0 4.8 163.2 4.6 164.4 4.4 165.4 4.0 166.9 3.8 168.2 3.5 169.3 3.0 170.3 2.7

x1/x2 = 0.16/0.64 Cp C pE 152.7 -1.9 154.4 -1.6 156.2 -1.3 157.6 -1.1 159.5 -0.9 161.3 -0.7 162.9 -0.5 165.0 -0.3 166.7 -0.2 168.5 -0.1 170.2 0.0

Standard uncertainties u are u (T) = 0.1 K, u (x) = 0.001, Uc (Cp) = 0.5 Jmol-1K-1 (level of confidence = 0.95). CpE/Jmol-1K-1 is a derived value from experimental Cp using eq. 4.

The temperature dependence of Bi and Ci are assumed as follows:

𝐵𝑖 = 𝑏𝑖,0 + 𝑏𝑖,1 (𝑇/K)

(8)

Molar Heat Capacity of Aqueous Blends …

43

𝐶𝑖 = 𝑐𝑖,0 + 𝑐𝑖,1 (𝑇/K)

(9)

where excess heat capacities of binary systems (Cp12E, Cp13E and Cp23E) were calculated using the Redlich-Kister relation as shown in equation 5. The coefficients regressed for all ternary systems using the experimental data are given in Table 11. Table 11. Parameters of Excess Molar Heat Capacity for Ternary System Ternary system

i

bi,0

Parameters bi,1

1 2 3

-36.68 -53.19 7784.92

-2.94  10-1 -8.23  10-1 3.11

1 2 MEA (1) + PZ 3 (2) + H2O (3) 1 2 3

-34.42 -55.16 7744.51

2.75 -8.69  10-1 -12.12

1306.57 -62.50 8017.33

-2.58 -4.90 -6.40

1 2 3

1610.07 -118.00 -236.44

-3.67 -15.08 22.85

ci,0

ci,1

x3 = 0.8 117.67 -11.57 8.58 -1.45  10-2 -6.23  10-4 -5.52  10-2 x3 = 0.6 178.30 -4.26 8.68 -1.44  10-2 -4 -6.23  10 -5.51  10-2 x3 = 0.4 623.28 -3.23 9.12 -1.45  10-2 -4 -6.23  10 -5.60  10-2 x3 = 0.2 831.53 5.74  10-2 8.17 -1.53  10-2

no. of data points

AAD% CpE Cp

44

1.7

0.2

44

1.3

0.1

44

1.4

0.1

44

1.0

0.1

-6.23  10-4 -4.47  10-2

Figures 6-9 show the measured molar heat capacities for ternary system with (x3 = 0.8,0.6,0.4 and 0.2) and the concentration dependency of the molar excess capacities at various temperatures for MEA + PZ + H2O. The molar excess heat capacity values were positive for all the temperatures from (303.15 to 353.15) K as shown in Figures 6 and 7, while a negative values was achieved in Figure 8 at a temperature of 353.15 K and at the mole fraction around 0.38 < x1 < 0.45. For Figure 9 the molar excess heat capacity values were only positive for all the temperatures at the mole fraction around

44

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al.

0.2 < x1 < 0.4 and it is negative for the other mole fractions. The solid lines in Figures 6-9 (a) were calculated by combining equations 4 and 7 while the solid lines in Figures 6-9 (b) were predicted using equation 7. The coefficients to predict the values are given in Table 11. From Figure 6 (a) it can be observed that the molar heat capacity values at lower temperatures are closer to each other compared to higher temperature values, while the vice-versa happened with Figure 7 (a). From Figure 8 and 9 (a) it can be observed as the Cp values of higher PZ blend intersect at temperatures between ((325 to 340) and (308 to 316) respectively)K and this indicates that the non-ideality (mixture of solid and liquid phases) of the solution due to blending the mixtures will be great in these regions. AAD% obtained for predicting CpE and Cp values of the ternary system MEA + PZ + H2O at (x3 = 0.8,0.6,0.4 and 0.2) were ((1.7% and 0.2%), (1.3% and 0.1%), (1.4% and 0.1%) and (1% and 0.1%) respectively). The isotherm for different CpE at constant temperature (325.15 K) for MEA + PZ + H2O blends were drawn using equation 7 for each CpE (Figure A in Supplementary Information). Matlab R2011bTM was used to program the CpE calculations for required CpE and temperature. Both negative and positive values of CpE occur for the blends. The lowest excess heat capacity occurs for the solution having lower water (concentrated solution of MEA and PZ) and the highest excess enthalpy was achieved for the solution having higher water (diluted solution of MEA and PZ). The isotherm curves having negative excess heat capacity (CPE = -5 Jmol-1K-1) have a maximum value at 80% MEA, 10% PZ and 10% H2O and have a minimum value for 10% MEA, 70% PZ and 20% H2O. The isotherm curve having a lower positive excess heat capacity (CpE = 2 Jmol-1K-1) has a maximum value at 53% MEA, 6.4% PZ and 40.6% H2O. The isotherm curve having a higher positive excess heat capacity (CpE = 5 Jmol-1K-1) has a maximum value at 94.3% MEA, 5.62% PZ and 0.08% H2O and a minimum value at 0.096% MEA, 29.769% PZ and 70.135% H2O. From this study, it can be concluded that highly concentrated blends are having lower heat capacity compared to diluted blends.

Molar Heat Capacity of Aqueous Blends …

45

120

Cp/(J.mol-1.K-1)

115

110

105

100

95 300

310

320

330

340

350

360

T/K 18 16

CpE/(J.mol-1.K-1)

14 12 10 8 6 4 2 0 0.00

0.02

0.04

0.06

0.08

0.10

xMEA

0.12

0.14

0.16

0.18

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al. 140

Cp/(J.mol-1.K-1)

135

130

125

120

115 300

310

320

330

340

350

360

T/K 18 16 14

CpE/(J.mol-1.K-1)

46

12 10 8 6 4 2 0 0.00

0.05

0.10

0.15

0.20

xMEA

0.25

0.30

0.35

Molar Heat Capacity of Aqueous Blends …

47

155

Cp/(J.mol-1.K-1)

150

145

140

135

130 300

310

320

330

340

350

360

T/K 10

CpE/(J.mol-1.K-1)

8

6

4

2

0

0.0

0.1

0.2

0.3

xMEA

0.4

0.5

Abdurahim Abdulkadir, Aravind V Rayer, Dang Viet Quang et al. 175

Cp/(J.mol-1.K-1)

170

165

160

155

150

145 300

310

320

330

340

350

360

T/K 6

4

CpE/(J.mol-1.K-1)

48

2

0

-2

-4 0.0

0.1

0.2

0.3

0.4

xMEA

0.5

0.6

0.7

Molar Heat Capacity of Aqueous Blends …

49

The excess heat capacity for MEA + PZ + H2O isotherms at lower and higher temperatures for (CpE = -10 and 5 Jmol-1K-1) were drawn using equation 7 for each CpE. Matlab R2011bTM was used to program the Cp+ calculations for required CpE and temperature (Figure B in Supplementary Information). At a constant negative excess heat capacity (CpE = -10 Jmol-1K-1) the isotherm curve has increase in trend with increasing temperature from 323.15 to 393.15 K. At a constant positive excess heat capacity (CpE = 5 Jmol-1K-1), the isotherm curve increases with temperature at highly concentrated blends and decreases for the diluted blends.

CONCLUSION A new set of experimental data on the heat capacities of aqueous mixtures of monoethanolamine (MEA) with Piperazine (PZ) were measured from (303.15 to 353.15) K with a micro reaction calorimeter. An excess molar heat capacity correlation using the Redlich-Kister equation for the composition dependence is used to denote the measured Cp of both binary and ternary blends of MEA, PZ and H2O. Total of 132 data points for binary system and 176 data points for ternary system were reported in this work with a correlation having less than 3% absolute average deviations (AAD%) for predicting CpE values and less than 1% predicting Cp values for different concentrations and temperatures. For all systems; the results showed that the molar heat capacity increased with increasing temperature. From this study, it can be concluded that the highly concentrated blends are more beneficial to reduce the excess heat capacity than the diluted blends at all temperatures. PZ blended with highly reactive solvents with CO2 (i.e., MEA) compared to the less reactive solvents with CO2 (i.e., AMP) exhibited the lower excess heat capacity. PZ blended with MEA from this study exhibits the lowest excess heat capacity compared to binary blends of MEA with other alkanolamines like MDEA, AMP and 2-PE.

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REFERENCES [1] Rayer, A. V., Sumon, K. Z., Sema, T., Henni, A., Idem, R. O., Tontiwachwuthikul, P., Part 5c: Solvent chemistry: Solubility of CO2 in reactive solvents for post-combustion CO2. Carbon Management 2012, 3, (5), 467-484. [2] Feron, P. H., ten Asbroek, N., New solvents based on amino-acid salts for CO2 capture from flue gases. Proceeding of GHGT 2004, 7, 5-9. [3] Chen, Y.R., Caparanga, A. R., Soriano, A. N., Li, M.-H., Liquid heat capacity of the solvent system (piperazine + n-methyldiethanolamine + water). The Journal of Chemical Thermodynamics 2010, 42, (1), 5459. [4] Adeosun, A., Abu-Zahra, M. R. M., Evaluation of amine-blend solvent systems for CO2 post-combustion capture applications. Energy Procedia 2013, 37, (0), 211-218. [5] Dang, H., Rochelle, G. T., CO2 Absorption Rate and Solubility in Monoethanolamine/Piperazine/Water. Separation Science and Technology 2003, 38, (2), 337-357. [6] Rayer, A. V., Henni, A., Tontiwachwuthikul, P., Molar heat capacities of solvents used in CO2 capture: A group additivity and molecular connectivity analysis. The Canadian Journal of Chemical Engineering 2012, 90, (2), 367-376. [7] Poozesh, S., Rayer, A. V., Henni, A., Molar Heat Capacity (Cp) of Aqueous Cyclic Amine Solutions from (298.15 to 353.15) K. Journal of Chemical & Engineering Data 2013, 58, (7), 1989-2000. [8] Riddick, J. A. B., W. B., Sakano, T. K., Organic Solvents. 4th ed.; Wiley: New York: 1986. [9] Chemical, U. C., Gas Treating Chemicals. 1957, 1. [10] Gas Treating Data Book; Texaco Chemical Co.: 1969. [11] Hayden, T. A., Smith, T. G. A., Mather, A. E., Heat capacity of aqueous methyldiethanolamine solutions. Journal of Chemical & Engineering Data 1983, 28, (2), 196-197. [12] Mundhwa, M., Elmahmudi, S., Maham, Y., Henni, A., Molar Heat Capacity of Aqueous Sulfolane, 4-Formylmorpholine, 1-Methyl-2-

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[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

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pyrrolidinone, and Triethylene Glycol Dimethyl Ether Solutions from (303.15 to 353.15) K. Journal of Chemical & Engineering Data 2009, 54, (10), 2895-2901. Mundhwa, M., Henni, A., Molar Heat Capacity of Various Aqueous Alkanolamine Solutions from 303.15 K to 353.15 K. Journal of Chemical & Engineering Data 2007, 52, (2), 491-498. Weiland, R. H., Dingman, J. C., Cronin, D. B., Heat Capacity of Aqueous Monoethanolamine, Diethanolamine, N-Methyldiethanolamine, and N-Methyldiethanolamine-Based Blends with Carbon Dioxide. Journal of Chemical & Engineering Data 1997, 42, (5), 10041006. Zhang, K., Hawrylak, B., Palepu, R., Tremaine, P. R., Thermodynamics of aqueous amines: excess molar heat capacities, volumes, and expansibilities of {water + methyldiethanolamine (MDEA)} and {water + 2-amino-2-methyl-1-propanol (AMP)}. The Journal of Chemical Thermodynamics 2002, 34, (5), 679-710. Chen, Y. J., Shih, T.W., Li, M. H., Heat Capacity of Aqueous Mixtures of Monoethanolamine with N-Methyldiethanolamine. Journal of Chemical & Engineering Data 2000, 46, (1), 51-55. Chen, Y. J., Li, M. H., Heat Capacity of Aqueous Mixtures of Monoethanolamine with 2-Amino-2-methyl-l-propanol. Journal of Chemical & Engineering Data 2000, 46, (1), 102-106. Shih, T. W., Chen, Y. J., Li, M. H., Heat capacity of aqueous mixtures of monoethanolamine with 2-piperidineethanol. Thermochimica Acta 2002, 389, (1–2), 33-41. Shih, T. W., Li, M. H., Heat capacity of aqueous mixtures of diethanolamine with 2-amino-2-methyl-l-propanol. Fluid Phase Equilibria 2002, 202, (2), 233-237. Shih, T. W., Li, M. H., Liquid Heat Capacity of Aqueous Solutions Containing Diethanolamine and 2-Piperidineethanol. Journal of Chemical Engineering of Japan 2008, 41, (11), 1011-1016. Wang, C. W., Soriano, A. N., Yang, Z. Y., Li, M. H., Solubility of carbon dioxide in the solvent system (2-amino-2-methyl-1-propanol + sulfolane + water). Fluid Phase Equilibria 2010, 291, (2), 195-200.

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[22] Lin, S.Y., Leron, R. B., Li, M. H., Molar heat capacities of diethylenetriamine and 3-(methylamino)propylamine, their aqueous binaries, and aqueous ternaries with piperazine. Thermochimica Acta 2014, 575, (0), 34-39. [23] Chen, Y. R., Caparanga, A. R., Soriano, A. N., Li, M.-H., Liquid heat capacity of the solvent system (piperazine + 2-amino-2-methyl-lpropanol + water). The Journal of Chemical Thermodynamics 2010, 42, (4), 518-523. [24] Osborne, N. S., Simson, H. F., Ginnings, D.C., Measurements of heat capacity and heat of vaporization of water in the range of 00C to 1000C. J. Res. Nat. Bur. Stand. 1939, 23, 197-260. [25] Chiu, L. F., Liu, H. F., Li, M. H., Heat Capacity of Alkanolamines by Differential Scanning Calorimetry. Journal of Chemical & Engineering Data 1999, 44, (3), 631-636. [26] Bishnoi, S., Rochelle, G. T., Thermodynamics of Piperazine/ Methyldiethanolamine/Water/Carbon Dioxide. Industrial & Engineering Chemistry Research 2002, 41, (3), 604-612.

In: Heat Capacity Editor: Søren A. Dam

ISBN: 978-1-53618-142-5 © 2020 Nova Science Publishers, Inc.

Chapter 3

STUDIES OF THERMAL ANALYSIS AND SPECIFIC HEAT CAPACITY FOR QUATERNARYAMMONIUM SALTS Gaurav R. Gupta1, Vasim R. Shaikh2, Sachin S. Kalas3, Dilip G. Hundiwale2 and Kesharsingh J. Patil2,* 1

2

Institute of Chemical Technology, Matunga, Mumbai, India School of Chemical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India 3 Common Facility Center, Shivaji University, Kolhapur, India

ABSTRACT Heat capacity is a substantial thermodynamic quantity because of its intrinsic significance and its connection with other thermodynamic properties like enthalpy, entropy and Gibbs energy. The measurement of heat capacity is an important application of differential scanning *

Corresponding Author’s Email: [email protected].

54

Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al. calorimetry, where results obtained with acceptable uncertainty and often with a negligible difficulty. In this contribution we report thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) profiles of tetraethyl, tetrapropyl, tetrabutyl, hexadecyltrimethylammonium bromide, tetrafluoroborate and hexafluorophosphate salts for a temperature range of 30 to 500oC (303-573 K). Furthermore, the exploration of heat flow data towards the calculations of specific heat capacity (Cp) at different temperatures has been accomplished by developing a simple mathematical operation. In addition to that, a suitable mechanism of thermal decomposition of the studied quaternary ammonium salts in the form of generation of PF5 and alkylhalide species with removal of trialkylamine for hexafluorophosphate salts has been proposed.

Keywords: quaternaryammonium salts, differential scanning calorimetry, specific heat capacity, thermo-gravimetric analysis

INTRODUCTION Microcalorimetry and differential scanning calorimetry (DSC) are the heat (enthalpy) measurement techniques to characterize the physical properties of the materials of high commercial importance, as well of use to derive information about molecular/ionic interactions. Also, DSC allows determining the heat capacities in both solid and liquid states and to probe phase transition temperatures (glass transition) and the data obtained have been explored for the calculations of corresponding enthalpy and entropy changes. These studies provides the information about changes in properties of the systems which are under consideration, and the data obtained are extended to examine enthalpy-entropy compensation phenomenon and biologically important phenomenon such as denaturation studies of proteins as well. Specific heat capacity (Cp) is the basic quantity derived from calorimetric measurements and is used in the description of its thermodynamics. For a full description of a system, heat capacity information is combined with heats of transition, reaction etc. [1] Increasing environmental consciousness within the scientific community has led chemists to search for environmentally friendly, nonpolluting media and processes for chemical synthesis as alternatives to

Studies of Thermal Analysis and Specific Heat Capacity …

55

conventional volatile organic solvents. Recently, ambient temperature liquids that consist only of cations and anions grabbing an attention of scientific community both from academia as well as industry, which are known variously as “room temperature molten salts”, “ambient temperature melts”, or, alternatively and increasingly, simply as “ionic liquids (IL's)”. [2-5] The unique properties of IL's, which can be tailored at the molecular level by an appropriate selection of its ionic units, have opened new avenues of processing options. Ionic liquids are now widely recognized as suitable for use in organic reactions and offer possibilities for improvement in the control of product distribution, enhanced reactivity, ease of product recovery, catalyst immobilization, and recycling, are considered as sustainable alternatives to environmentally hazardous metal precursors in the formulation of polymers. [6-10] The tuning ability of these salts provides them a broad spectrum of applications in every domain of present day science. [11-15] Particularly in materials science the salts having combination of organic as well as inorganic cations and with hexafluorophosphate anion show remarkable electrochemical properties. However, it was found that hexafluorophosphate anion with LiPF6 is not stable and at elevated temperature it decomposes into PF5 gas. [16] A number of engineering parameters need to be determined for the ionic liquids in order to measure their suitability for materials applications, and for process design. In particular, the absence of Cp data is a substantial obstacle for the design of chemical reactors and heat transfer systems, required if any ionic liquid processes are to be developed beyond the laboratory scale. Specific heat capacities of pure substances further utilized for the calculations of number of thermodynamic parameters like relative entropy, free energy and enthalpy changes for the systems. [17, 18] The specific heat capacities of ionic liquids and their mixtures are having significant importance in chemical engineering work accompanying with the design and operation of reactors and heat related operations required for scale-up, pilot-plant, and commercialization of ionic liquids and technologies associated with ionic liquids. In the next, the data of specific heat capacities over a wide range of operating temperatures are also helpful for the use of ionic liquids for low temperature operations and/or as reaction

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al.

medium or as heat transfer fluids where high temperature conditions are considered. [19-24] As far the concerns of scientific studies related to the structural characterizations of the material or of an organic compound, thermal methods of analysis have been developed for the scientific study about the changes in the properties of a material which occur on heating. Thermal gravimetric analysis (TGA) is a technique which dealt with the mass change of a substance which has been measured as a function of temperature whilst the substance is being subjected to a controlled temperature programme, and the data obtained provide information about the solid state reaction kinetics. [25-29] On the other hand, the thermal data obtained from the DSC experimentation have been utilized for the calculations of the Cp with the help of our own developed protocol. [30, 31] Many years earlier Ubbelohde [32] has discussed melting mechanism of ionic crystals. According to him, the melt always exhibits more randomness or disorder than the crystal. This causes a marked increase in vibrational entropy on melting due to greater excitation of vibrations. For these calculations, the data for Cp are always useful. Practically, very little information is yet available about Cp α temperature variations of ionic solids comprising polyatomic ions. Also it has been suggested that configurational entropy changes may be important in the melting of ions containing flexible groups such as [N(C4H9)4]+, but cannot be probed due to absence of Cp data. Herein, we are describing our thermal studies towards tetraethylammonium bromide (TEABr), tetrapropylammonium bromide (TPABr), tetrabutylammonium bromide (TBABr), hexadecyltrimethylammonium bromide (HDTMABr), tetrapropylammonium tetrafluo-roborate (TPABF4), tetrabutylammonium tetrafluoroborate (TBABF4), hexadecyltrimethylammonium tetrafluoroborate (HDTMABF4), tetraethylammonium hexafluorophosphate (TEAPF6), tetrapropylammonium hexafluorophosphate (TPAPF6), tetrabutylammonium hexafluorophosphate (TBAPF6), and hexadecyltrimethylammonium hexafluorophosphate (HDTMAPF6) in the temperature range of 30 to 500oC (303-573 K). The results of thermal analysis reveal the in-situ formation of alkyl fluorides,

Studies of Thermal Analysis and Specific Heat Capacity …

57

tertiary amine and PF5 gas which impart high specific heat capacity for hexadecyltrimethylammonium hexafluorophosphate salt.

EXPERIMENTAL SECTION Materials The potassium hexafluorophosphate (KPF6), HDTMABr were purchased from SigmaAldrich having purity 99%, and sodium tetrafluoroborate (NaBF4), TEABr, TPABr, TBABr of analytical grade were procured from s d Fine Chemicals Pvt. Ltd., Mumbai (India) having purity98%. All the chemicals were used without further purifications. Quartz doubly distilled water was used for anion metathesis reaction. The salts were dried in vacuum at 60oC (333 K) for 24 hours and stored in vacuum desiccator. For TGA and DSC work the samples were loaded into aluminum crucibles in air for 1520 seconds, then hermitically sealed.

Methodology General Procedure for Anion Metathesis Reaction An aqueous solution of NaBF4/KPF6 was gradually added to the stirred aqueous solution of tetraalkylammonium bromide. White crystals of tetraalkylammonium terafluoroborate/hexafluorophosphate separated out rapidly from the reaction mixture. Thereafter the crystals were collected and washed with plenty of water over Buchner funnel and then kept for drying in a vacuum desiccator. The general procedure is summarized in Figure 1.

Figure 1. General procedure for anion metathesis of tetraalkylammonium bromides.

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al.

Thermal Analysis of Quaternary Ammonium Salts The TGA-DSC analysis of tetraalkylammonium halides, tetrafluoroborates and hexafluorophosphates were performed on TA instrument (Model: SDT Q 600 V 20.9) with temperature accuracy ± 0.5 K under N2 atmosphere, which was kept in air conditioned lab having humidity of 5-10%. Samples having weights in the range of 4 to 10 mg were used for the measurements. The sample volumes of the alumina pans were 0.01 mL with a cell volume of 3.4 mL and were subjected to nitrogen purging with a flow rate of 50 mL·min1. The heating rate of the sample was always maintained at 5 K·min1. The instrument was calibrated for differential temperature using the empty pan, sapphire and fusion point of Zn, while heat flow measurements in the range of 40-800oC (313-1073 K) were made. The parameters: uncalibrated temperature difference and actual temperature, were measured with reference to standard sample of sapphire (59.719 mg). Calculations of Specific Heat Capacity (Cp) The samples of quaternary ammonium salts as well as sample of KCl, cyclodextirns [30] and urea [31] as standard were subjected to DSC analysis over a temperature range of 30-500oC (303-773 K). A systematic and efficient mathematical programme was advanced to calculate the specific heat capacity of the solid samples, [30, 31] and the details of the calculations are described below: A. Performance of thermistors was checked for a selected temperature range and obtained the signal in V. B. The calibrated weight analysis was performed for a selected temperature range and data was obtained in V/mg. C. A measure of empty pan signal was studied and its contribution in V at different temperatures was obtained. D. Sapphire was studied as a calibrant standard and its DSC profile was obtained in a temperature range in between 55 and 400oC (328-673 K). The corresponding signal was obtained in terms of V/mg.

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59

E. The correction for pan signal data was applied by appropriate corrections due to matching of thermistors. F. The signal of weights was subtracted from the signal due to sapphire. The resulting signal was multiplied by weight of sapphire and finally converted the emf into Volts (V). Then the pan signal in volts was subtracted from sapphire signal in volts. G. Zinc metal was used to assess the temperature difference i.e., dT (oC) between two pans. A DSC scan of zinc metal was obtained in a temperature range of 55-500oC (328-773 K). The zinc melts at 425oC (698 K). The area under the endothermic curve was calculated and further used to obtain heat of fusion of zinc metal as 107.1 J∙g1. The data is in excellent agreement with literature data. [33] H. From the specific heat capacity values for sapphire, and measured dT values at different temperatures, the enthalpy change for sapphire as a function of temperature was calculated in J∙sec1. The data yielded the values of current (I) generated via the use of equation H = I2Rt. Using the average of current values, signal values for sapphire were converted into power (watt) values at the studied temperatures. From the measured current, the DSC signals for pan and sapphire were appropriately converted into the power unit of watt. The appropriate amplitudes for sapphire and pan were obtained and a pan correction for amplitude data of sapphire was applied. I. The amplitude ratios for salt/sapphire (corrected) as well as the weight ratio (sapphire/salt) were calculated and further used to obtain specific heat capacity at constant pressure (Cp) as a function of temperature for the studied salts, using the equation; Amplitude ratio  weight ratio =K  C p Scanning rate where, K is the sensitivity in J1∙g∙sec. which has been taken as unity (i.e., 1). The above methodology was applied to the data of KCl. The calculated values of specific heat capacity for KCl (Figure 2) show

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al. excellent agreement above 65oC (338 K) up to 345oC (618 K). [33, 34]

Figure 2. Comparison of specific heat capacity (Cp) data for KCl (; KCl Expt.) with literature (∆; Burns and Verall [34], □; Dortmund Data Bank (Skuratov et al.) [35], ; Dortmund Data Bank (Egorov et al.) [35]

We observed that sapphire as a standard for specific heat capacity measurements yielded reliable results above 65oC (338 K), as there are structural transitions reported at about 40-50oC (313-323 K) for sapphire.

RESULTS AND DISCUSSION The suggested methodology offers excellent agreement for the specific heat capacity values for KCl above 65oC (338 K) up to 345oC (618 K) with the values reported in the literature. [34, 35] The comparison of Cp data for KCl with literature data [34, 35] as a function of temperature is shown in Figure 1.

Studies of Thermal Analysis and Specific Heat Capacity …

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

61

Figure 3. a-h: Thermograms of tetraalkylammonium salts.

Although, in literature a systematic thermal analysis of the tetraalkylammonium salts using thermogravimetry has already been

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performed and the results were nicely discussed. [36] In the present work, Thermal gravimetry analysis of tetraalkylammonium bromide, tetrafluoroborate and hexafluorophosphate salts (Figure 3a-h) reveals that tetrafluoroborates are thermally more stable salts as compared to the corresponding bromide and hexafluorophosphate salts. The high thermal stability of tetrafluoroborate over bromide and hexafluorophosphate salts is observed and can be attributed to the possibility of isomorphism, while the hexafluorophosphate salts of tetraalkylammonium cations except tetraethylammonium cation undergoes decomposition to give fluoride anion (which serves as a base and accomplishes a rapid abstraction of proton, is followed by thermally induced addition of HF across carbon double bond carbon which yields 1fluoroalkane and tertiary amine as products) along with thermally stable pentafluorophosphate (PF5) (Figure 4). [PF6]anionof tetraalkylammonium cation salt decomposes with heat to give PF5 and F PF5 is a thermally stable species up to 300oC (573 K), while the tetraalkylammonium salt with basic fluoride anion initiates elimination yielding alkene and HF, which is followed by addition leading to the formation of an alkyl fluoride and trialkylamine as volatile products. The summary of decomposition pathways is given in Figure 4.

Figure 4. Plausible mechanism for the thermally assisted elimination-addition reaction for the formation of alkyl fluoride and trialkyl amine.

Studies of Thermal Analysis and Specific Heat Capacity … Table 1. Thermal response of the tetraalkyl ammonium salts

Salt

Onset temperature for decomposition from TGA (T/K)

(C2H5)4N+Br (C3H7)4N+Br (C4H9)4N+Br (C16H33)(CH3)3N+Br (C3H7)4N+BF4 (C4H9) 4N+BF4 (C16H33)(CH3)3N+BF4 (C2H5)4N+PF6 (C3H7)4N+PF6 (C4H9)4N+PF6 (C16H33)(CH3)3N+PF6

523 481 433 422 575 595 490 655 507 515 323

Thermal Transitions observed at temperature from DSC (T/K) st I IInd IIIrd IVth 446 563 --381 531 541 -364 376 392 493 379 526 --400 518 665 -345 435 661 -373 520 693 -348 668 --326 468 507 663 310 362 515 -346 ----

Table 2. Specific heat capacity (Cp) data for tetraalkylammonium bromide salts Temperature /K

TEABr 298* 1.23 348 1.28 358 1.30 368 1.31 378 1.31 388 1.31 398 1.31 408 1.32 418 1.32 428 1.33 438 1.35 448 1.44 458 1.38 468 1.37 *Extrapolated value at 298 K.

TPABr 1.45 1.49 1.51 1.51 1.52 1.58 1.54 1.54 1.55 1.56 1.57 1.58 1.59 1.61

Cp /J∙K1∙g1 TBABr 2.26 2.56 2.62 2.66 2.74 2.68 2.74 2.68 2.67 2.67 2.69 2.73 2.84 --

HDTMABr 2.28 2.82 2.84 2.84 3.06 2.91 2.87 2.89 2.91 2.94 2.98 3.02 3.07 3.12

63

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al.

We suggest that after decomposition of these salts, the remains consist of PF5 gas which is being confirmed on the basis of stoichiometric concentrations from TGA weight loss data. The data regarding onset of decomposition temperature (TGA) and thermal transitions noted from DSC profiles are collected in Table 1. It is to be noted that the specific heat capacity data for studied tetraalkylammonium bromide salts were obtained with appropriate weight corrections through TGA thermograms is tabulated in Table 2. The closer scrutiny of Figure 5 and Table 2 reveal that the Cp data of the tetraethylammonium bromide are in harmony with the data reported by Burns and Verrall. [34]

Figure 5. Variation of specific heat capacity (Cp) for studied tetraalkylammonium bromide salts as a function of temperature: ; TEABr,; TEABr Lit. [34], ; TPABr, ∆; TBABr, □; HDTMABr.

It is to be noted that one endothermic mesotropic transition in heat flow is observed for TEABr at 173oC (446 K), while it is having onset of decomposition temperature at 250oC (523 K). Similar behaviour is observed for TPABr having mesotropic endotherm at 108oC (381 K) and the onset of decomposition at 208oC (481 K). The case of thermal behaviour of TBABr is interesting. The melting point of this compound is known to be 104-106oC (377 to 379 K). We observe from our DSC data that it has three endotherms

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at 91, 103, 119oC (364, 376 and 392 K), respectively. Therefore, it is certain that molten form of TBABr as a liquid which is stable up to 160oC (433 K), and hence we have an ionic liquid TBABr for a temperature range of 104160oC (377 to 433 K). The specific heat capacity values are found to be lowest for TEABr. It has been proposed that tetraalkylammonium salts as they exhibit multiple step melting behaviour having layered structures show thermal transitions in the form of peculiar solid polymorphs or formation of smectic mesophases. [38] Thus, the quaternary N centre in a salt exhibiting electrostatic interaction with the halide anions is affected by the thermal energy of which extent and strength depends upon the chain length involved and symmetry properties of the molecules as a whole. We can compare the above data with similar data for HDTMABr. This salt melts at 248 to 251oC (521 to 524 K), while we observe from TGA and DSC, an endothermic transition at 253oC (526 K). It also exhibits a mesophasic transition at 106oC (379 K). The heat of decomposition is lower and specific heat capacity values are more than the other tetraalkylammonium bromide salts. The chain movement and melting show appreciable effect on specific heat capacity as well on heat of decomposition as a function of temperature for this salt. Such an observation probably indicates rotational and vibrational energy changes contribution to the total heat capacity due to segmental chain dynamics. The variation in specific heat capacity values for both the tetrafluoroborates and hexafluorophosphates are shown in Figure 6 and the data are tabulated in Table 3. In comparison with hexafluorophosphates the specific heat capacity values of tetrafluoroborate salts are quite low. The specific heat capacity data for HDTMABF4 are not found anywhere in literature and the reason behind this may be the thermal lability of the salt, which shows decomposition at or below 33oC (306 K) and only PF5 remains. An attempt has been made to calculate the specific heat capacity values. We found that the values are too high as compared to any other salt. Presently, we cannot offer any detailed interpretation for this because of limited information available for fluorinated compounds.

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al. Table 3. Specific heat capacity (Cp) data for tetraalkylammonium tetrafluoroborate and hexafluorophosphate salts

Temperature/K TPABF4 1.65 348 1.71 358 1.75 368 1.76 378 1.76 388 1.77 398 1.86 408 1.85 418 1.81 428 1.80 438 1.80 448 1.81 458 1.81 468 1.82 * Extrapolated value at 298 K. 298*

TBABF4 1.42 1.52 1.58 1.60 1.60 1.61 1.62 1.63 1.64 1.64 1.68 1.66 1.66 1.67

Cp /J∙K1∙g1 HDTMABF4 TEAPF6 3.10 0.81 3.51 0.89 3.58 0.92 3.71 0.94 3.76 0.95 3.65 0.96 3.62 0.97 3.61 0.98 3.62 1.00 3.62 1.01 3.63 1.02 3.65 1.03 3.66 1.04 3.66 1.04

TPAPF6 2.21 2.30 2.31 2.33 2.35 2.37 2.40 2.42 2.45 2.47 2.48 2.50 2.52 2.64

TBAPF6 2.30 3.44 3.80 3.98 4.05 4.11 4.17 4.23 4.29 4.34 4.39 4.44 4.49 4.54

Figure 6. Variation of specific heat capacity (Cp) for tetraalkylammonium tetrafluoroborate and hexafluorophosphate salts as a function of temperature: (; TPABF4, ; TBABF4, ∎; HDTMABF4) (∆; TEAPF6, ; TPAPF6, ; TBAPF6).

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A book by Gaune-Escard and Seddon [39] is an excellent source of literature for the properties of fluorinated molten salts and ionic liquids. The fluorinated species [BF4] and [PF6], however, are un-polarizable, and so minimize the effect of the van der Waals contributions to the liquid cohesion. The DSC thermograms of all studied salts show mesophasic transitions before melting point of the salts (Table 1). As the tetraalkylammonium hexafluorophosphate salts have poor thermal stability (except TEAPF6) the mesophasic changes are encountered at low temperature (< 100oC,  373 K), while for tetraalkylammonium tetrafluoroborates a possibility of isomorphism is responsible for the thermal inflections occurred in the heat flow profiles. We note from Figure 3h that Bu4NPF6 exhibits two thermal transitions at 37 and 89oC (310 and 362 K), respectively, which have also been observed by Coutinho et al. [40] The thermograph and heat flow measurement data for tetraalkylammonium salts with BF4 anion show that they are also having mesophasic and decomposition transitions. For the TPABF4 salt the onset of decomposition is at 302oC (575 K) but before that two more transitions are noted at 127 and 245oC (400 and 518 K), respectively. The reported melting temperature is 245oC (518 K), thus between 245 and 302oC (518 and 575 K) this salt exists as an ionic melt. It decomposes completely at about 392oC (665 K). The TBABF4 melts at 161oC (434 K), while we observe the thermal transitions at 72 and 162oC (345 and 435 K), finally a complete decomposition occurs at 388oC (661 K). This salt thus exists as an ionic melt over a large temperature range (162 to 322oC, 435 to 595 K). The unsymmetrical HDTMABF4 melts at 240oC (513 K), while we observe a thermal transition at 247oC (520 K). The salt exhibits a mesophasic heat transition at 100oC (373 K). It can be attributed to longchain melting and asymmetry, the ionic melt existence even for a limited temperature is not being observed. One of the most sensitive probe for studies of structural effects in water 0

0

is the limiting partial molar heat capacity of the solute C P2 . The C P2 values also can be obtained by measuring the integral enthalpy of solution at infinite

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al. 0

dilution as a function of temperature which provide C P2  CPPure where CPPure is the heat capacity of the pure crystalline salt in its standard state or at 298 K. In general CPPure data for many of the salts are not available easily although pioneering work in this direction has been reported by Burns and Verrall [34] as well by Manin et al. [41] Our present studies of thermal 0

behavior of these salts also provide information about C P2 values required 0

to calculate CP02  C P2  CPPure values in aqueous solutions. Although there is a question of defining standard state for solids (pressure and temperature specifications), the use of 298 K and 1 atmosphere suffices the need of estimating deviation. That is the reason for reporting the thermodynamic data of enthalpy, entropy changes etc. at 298 K in standard 0

textbooks. We think that the C P2 obtained in this work, extrapolated to 298 K may fulfill the need of solution chemists to obtain meaningful values of 0

C P2  CPPure which can be compared with those obtained using adiabatic calorimetry.

CONCLUSION If the fused organic salts or ionic liquids are to be applied in industrial processes, their heat transfer and specific heat capacity properties along with other thermodynamic properties are needed for the design of a chemical facility. We obtained such data from thermal techniques, the weight loss and heat flow data for TEABr, TPABr, TBABr, HDTMABr, TPABF4, TBABF4, HDTMABF4, TEAPF6, TPAPF6, TBAPF6 and HDTMAPF6, salts over the temperature range of 303 to 773 K. The calculations of specific heat capacity values as a function of temperature were made. The decomposition of TPAPF6, TBAPF6, and HDTMAPF6 in terms of generation of 1fluoroalkane, tertiary amine and thermally stable PF5 species with temperature increase is explained by proposing a suitable mechanism. The

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69

complex thermal behavior observed on the basis of heat flow and weight loss measurements for most of the compounds suggests presence of mesophases between the true solid and isotropic liquid. The information of melting point and observed decomposition temperatures for TBABr, TBABF4, and TPABF4 led us to suggest that these compounds exist as ionic melt for a limited temperature interval. It has been observed that in the series of tetraalkylammonium cations, when bromide anions are associated with a tetraethylammonium ion, lowest specific heat capacity value is obtained, while specific heat capacity values for other salts increase in magnitude with increase in molecular weight of the salt. We obtained highest specific heat capacity values for HDTMAPF6 which is anomalous. Thus the magnitude of specific heat capacity values are indicative of effects due to the chain length of non-polar groups and symmetry of the cations while the nature of anions also point out the importance of coloumbic interactions. More detailed studies of spectroscopic properties at different temperatures are required to understand the thermally induced transitions for the studied salts.

ACKNOWLEDGMENT Authors Dr. G. R. Gupta and Prof. D. G. Hundiwale are thankful to Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon425001, Maharashtra (India) for granting a fund in terms of a project entitled “Synthesis and use of ionic liquids in organic reactions ” under the scheme of “Vice Chancellor Research Promotion Scheme (VCRMS).”

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Cheng, S. Z. D. (2002). Handbook of Thermal Analysis and Calorimetry, Elsevier, UK. Tomar, P. A., Yadav, S. M. and Gupta, G. R. (2014). The thermal gravimetric studies for polymer samples of polyvinyl chloride (PVC)

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and polyvinyl alcohol (PVA) obtained by treatment with ionic liquid [bmim] Br. Polym. Bull., 71: 1349-1358. [3] Ohno, H. (2011). Electrochemical Aspects of Ionic Liquids, John Wiley and Sons, New York. [4] Patil, P. P., Shaikh, V. R., Gupta, G. R., Patil, P. D., Borse, A. U. and Patil, K. J. (2018). Studies of Viscosity Coefficient and Density Properties of Imidazolium Based Ionic Liquids in Aqueous Solutions at Different Temperatures. ChemistrySelect, 3: 5593-5599. [5] Patil, P. D., Shaikh, V. R., Gupta, G. R., Hundiwale, D. G. and Patil K. J. (2018). Studies of Volumetric and Viscosity Properties in Aqueous Solutions of Imidazolium Based Ionic Liquids at Different Temperatures and at Ambient Pressure. J. Sol. Chem. (Accepted). [6] Sarode, C. H., Gupta, G. R., Chaudhari, G. R. and Waghulde, G. P. (2018). Synthesis of 2-amino-4-aryl-thiazoles using ionic liquids and molten salts. Curr. Green Chem. 5: 191-197. [7] MacFarlane, D. R., Tachikawa, N., Forsyth, M., Pringle, J. M., Howlett, P. C., Elliott, G. D., Davis, Jr. J. H., Watanabe, M., Simon, P. and Angell, C. A. (2014). Energy applications of ionic liquids. Energy Environ. Sci., 2014, 7, 232-250. [8] Dupont, J., Itoh, T., Lozano, P. and Malhotra, S. (2014). Environmentally Friendly Syntheses Using Ionic Liquids, CRC Press, London. [9] Hardacre, C. and Parvulescu, V. (2014). Catalysis in Ionic Liquids From Catalyst Synthesis to Application, The Royal Society of Chemistry, London. [10] Kirchner, B. (2010). Ionic Liquids, Springer-Verlag Berlin Heidelberg. [11] Torriero, A. A. J. (2015). Electrochemistry in Ionic Liquids, volume 1, Springer, Switzerland. [12] Ventura, S. P. M., eSilva, F. A., Quental, M. V., Mondal, D., Freire, M. G. and Coutinho, J. A. P. (2017). Ionic-Liquid-Mediated Extraction and Separation Processes for Bioactive Compounds: Past, Present, and Future Trends. Chem. Rev., 117: 6984-7052.

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[13] Schneider, S., Hawkins, T., Rosander, M., Vaghjiani, G., Chambreau, S. and Drake, G. (2008). Ionic Liquids as Hypergolic Fuels. Energ. Fuels, 22: 2871-2872. [14] Calzaa, P., Noe, G., Fabbri, D., Santoro, V., Minero, C., Vione, D. and Medana, C. (2017). Photoinduced transformation of pyridinium-based ionic liquids, and implications for their photochemical behavior in surface waters. Water Res., 122: 194-206. [15] Watanabe, M., Thomas, M. L., Zhang, S., Ueno, K., Yasuda, T. and Dokko, K. (2017). Application of Ionic Liquids to Energy Storage and Conversion Materials and Devices. Chem. Rev., 117: 7190-7239. [16] Xu, W., Cooper, E. I. and Angell, C. A. (2003). Ionic liquids:  Ion mobilities, glass temperatures, and fragilities. J. Phys. Chem. B, 107: 6170-6178. [17] Privalov, P. L. (2012). Microcalorimetry of Macromolecules: The Physical Basis of Biological Structures, John Wiley and Sons, New York. [18] Malhotra, S. V. (2007). Ionic Liquids in Organic Synthesis, volume 950, American Chemical Society, USA. [19] Fredlake, C. P., Crosthwaite, J. M., Hert, D. G., Aki, S. N. V. K. and Brennecke, J. F. (2004). Thermophysical Properties of ImidazoliumBased Ionic Liquids. J. Chem. Eng. Data, 49: 954-964. [20] Verevkin, S. P., Ralys, R. V., Emelyanenko, V. N., Zaitsau, D. H. and Schick, C. (2013). Thermochemistry of the pyridinium- and pyrrolidinium-based ionic liquids. J. Therm. Anal. Calorim., 112: 353358. [21] Rostami, A., Hemmati-Sarapardeh, A., Karkevandi-Talkhooncheh, A., Husein, M. M., Shamshirband S. and Rabczuk, T. (2019). Modeling heat capacity of ionic liquids using group method of data handling: A hybrid and structure-based approach. Int. J. Heat Mass Transf., 129: 7-17. [22] Troncoso, J., Cerdeirina, C. A., Sanmamed, Y. A., Romanı L., Paulo L. and Rebelo, N. (2006). Thermodynamic Properties of ImidazoliumBased Ionic Liquids:  Densities, Heat Capacities, and Enthalpies of

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Gaurav R. Gupta, Vasim R. Shaikh, Sachin S. Kalas et al. Fusion of [bmim] [PF6] and [bmim][NTf2]. J. Chem. Eng. Data, 51: 1856-1859. Paulechka, Y. U., Kabo, A. G., Blokhin, A. V., Kabo, G. J. and Shevelyova, M. P. (2010). Heat Capacity of Ionic Liquids: Experimental Determination and Correlations with Molar Volume. J. Chem. Eng. Data, 55: 2719-2724. Ge, R., Hardacre, C., Jacquemin, J., Nancarrow, P. and Rooney, D. W. (2008). Heat Capacities of Ionic Liquids as a Function of Temperature at 0.1 MPa. Measurement and Prediction. J. Chem. Eng. Data, 53: 2148-2153. Shirsath, N. B., Gupta, G. R., Gite, V. V., Meshram, J. S. (2018). Studies of thermally assisted interactions of polysulphide polymer with ionic liquids. Bull. Mater. Sci., 41:63-70. Gupta, G. R., Nevare, M. R., Patil, A. M. and Gite, V. V. (2019). Unprecedented exploration of ionic liquids as an additive which astonishes thermal stability of the PVC formulations. Bull. Mater. Sci. Accepted. Khawam, A. and Flanagan, D. R. (2005). Role of isoconversional methods in varying activation energies of solid-state kinetics: II. Nonisothermal kinetic studies. Thermochimica Acta, 436:101-112. Khawam, A. and Flanagan, D. R. (2006). Solid-State Kinetic Models:  Basics and Mathematical Fundamentals. J. Phys. Chem. B, 110: 17315-17328. Khawam, A. and Flanagan, D. R. (2006). Basics and Applications of Solid-State Kinetics: A Pharmaceutical Perspective. J. Pharam. Sci., 95: 472-498. Gupta, G. R., Patil, P. D., Shaikh, V. R., Kolhapurkar, R. R., Dagade, D. H. and Patil, K. J. (2018). Analytical estimation of water contents, specific heat capacity and thermal profiles associated with enzymatic model compound -cyclodextrin. Curr. Sci., 114: 2525-2529. Gupta, G. R., Shaikh, V. R. and Patil, K. J. (2018). Synchronous thermogravimetry and differential scanning calorimetry estimates of urea inclusion complexes using TGA/DSC. Curr. Phys. Chem., 8: 175-185.

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[32] Ubbelohde, A. R. (1959). Melting Mechanism of Ionic Crystals, In The Structure of Electrolytic Solutions, (Ed. W. J. Hamer), John Wiley and Sons, New York. [33] Haines, P. J. (1995). Thermal Methods of Analysis, Principles, Applications and Problems, Springer, The Netherlands. [34] Burns, J. A. and Verrall, R. E. (1974). Thermodynamics of tetraalkyland bis-tetraalkylammonium bromides: II. Heat capacities of solid state from 273 to 373 K. Thermochim. Acta, 9: 277288. [35] Dortmund Data Bank. http://www.ddbst.com/en/EED/PCP/HCP_ C4577.php. [36] Zhuravlev, O. E., Nikolskii, V. M. and Voronchikhina, L. I. (2013). Thermal Stability of Quaternary Ammonium Hexafluorophosphates and Halides. Russ. J. Appl. Chem., 86: 824−830. [37] Corbridge, D. E. C. (2013). Phosphorus Chemistry, Biochemistry and Technology, CRC Press, London. [38] Leonidopoulou, G. M., Malliaris, A. and Paleos, C. M. (1985). Thermal behavior of some long-chain quaternary ammonium salts. Thermochim. Acta, 85: 147-150. [39] Gaune-Escard, M. and Seddon, K. R. (2010). Molten Salts and Ionic Liquids: Never the Twain, John Wiley and Sons, New York. [40] Neves, C. M. S. S., Rodrigues, A. R., Kumia, K. A., Esperanca, J. M. S. S., Freire, M. G. and Coutinho, J. A. P. (2013). Solubility of nonaromatic hexafluorophosphate-based salts and ionic liquids in water determined by electrical conductivity. Fluid Phase Equilib., 358: 5055. [41] Manin, N. G., Kustov, A. V. and Antonova, O. A. (2012). Heat capacities of crystalline tetraalkylammonium salts. Russ. J. Phys. Chem. A, 86: 878-880.

In: Heat Capacity Editor: Søren A. Dam

ISBN: 978-1-53618-142-5 © 2020 Nova Science Publishers, Inc.

Chapter 4

THE EXCESS PARTIAL MOLAR HEAT CAPACITY OF WATER IS A MEASURE OF ITS STRUCTURE IN BINARY AQUEOUS SOLVENT MIXTURES Yizhak Marcus Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

ABSTRACT The excess partial molar heat capacity of the water in binary aqueoussolvent mixtures (W + S), CPWE, provides insight into the water structure enhancement, if present. A cubic representation of CPE of binary aqueoussolvent mixtures CpE = b0 + b1xS + b2xS2 + b3xS3 is valid for water-rich mixtures, xS ≤ 0.3, hence also CPWE = –b2xS2 – 2b3xS3 is readily obtained. Values of CPWE(xS) were obtained for many aqueous co-solvent mixtures 

Corresponding Author’s Email: [email protected].

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Yizhak Marcus from literature data beyond those dealt with in the author’s previous publication. Typical values of the maximal CPWE are 10 to 20 J K-1 mol-1 or 24 to 48% of the difference ΔCPl-ig = CP(liq) – CP(id.gas), which for water at 25°C is 42 J K-1 mol-1. However, energy input into the water entails not only ordering of the water, but also input into vibrational modes. Therefore, only a fraction of the heat capacity of ideal gas water needs to be subtracted from CPWE in order that only structure (order) enhancement is reckoned. Empirically, a fraction of 0.3 appears to be satisfactory. A mixture model for water structure in terms of compact and bulky hydrogen bonded domains allows structure enhancement to be interpreted as transfer of molecules between them. Strong, small hydrogen bonding solutes do not enhance the structure, fitting well into it. Solutes with many methyl groups, though miscible with water, do enhance its structure.

INTRODUCTION The hydrogen-bonded structure of water is manifested in there being domains where all the water molecules are hydrogen-bonded to each other beside domains where many free, non-hydrogen-bonded, water molecules exist. Enhancement of the water structure by the presence of a co-solvent means that water molecules are transferred from the non-bonded domain to the highly hydrogen-bonded domain. One measure of the occurrence of such a transfer in binary water/co-solvent mixtures is a positive excess partial molar volume of the water [1] and another one is a positive partial molar heat capacity of the water [2], i.e., enhanced water structure results in CPW > 0. This is because highly hydrogen bonded domains have a larger heat capacity than the mean one of pure water. The partial molar heat capacity of the water in binary water/co-solvent mixtures, CPW, has not generally been reported in literature. It is, therefore, necessary to obtain this from published data of the total specific heats, of excess heat capacities of the mixtures, or of the apparent molar heat capacities of the mixtures.

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DATA Excess molar isobaric heat capacity data of mixtures of water, subscript W, with co-solvents, subscript S, were obtained from the literature, as far as available, for 25°C. Only water-rich mixtures, that is, mole fractions of the co-solvent xS ≤ 0.3, are of interest. The excess molar heat capacity of the binary mixture is obtained from its molar heat capacity CP = cP[(1–xS)MW + xSMS]

(1)

where cP is its specific heat of the mixture and the Ms denote the molar masses, as: CPE=CP–(1–xS)CPWo–xSCPSo

(2)

If the reported quantity is the apparent molar heat capacity of the mixture, CPϕ, then the excess molar heat capacity of the mixture is: CPE = xS(CPϕ – CPSo)

(3)

When CPE = f(xS) values for the mixtures are the reported data or are derived from the apparent molar heat capacity as above, the excess partial isobaric molar heat capacity of the water is obtained from CPE as: CPWE = CPE – xS(∂CPE/∂xS)T

(4)

Data that were only available at xS < 0.1 or at co-solvent molalities mS < 6 mol kg−1 could not be used properly for the derivation of CPWE values. The excess heat capacities of the mixtures can generally be described as a cubic function:

78

Yizhak Marcus CPE = axS + bx2 + cx3

(5)

the curve passing through the origin, with a correlation coefficient rcorr > 0.995. Then: CPWE = −bxS2 – 2cxS3

(6)

This quantity is positive in water-rich mixtures if b < 0. However, CPWE becomes negative if c > 0 beyond xSlim = −b/2c. In such cases CPWE reaches a maximal positive value, CPWmax, at xSmax = −b/3c. Given the molar heat capacity of pure water, CPW°=75.33 J∙K−1∙mol−1 at 25 °C, the partial molar heat capacity of the water in the mixtures is then: CPW = CPW° + CPWE

(7)

The required isobaric heat capacity data for the binary aqueous mixtures considered in this review, whether the specific heat capacities cP, the molar ones CP, or the apparent ones CPϕ, are from the following sources, although some other sources provided equivalent data. The co-solvents considered are: methanol [3], ethanol [3], 1-propanol [4], 2-propanol [3], t-butanol [3], ethylene glycol [5], 2-methoxyethanol [6], 1,2-dimethoxyethane [7], triethylene glycol dimethyl ether [8], glycerol [9], 2-ethanolamine [10], diethanolamine [11], triethamolamine [11], methyldiethanolamine [11], tetrahydrofuran [12], 1,4-dioxane [12], acetone [3], formic acid [13], acetic acid [13], propanoic acid [13], N-methylmorpholine [8], formamide [14], Nmethylformamide [12], N,N-dimethylformamide [14], N,Ndimethylacetamide [14], N-methylpyrrolidinone [8], hexamethyl phosphoric triamide [15], pyridine [16], acetonitrile [14], dimethylsulfoxide [14], and sulfolane [8].

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79

Table 1. The coefficients b and c of eq. (6) CPWE = −bxS2 – 2cxS3 and the co-solvent mole fraction xSmax at which The partial molar excess heat capacity of the water reaches a maximal value, CPWEmax Co-solvent Methanol Ethanol 1-Propanol 2-Propanol t-Butanol Ethylene glycol 1,2-Propanediol 1,3-Propanediol 1,4-Butanediol 2-Methoxyethanol 2-Ethoxyethanol Glycerol Ethanolamine Diethanolamine Triethanolamine Methyldiethanolamine 1,2-dimethoxyethane TEGDMEa Tetrahydrofuran 1,4-Dioxane Acetone Formic acid Acetic acid Propanoic acid Butanoic acid Ethylene carbonate Morpholine N-formylmorpholine Formamide N-methylformamide N,N-Dimethylformamide N,N-Dimethylacetamide N-Methylpyrrolidinone Tetramethylurea HMPTb Pyridine Acetonitrile Dimethylsulfoxide Sulfolane

b/J K–1 mol–1 –373 –680 –1776 –1941 –3652 –220 –200 –395 –707 –495 –1250 –206 –86 –6 16 –138 –1817 –943 –598 –791 –412 21 –131 –359 –479 –243 –1021 136 13 –388 –156 –419 –157 –1187 –3518 –1790 –463 –53 37

c/J K–1 mol–1 873 1576 10380 3500 8618 692 254 656 1102 1360 2239 707 180 –5 –13 91 2254 995 818 1422 973 –1 165 536 788 29 1560 –168 40 670 208 1157 102 3041 7780 –4558 1733 127 –70

xSmax 0.142 0.144 0.057 0.185 0.141

CPWEmax 2.5 4.7 3.8 22.1 24.3

0.262 0.201 0.214 0.243 0.186 0.097

4.6 5.0 10.8

CPWE < 0 0.505 0.242 0.316 0.243 0.185 0.141 CPWE < 0 0.265 0.223 0.203 0.218 CPWE < 0 CPWE < 0 0.193 0.250 0.121 0.513 0.130 0.151 0.131 0.089 0.139 CPWE < 0

14.4 0.6

11.7 42.5 31.4 11.8 16.7 2.7 3.1 14.9 6.6 16.2

4.8 3.3 2.0 13.8 7.0 26.6 10.2 1.2 0.3

a TEGDME = Triethylene glycol dimethyl ether. b HMPT = Hexamethyl phosphoric triamide

80

Yizhak Marcus

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BIBLIOGRAPHY A project guide to Earth's waters LCCN 2010011150 Type of material Book Personal name Petersen, Christine. Main title A project guide to Earth's waters / Christine Petersen. Published/Created Hockessin, Del.: Mitchell Lane Publishers, c2011. Description 47 p.: col. ill.; 25 cm. ISBN 9781584158714 LC classification GB848 .P48 2011 Summary Introduces basic scientific principles about water and the water cycle, providing instructions for simple experiments that examine such topics as solubility, density, the pH scale, and capillarity. Contents The water cycle -- Desalination -- Solubility -Groundwater -- Water's freezing point -- Specific heat capacity -- Density -- Acid rain -- Capillarity -- Life in the water -- Water power. Subjects Hydrologic cycle--Juvenile literature.

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AP chemistry LCCN Type of material Personal name Main title Edition Published/Produced Description ISBN LC classification Variant title Related names Contents

Bibliography Water--Juvenile literature. Includes bibliographical references and index. Earth science projects for kids Earth science projects for kids.

2013954713 Book Dingle, Adrian, 1967- author. AP chemistry / Adrian Dingle, The Westminster Schools, Atlanta, Georgia. 2nd edition. Piscataway, New Jersey: Research & Education Association, [2014] vi, 259 pages: illustrations; 23 cm. 9780738611549 (pbk.) 0738611549 (pbk.) QD42 .D547 2014 A.P. chemistry Advanced Placement chemistry Research and Education Association, publisher. Keys for success on the AP Chemistry exam -Atoms and elements. Atoms and moles; Electrons; Periodicity; Atomic models; Conservation of atoms and mass -- Bonding. Solids, liquids, gases, and solutions; Intermolecular forces; Intra forces, VSEPR, and shape; Bonding and properties of solids -Chemical reactions. Chemical reactions; Classifying chemical reactions; Energy changes in chemical reactions -- Rates of reaction. Factors affecting rates of reaction; Collision theory; Mechanisms; Catalysts -Chemical thermodynamics. Temperature, heat, and specific

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heat capacity; Conservation of energy, work, and calorimetry; Bond making and bond breaking; Inter and intra forces and physical and chemical change; Entropy and free energy -- Equilibrium. Dynamic equilibrium; Le Chatelier's principle; Acids, bases, and solubility equilibrium; Equilibrium and Gibbs free energy -- Overarching themes. Laboratory work in AP chemistry; Writing good free-response answers -- Periodical table of the elements -- AP chemistry equations and constants. Chemistry--Examinations--Study guides. Chemistry--Examinations, questions, etc. Advanced placement programs (Education)-Examinations--Study guides. Universities and colleges--United States-Entrance examinations--Study guides. College entrance achievement tests--United States--Study guides. Advanced placement programs (Education)-Examinations. Chemistry--Examinations. College entrance achievement tests. Universities and colleges--Entrance examinations. United States. Examinations, questions, etc. Study guides. Crash course

Chemical thermodynamics: for process simulation LCCN 2012405553 Type of material Book

84 Main title Published/Created Description Links

ISBN LC classification Related names Summary

Contents

Bibliography Chemical thermodynamics: for process simulation / Jurgen Gmehling ... [et al.]. Weinheim: Wiley-VCH, c2012. xxv, 735 p.: ill.; 24 cm. Publisher description http://www.loc.gov/catdir/ enhancements/fy1214/2012405553-d.html Table of contents http://www.loc.gov/catdir/ enhancements/fy1214/2012405553-t.html Contributor biographical information http:// www.loc.gov/catdir/enhancements/fy1214/20124 05553-b.html 9783527312771 3527312773 TJ265 .C494 2012 Gmehling, Jürgen, 1946This is the only book to apply thermodynamics to real-world process engineering problems. It comprises numerous solved examples, as well as estimation methods for thermophysical properties and phase equilibria, thermodynamics of alternative separation processes, and recent developments. Written for teaching students the engineering perspective of thermodynamics, this is also of interest to all companies active in chemistry, pharmacy, oil and gas processing, petrochemistry, refinery, food production, environmental protection and engineering-Source other than Library of Congress. 1. Introduction -- 2. PvT behavior of pure components -- 3. Correlation and estimation of pure component properties -- 4. Properties of mixtures -- 5. Phase equilibria in fluid systems -6. Caloric properties -- 7. Electrolyte solutions -8. Solid-liquid equilibria -- 9. Membrane

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processes -- 10. Polymer thermodynamics -- 11. Applications of thermodynamics in separation technology -- 12. Enthalpy of reaction and chemical equilibria -- 13. Special applications -14. Practical applications -- 15. Introduction to the collection of example problems --Appendices: A. Pure component parameters -- B. Coefficients for high precision equations of state -- C. Useful derivations -- D. Standard thermodynamic properties for selected electrolyte compounds -E. Regression technique for pure component data -- F. Regression techniques for binary parameters -- G. Ideal gas heat capacity polynomial coefficients for selected compounds -- H. UNIFAC parameters -- I. Modified UNIFAC parameters -- J. PSRK parameters -- J. PSRK parameters -- K. VTPR parameters. Thermodynamics--Simulation methods. Production engineering. Includes bibliographical references and index.

Einstein's other theory: the Planck-Bose-Einstein theory of heat capacity LCCN 2004042068 Type of material Book Personal name Rogers, Donald, 1932Main title Einstein's other theory: the Planck-Bose-Einstein theory of heat capacity / Donald W. Rogers. Published/Created Princeton, N.J.: Princeton University Press, c2005. Description xii, 181 p.: ill.; 24 cm. Links Table of contents http://www.loc.gov/catdir/ toc/fy0612/2004042068.html

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ISBN LC classification Portion of title Contents

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Notes

Bibliography Publisher description http://www.loc.gov/cat dir/enhancements/fy0668/2004042068-d.html Contributor biographical information http:// www.loc.gov/catdir/enhancements/fy0734/20040 42068-b.html 0691118264 (acid-free paper) QC484 .R64 2005 Planck-Bose-Einstein theory of heat capacity History -- Background -- Experimental background -- The Planck equation -- The Einstein's equation -- The Debye equation -Quantum statistics -- Consequences of the FermiDirac distribution -- Consequences of the BoseEinstein distribution. Blackbody radiation. Specific heat. Bose-Einstein condensation. Includes bibliographical references (p. [177]) and index.

Enthalpy and internal energy: liquids, solutions and vapours LCCN 2017275733 Type of material Book Main title Enthalpy and internal energy: liquids, solutions and vapours / edited by Emmerich Wilhelm, University of Vienna, Austria, and Trevor M. Letcher, University of Kwa-Zulu-Natal, South Africa. Published/Produced London, UK: Royal Society of Chemistry, [2018] Description xxi, 618 pages: illustrations (some color); 24 cm ISBN 9781782627111 hardcover 1782627111 hardcover electronic PDF electronic PUB

Bibliography LC classification Related names Summary

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QC318.E55 E58 2018 Wilhelm, Emmerich, editor. Letcher, T. M. (Trevor M.), editor. "Containing the very latest information on all aspects of enthalpy and internal energy as related to fluids, this book brings all the information into one authoritative survey in this well-defined field of chemical thermodynamics."--Page 4 of cover. Internal Energy and Enthalpy: Introduction, Concepts and Selected Applications / Emmerich Wilhelm -- Macroscopic Energy and Entropy Balances in Phase Equilibrium Studies / J. David Raal and Deresh Ramjugernath -- Enthalpy Measurements of Condensed Matter by Peltierelement-based Adiabatic Scanning Calorimetry (pASC) / Jan Thoen, Jan Leys, Patricia LosadaPérez and Christ Glorieux -- Isothermal Titration Calorimetry / José Manuel del Río and Jean-Pierre E. Grolier -- Calorimetric Determination of Enthalpies of Vaporization / Dzmitry H. Zaitsau and Eugene Paulechka -- Energetic Effects in Hydrogen-bonded Liquids and Solutions / Claudio A. Cerdeirin̋a, Kateřina Zemánková and Miguel Costas -- Thermodynamic Studies of Inclusion Compounds of Cyclodextrin / Takayoshi Kimura -- Thermodynamic Studies of Chiral Compounds / Takayoshi Kimura -Temperature Dependence of the Enthalpy of Alkanes and Related Phase Change Materials (PCMs) / Jan Leys, Patricia Losada-Pérez, Christ Glorieux and Jan Thoen -- Enthalpy Changes on Solution of Gases in Liquids / Emmerich Wilhelm and Rubin Battino -- Titration Calorimetry and Differential Scanning Calorimetry of Lipid-

88

Bibliography Protein Interactions / Joachim Seelig -Biocalorimetry: Differential Scanning Calorimetry of Protein Solutions / Pedro L. Mateo, Francisco Conejero-Lara, Irene Luque, Javier Ruiz-Sanz, Jose C. Martinez, Ana I. Azuaga and Eva S. Cobos -- Biocalorimetry of Plants, Insects and Soil Microorganisms / Lee D. Hansen, Amaia Nogales, Birgit ArnholdtSchmitt, Lisa G. Neven and Nieves Barros -Temperature Dependence of the Enthalpy Near Critical and Tricritical Second-order and Weakly First-order Phase Transitions / Patricia LosadaPérez, Jan Leys, George Cordoyiannis, Christ Glorieux and Jan Thoen -- Yang-Yand Critical Anomaly / Ilmutdin M. Abdulagatov, Joseph W. Magee, Nikolai G. Polikhronidi and Rabiyat G. Batyrova -- Internal Pressure and Internal Energy of Saturated and Compressed Phases / Ilmutdin M. Abdulagatov, Joseph W. Magee, Nikolai G. Polikhronidi and Rabiyat G. Batyrova -Solubility Parameters: A Brief Review / Emmerich Wilhelm -- Internal Pressure of Liquids: A Review / Yizhak Marcus -- Excess Enthalpies for Binary Systems Containing Ionic Liquids / Jacobo Troncoso -- Electrolyte Solutions: Standard State Partial Molar Enthalpies of Aqueous Solution up to High Temperatures / Essmaiil Djamali and Walter G. Chapman -- Correlation and Prediction of Excess Molar Enthalpies Using DISQUAC / Juan Antonio González, Isaías García de la Fuente and José Carlos Cobos -- Molecular Thermodynamics of Solutions / Ioannis Tsivintzelis and Costas Panayiotou -- Measurement of Heat Capacity and

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Phase Transition Enthalpy for Condensed Materials by Precision Adiabatic Calorimetry / Z.C. Tan, Q. Shi, Z.D. Nan and Y.Y. Di. Enthalpy. Thermodynamics. Liquids. Gases. Enthalpy. Gases. Liquids. Thermodynamics. Includes bibliographical references and index.

Essentials of oceanography LCCN 2016948993 Type of material Book Personal name Garrison, Tom, 1942-2016, author. Main title Essentials of oceanography / Tom Garrison, Orange Coast College, University of Southern California, Robert Ellis, Orange Coast College. Edition Eighth edition. Published/Produced Boston, MA: National Geographic Learning, [2018] ©2018 Description xxi, 298 pages: color illustrations, color maps; 28 cm ISBN 9781337098649 (paperback; student edition) 9781337098656 (loose leaf edition) LC classification GC11.2 .G36 2018 Related names Ellis, Robert (College teacher), author. National Geographic Learning (Firm), issuing body. Contents Machine generated contents note: 1. Earth and Ocean -- 1.1. Earth Is an Ocean World -- 1.2.

90

Bibliography Marine Scientists Use the Logic of Science to Study the Ocean -- Spotlight Figure 1.3 Earth's Most Prominent Features -- 1.3. Stars Form Seas -- Stars Formed Early in the History of the Universe -- Stars and Planets Are Contained within Galaxies -- Stars Make Heavy Elements from Lighter Ones -- Solar Systems Form by Accretion -- 1.4. Earth, Ocean, and Atmosphere Accumulated in Layers Sorted by Density -- 1.5. Life Probably Originated in the Ocean -- A Closer Look 1.1 How Do We Know the Age of Earth and the Ocean? -- 1.6. What Will Be Earth's Future? - 1.7. Are There Other Ocean Worlds? -- Our Solar System's Outer Moons -- Mars -- Titan -Insight from a National Geographic Explorer 1.1 -- Extrasolar Planets -- Life and Oceans? -Questions from Students -- Terms and Concepts to Remember -- Chapter in Perspective -- Study Questions -- Global Environment Watch -- 2.A History of Marine Science -- 2.1. Understanding the Ocean Began with Voyaging for Trade and Exploration -- Early Peoples Traveled the Ocean for Economic Reasons -- Systematic Study of the Ocean Began at the Library of Alexandria -Eratosthenes Accurately Calculated the Size and Shape of Earth -- A Closer Look 2.1 Latitude and Longitude -- 2.2. Seafaring Expanded Human Horizons -- 2.3. The Chinese Undertook Organized Voyages of Discovery -- 2.4. Prince Henry Launched the Age of European Discovery -- Insight from a National Geographic Explorer 2.1 -- 2.5. Voyaging Combined with Science to Advance Ocean Studies -- Captain James Cook Was the First Marine Scientist -- Accurate

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Determination of Longitude Was the Key to Oceanic Exploration and Mapping -- Matthew Maury Discovered Worldwide Patterns of Winds and Ocean Currents -- The Challenger Expedition Was Organized from the First as a Scientific Expedition -- 2.6. Contemporary Oceanography Makes Use of Modern Technology -- New Ships for New Tasks -- Oceanographic Institutions Arose to Oversee Complex Research Projects -Robot Devices Are Becoming More Capable -Satellites Have Become Important Tools in Ocean Exploration -- Questions from Students -- Chapter in Perspective -- Terms and Concepts to Remember -- Study Questions -- Global Environment Watch -- 3. Earth Structure and Plate Tectonics -- 3.1. Pieces of Earth's Surface Look Like They Once Fit Together -- 3.2. Earth's Interior Is Layered -- A Closer Look 3.1 How Deep in the Earth Have People Gone? -- Each of Earth's Inner Layers Has Unique Characteristics - Radioactive Elements Generate Heat Inside Earth -- Continents Rise above the Ocean Because of Isostatic Equilibrium -- 3.3. Wegener's Idea Is Transformed -- 3.4. The Breakthrough: From Seafloor Spreading to Plate Tectonics -- Plates Interact at Plate Boundaries -- Insight from a National Geographic Explorer 3.1 -- Ocean Basins Form at Divergent Plate Boundaries -Island Arcs Form, Continents Collide, and Crust Recycles at Convergent Plate Boundaries -- Crust Fractures and Slides at Transform Plate Boundaries -- 3.5. Confirmation of Plate Tectonics -- A History of Plate Movement Has Been Captured in Residual Magnetic Fields --

92

Bibliography Plate Movement above Mantle Plumes and Hot Spots Provides Evidence of Plate Tectonics -Sediment Age and Distribution, Oceanic Ridges, and Terranes Are Explained by Plate Tectonics -3.6. Scientists Still Have Much to Learn about the Tectonic Process -- Questions from Students -Terms and Concepts to Remember -- Study Questions -- Global Environment Watch -Chapter in Perspective -- 4. Ocean Basins -- 4.1. The Ocean Floor Is Mapped by Bathymetry -Echo Sounders Bounce Sound off the Seabed -Multibeam Systems Combine Many Echo Sounders -- Satellites Can Be Used to Map Seabed Contours -- Robots Descend to Observe the Details -- Insight from a National Geographic Explorer 4.1 -- 4.2. Ocean-Floor Topography Varies with Location -- 4.3. Continental Margins May Be Active or Passive -- Continental Shelves Are Seaward Extensions of the Continents -Continental Slopes Connect Continental Shelves to the Deep-Ocean Floor -- Spotlight Figure 4.8 Major Features of Ocean Basins -- Submarine Canyons Form at the Junction between Continental Shelf and Continental Slope -Continental Rises Form As Sediments Accumulate at the Base of the Continental Slope -- 4.4. The Topology of Deep-Ocean Basins Differs from That of the Continental Margin -Oceanic Ridges Circle the World -- Hydrothermal Vents Are Hot Springs on Active Oceanic Ridges -- Abyssal Plains and Abyssal Hills Cover Most of Earth's Surface -- Volcanic Seamounts and Guyots Project above the Seabed -- Trenches and Island Arcs Form in Subduction Zones -- 4.5. The

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Grand Tour -- Questions from Students -- Terms and Concepts to Remember -- Chapter in Perspective -- Study Questions -- Global Environment Watch -- 5. Ocean Sediments -- 5.1. Sediments Vary Greatly in Appearance -- 5.2. Sediments May Be Classified by Particle Size -5.3. Sediments Are Classified by Source -Terrigenous Sediments Come from Land -Biogenous Sediments Form from the Remains of Marine Organisms -- Hydrogenous Sediments Form Directly from Seawater -- Cosmogenous Sediments Come from Space -- Marine Sediments Are Usually Combinations of Terrigenous and Biogenous Deposits -- 5.4. Neritic Sediments Overlie Continental Margins -- 5.5. Pelagic Sediments Vary in Composition and Thickness -Turbidites Are Deposited on the Seabed by Turbidity Currents -- Clays Are the Finest and Most Easily Transported Terrigenous Sediments - Oozes Form from the Rigid Remains of Living Creatures -- Hydrogenous Materials Precipitate out of Seawater Itself -- Researchers Have Mapped the Distribution of Deep-Ocean Sediments -- 5.6. Scientists Use Specialized Tools to Study Ocean Sediments -- 5.7. Sediments Are Historical Records of Ocean Processes -- A Closer Look 5.1 Could Sediment Cores Tell Us Something about Earth's History, and Thus Offer Insight into Future Change? -- Questions from Students -- Chapter in Perspective -- Terms and Concepts to Remember -- Study Questions -Global Environment Watch -- 6. Water and Ocean Structure -- 6.1. Familiar, Abundant, and Odd -6.2. The Water Molecule -- A Closer Look 6.1

94

Bibliography How Do We Know the Nature of Water? -- 6.3. Water Has Unusual Thermal Characteristics -Heat and Temperature Are Not the Same Thing - Not All Substances Have the Same Heat Capacity -- Water's Temperature Affects Its Density -- Water Becomes Less Dense When It Freezes -- Water Removes Heat from Surfaces As It Evaporates -- 6.4. Surface Water Moderates Global Temperature -- Movement of Water Vapor from Tropics to Poles Also Moderates Earth's Temperature -- Global Warming Is Influencing Ocean-Surface Temperature -- 6.5. Water Is a Powerful Solvent -- Salinity Is a Measure of Seawater's Total Dissolved Organic Solids -- The Components of Ocean Salinity Came From, and Have Been Modified by, Earth's Crust -- The Ratio of Dissolved Solids in the Ocean Is Constant -- Salinity Is Calculated by Seawater's Conductivity -- The Ocean Is in Chemical Equilibrium -- The Ocean's Mixing Time Is Short -- 6.6. Gases Dissolve in Seawater -- Nitrogen -Oxygen -- Carbon Dioxide -- 6.7. Acid-Base Balance -- 6.8. The Ocean Is Stratified by Density -- The Ocean Is Stratified into Three Density Zones by Temperature and Salinity -- Water Masses Have Characteristic Temperature, Salinity, and Density -- 6.9. Light Does Not Travel Far through the Ocean -- The Photic Zone Is the Sunlit Surface of the Ocean -- Water Transmits Blue Light More Efficiently Than Red -- Insight from a National Geographic Explorer 6.1 -- 6.10. Sound Travels Much Farther Than Light in the Ocean -- Refraction Can Bend the Paths of Light and Sound through Water --

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Refraction Causes SOFAR Layers and Shadow Zones -- Sonar Systems Use Sound to Detect Underwater Objects -- Questions from Students - Chapter in Perspective -- Terms and Concepts to Remember -- Study Questions -- Global Environment Watch. 7. Atmospheric Circulation -- 7.1. The Atmosphere and Ocean Interact with Each Other -- 7.2. The Atmosphere Is Composed Mainly of Nitrogen, Oxygen, and Water Vapor -7.3. The Atmosphere Moves in Response to Uneven Solar Heating and Earth's Rotation -- The Solar Heating of Earth Varies with Latitude -- The Solar Heating of Earth Also Varies with the Seasons -- Earth's Uneven Solar Heating Results in Large-Scale Atmospheric Circulation -- 7.4. The Coriolis Effect Deflects the Path of Moving Objects -- The Coriolis Effect Influences the Movement of Air in Atmospheric Circulation Cells -- Three Atmospheric Circulation Cells Circulate in Each Hemisphere -- 7.5. Atmospheric Circulation Generates Large-Scale Surface Wind Patterns -- Monsoons Are Wind Patterns That Change with the Seasons -- El Nino, La Nina -7.6. Storms Are Variations in Large-Scale Atmospheric Circulation -- Storms Form within or between Air Masses -- Extratropical Cyclones Form between Two Air Masses -- Tropical Cyclones Form in One Air Mass -- 7.7. Katrina and Sandy -- Spotlight Figure 7.24 Comparing Hurricane Katrina and Superstorm Sandy -Questions from Students -- Terms and Concepts to Remember -- Chapter in Perspective -- Study Questions -- Global Environment Watch -- 8. Ocean Circulation -- 8.1. Mass Flow of Ocean

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Bibliography Water Is Driven by Wind and Gravity -- 8.2. Surface Currents Are Driven by the Winds -Surface Currents Flow around the Periphery of Ocean Basins -- Seawater Flows in Six Great Surface Circuits -- Boundary Currents Have Different Characteristics -- A Final Word on Gyres -- 8.3. Surface Currents Affect Weather and Climate -- 8.4. Wind Can Cause Vertical Movement of Ocean Water -- Nutrient-Rich Water Rises Near the Equator -- Wind Can Induce Upwelling Near Coasts -- Wind Can Also Induce Coastal Downwelling -- 8.5. El Nino and La Nina Are Exceptions to Normal Wind and Current Flow -- 8.6. Thermohaline Circulation Affects All the Ocean's Water -- Water Masses Have Distinct, Often Unique Characteristics. Oceanography. Oceanography. Includes bibliographical references and index.

Experimental studies of boson fields in solids LCCN 2018019172 Type of material Book Personal name Köbler, Ulrich, author. Main title Experimental studies of boson fields in solids / Ulrich Köbler (Forschungszentrum Jülich GmbH, Germany), Andreas Hoser (Helmholtz-ZentrumBerlin GmbH, Germany). Published/Produced Singapore; Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd., [2018] ©2018 Description xi, 949 pages; 26 cm ISBN 9789813235489 (hardcover alk. paper) 9813235489 (hardcover alk. paper)

Bibliography LC classification Related names Summary

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QC176.8.M3 K63 2018 Hoser, Andreas, author. "This book provides a new understanding of the large amount of experimental results gained in solid state physics during the last seven decades. For more than 160 different materials, data analyses shown in terms of atomistic models (Hamiltonians) have not provided a quantitatively satisfactory description of either excitation spectra or dynamic properties. Instead, the experimental evidences have elaborated that field theories are necessary. However, most experimentalists are not familiar with field theories, and realistic field theories of magnetism are absent. The book illustrates in an empirical way the elements of future field theories of solid state physics with special emphasis on magnetic materials. In contrast to the many available textbooks on quantum field theories that emphasize more on algorithmic formalities rather than referring to the experimental facts, the approach in this book is pragmatic instead of abstract theoretic. This methodical concept considerably facilitates experimentalists to get acquainted with the basic ideas of field theories, even if a ready field theory is not provided by this experimental study"-- Provided by publisher. History of conventional spin wave theory -- Basic issues of renormalization group (RG) theory -Universality -- Microscopic processes -- Relevant and non-relevant magnons -- Crossover phenomena -- Metastability of universality classes -- Relevant and non-relevant interactions -Temperature dependence of the magnon

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Bibliography excitation spectra -- Magnetic heat capacity -Experimental verification of GSW bosons -Magnets with and without magnon gap -Microscopic details: spin structure, site disorder, two order parameters -- The boson fields at the magnetic ordering transition -- Thermal lattice expansion and magnetostriction -- Boson fields near melting transition -- Boson fields in superconductors -- Summary. Solids--Magnetic properties. Magnetism. Renormalization group. Solid state physics. Includes bibliographical references (pages 921944) and index.

Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties LCCN 2010938473 Type of material Book Main title Glassy, amorphous and nano-crystalline materials: thermal physics, analysis, structure and properties / Jaroslav Šesták, Jiří J. Mareš, Pavel Hubík, editors. Published/Created Dordrecht; New York: Springer, 2010. Description xvii, 380 p.: ill,; 24 cm. ISBN 9789048128815 (hbk.) 9048128811 (hbk.) LC classification QC611.8.N33 G53 2010 Related names Šesták, Jaroslav, 1938Mareš, J. (Jiří), 1959Hubík, Pavel. Contents Introduction: Some essential attributes of glassiness regarding the nature of non-crystalline

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solids / Hiroshi Suga -- Heat capacity and entropy functions in strong and fragile glass-formers, relative to those of disordering crystalline materials / C. Austen Angell -- Vibration forms in the vicinity of glass transition, structural changes and the creation of voids when assuming the role of polarizability / Jaroslav Šesták ... [et al.] -Some aspects of vitrification, amorphisation and disordering and the generated extent of nanocrystallinity / Jaroslav Šestak ... [et al.] -- Basic role of thermal analysis in polymer physics / Adam L. Danch -- Phases of amorphous, crystalline, and intermediate order in microphase and nanophase systems / Bernhard Wunderlich -Thermal portrayal of phase separation in polymers producing nanophase separated materials / Ivan Krakovský and Yuko Ikeda -Solid forms of pharmaceutical molecules / Bohumil Kratochvíl -- Chalcogenide glasses selected as a model system for studying thermal properties / Zdeněk Černošek, Eva Černošková, and Jana Holubová -- Viscosity measurements applied to chalcogenide glass-forming systems / Peter Koštál, Jana Shánělová, and Jiří Málek -Thermal properties and related structural study of oxide glasses / Marek Liška and Mária Chromčíková -- Oxide glass structure, nonbridging oxygen and feasible magnetic properties due to the addition of Fe/Mn oxides / Jaroslav Šesták, Marek Liška, and Pavel Hubík. New approach to viscosity of glasses / Isak Avramov - Transport constitutive relations, quantum diffusion and periodic reactions / Jiří J. Mareš, Jaroslav Šesták, and Pavel Hubík -- In-situ

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Bibliography investigation of the fast lattice recovery during electropulse treatment of heavily cold drawn nanocrystaline Ni-Ti wires / Petr Šittner ... [et al.] -- Emanation thermal analysis as a method for diffusion structural diagnostics of zircon and brannerite minerals / Vladimír Balek, Iraida M. Bounstseva, and Igor von Beckman -- Scanning transitiometry and its application in petroleum industry and in polymer and food science / JeanPierre E. Grolier -- Constrained states occurring in plants cryo-processing and the role of biological glasses / Jiří Zámečník and Jaroslav Šesták -- Thermophysical properties of natural glasses at the extremes of the thermal history profile / Paul Thomas ... [et al.] -- Hotness manifold, phenomenological temperature and other related concepts of thermal physics / Jiří J. Mareš -- Historical roots and development of thermal analysis and calorimetry / Jaroslav Šesták, Pavel Hubík, and Jiří J. Mareš. Semiconductor nanocrystals. Amorphous semiconductors. Nanostructured materials. Includes bibliographical references and index. Hot topics in thermal analysis and calorimetry; 8 Hot topics in thermal analysis and calorimetry; v. 8.

Harmonic oscillators: types, functions and applications LCCN 2019024814 Type of material Book Main title Harmonic oscillators: types, functions and applications / Yilun Shang. Published/Produced New York: Nova Science Publishers, [2019]

Bibliography ISBN LC classification Related names Summary

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9781536158106 (hardcover) (adobe pdf) TK7872.O7 H36 2019 Shang, Yilun, editor. "This book gathers state-of-the-art advances on harmonic oscillators including their types, functions, and applications. In Chapter 1, Neetik and Amlan have discussed the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology, etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy, Onicescu energy and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been invoked to explain several physic-chemical properties of a system under investigation. Kullback Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the

102

Bibliography change of information in going from one state to another. In Chapter 2, Nabakumar, Subhasree, and Paulami have revisited classical-quantum correspondence in the context of linear Simple Harmonic Oscillator (SHO). According to Bohr's correspondence principle, quantum mechanically calculated results match with the classically expected results when quantum number is very high. Classical quantum correspondence may also be visualized in the limit when the action integral is much greater than Planck's constant. When deBroglie wave length associated with a particle is much larger than system size, then quantum mechanical results also match with the classical results. In the context of dynamics, Ehrenfest equation of motion is used in quantum domain, which is analogous to classical Newton's equation of motion. SHO is one of the most important systems for several reasons. It is one of the few exactly solvable problems. Any stable molecular potential can be approximated by SHO near the equilibrium point. This builds the foundation for the understanding of complex modes of vibration in large molecules, the motion of atoms in a solid lattice, the theory of heat capacity, vibration motion of nuclei in molecule etc. The authors have revisited the common solution techniques and important properties of both classical and quantum linear SHO. Then they focused on probability distribution, quantum mechanical tunneling, classical and quantum dynamics of position, momentum and their actuations, viral theorems, etc. and also analyzed how quantum mechanical results finally tend to classical results

Bibliography

Subjects Notes Additional formats

Series

103

in the high quantum number limit. In Chapter 3, Neeraj has discussed the nature of atomic motions, sometimes referred to as lattice vibrations. The lattice dynamics deals with the vibrations of the atoms inside the crystals. In order to write the dynamic equations of the motion of crystal atoms, we need to describe an inter-atomic interaction. Therefore, it is natural to start the study of the lattice dynamics with the case of small harmonic vibrations. The dynamics of onedimensional and two-dimensional vibrations of monatomic and diatomic crystals can be understood by using the simple model forces based on harmonic approximation. This harmonic approximation is related to a simple ball-spring model. According to this model, each atom is coupled with the neighboring atoms by spring constants. The collective motion of atoms leads to a distinct traveling wave over the whole crystal, leading to the collective motion, so-called phonon. The simple ball-spring model enlightens us some of the significant common features of lattice dynamics that have been discussed throughout this chapter. Further, this chapter helps in understanding the quantization energy of a harmonic oscillation and the concept of phonon"-- Provided by publisher. Harmonic oscillators. Includes bibliographical references and index. Online version: Harmonic oscillators: Hauppauge: Nova Science Publishers, 2019. 9781536158113 (DLC) 2019024815 Physics research and technology

104

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Harmonic oscillators: types, functions and applications LCCN 2019024815 Type of material Book Main title Harmonic oscillators: types, functions and applications / Yilun Shang. Published/Produced New York: Nova Science Publishers, [2019] Description 1 online resource ISBN 9781536158113 (adobe pdf) (hardcover) LC classification TK7872.O7 Related names Shang, Yilun, editor. Summary "This book gathers state-of-the-art advances on harmonic oscillators including their types, functions, and applications. In Chapter 1, Neetik and Amlan have discussed the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology, etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both free and constrained situations. The most prominent amongst these are: Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy, Onicescu energy and several complexities. Arguably, these are the most effective measures of uncertainty, as they do not make any reference to some specific points of a respective Hilbert space. These have been

Bibliography

105

invoked to explain several physic-chemical properties of a system under investigation. Kullback Leibler divergence or relative entropy describes how a given probability distribution shifts from a reference distribution function. This characterizes a measure of discrimination between two states. In other words, it extracts the change of information in going from one state to another. In Chapter 2, Nabakumar, Subhasree, and Paulami have revisited classical-quantum correspondence in the context of linear Simple Harmonic Oscillator (SHO). According to Bohr's correspondence principle, quantum mechanically calculated results match with the classically expected results when quantum number is very high. Classical quantum correspondence may also be visualized in the limit when the action integral is much greater than Planck's constant. When deBroglie wave length associated with a particle is much larger than system size, then quantum mechanical results also match with the classical results. In the context of dynamics, Ehrenfest equation of motion is used in quantum domain, which is analogous to classical Newton's equation of motion. SHO is one of the most important systems for several reasons. It is one of the few exactly solvable problems. Any stable molecular potential can be approximated by SHO near the equilibrium point. This builds the foundation for the understanding of complex modes of vibration in large molecules, the motion of atoms in a solid lattice, the theory of heat capacity, vibration motion of nuclei in molecule etc. The authors have revisited the common solution techniques

106

Bibliography and important properties of both classical and quantum linear SHO. Then they focused on probability distribution, quantum mechanical tunneling, classical and quantum dynamics of position, momentum and their actuations, viral theorems, etc. and also analyzed how quantum mechanical results finally tend to classical results in the high quantum number limit. In Chapter 3, Neeraj has discussed the nature of atomic motions, sometimes referred to as lattice vibrations. The lattice dynamics deals with the vibrations of the atoms inside the crystals. In order to write the dynamic equations of the motion of crystal atoms, we need to describe an inter-atomic interaction. Therefore, it is natural to start the study of the lattice dynamics with the case of small harmonic vibrations. The dynamics of onedimensional and two-dimensional vibrations of monatomic and diatomic crystals can be understood by using the simple model forces based on harmonic approximation. This harmonic approximation is related to a simple ball-spring model. According to this model, each atom is coupled with the neighboring atoms by spring constants. The collective motion of atoms leads to a distinct traveling wave over the whole crystal, leading to the collective motion, so-called phonon. The simple ball-spring model enlightens us some of the significant common features of lattice dynamics that have been discussed throughout this chapter. Further, this chapter helps in understanding the quantization energy of a harmonic oscillation and the concept of phonon"-- Provided by publisher.

Bibliography Subjects Notes Additional formats

Series

107

Harmonic oscillators. Includes bibliographical references and index. Print version: Harmonic oscillators New York: Nova Science Publishers, [2019] 9781536158106 (DLC) 2019024814 Physics research and technology

Heat capacities: liquids, solutions and vapours LCCN 2012382424 Type of material Book Main title Heat capacities: liquids, solutions and vapours / edited by Emmerich Wilhelm, Trevor M. Letcher. Published/Created Cambridge: Royal Society of Chemistry, c2010. Description xiv, 516 p.: ill.; 24 cm. ISBN 9780854041763 (hbk.) 0854041761 (hbk.) LC classification QD511 .H43 2010 Portion of title Liquids, solutions and vapours Related names Wilhelm, Emmerich. Letcher, T. M. (Trevor M.) Royal Society of Chemistry (Great Britain) Contents Heat capacities: introduction, concepts and selected applications / Emmerich Wilhelm -Calorimetric methods for measuring heat capacities of liquids and liquid solutions / Lee D. Hansen and Donald J. Russell -- An analysis of conductive heat losses in a flow calorimeter for heat capacity measurement / J. David Raal -- Heat capacities and related properties of liquid mixtures / Emmerich Wilhelm and Jean-Pierre E. Grolier -- Heat capacity of non-electrolyte solutions / Amr Henni -- Heat capacities and related properties of vapours and vapour mixtures / Christopher J. Wormald -- Heat capacity of

108

Bibliography electrolyte solutions / Andrew W. Hakin and Mohammad M.H. Bhuiyan -- Scanning transitiometry and its use to determine heat capacities of liquids at high pressures / Stanislaw L. Randzio -- Speed of sound measurements and heat capacities of gases / Anthony R.H. Goodwin and J.P. Martin Trusler -- Speed-of-sound measurements and heat capacities of liquid systems at high pressure / Toshiharu Takagi and Emmerich Wilhelm -- Heat capacities and Brillouin scattering in liquids / Emmerich Wilhelm and Augustinus Asenbaum -Photothermal techniques for heat capacities / Jan Thoen and Christ Glorieux -- High resolution adiabatic scanning calorimetry and heat capacities / Jan Thoen -- Heat capacities in the critical region / Mikhail Anisimov and Jan Thoen -- Heat capacity of polymeric systems / Marek Pyda -Protein heat capacity / Werner W. Streicher and George I. Makhatadze -- Heat capacity in liquid crystals / M. Marinelli, F. Mercuri and U. Zammit -- Heat capacities and phase transitions for the dynamic chemical systems: conformers, tautomers, plastic crystals and ionic liquids / Gennady Kabo, Eugene Paulechka and Michael Frenkel -- The estimation of heat capacities of pure liquids / Milan Zábranský ... [et al.] -Computer simulation studies of heat capacity effects associated with hydrophobic effects / Dietmar Paschek, Ralf Ludwig and Jörg Holzmann -- Partial molar heat capacity changes of gases dissolved in liquids / Emmerich Wilhelm and Rubin Battino -- Heat capacities of molten salts / Yizhak Marcus.

Bibliography Subjects Notes Heat LCCN Type of material Personal name Main title Edition Published/Created Description Links ISBN LC classification Contents

Subjects Notes Series

109

Thermochemistry. Includes bibliographical references and index.

2005029476 Book Mahaney, Ian F. Heat / Ian F. Mahaney. 1st ed. New York: Rosen Pub. Group's PowerKids Press, 2007. 24 p.; 24 cm. Table of contents http://www.loc.gov/catdir/ toc/ecip061/2005029476.html 1404234772 (library binding) 1404221867 (pbk.) QC256 .M34 2007 Energy -- Heat is a type of energy -- Measuring heat -- The science of heat -- Conduction -Convection -- Radiation -- Heat capacity -- An experiment -- Let's use heat energy -- Glossary -Index. Heat--Juvenile literature. Includes index. Energy in action

Introduction to the thermodynamics of materials LCCN 2008001951 Type of material Book Personal name Gaskell, David R., 1940Main title Introduction to the thermodynamics of materials / David R. Gaskell. Edition 5th ed. Published/Created New York: Taylor & Francis, 2008.

110 Description Links

ISBN LC classification Contents

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Bibliography xv, 618 p.: ill.; 24 cm. + 1 CD-ROM (4 3/4 in.) Table of contents only http://www.loc.gov/catdir/ toc/ecip088/2008001951.html Publisher description http://www.loc.gov/catdir/ enhancements/fy0913/2008001951-d.html 9781591690436 1591690439 TN673 .G33 2008 Introduction and definition of terms -- The first law of thermodynamics -- The second law of thermodynamics -- The statistical interpretation of entropy -- Auxiliary functions -- Heat capacity, enthalpy, entropy -- Phase equilibrium in a onecomponent system -- The behavior of gases -- The behavior of solutions -- Gibbs free energy composition and phase diagrams of binary systems -- Reactions involving gases -- Reactions involving pure condensed phases and a gaseous phase -- Reaction equilibria in systems containing components in condensed solution -- Phase diagrams for binary systems in pressuretemperature-composition space -Electrochemistry. Thermodynamics. Materials--Thermal properties. Metallurgy. Includes bibliographical references and index.

Isochoric heat capacity of fluids and fluid mixtures in the critical and supercritical regions: experiment and theory LCCN 2011024418 Type of material Book Main title Isochoric heat capacity of fluids and fluid mixtures in the critical and supercritical regions:

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Published/Created Description ISBN LC classification Related names

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111

experiment and theory / Ilmutdin M. Abdulagatov and Gennadii V. Stepanov and Aziz I. Abdulagatov, editors. New York: Nova Science Publishers, c2012. vii, 356 p.: ill.; 26 cm. 9781614705598 (pbk.) QC145.4.T5 I86 2012 Abdulagatov, I. M. Stepanov, Gennadiĭ Vladimirovich. Abdulagatov, A. I. Fluids--Thermal properties. Supercritical fluids. Hydrostatics. High pressure (Technology) Includes bibliographical references (p. 329-349) and index.

Modern thermodynamics: from heat engines to dissipative structures LCCN 2014021349 Type of material Book Personal name Kondepudi, Dilip, 1952- author. Main title Modern thermodynamics: from heat engines to dissipative structures / Dilip Kondepudi, Wake Forest University, USA, Ilya Prigogine, formerly Director, International Solvay Institutes, Belgium. Edition Second edition. Published/Produced Chichester, West Sussex; Hoboken, NJ: Wiley & Sons, 2015. Description xxvi, 523 pages: illustrations; 25 cm ISBN 9781118371817 (pbk.) 111837181X (pbk.) LC classification QC311 .K66 2015 Related names Prigogine, I. (Ilya), author.

112 Contents

Subjects Notes Additional formats

Bibliography I Historical roots: from heat engines to cosmology -- 1. Basic Concepts and the Laws of Gases -- 2. The First Law of Thermodynamics -- 3. The Second Law of Thermodynamics and the Arrow of Time -- 4. Entropy in the Realm of Chemical Reactions -- II Equilibrium Thermodynamics -- 5. Extremum Principles and General Thermodynamic Relations -- 6. Basic Thermodynamics of Gases, Liquids and Solids -7. Thermodynamics of Phase Change -- 8. Thermodynamics of Solutions -9. Thermodynamics of Chemical Transformations - 10 Fields and Internal Degrees of Freedom -- 11. Thermodynamics of Radiation -- III Fluctuations And Stability -- 12. The Gibbs Stability Theory -13. Critical Phenomena and Configurational Heat Capacity -- 14. Entropy Production, Fluctuations and Small Systems -- IV Linear Nonequilibrium Thermodynamics -15. Nonequilibrium Thermodynamics: The Foundations -- 16. Nonequilibrium Thermodynamics: The Linear Regime -- 17. Nonequilibrium Stationary States and Their Stability: Linear Regime -- V Order Through Fluctuations -- 18. Nonlinear Thermodynamics -- 19. Dissipative Structures -20. Elements of Statistical Thermodynamics -- 21. Self-Organization and Dissipative Structures in Nature. Thermodynamics. Includes bibliographical references and author index. Online version: Kondepudi, Dilip, 1952- author. Modern thermodynamics Second edition. Chichester, West Sussex; Hoboken, NJ: John

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113

Wiley & Sons Inc., 2015 9781118698709 (DLC) 2014022007 Physical chemistry: how chemistry works LCCN 2016015389 Type of material Book Personal name Kolasinski, Kurt W. Main title Physical chemistry: how chemistry works / Kurt W. Kolasinski, Department of Chemistry, West Chester University, USA. Published/Produced Chichester, West Sussex: John Wiley & Sons, Inc., 2016. Description xvii, 726 pages: color illustrations; 28 cm ISBN 9781118751121 (pbk.) 9781118751213 (adobe PDF) LC classification QD453.3 .K65 2016 Portion of title How chemistry works Contents Introduction -- Statistical mechanics -- Ideal gases -- Non-ideal gases and intermolecular interactions -- Liquids, liquid crystals, and ionic liquids -Solids, nanoparticles, and interfaces -- First law of thermodynamics -Second law of thermodynamics -- Third law of thermodynamics and temperature dependence of heat capacity, enthalpy, and entropy -- Thermochemistry: the role of heat in chemical and physical changes -Chemical equilibrium -- Phase stability and phase transitions -- Solutions and mixtures: nonelectrolytes -- Solutions of electrolytes -Electrochemistry: the chemistry of free charge exchange -- Empirical chemical kinetics -Reaction dynamics: mechanisms and rates -Complex reactions mechanisms: catalysis, photochemistry and charge transfer -- Developing

114

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Bibliography quantum mechanical intuition -- The quantum mechanical description of nature -- Model quantum systems -- Atomic structure -Introduction to spectroscopy and atomic spectroscopy -- Molecular bonding and structure -- Molecular spectroscopy & excited state dynamics: diatomics -- Polyatomic molecules and group theory -- Light-matter interactions: lasers, laser spectroscopy, and photodynamics. Chemistry, Physical and theoretical--Textbooks. Chemistry--Textbooks. Includes index.

Polyoxymethylene handbook: structure, properties, applications and their nanocomposites LCCN 2014012373 Type of material Book Main title Polyoxymethylene handbook: structure, properties, applications and their nanocomposites / edited by Sigrid Luftl, Visakh P.M. and C. Sarathchandran. Published/Produced Hoboken, New Jersey: Salem, MA: John Wiley & Sons, Scrivener Publishing, [2014] Description 1 online resource. Links Cover image http://catalogimages.wiley.com/ images/db/jimages/9781118385111.jpg ISBN 9781118914427 (epub) 9781118914434 (pdf) LC classification TA455.P58 Related names Luftl, Sigrid, 1966P. M., Visakh. Sarathchandran, C., 1978Summary "In recent decades, Polyoxmethylene (POM) has been positioned as a high performance

Bibliography

Contents

115

engineering polymer with increasing worldwide demand, particularly in the automotive, electronics, medical, and consumer goods industries. Despite this interest in POM, there has not been a book devoted to this compound. This volume rectifies this situation by bringing together the knowledge of leading scientists from industry and academia to present research results and applications of POM, including their structure, properties, manufacture, additives, processing and applications, as well their nanocomposites and other compounds"-Provided by publisher. "This book rectifies this situation by bringing together the knowledge of leading scientists from industry and academia to present research results and applications of POM, including their structure, properties, manufacture, additives, processing and applications, as well their nanocomposites and other compounds"-Provided by publisher. Machine generated contents note: Preface xiii 1 Polyoxymethylene: State of Art, New Challenges and Opportunities 1 Sigrid Luft l and Visakh. P.M. 1.1 Scope 2 1.2 History 2 1.3 Commercial Significance 7 References 13 2 Polymerization and Manufacture of Polyoxymethylene 21 Johannes Karl Fink 2.1 Introduction 21 2.2 Monomers 22 2.3 Comonomers 25 2.4 Polymerization and Fabrication 28 2.5 Special Additives 44 References 46 3 Polyoxymethylene Additives 53 Emmanuel Richaud 3.1 Introduction 53 3.2 Antioxidants 54 3.3 Compounds Reacting with Secondary Reaction Products 59 3.4 UV

116

Bibliography Stabilization 60 3.5 Impact Modifier 65 3.6 Nucleating Agent 67 3.7 Pigments and Dyes 72 3.8 Flame Retardants 75 3.9 Antistatic Agents 79 3.10 Lubricating Agents 80 3.11 Fillers 82 3.12 Processing Aids 90 References 91 Appendix 3.1: List of Stabilizers 100 4 Polyoxymethylene Processing 107 Kinga Pielichowska 4.1 Introduction 107 4.2 Injection Molding 109 4.3 Melt Extrusion 116 4.4 Solid-State Extrusion 118 4.5 Extrusion Assisted by Supercritical Carbon Dioxide 120 4.6 Blow Molding 121 4.7 Others Methods 123 4.8 Highly Oriented Products 132 4.9 Recycling of Production Waste 136 4.10 Finishing and Machining of POM 138 4.11 Conclusions 141 References 142 5 Polyoxymethylene Applications 153 Lidia Tokarz, Slawomir Pawlowski and Michal Kedzierski 5.1 Introduction 153 5.2 Automotive Industry, Mechanical Engineering 156 5.3 Electrical and Electronic Industry, Fancy Goods 157 5.4 Medical Applications 158 5.5 Future Trends 160 References 160 6 Structure and Morphology of Polyoxymethylene 163 Maria Raimo 6.1 Introduction 163 6.2 Crystalline Structure of POM: Orthorhombic and Hexagonal Phases 165 6.3 Crystal Structure Determination 170 6.4 Morphology of Orthorhombic and Hexagonal POM 173 6.5 Morphology of RubberModified POM 179 6.6 Structure-Properties Relationships 181 References 186 7 Crystal Structure and Crystallization Behavior of POM and its Microscopically-Viewed Relation with the Physical and Thermal Properties on the Basis of X-ray Scattering, Vibrational Spectroscopy and

Bibliography

117

Lattice Dynamical Theory 193 Kohji Tashiro 7.1 Introduction 194 7.2 Crystal Structure Analysis of POM 195 7.3 Vibrational Spectra of POM 204 7.4 Structural Evolution in Isothermal Crystallization 207 7.5 Microscopically-Viewed Mechanical Property of POM 216 7.6 Conclusions 223 Acknowledgements 224 References 224 8 Physical Properties of Polyoxymethylene 227 Johannes Karl Fink 8.1 Introduction 227 8.2 Density 228 8.3 Hardness 230 8.4 Heat Capacity 231 8.5 Melt Flow 231 8.6 Water Absorption 235 8.7 Gas Permeability 236 8.8 Specific Absorption 238 References 239 9 POM Mechanical Properties 241 Fahmi Bedoui and Bruno Fayolle 9.1 Short Term Properties 242 9.2 Long-Term Properties 249 9.3 Conclusion 252 Acknowledgement 253 References 253 10 Thermal Properties and Flammability of Polyoxymethylene 257 Vasiliki-Maria Archodoulaki and Sigrid Luft l 10.1 Glass Transition and Melting Temperature 257 10.2 Coefficient of Linear Thermal Expansion 260 10.3 Thermal Conductivity and Specific Heat 260 10.4 HDT and Vicat 261 10.5 Thermo-Oxidative Degradation Behavior and Aging 261 10.6 Testing of Long-Term Heat Aging 266 10.7 Flammability 267 10.8 Hot Sterilization 270 References 271 11 Chemical Resistance of Polyoxymethylene 277 Sigrid Luft l and Emmanuel Richaud 11.1 Intoduction 277 11.2 Degradation and Oxidation Mechanisms in POM 278 11.3 Resistance to Chemicals 283 References 295 12 The Electrical Response of Polyoxymethylene (POM) 301 D.A. Wasylyshyn

118

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Notes

Bibliography 12.1 Introduction 301 12.2 Interactions between POM and Electromagnetic Waves 302 12.3 Interactions between POM and Arc Plasma 313 References 318 13 Electrical and Optical Properties of Polyoxymethylene 321 Natamai Subramanian Muralisrinivasan 13.1 Introduction 321 13.2 Electrical Properties 322 13.3 Optical Properties 327 References 329 14 Nanocomposites of Polyoxymethylene 331 Agnieszka Leszczyñska and Krzysztof Pielichowski 14.1 Introduction 331 14.2 Preparation and Structure of POM Nanocomposites with Different Nanoadditives 332 14.3 Properties of Polyoxymethylene-Based Nanocomposites 347 14.4 POM Blends as Matrices in Nanocomposite Materials 376 14.5 POM Nanostructures - Electrospun POM Nanofibers 381 14.6 Applications of POM-Based Nanocomposites and Future Trends 385 14.7 Conclusions 386 List of acronyms 387 References 388 15 Future, Environmental Impact and Suppliers 399 Takashi Iwamoto and Junzo Masamoto 15.1 Introduction 400 15.2 Developments and Specialty Resins 400 15.3 Safety (Regulation and Approvals) 421 15.4 Environmental Impact 424 15.5 Suppliers and Commercial Grades 426 15.6 Future 426 References 432 Index 435 . Polyoxymethylene. Technology & Engineering / Chemical & Biochemical. Includes bibliographical references and index.

Bibliography Additional formats

119

Print version: Polyoxymethylene handbook Hoboken, New Jersey: John Wiley & Sons, [2014] 9781118385111 (DLC) 2014002685

Polyoxymethylene handbook: structure, properties, applications and their nanocomposites LCCN 2014002685 Type of material Book Main title Polyoxymethylene handbook: structure, properties, applications and their nanocomposites / edited by Sigrid Lüftl, Visakh P.M., and Sarath Chandran. Published/Produced Hoboken, New Jersey: Scrivener Publishing/Wiley, [2014] Description xv, 442 pages: illustrations; 25 cm Links Cover image http://catalogimages.wiley.com/ images/db/jimages/9781118385111.jpg ISBN 9781118385111 (hardback) LC classification TA455.P58 P69585 2014 Related names Luftl, Sigrid, 1966P. M., Visakh. Sarathchandran, C., 1978Summary "In recent decades, Polyoxmethylene (POM) has been positioned as a high performance engineering polymer with increasing worldwide demand, particularly in the automotive, electronics, medical, and consumer goods industries. Despite this interest in POM, there has not been a book devoted to this compound. This volume rectifies this situation by bringing together the knowledge of leading scientists from industry and academia to present research results and applications of POM, including their structure, properties, manufacture, additives,

120

Contents

Bibliography processing and applications, as well their nanocomposites and other compounds"-Provided by publisher. "This book rectifies this situation by bringing together the knowledge of leading scientists from industry and academia to present research results and applications of POM, including their structure, properties, manufacture, additives, processing and applications, as well their nanocomposites and other compounds"-Provided by publisher. Machine generated contents note: Preface xiii 1 Polyoxymethylene: State of Art, New Challenges and Opportunities 1 Sigrid Luft l and Visakh. P.M. 1.1 Scope 2 1.2 History 2 1.3 Commercial Significance 7 References 13 2 Polymerization and Manufacture of Polyoxymethylene 21 Johannes Karl Fink 2.1 Introduction 21 2.2 Monomers 22 2.3 Comonomers 25 2.4 Polymerization and Fabrication 28 2.5 Special Additives 44 References 46 3 Polyoxymethylene Additives 53 Emmanuel Richaud 3.1 Introduction 53 3.2 Antioxidants 54 3.3 Compounds Reacting with Secondary Reaction Products 59 3.4 UV Stabilization 60 3.5 Impact Modifier 65 3.6 Nucleating Agent 67 3.7 Pigments and Dyes 72 3.8 Flame Retardants 75 3.9 Antistatic Agents 79 3.10 Lubricating Agents 80 3.11 Fillers 82 3.12 Processing Aids 90 References 91 Appendix 3.1: List of Stabilizers 100 4 Polyoxymethylene Processing 107 Kinga Pielichowska 4.1 Introduction 107 4.2 Injection Molding 109 4.3 Melt Extrusion 116 4.4 Solid-State Extrusion 118 4.5 Extrusion Assisted by Supercritical Carbon

Bibliography

121

Dioxide 120 4.6 Blow Molding 121 4.7 Others Methods 123 4.8 Highly Oriented Products 132 4.9 Recycling of Production Waste 136 4.10 Finishing and Machining of POM 138 4.11 Conclusions 141 References 142 5 Polyoxymethylene Applications 153 Lidia Tokarz, Slawomir Pawlowski and Michal Kedzierski 5.1 Introduction 153 5.2 Automotive Industry, Mechanical Engineering 156 5.3 Electrical and Electronic Industry, Fancy Goods 157 5.4 Medical Applications 158 5.5 Future Trends 160 References 160 6 Structure and Morphology of Polyoxymethylene 163 Maria Raimo 6.1 Introduction 163 6.2 Crystalline Structure of POM: Orthorhombic and Hexagonal Phases 165 6.3 Crystal Structure Determination 170 6.4 Morphology of Orthorhombic and Hexagonal POM 173 6.5 Morphology of RubberModified POM 179 6.6 Structure-Properties Relationships 181 References 186 7 Crystal Structure and Crystallization Behavior of POM and its Microscopically-Viewed Relation with the Physical and Thermal Properties on the Basis of X-ray Scattering, Vibrational Spectroscopy and Lattice Dynamical Theory 193 Kohji Tashiro 7.1 Introduction 194 7.2 Crystal Structure Analysis of POM 195 7.3 Vibrational Spectra of POM 204 7.4 Structural Evolution in Isothermal Crystallization 207 7.5 Microscopically-Viewed Mechanical Property of POM 216 7.6 Conclusions 223 Acknowledgements 224 References 224 8 Physical Properties of Polyoxymethylene 227 Johannes Karl Fink 8.1 Introduction 227 8.2 Density 228 8.3 Hardness 230 8.4 Heat Capacity

122

Bibliography 231 8.5 Melt Flow 231 8.6 Water Absorption 235 8.7 Gas Permeability 236 8.8 Specific Absorption 238 References 239 9 POM Mechanical Properties 241 Fahmi Bedoui and Bruno Fayolle 9.1 Short Term Properties 242 9.2 Long-Term Properties 249 9.3 Conclusion 252 Acknowledgement 253 References 253 10 Thermal Properties and Flammability of Polyoxymethylene 257 Vasiliki-Maria Archodoulaki and Sigrid Luft l 10.1 Glass Transition and Melting Temperature 257 10.2 Coefficient of Linear Thermal Expansion 260 10.3 Thermal Conductivity and Specific Heat 260 10.4 HDT and Vicat 261 10.5 Thermo-Oxidative Degradation Behavior and Aging 261 10.6 Testing of Long-Term Heat Aging 266 10.7 Flammability 267 10.8 Hot Sterilization 270 References 271 11 Chemical Resistance of Polyoxymethylene 277 Sigrid Luft l and Emmanuel Richaud 11.1 Intoduction 277 11.2 Degradation and Oxidation Mechanisms in POM 278 11.3 Resistance to Chemicals 283 References 295 12 The Electrical Response of Polyoxymethylene (POM) 301 D.A. Wasylyshyn 12.1 Introduction 301 12.2 Interactions between POM and Electromagnetic Waves 302 12.3 Interactions between POM and Arc Plasma 313 References 318 13 Electrical and Optical Properties of Polyoxymethylene 321 Natamai Subramanian Muralisrinivasan 13.1 Introduction 321 13.2 Electrical Properties 322 13.3 Optical Properties 327 References 329 14 Nanocomposites of Polyoxymethylene 331 Agnieszka Leszczyñska and Krzysztof

Bibliography

Subjects

Notes Additional formats

Quantum oscillators LCCN Type of material Personal name Main title Published/Created Description

123

Pielichowski 14.1 Introduction 331 14.2 Preparation and Structure of POM Nanocomposites with Different Nanoadditives 332 14.3 Properties of Polyoxymethylene-Based Nanocomposites 347 14.4 POM Blends as Matrices in Nanocomposite Materials 376 14.5 POM Nanostructures - Electrospun POM Nanofibers 381 14.6 Applications of POM-Based Nanocomposites and Future Trends 385 14.7 Conclusions 386 List of acronyms 387 References 388 15 Future, Environmental Impact and Suppliers 399 Takashi Iwamoto and Junzo Masamoto 15.1 Introduction 400 15.2 Developments and Specialty Resins 400 15.3 Safety (Regulation and Approvals) 421 15.4 Environmental Impact 424 15.5 Suppliers and Commercial Grades 426 15.6 Future 426 References 432 Index 435 . Polyoxymethylene. Technology & Engineering / Chemical & Biochemical. Includes bibliographical references and index. Online version: Polyoxymethylene handbook Hoboken, New Jersey: John Wiley & Sons, [2014] 9781118914434 (DLC) 2014012373

2011008577 Book Henri-Rousseau, Olivier. Quantum oscillators / Olivier Henri-Rousseau and Paul Blaise. Hoboken, N.J.: Wiley, c2011. xxiii, 647 p.: ill. (some col.); 25 cm.

124 ISBN LC classification Related names Summary

Contents

Bibliography 9780470466094 (cloth) 047046609X (cloth) QC174.2 .H45 2011 Blaise, Paul. "Quantum Oscillators is a valuable source of information and an excellent supplementary text in courses on spectroscopy of hydrogen-bonded systems, one of the unsolved problems of science. This reference provides a reasonable and accessible entrance to the difficult subject of nonequilibrium quantum mechanics and is a timely update of classical works while, at the same time, providing a comprehensive treatment of hydrogen bonding. Also included is an appendix that summarizes mathematical concepts needed to understand the basis of the theory"-Provided by publisher. "The book is divided into four parts. The first part is devoted to the concepts of quantum mechanics the knowledge of which is necessary for a good understanding of the dynamics of quantum oscillator which may be damped, and deals with time independent quantum mechanics and time dependent quantum mechanics"--Provided by publisher. Machine generated contents note: pt. I BASIS REQUIRED FOR QUANTUM OSCILLATOR STUDIES -- ch. 1 Basic Concepts Required For Quantum Mechanics -- 1.1.Basic Concepts of Complex Vectorial Spaces -- 1.2.Hermitian Conjugation -- 1.3.Hermiticity and Unitarity -1.4.Algebra Operators -- ch. 2 Basis For Quantum Approaches Of Oscillators -- 2.1.Oscillator Quantization at the Historical Origin of Quantum

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Mechanics -- 2.2.Quantum Mechanics Postulates and Noncommutativity -- 2.3.Heisenberg Uncertainty Relations -- 2.4.Schrodinger Picture Dynamics -- 2.5.Position or Momentum Translation Operators -- 2.6.Conclusion -Bibliography -- ch. 3 Quantum Mechanics Representations -- 3.1.Matrix Representation -3.2.Wave Mechanics -- 3.3.Evolution Operators - 3.4.Density operators -- 3.5.Conclusion -Bibliography -- ch. 4 Simple Models Useful For Quantum Oscillator Physics -- 4.1.Particle-in-aBox Model -- 4.2.Two-Energy-Level Systems -4.3.Conclusion -- Bibliography -- pt. II SINGLE QUANTUM HARMONIC OSCILLATORS -ch. 5 Energy Representation For Quantum Harmonic Oscillator -- 5.1.Hamiltonian Eigenkets and Eigenvalues -5.2.Wavefunctions Corresponding to Hamiltonian Eigenkets -5.3.Dynamics -- 5.4.Boson and fermion operators -- 5.5.Conclusion -- Bibliography -- ch. 6 Coherent States And Translation Operators -6.1.Coherent-State Properties -- 6.2.Poisson Density Operator -- 6.3.Average and Fluctuation of Energy -- 6.4.Coherent States as Minimizing Heisenberg Uncertainty Relations -6.5.Dynamics -- 6.6.Translation Operators -6.7.Coherent-State Wavefunctions -- 6.8.FranckCondon Factors -- 6.9.Driven Harmonic Oscillators -- 6.10.Conclusion -- Bibliography -ch. 7 Boson Operator Theorems -- 7.1.Canonical Transformations -- 7.2.Normal and Antinormal Ordering Formalism -- 7.3.Time Evolution Operator of Driven Harmonic Oscillators -7.4.Conclusion -- Bibliography -- ch. 8 Phase

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Bibliography Operators And Squeezed States -- 8.1.Phase Operators -8.2.Squeezed States -8.3.Bogoliubov-Valatin transformation -8.4.Conclusion -- Bibliography -- pt. III ANHARMONICITY -- ch. 9 Anharmonic Oscillators -- 9.1.Model for Diatomic Molecule Potentials -- 9.2.Harmonic oscillator perturbed by a Q3 potential -- 9.3.Morse Oscillator -9.4.Quadratic Potentials Perturbed by Cosine Functions -- 9.5.Double-well potential and tunneling effect -- 9.6.Conclusion -- Bibliography -- ch. 10 Oscillators Involving Anharmonic Couplings -- 10.1.Fermi resonances -10.2.Strong Anharmonic Coupling Theory -10.3.Strong Anharmonic Coupling within the Adiabatic Approximation -10.4.Fermi Resonances and Strong Anharmonic Coupling within Adiabatic Approximation -- 10.5.Davydov and Strong Anharmonic Couplings -10.6.Conclusion -- Bibliography -- pt. IV OSCILLATOR POPULATIONS IN THERMAL EQUILIBRIUM -- ch. 11 Dynamics Of A Large Set Of Coupled Oscillators -- 11.1.Dynamical Equations in the Normal Ordering Formalism -11.2.Solving the linear set of differential equations (11.27) -- 11.3.Obtainment of the Dynamics -- 11.4.Application to a Linear Chain - 11.5.Conclusion -- Bibliography -- ch. 12 Density Operators For Equilibrium Populations Of Oscillators -- 12.1.Boltzmann's H-Theorem -12.2.Evolution Toward Equilibrium of a Large Population of Weakly Coupled Harmonic Oscillators -- 12.3.Microcanonical Systems -12.4.Equilibrium Density Operators from Entropy

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Maximization -- 12.5.Conclusion -- Bibliography -- ch. 13 Thermal Properties Of Harmonic Oscillators -- 13.1.Boltzmann Distribution Law inside a Large Population of Equivalent Oscillators -- 13.2.Thermal properties of harmonic oscillators -- 13.3.Helmholtz Potential for Anharmonic Oscillators -- 13.4.Thermal Average of Boson Operator Functions -13.5.Conclusion -- Bibliography -- pt. V QUANTUM NORMAL MODES OF VIBRATION -- ch. 14 Quantum Electromagnetic Modes -14.1.Maxwell Equations -14.2.Electromagnetic Field Hamiltonian -14.3.Polarized Normal Modes -- 14.4.Normal Modes of a Cavity -- 14.5.Quantization of the Electromagnetic Fields -- 14.6.Some Thermal Properties of the Quantum Fields -14.7.Conclusion -- Bibliography -- ch. 15 Quantum Modes In Molecules And Solids -15.1.Molecular Normal Modes -- 15.2.Phonons and Normal Modes in Solids -- 15.3.Einstein and Debye Models of Heat Capacity -15.4.Conclusion -- Bibliography -- pt. VI DAMPED HARMONIC OSCILLATORS -- ch. 16 Damped Oscillators -- 16.1.Quantum Model for Damped Harmonic Oscillators -- 16.2.SecondOrder Solution of Eq. (16.41) -- 16.3.FokkerPlanck Equation Corresponding to (16.114) -16.4.Nonperturbative Results for Density Operator -- 16.5.Langevin Equations for Ladder Operators -- 16.6.Evolution Operators of Driven Damped Oscillators -- 16.7.Conclusion -Bibliography -- pt. VII VIBRATIONAL SPECTROSCOPY -- ch. 17 Applications To

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Bibliography Oscillator Spectroscopy -- 17.1.IR Selection Rules for Molecular Oscillators -- 17.2.IR Spectra within the Linear Response Theory -- 17.3.IR Spectra of Weak H-Bonded Species -- 17.4.SD of Damped Weak H-Bonded Species -17.5.Approximation for Quantum Damping -17.6.Damped Fermi Resonances -- 17.7.HBonded IR Line Shapes Involving Fermi Resonance -- 17.8.Line Shapes of H-Bonded Cyclic Dimers -- Bibliography -- ch. 18 Appendix -- 18.1.An Important Commutator -- 18.2.An Important Basic Canonical Transformation -18.3.Canonical Transformation on a Function of Operators -- 18.4.Glauber-Weyl Theorem -18.5.Commutators of Functions of the P and Q operators -- 18.6.Distribution Functions and Fourier Transforms -- 18.7.Lagrange Multipliers Method -- 18.8.Triple Vector Product -18.9.Point Groups -- 18.10.Scientific Authors Appearing in the Book. Harmonic oscillators. Spectrum analysis. Wave mechanics. Hydrogen bonding. Science / Chemistry / Physical & Theoretical Includes bibliographical references and index.

Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron LCCN 2007932415 Type of material Book Personal name Fujita, Shigeji.

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Quantum theory of conducting matter: Newtonian equations of motion for a Bloch electron / Shigeji Fujita and Kei Ito. New York: Springer, c2007. xix, 244 p.: ill.; 25 cm. Contributor biographical information http://www. loc.gov/catdir/enhancements/fy0823/200793241 5-b.html Publisher description http://www.loc.gov/catdir/ enhancements/fy0823/2007932415-d.html Table of contents only http://www.loc.gov/catdir/ enhancements/fy0823/2007932415-t.html 9780387741024 038774102X QC680 .F84 2007 Ito, Kei, 1971Introduction -- Lattice vibrations and heat capacity -- Free electrons and heat capacity -Electric conduction and the Hall effect -Magnetic susceptibility -- Boltzmann equation method -- Bloch theorem -- The Fermi liquid model -- The Fermi surface -- Bloch electron dynamics -- De Haas-Van Alphen oscillations -Magnetoresistance -- Cyclotron resonance -Seebeck coefficient (Thermopower) -- Infrared Hall effect. Quantum electrodynamics. Conduction electrons--Mathematics. Equations of motion. Includes bibliographical references (p. 227-235) and index.

Refractory materials: characteristics, properties and uses LCCN 2018946817

130 Type of material Main title Published/Produced Description ISBN LC classification Related names Contents

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Bibliography Book Refractory materials: characteristics, properties and uses / Christopher Bryant, editor. New York: Nova Science Publishers, Inc., [2018] xii, 238 pages: illustrations; 24 cm. 9781536138627 TA418.26 .R455 2018 Bryant, Christopher, 1975- editor. Chapter 1. Cement Refractory Bricks Characteristics: The Importance of Mineralogical Quantification in the Evaluation of the Refractory Bricks Corrosion / Sahar Belgacem and Haykel Galai -- chapter 2. Mechanical and Thermomechanical Behavior of Refractories: From Basic Concepts to Effective Property Calculations / Willi Pabst, Eva Gregorová, Tereza Uhliřová, and Vojtěch Nečina -- chapter 3. A BiLinear Model of the Correlation between Heat Capacity and Volume Thermal Expansivity of Refractories as a Novel Tool for the Evaluation of the Reliable Numerical Data for Chemical and Physical Thermodynamics: part I. Grounds and Modelling / Vladimir Yu. Bodryakov -- chapter 4. A Bi-Linear Model of the Correlation between Heat Capacity and Volume Thermal Expansivity of Refractories as a Novel Tool for the Evaluation of the Reliable Numerical Data for Chemical and Physical Thermodynamics: part II. Application to Periclase and Corundum / Vladimir Yu. Bodryakov. Refractory materials. Includes bibliographical references and index. Construction materials and engineering

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Statistical thermodynamics LCCN 2017932602 Type of material Book Personal name Maczek, Andrew, author. Main title Statistical thermodynamics / Andrew Maczek, Anthony Meijer. Edition Second edition. Published/Produced Oxford: Oxford University Press, [2017] ©2017 Description x, 120 pages: illustrations; 25 cm. ISBN 9780198777489 (pbk.) 0198777485 (pbk.) LC classification QD504 .M23 2017 Related names Meijer, Anthony, author. Summary "'Statistical thermodynamics' gives a concise and accessible account of this fundamental topic by emphasizing the underlying physical chemistry at the atomic and molecular level, while introducing the mathematical concepts in an approachable way. The material is presented in short, selfcontained sections, making it flexible both for learning and for teaching. The separate sections are finally brought together by a series of detailed applications to real systems. Throughout the text, frequent diagrams and marginal notes are provided to support learning. End-of-chapter problems are included to encourage active participation and thus promote deeper understanding. New to this edition: an online resource centre with interactive questions for students and downloadable figures for instructors; new end-ofchapter summaries help you understand the key 'take home' points for each topic; new numerical

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Bibliography problems at the end of the book enable you to practice using the material covered in the primer to solve novel problems; [and] an appendix covering additional mathematics, for those who wish to extend their understanding in a more formal and detailed manner." -- rear cover. The Boltzmann law -- Sum over states: the molecular partition function -- Applications of the molecular partition function -- From molecule to mole: the canonical partition function -Distinguishable and indistinguishable particles -Two-level systems: a case study -Thermodynamic functions: towards a statistical toolkit -- The ideal monatomic gas: the translational partition function -- The ideal diatomic gas: internal degrees of freedom -- The ideal diatomic gas: the rotational partition function -- ortho and para spin states: a case study -- The ideal diatomic gas: the vibrational partition function -- The electronic partition function -Heat capacity and Third Law entropy: two case studies -- Calculating equilibrium constants. Statistical thermodynamics. Statistical thermodynamics. Textbooks. Textbooks. Previous edition: 1998. Includes bibliographical references and index. Oxford chemistry primers Oxford chemistry primers.

Steam Systems: Performance Improvement Opportunities LCCN 2014395226 Type of material Book

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Steam Systems: Performance Improvement Opportunities / Sadie M. Baker and Valerie Parker, Editors. New York: Nova Science Publishers, Inc. [2012] xvi, 181 pages: illustrations; 27 cm. 9781620815632 162081563X TJ277 .S826 2012 Baker, Sadie M., editor. Parker, Valerie, editor. "There are three principal forms of energy used in industrial processes: electricity, direct-fired heat, and steam. Steam provides process heating, pressure control, mechanical drive, and component separation, and is a source of water for many process reactions. Steam has many performance advantages that make it an indispensable means of delivering energy. These advantages include low toxicity, ease of transportability, high efficiency, high heat capacity, and low cost with respect to the other alternatives. This book is designed to provide steam system users with a reference that describes the basic steam system components, outlines opportunities for energy and performance improvements, and discusses the benefits of a systems approach in identifying and implementing these improvement opportunities"-Page [ix]. Steam engineering. Steam-heating. Includes index. Energy Science, Engineering and Technology

134 Superconductors LCCN Type of material Personal name Main title Edition Published/Produced Description Links

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2014933417 Book Narlikar, A. V., 1940- author. Superconductors / A.V. Narlikar. First edition. Oxford, United Kingdom: Oxford University Press, 2014. xii, 477 pages: illustrations; 26 cm. Contributor biographical information http://www. loc.gov/catdir/enhancements/fy1604/201493341 7-b.html Publisher description http://www.loc.gov/catdir/ enhancements/fy1604/2014933417-d.html Table of contents only http://www.loc.gov/catdir/ enhancements/fy1604/2014933417-t.html 9780199584116 0199584117 QC611.95 .N37 2014 "Superconductors is neither about basic aspects of superconductivity nor about its applications, but its main focus is on superconducting materials themselves. Unusual and unconventional features of a large variety of novel superconductors are presented and their technological potential as practical superconductors assessed. The presentation is readily accessible to readers from a diverse range of scientific and technical disciplines, such as metallurgy, materials science, materials engineering, electronic and device engineering, and chemistry. The derivation of mathematical formulas and equations has been kept to a minimum and, wherever necessary, short appendices with essential mathematics have been

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added at the end of the text. The book is not meant to serve as an encyclopaedia, describing each and every superconductor that exists, but focuses on important milestones in their exciting development."-- Page 4 of cover. 1. Onnes' discovery and one hundred years of superconductors. Onnes' discovery -- One hundred years of superconductors -- Progress with LTS and HTS applications -- This book -Summary -- 2. The superconducting state. Electrical conduction in metals and the origin of resistance -Microscopic nature of superconducting state -- Summary -- Appendix 2A. BCS ground state and the energy gap -- 3. The superconducting transition and its basic phenomenology. Fundamental characteristics of the superconducting transition -- The critical field Hc -- The critical current -- Resistive transition -Implications of perfect conductivity -- Meissner-Ochsenfeld effect -- London phenomenology -Penetration depth -- Departing current density -Shortcomings of the London phenomenology -Intermediate state -- Filamentary superconductors and Mendelssohn's sponge -- Range of coherence and non-local theory -- Interface boundary energy -- Summary -- Appendix 3A. Electrodynamics of a perfect conductor and London phenomenology -- 4. Thermodynamics and general properties. Thermodynamic aspects of the transition -Thermal properties -- Ultrasonic behaviour -- AC and optical properties -- Tunnelling in the superconducting state -- Summary -- Appendix 4A. Condensation energy -- Entropy -- Heat capacity -- 5. Advent of type II superconductors.

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Bibliography Ginzburg--Landau phenomenology -- Sign of the surface energy and superconductor types -- Mixed state and other characteristics -- Summary -Appendix 5A. Ginzburg--Landau equations -- 6. Critical current and flux pinning. Transport current in the mixed state -- Driving force and the critical state -- Vortex motion -- Stabilisation of superconductors -- Pinning centres -- Pinning interactions -- AC losses -- Summary -- 7. Superconductors in abundance. Low-temperature superconductors (LTS) -- High-temperature superconductors (HTS) -- Summary -- 8. Niobium--zirconium and niobium--titanium alloys. The niobium--zirconium system -- The niobium--titanium system -- Summary --9. A-15 superconductors. Crystal structure, stoichiometry, and ordering -- Long-range order and Tc -Structural instability at low temperature -Potential binary systems -- Pseudo-binaries -- A15 phase formation -- Upper critical field and paramagnetic limitation -- Critical current density and the nature of pinning centres in A-15s -Strain sensitivity -- Summary -- 10. Conductor development of A-15 superconductors. Liquidsolute diffusion -- CVD process -- The bronze process and formation of A-15 phase by solid state diffusion -- Thermodynamics and kinetics of compound-layer formation in the bronze process -- Modifications of the bronze process -Fabrication of Nb3Al conductor -- Summary -11. Chevrel-phase superconductors. Crystal structure and stoichiometry -- Occurrence of superconductivity in Chevrel phases -- Synthesis of bulk samples -- Upper critical field -- Critical

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current density: inherent problems and progress in raisingJc -- Conductor development of Chevrelphase compounds -- Nature of superconductivity of Chevrel-phase compounds -- Summary -- 12. Rare-earth-based ternary superconductors and quaternary borocarbides. LTS systems with magnetic order -- The interplay -- Various ternary materials and their interplay behaviour -Quaternary borocarbides -- Crystal structure and related aspects -- Coexistence and interplay of Tc and Tm -- Summary --13. Heavy fermion superconductors. Discovery of HF superconductors -- Quantum phase transition and quantum critical point -- General features of anomalous normal state and unusual superconductivity -- Short description of various HF superconductors -- Special features of HF superconductors -- Summary -- 14. Organic superconductors. Evolution of organic superconducting salts -- The (TM)2 family of quasi-one-dimensional superconductors -- The (ET)2 family of quasi-two-dimensional superconductors -- Superconducting fullerides -Graphite intercalation compounds (GICs) -Summary -- 15. Superconducting magnesium diboride. Crystal structure and Tc -- Conventional superconductivity of MgB2 -- Band structure and two superconducting gaps -- Implications of two gaps -- MgB2 for practical applications -Material synthesis -- Nanoparticle doping for enhancingJc -- Conductor development: wires and tapes of MgB2 -- Summary -- 16. Hightemperature cuprate superconductors. Genesis of HTS cuprates -- General features of HTS cuprates

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Bibliography -- Prominent HTS cuprate systems -- Substitution studies in HTS -- Summary --17. Thin-film technology and conductor development of HTS cuprates. Microstructural aspects -- Prominent techniques for depositing HTS films -- Conductor development -- Summary -- 18. Bulk HTS cuprates. General considerations -- Melt processing of bulk YBCO samples -- Effective pinning centres in bulk HTS -- Ternary 123 bulk compounds -- Trapped field -- Mechanical strengthening -- Summary -- 19. Ruthenates and ruthenocuprates. A superconductor in the ruthenate family: Sr2RuO4 -- Unconventional superconductivity -- Summary of the current status of ruthenate superconductors -Superconducting ruthenocuprates -Superconductivity, general features -- Magnetic states and coexistence of TM and Tc -- Cationic substitutions in Ru-1212 and Ru-1222, effect on Tc and TM -- Summary -- 20. Iron-based superconductors. Different FBS families, their crystal structures, and their general features -Electronic structure -- Phase diagrams -Unconventional superconductivity of FBS -Materials synthesis -- Upper critical field, anisotropy, and potential for applications -Summary -- 21. Miscellaneous superconductors. Superconducting bismuthates -- Cobalt oxide hydrate -- Intermetallic perovskites free from oxygen: MgCNi3 and related superconducting compounds -- Metallonitride halides -- Pyrochlore oxides -- Layered transition metal chalcogenides -- BiS2-based superconductors. Superconductors.

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The basics of heat LCCN Type of material Personal name Main title Edition Published/Produced Description ISBN LC classification Summary

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Materials science. Materials science. Superconductors. Supraleiter. Includes bibliographical references (pages 431470) and index.

2014005199 Book Clark, John O. E., 1937- author. The basics of heat / John O.E. Clark. 2015 edition. New York: Rosen Publishing, 2015. 96 pages: illustrations (some color); 25 cm. 9781477777640 (library bound) 1477777644 (library bound) QC256 .C53 2015 "We often automatically equate heat with temperature to such a degree that we may not take the time to consider what heat really is. Heat refers to the energy that is transferred from one body to another that is at a lower temperature. This transfer occurs often without us knowing it, but it is ever-present and crucial to all life. This volume examines the basics of heat and the related concept of temperature. Detailed diagrams help illustrate such concepts as specific heat capacity and latent heat. Clear text explains the difference between conduction, convection, and radiation, as well as emitters, absorbers, and more"-- Provided by publisher. The power of heat -- How is heat produced? -Measuring heat -- How thermometers work --

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Bibliography Reacting to heat -- Changing states -- Fluid and gas expansion -- Expanding solids -- Conductors and insulators -- Circulating heat -- Radiation and infrared rays -- Trapping and emitting radiation -From hot to cold -- Biography: James Watt. Heat--Juvenile literature. Heat--Transmission--Juvenile literature. Includes bibliographical references (page 90) and index. Grades 7-12. Core concepts

The science and engineering of materials LCCN 2010932702 Type of material Book Personal name Askeland, Donald R. Main title The science and engineering of materials / Donald R. Askeland, Pradeep P. Fulay, Wendelin J. Wright. Edition 6th ed. [SI ed.]. Published/Created Stamford, CT: Cengage Learning, c2011. Description xxi, 921 p.: ill. (some col.); 27 cm. ISBN 0495296023 (hbk.) 9780495668022 (pbk.: SI ed.) 0495668028 (pbk.: SI ed.) LC classification TA403 .A74 2011 Related names Fulay, Pradeep P., 1960Wright, Wendelin J. Contents Machine generated contents note: ch. 1 Introduction to Materials Science and Engineering -- 1. What is Materials Science and Engineering? -- 1-2. Classification of Materials -1-3. Functional Classification of Materials -- 1-4. Classification of Materials Based on Structure --

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1-5. Environmental and Other Effects -- 1-6. Materials Design and Selection -- Summary -Glossary -- Problems -- ch. 2 Atomic Structure -2-1. The Structure of Materials: Technological Relevance -- 2-2. The Structure of the Atom -- 23. The Electronic Structure of the Atom -- 2-4. The Periodic Table -- 2-5. Atomic Bonding -- 26. Binding Energy and Interatomic Spacing -- 27. The Many Forms of Carbon: Relationships Between Arrangements of Atoms and Materials Properties -- Summary -- Glossary -- Problems -ch. 3 Atomic and lonic Arrangements -- 3-1. Short-Range Order versus Long-Range Order -3-2. Amorphous Materials -- 3-3. Lattice, Basis, Unit Cells, and Crystal Structures -- 3-4. Allotropic or Polymorphic Transformations 3-5. Points, Directions, and Planes in the Unit Cell -3-6. Interstitial Sites -- 3-7. Crystal Structures of Ionic Materials -- 3-8. Covalent Structures -- 3-9. Diffraction Techniques for Crystal Structure Analysis -- Summary -- Glossary -- Problems -ch. 4 Imperfections in the Atomic and lonic Arrangements -- 4-1. Point Defects -- 4-2. Other Point Defects -- 4-3. Dislocations -- 4-4. Significance of Dislocations -- 4-5. Schmid's Law -- 4-6. Influence of Crystal Structure -- 4-7. Surface Defects -- 4-8. Importance of Defects -Summary -- Glossary -- Problems -- ch. 5 Atom and lon Movements in Materials -- 5-1. Applications of Diffusion -- 5-2. Stability of Atoms and Ions -- 5-3. Mechanisms for Diffusion -- 5-4. Activation Energy for Diffusion -- 5-5. Rate of Diffusion [Fick's First Law] -- 5-6. Factors Affecting Diffusion -- 5-7. Permeability of

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Bibliography Polymers -- 5-8. Composition Profile [Fick's Second Law] -- 5-9. Diffusion and Materials Processing -- Summary -- Glossary -- Problems - ch. 6 Mechanical Properties: Part One -- 6-1. Technological Significance6-2. Terminology for Mechanical Properties -- 6-3. The Tensile Test: Use of the Stress-Strain Diagram -- 6-4. Properties Obtained from the Tensile Test -- 6-5. True Stress and True Strain -- 6-6. The Bend Test for Brittle Materials -- 6-7. Hardness of Materials -- 6-8. Nanoindentation -- 6-9. Strain Rate Effects and Impact Behavior -- 6-10. Properties Obtained from the Impact Test -- 6-11. Bulk Metallic Glasses and Their Mechanical Behavior -- 6-12. Mechanical Behavior at Small Length Scales -Summary -- Glossary -- Problems -- ch. 7 Mechanical Properties: Part Two -- 7-1. Fracture Mechames -- 7-2. The Importance of Fracture Mechanics -- 7-3. Microstructural Features of Fracture in Metallic Materials -- 7-4. Microstructural Features of Fracture in Ceramics, Glasses, and Composites -- 7-5. Weibull Statistics for Failure Strength Analysis -- 7-6. Fatigue -- 77. Results of the Fatigue Test -- 7-8. Application of Fatigue Testing -- 7-9. Creep, Stress Rupture, and Stress Corrosion -- 7-10. Evaluation of Creep Behavior -- 7-11. Use of Creep Data -- Summary -- Glossary -- Problems Ch. 8 Strain Hardening and Annealing -- 8-1. Relationship of Cold Working to the Stress-Strain Curve -- 8-2. StrainHardening Mechanisms -- 8-3. Properties versus Percent Cold Work -- 8-4. Microstructure, Texture Strengthening, and Residual Stresses -- 85. Characteristics of Cold Working -- 8-6. The

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Three Stages of Annealing -- 8-7. Control of Annealing -- 8-8. Annealing and Materials Processing -- 8-9. Hot Working -- Summary -Glossary -- Problems -- ch. 9 Principles of Solidification -- 9-1. Technological Significance - 9-2. Nucleation -- 9-3. Applications of Controlled Nucleation -- 9-4. Growth Mechanisms -- 9-5. Solidification Time and Dendrite Size -- 9-6. Cooling Curves -- 9-7. Cast Structure -- 9-8. Solidification Defects -- 9-9. Casting Processes for Manufacturing Components -- 9-10. Continuous Casting and Ingot Casting -- 9-11. Directional Solidification [DS], Single Crystal Growth, and Epitaxial Growth -- 9-12. Solidification of Polymers and Inorganic Glasses -- 9-13. Joining of Metallic Materials -- Summary -- Glossary -- Problems -ch. 10 Solid Solutions and Phase Equilibrium 101. Phases and the Phase Diagram -- 10-2. Solubility and Solid Solutions -- 10-3. Conditions for Unlimited Solid Solubility -- 10-4. SolidSolution Strengthening -- 10-5. Isomorphous Phase Diagrams -- 10-6. Relationship Between Properties and the Phase Diagram -- 10-7. Solidification of a Solid-Solution Alloy -- 10-8. Nonequilibrium Solidification and Segregation -Summary -- Glossary -- Problems -- Chatper 11 Dispersion Strengthening and Eutectic Phase Diagrams -- 11-1. Principles and Examples of Dispersion Strengthening -- 11-2. Intermetallic Compounds -- 11-3. Phase Diagrams Containing Three-Phase Reactions -- 11-4. The Eutectic Phase Diagram -- 11-5. Strength of Eutectic Alloys -- 11-6. Eutectics and Materials Processing

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Bibliography -- 11-7. Nonequilibrium Freezing in the Eutectic System -- 11-8. Nanowires and the Eutectic Phase Diagram -- Summary -- Glossary -- Problems -ch. 12 Dispersion Strengthening by Phase Transformations and Heat Treatment -- 12-1. Nucleation and Growth in Solid-State Reactions - 12-2. Alloys Strengthened by Exceeding the Solubility Limit12-3. Age or Precipitation Hardening -- 12-4. Applications of Age-Hardened Alloys -- 12-5. Microstructural Evolution in Age or Precipitation Hardening -- 12-6. Effects of Aging Temperature and Time -- 12-7. Requirements for Age Hardening -- 12-8. Use of Age-Hardenable Alloys at High Temperatures -12-9. The Eutectoid Reaction -- 12-10. Controlling the Eutectoid Reaction -- 12-11. The Martensitic Reaction and Tempering -- 12-12. The Shape-Memory Alloys [SMAs] -- Summary -- Glossary -- Problems -- ch. 13 Heat Treatment of Steels and Cast Irons -- 13-1. Designations and Classification of Steels -- 13-2. Simple Heat Treatments -- 13-3. Isothermal Heat Treatments - 13-4. Quench and Temper Heat Treatments -13-5. Effect of Alloying Elements -- 13-6. Application of Hardenability -- 13-7. Specialty Steels -- 13-8. Surface Treatments -- 13-9. Weldability of Steel -- 13-10. Stainless Steels -13-11. Cast Irons -- Summary -- Glossary -Problems -- ch. 14 Nonferrous Alloys -- 14-1. Aluminum Alloys -- 14-2. Magnesium and Beryllium Alloys14-3. Copper Alloys -- 14-4. Nickel and Cobalt Alloys -- 14-5. Titanium Alloys -- 14-6. Refractory and Precious Metals -Summary -- Glossary -- Problems -- ch. 15

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Ceramic Materials -- 15-1. Applications of Ceramies -- 15-2. Properties of Ceramics -- 15-3. Synthesis and Processing of Ceramic Powders -15-4. Characteristics of Sintered Ceramics -- 155. Inorganic Glasses -- 15-6. Glass-Ceramics -15-7. Processing and Applications of Clay Products -- 15-8. Refractories -- 15-9. Other Ceramic Materials -- Summary -- Glossary -Problems -- ch. 16 Polymers -- 16-1. Classification of Polymers -- 16-2. Addition and Condensation Polymerization -- 16-3. Degree of Polymerization -- 16-4. Typical Thermoplastics - 16-5. Structure -- Property Relationships in Thermoplastics -- 16-6. Effect of Temperature on Thermoplastics -- 16-7. Mechanical Properties of Thermoplastics -- 16-8. Elastomers [Rubbers] -16-9. Thermosetting Polymers -- 16-10. Adhesives -- 16-11. Polymer Processing and Recycling -- Summary -- Glossary -- Problems Ch. 17 Composites: Teamwork and Synergy in Materials -- 17-1. Dispersion-Strengthened Composites -- 17-2. Particulate Composites -- 173. Fiber-Reinforced Composites -- 17-4. Characteristics of Fiber-Reinforced Composites - 17-5. Manufacturing Fibers and Composites -17-6. Fiber-Reinforced Systems and Applications -- 17-7. Laminar Composite Materials -- 17-8. Examples and Applications of Laminar Composites -- 17-9. Sandwich Structures -Summary -- Glossary -- Problems -- ch. 18 Construction Materials -- 18-1. The Structure of Wood -- 18-2. Moisture Content and Density of Wood -- 18-3. Mechanical Properties of Wood -18-4. Expansion and Contraction of Wood -- 18-

146

Bibliography 5. Plywood -- 18-6. Concrete Materials -- 18-7. Properties of Concrete -- 18-8. Reinforced and Prestressed Concrete -- 18-9. Asphalt -- Summary -- Glossary -- Problems -- ch. 19 Electronic Materials -- 19-1. Ohm's Law and Electrical Conductivity -- 19-2. Band Structure of Solids -19-3. Conductivity of Metals and Alloys -- 19-4. Semiconductors19-5. Applications of Semiconductors -- 19-6. General Overview of Integrated Circuit Processing -- 19-7. Deposition of Thin Films -- 19-8. Conductivity in Other Materials -- 19-9. Insulators and Dielectric Properties -- 19-10. Polarization in Dielectrics -19-11. Electrostriction, Piezoelectricity, and Ferroelectricity -- Summary -- Glossary -Problems -- ch. 20 Magnetic Materials -- 20-1. Classification of Magnetic Materials -- 20-2. Magnetic Dipoles and Magnetic Moments -- 203. Magnetization, Permeability, and the Magnetic Field -- 20-4. Diamagnetic, Paramagnetic, Ferromagnetic, Ferrimagnetic, and Superparamagnetic Materials -- 20-5. Domain Structure and the Hysteresis Loop -- 20-6. The Curie Temperature 20-7. Applications of Magnetic Materials -- 20-8. Metallic and Ceramic Magnetic Materials -- Summary -- Glossary -Problems -- ch. 21 Photonic Materials -- 21-1. The Electromagnetic Spectrum -- 21-2. Refraction, Reflection, Absorption, and Transmission -- 21-3. Selective Absorption, Transmission, or Reflection -- 21-4. Examples and Use of Emission Phenomena -- 21-5. Fiber-Optic Communication System -- Summary -- Glossary -- Problems -- ch. 22 Thermal Properties of Materials -- 22-1. Heat

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Capacity and Specific Heat -- 22-2. Thermal Expansion -- 22-3. Thermal Conductivity -- 22-4. Thermal Shock -- Summary -- Glossary -Problems -- ch. 23 Corrosion and Wear -- 23-1. Electrochemical Corrosion -23-2. Electrochemical Corrosion -- 23-3. The Electrode Potential in Electrochemical Cells -- 23-4. The Corrosion Current and Polarization -- 23-5. Types of Electrochemical Corrosion -- 23-6. Protection Against Electrochemical Corrosion -- 23-7. Microbial Degradation and Biodegradable Polymers -- 23-8. Oxidation and Other Gas Reactions -- 23-9. Wear and Erosion -- Summary -- Glossary -- Problems. Materials. Materials science. Includes index.

The science of construction materials LCCN 2009935456 Type of material Book Personal name Hansen, Per Freiesleben. Uniform title Materialefysik for Bygningsingeniører. English Main title The science of construction materials / Per Freiesleben Hansen; edited by Ole Mejlhede Jensen. Edition [English ed.]. Published/Created Heidelberg; New York: Springer, c2009. Description 1 v. (various pagings): ill.; 29 cm. Links Contributor biographical information http://www. loc.gov/catdir/enhancements/fy1109/200993545 6-b.html Publisher description http://www.loc.gov/catdir/ enhancements/fy1109/2009935456-d.html

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Bibliography Table of contents only http://www.loc.gov/catdir/ enhancements/fy1109/2009935456-t.html 9783540708971 3540708979 9783540708988 (e-ISBN) 3540708987 (e-ISBN) TA403.6 .H36513 2009 Jensen, Ole Mejlhede. 1. System of matter: Atoms; Relative atomic mass; Relative molecular mass; Amount of substance: the mole; Molar mass; Mixture of substances; The ideal gas law; Ideal gas mixture; Real gases; Intermolecular forces; Critical temperature; SI units -- 2. Thermodynamic concepts: Thermodynamic system; Description of state; Thermodynamic variables; Work; Heat; Thermodynamic process -- 3. First law: Energy; First law; Internal energy U; Enthalpy H; Ideal gas; Isothermal change of state; A diabatic change of state; Thermochemical equation; Standard enthalpy; Reactive enthalpy -- 4. Second law: Introduction; The Carnot cycle; Second law; Temperature dependence of entropy; Entropy change, ideal gas; Entropy change by phase transformation; Standard entropy; Reaction entropy; Chemical equilibrium; The concept of entropy -- 5. Calculations of equilibrium: The Gibbs free energy; THe Clapeyron equation; The Clausius- Clapeyron equation -- Activity -Thermodynamic equilibrium constant -Temperature dependence of equilibrium -- 6. Electrochemistry: Electric current and charge; Electric potential; Electric conductivity; Electrochemical reaction; Electrochemical

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potential; The Nernst equation; Temperature dependence of the potential; Notation rules; Standard potential; Passivation -- App.A. Mathematical appendix: Numerical calculations; Dimensional analysis; Newton-Raphson iteration; Cramer's formula; Linear regression; Exact differential; Gradient field; Maxwell's relations; Debye-Hückel's law; App.B. Tables: Physical constants; Elements; Vander Waals constants; Thermochemical data 1. Inorganic compounds; Thermochemical data 2. Cement-chemical compounds; Thermochemical data 3. Organic compounds; Molar heat capacity; Surface tension; Electrochemical standard potential; Water and water vapour -- App.C. Solutions to check-up questions and exercises. Building materials. Materials science. Building materials--Problems, exercises, etc. Building materials--Effect of temperature on. Includes bibliographical references and index.

Thermal physics: concepts and practice LCCN 2011036379 Type of material Book Personal name Wasserman, Allen L. Main title Thermal physics: concepts and practice / Allen L. Wasserman. Published/Created Cambridge, UK; New York: Cambridge University Press, 2012. Description xiii, 303 p.; 26 cm. Links Cover image http://assets.cambridge.org/9781 1070/06492/cover/9781107006492.jpg ISBN 9781107006492 (hardback)

150 LC classification Summary

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Bibliography QC311 .W37 2012 "Thermodynamics has benefited from nearly 100 years of parallel development with quantum mechanics. As a result, thermal physics has been considerably enriched in concepts, technique and purpose, and now has a dominant role in the developments of physics, chemistry and biology. This unique book explores the meaning and application of these developments using quantum theory as the starting point. The book links thermal physics and quantum mechanics in a natural way. Concepts are combined with interesting examples, and entire chapters are dedicated to applying the principles to familiar, practical and unusual situations. Together with end-of-chapter exercises, this book gives advanced undergraduate and graduate students a modern perception and appreciation for this remarkable subject"-- Provided by publisher. Machine generated contents note: 1. Introducing thermodynamics; 2. Onward to thermodynamics; 3. The First Law; 4. A mathematical digression; 5. Thermodynamics potentials; 6. On knowing the unknowable; 7. The ideal gas; 8. The 2-level system; 9. Lattice heat capacity; 10. Elastomers entropy springs; 11. Thermodynamics of magnetism; 12. Open systems; 13. The amazing chemical potential; 14. Thermodynamics of radiation; 15. Ideal Fermi gas; 16. Ideal BoseEinstein system; 17. Thermodynamics and the CMB; Appendices; Index. Thermodynamics. Entropy. Statistical mechanics.

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Science / Physics Includes bibliographical references and index.

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BI-LINEAR MODEL OF CORRELATION BETWEEN HEAT CAPACITY AND VOLUME THERMAL EXPANSIVITY OF SOLIDS AS A NOVEL TOOL FOR EVALUATION THE RELIABLE NUMERICAL DATA FOR PURPOSES OF CHEMICAL THERMODYNAMICS: APPLICATION TO RARE GAS SOLIDS

Vladimir Yu. Bodryakov Head of the Department of Higher Mathematics, Ural State Pedagogical University, Yekaterinburg, Russia

Series: Physics Research and Technology ISBN: 978-1-53613-387-5 Binding: e-Book Publication Date: 2018

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A systematic study of basic thermodynamic functions of Rare Gas Solids (RGS) has been undertaken through the whole range of their solid states. These functions were: isobaric molar heat capacity CP(T), volume coefficient of thermal expansion β(T), molar volume V(T), differential Grüneisen parameter γ′(T), etc. In the first section of the monograph, the thermodynamic grounds are considered for hypothesizing bi-linear correlation β(CP) between heat capacities and volume thermal expansivities of non-metal solids up to the melting points (the B-model). Theoretical consideration is made within anharmonic Debye-Grüneisen model without taking into account and taking into account of the Frenkel defects that influences in the premelting range. Mathematical relations for the B-model are also formulated. The algorithm has been described in detail of the B-model application with the use of least squares method for computer analysis of scattered primary experimental data (CP(T), β(T), β(CP)), etc. In the second section of the monograph, the computer thermodynamic model calculations have been done within the anharmonic Debye model without taking into account and taking into account the influence of Frenkel defects in the premelting range. The validity of the B-model was verified in respect of the results of model calculations. The effect of changing model parameters is evaluated within the framework of the model. In the third section of the monograph, the thermodynamic functions of RGS Ne, Ar, Kr, and Xe were estimated up to the melting points Tm using the B-model. The choice of RGS as model objects is due to the fact that they have quite representative thermodynamic data, they are not subjected to polymorphic transformations in the solid state, they do not have conduction electrons, the effects of anharmonicity and premelting processes are most obvious in RGS. A detailed critical analysis has been carried out of the available primary sources of various data on thermodynamic properties of RGS.

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HEAT CAPACITY OF RARE-EARTH ALUMINUM GARNETS AND PECULIARITIES OF TRANSPORT CHARACTERISTICS OF PHONONS CAUSED BY THE SCHOTTKY ANOMALIES AT LOW TEMPERATURES *

E. N. Khazanov1, A. V. Taranov1,†, E. V. Charnaya2 and E. V. Shevchenko2 1

Kotel’nikov Institute of Radio Engineering and Electronics, Moscow, Russia 2 St. Petersburg State University, St. Petersburg, Russia

Materials with a complex structure, such as single crystals of yttrium– rare earth–aluminum garnet solid solutions Y3-xRexAl5O12 (YAG:Re), are widely used in engineering and physical investigations. Measurements of heat capacity of Y3-xErxAl5O12 (x = 0, 0.6, 1.1, 3), and mixed Er3-xTmx Al5O12, (x = 0, 1, 2, 3) and Er2HoAl5O12 solid solutions were carried out in the temperature range from 1.9 to 220 K in zero magnetic field and in magnetic fields up to 9T. The heat capacity variations at low temperatures were dominated by the Schottky anomalies. At higher temperatures the phonon contribution played the major role. The heat capacity was fitted by a sum of the Debye, Einstein, and Schottky contributions. The entropy and magnetic entropy were evaluated. The magnetic entropy magnitude suggests the application of these garnets in adiabatic demagnetization refrigerators. In addition, anomalous sharp steps in temperature dependence of the heat capacity were observed in Er2HoAl5O12 in magnetic fields stronger than 8 T upon cooling as well as upon warming. The temperatures at which occur

*

The full version of this chapter can be found in Crystal Structure: Properties, Characterization and Determination, edited by Damon Richards, published by Nova Science Publishers, Inc, New York, 2018. † Corresponding Author’s Email: [email protected].

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these steps increase with increasing magnetic field. The steps were shifted relative to each other upon cooling and warming showing the thermal hysteresis. The sharp decrease in the heat capacity at low temperatures suggested the blocking of magnetic flips induced by strong enough magnetic fields. The temperature and concentration dependences of the transport characteristics of thermal frequency phonons were measured in the same solid solutions. The temperature dependences of the heat capacity and the kinetic characteristics are similar at helium temperatures. It was found that these dependences are caused by the presence of low energy levels. The peculiarities of transport characteristics of phonons at low temperatures caused by the Schottky anomalies were investigated.

A BI-LINEAR MODEL OF THE CORRELATION BETWEEN HEAT CAPACITY AND VOLUME THERMAL EXPANSIVITY OF REFRACTORIES AS A NOVEL TOOL FOR THE EVALUATION OF THE RELIABLE NUMERICAL DATA FOR CHEMICAL AND PHYSICAL THERMODYNAMICS PART I. GROUNDS AND MODELLING *

Vladimir Yu. Bodryakov† Head of the Department of Higher Mathematics, Ural State Pedagogical University, Yekaterinburg, Russia A systematic joint study of the temperature dependences of the isobaric molar heat capacity CP(T) and the thermal expansion coefficient β(T) of polyatomic solids was carried out using the example of refractory oxide *

The full version of this chapter can be found in Refractory Materials: Characteristics, Properties and Uses, edited by Christopher Bryant, published by Nova Science Publishers, Inc, New York, 2018. † Corresponding Author: Vladimir Yu. Bodryakov. Ural State Pedagogical University, prosp. Kosmonavtov, 26, 620017 Yekaterinburg, Russia. Email: [email protected].

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ceramics: periclase, MgO and corundum, Al2O3. Both ceramics have the widest practical applications and are considered reference materials, which justifies their choice for research. A systematic study of the thermodynamic properties associated with the heat capacity and volumetric expansion (namely, a change in the molar enthalpy, molar entropy, molar volume, etc.) was carried out. The chapter consists of two interrelated, but self-sufficient parts. The experimental and theoretical grounds for the hypothesis of a twoline correlation model (the B-model) added with computer simulation are considered in Part I. The B-model is used for a systematic analysis of the thermodynamic properties of refractory solids in Part II using refractory oxide ceramics, periclase, MgO and corundum, Al2O3. A preliminary analysis within the Debye-Grüneisen anharmonic model showed, in particular, that the existing numerous and widely used interpolations of the observed heat capacity CP(T) at elevated and high temperatures do not have a proper thermodynamic justification. Taking into account the temperature dependence of the Debye temperature θ = θ(T), the change in the molar enthalpy ΔH(T) = H(T) – H0 was expanded in a series in integral powers of the temperature T. The corresponding representation for the molar heat capacity assumes a thermodynamically single-valued form of CP(T) = a + bT – cT–2 + dT2 + ..., where the constant, with respect to the T, coefficients a, b, c, d, ..., depend on the pressure P and, as a rule, is nonnegative. An analogous expansion was obtained for the volume thermal expansion coefficient β(T). It is noted that the correct choice of the temperature range in which such an expansion is carried out is important. Model calculations show that there is a close relationship between the molar heat capacity of CP(T) and the volume expansivity β(T) from the selected refractory oxide ceramics, as well as for many other previously considered simple solids; the correlation has a characteristic two-line shape (the B-model). More precisely, the correlation dependence of β(CP) consists of two smoothly conjugate linear segments with “upward bend” (kink up),

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occurring approximately at the classical Dulong and Petit limit 3νR for the heat capacity; ν is the number of atoms per unit of the formula, and R is the gas constant. With the example of ceramic MgO and Al2O3, it is convincingly shown that the bi-linear correlation β(CP) can serve as a reliable modern tool for obtaining missing and checking the existing quantitative data for chemical and physical thermodynamics. In the control of the B-model, mutually consistent calorimetric (change in molar enthalpy, molar entropy, reduced thermodynamic potential) and dilatometry data (molar volume, volume expansion coefficient) were obtained and tabulated in the whole solid state range of the ceramics. Other important thermodynamic values for the ceramics were also established. The approach based on the B-model is universal and easy to use. It can be successfully applied to obtain missing and / or validated information on the thermodynamic properties of substances of various types, to replenish thermodynamic databases with reliable data.

A BI-LINEAR MODEL OF THE CORRELATION BETWEEN HEAT CAPACITY AND VOLUME THERMAL EXPANSIVITY OF REFRACTORIES AS A NOVEL TOOL FOR THE EVALUATION OF THE RELIABLE NUMERICAL DATA FOR CHEMICAL AND PHYSICAL THERMODYNAMICS. PART II. APPLICATION TO PERICLASE AND CORUNDUM *

Vladimir Yu. Bodryakov† Head of the Department of Higher Mathematics, Ural State Pedagogical University, Yekaterinburg, Russia *

The full version of this chapter can be found in Refractory Materials: Characteristics, Properties and Uses, edited by Christopher Bryant, published by Nova Science Publishers, Inc, New York, 2018. † Corresponding author: Vladimir Yu. Bodryakov. Ural State Pedagogical University, prosp. Kosmonavtov, 26, 620017 Yekaterinburg, Russia. E-mail address: [email protected].

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In Part II, the B-model is applied to a joint study of the temperature dependences of the basic thermodynamic functions of the selected refractory oxide ceramics, namely, periclase, MgO, and corundum, Al2O3. First of all, the isobaric molar heat capacity CP(T), the thermal expansion coefficient β(T), and their correlation, β(CP), between T = 0 and the melting temperature Tm were investigated. In the control of the B-model, mutually consistent calorimetric (change of the molar enthalpy, the molar entropy, the reduced thermodynamic potential) and dilatometric (the molar volume, the volume coefficient of thermal expansion) quantitative data were obtained and tabulated for MgO and Al2O3. Other important thermodynamic values for the ceramics were also established. A detailed comparison was made with the corresponding literary data.

UNFOLDING THERMODYNAMICS OF NUCLEIC ACIDS: DETERMINING HEAT CAPACITY EFFECTS USING DIFFERENTIAL SCANNING CALORIMETRY (DSC) *

Carolyn E. Carr1, Calliste Reiling-Steffensmeier1, Irine Khutsishvili2 and Luis A. Marky1,† 1

Department of Pharmaceutical Sciences, University of Nebraska Medical Center, Omaha, NE, US 2 Current Address: Institute of Physics, Javakhishvili State University, Tbilisi, Goergia The heat capacity (ΔCP) effects on the unfolding of a macromolecule play a significant role in the magnitude of their standard thermodynamic profiles; all three thermodynamic parameters (enthalpy, entropy and free energy) are dependent on temperature. The ΔCP of proteins is typically

*

The full version of this chapter can be found in Differential Scanning Calorimetry: Basics and Applications, edited by Amy Woods and Lila Chavez, published by Nova Science Publishers, Inc, New York, 2018. † Corresponding Author: Tel.: (402) 559-4628. Fax: (402) 559-9543. Email: [email protected].

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significant and is easily obtained using DSC by taking the difference in the ΔCP values of the pre- and post-transitional baselines. This ΔCP effect is due to the exposure and subsequent hydration of hydrophobic groups. However, for nucleic acids the ΔCP is typically very small and is within the noise level of the baseline. One way to indirectly determine ΔCP is by measuring the unfolding enthalpy, HDSC, and the transition temperature, TM, as a function of salt concentration; the slope of the HDSC versus TM plot is equal to ΔCP. Furthermore, the slope of the TM versus salt concentration plot can be used in conjunction with the thermodynamic parameters obtained from analysis of the DSC thermograms to determine the differential binding of counterions accompanying the unfolding of a macromolecule. In this work, we use DSC to determine ΔCPs for a series of DNA molecules, including ST-DNA, DNA duplexes, stem-loop motifs, hairpins with bulges, intramolecular three- and four-way junctions, triplexes and pseudoknots. In all cases, the resultant ΔCP is small and well within the baseline signal of the DSC and the unfolding of DNA molecules leads to a release of counterions.

THE PHASE COMPOSITION, GRAIN STRUCTURE, DIELECTRIC SPECTRA AND THE HEAT CAPACITY OF BI1–XGDXFEO3 SOLID SOLUTIONS *

S. V. Khasbulatov1, , A. A. Pavelko1, L. A. Reznichenko1, L. A. Silkina1, Z. M. Omarov2 and V. A. Aleshin1 †

1

Research Institute of Physics, Southern Federal University, Rostov-on-Don, Russia 2 H. I. Amirkhanov Institute of Physics of the Daghestanian Scientific Center of the Russian Academy of Sciences, Makhachkala, Russia *

The full version of this chapter can be found in Proceedings of the 2016 International Conference on "Physics, Mechanics of New Materials and Their Applications", edited by Ivan A. Parinov, Shun-Hsyung Chang and Muaffaq A. Jani, published by Nova Science Publishers, Inc, New York, 2017. † Corresponding author: S. V. Khasbulatov. E-mail: [email protected].

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The chapter presents the results of a comprehensive study of the crystal structure, grain structure, dielectric and thermal properties of hightemperature multiferroics Bi1-xGdxFeO3 (x = 0.05-0.20). The regularities of formation of the phase and grain structure, electrical and dielectric properties of objects at room temperature were established. The assumptions about the nature of the observed phenomena were suggested.

A STUDY OF THE HEAT CAPACITY OF RIBONUCLEASE A – WATER MIXTURES *

Vladimir A. Sirotkin† Kazan Federal University, A.M. Butlerov Chemical Institute, Kazan, Russia, Excess heat capacities of the binary system of bovine pancreatic ribonuclease A (RNase A) with water were obtained as a function of composition at 25 oC. Differential scanning calorimetry was applied to study hydration dependencies of the excess thermodynamic functions. A major focus of this study aims to show how these thermodynamic quantities correlate with coverage of the protein by the water molecules. The excess partial quantities are found to be sensitive to changes in the water and protein states. At the lowest water weight fractions (w1), the changes of the excess functions can mainly be attributed to water addition. A transition from the glassy to the flexible state of the protein is accompanied by significant changes in the excess partial quantities of water and lysozyme. This transition appears at w1> of 0.05 when charged groups of the protein are covered. Excess partial quantities reach their fully hydrated values at w1> 0.5 when coverage of both polar and weakly interacting surface elements is complete. At the highest water contents, water addition The full version of this chapter can be found in Protein – Water Interactions: A Differential Approach, edited Vladimir A. Sirotkin, published by Nova Science Publishers, Inc, New York, 2014. † Email: [email protected] *

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has no significant effect on the excess quantities. At w1 > 0.5, changes in the excess functions can solely be attributed to changes in the state of the protein.

INDEX # 1-amino-2-methyl-1-propanol, ix, 28

A absolute average deviations, 31, 49 absorption, 5, 6, 28, 50, 117, 122, 146 acid, 26, 50, 78, 79, 86 additives, 115, 119, 120 amine(s), viii, ix, 28, 29, 38, 40, 50, 51, 57, 62, 68 amino, ix, 28, 50, 51, 52, 70 ammonium, ix, 54, 56, 63, 67 atmosphere, 28, 58, 68 atoms, 7, 8, 82, 102, 105, 158

B base, 14, 19, 22, 62 blends, viii, 28, 29, 44, 49 Boltzmann constant, 17 Boltzmann H, viii, 2, 6, 16, 17, 126, 129, 132

Boltzmann H-irreversible heat capacity analogy, 2 Boltzmann H-temperature dependence, 2 bonding, x, 8, 76, 114, 124, 128

C calorimetry, ix, 54, 68, 83, 100 capture CO2, 28 chemical(s), 5, 8, 9, 28, 29, 54, 55, 57, 68, 82, 85, 87, 101, 104, 108, 113, 149, 150, 158 chemical reactions, 5, 8, 82 classification, 81, 82, 84, 86, 87, 89, 97, 98, 101, 104, 107, 109, 110, 111, 113, 114, 119, 124, 129, 130, 131, 133, 134, 139, 140, 148, 150 CO2, 28, 29, 41, 49, 50 color, 86, 89, 113, 139 composition, viii, 3, 28, 49, 110, 161 compounds, 65, 69, 85, 115, 120, 137, 149 conduction, 129, 135, 139, 154 conformity, 3, 10, 12, 14 correlation, 18, 22, 49, 78, 154, 157, 158, 159

164

Index

correlations, viii, 11, 28 criterion to equilibrium, 6 crystalline, 68, 73, 98 crystals, 56, 57, 103, 106, 108

D DEA, ix, 28, 29, 51 decomposition, 62, 63, 64, 65, 67, 68 deduction, 5, 9, 11, 16 deviation, viii, 25, 28, 31, 68 differential scanning, ix, 54, 72 differential scanning calorimetry, ix, 54, 72, 161 dimethylformamide, 78, 79 distribution, 55, 86, 101, 105 DSC, ix, 54, 56, 57, 58, 59, 63, 64, 65, 67, 72, 159, 160

E electron(s), 128, 129, 154 endothermic, 59, 64, 65 energy, ix, 2, 3, 4, 5, 7, 8, 10, 16, 19, 65, 76, 83, 86, 87, 101, 104, 109, 133, 135, 139, 148, 156 energy, internal, 2, 3, 10, 16, 86, 87, 148 engineering, 55, 84, 85, 115, 119, 130, 133, 134, 140, 155 entropy, vii, ix, 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 29, 53, 54, 55, 56, 68, 99, 101, 104, 110, 113, 132, 148, 150, 155, 157, 158, 159 equality, 10, 14, 17 equilibrium, viii, 2, 5, 6, 14, 15, 16, 17, 23, 83, 102, 105, 110, 113, 132, 148 equivalence of heat capacity and entropy, v, 9, 14 ester, 8, 18, 20, 25 ethanol, ix, 28, 78

evolution, vii, 1, 3 excess heat capacities, viii, 28, 33, 43, 76, 77, 161 excitation, 56, 97, 98

F Fabrication, 115, 120, 136 force, 7, 8, 16, 136 formation, 56, 62, 65, 136, 161 formula, 19, 23, 149, 158 free energy, 55, 83, 110, 148, 159

G gas heat capacity, viii, 2, 8, 26, 85 gas vibrational entropy, viii, 2, 8 gaseous ester, 20, 25 Gibbs energy, vii, ix, 29, 53 gravimetric analysis, ix, 54, 56

H heat capacity, v, vi, vii, viii, ix, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 35, 38, 40, 41, 43, 44, 49, 50, 51, 52, 53, 54, 63, 65, 66, 68, 71, 72, 75, 76, 77, 78, 79, 80, 81, 83, 85, 86, 88, 94, 98, 99, 102, 105, 107, 109, 110, 112, 113, 117, 121, 127, 129, 130, 132, 133, 135, 147, 149, 150, 153, 154, 155, 156, 157, 158, 159, 160, 161 heat capacity criterion to equilibrium, 14 heat capacity equilibrium criterion, 2 heat capacity of a molecular gas, 18 heat capacity-entropy equivalence, 2 heat capacity-pressure correlation, 21 heat transfer, vii, 1, 5, 55, 68 heat, internal, 4, 10, 12, 13, 14, 25

Index hindered amine, 40 hydrogen, ix, 76, 124

I ideal, ix, 6, 76, 113, 132, 148, 150 image, 114, 119, 149 incidence, vii, 1, 23 India, 53, 57, 69 industry, 55, 100, 115, 119, 120 internal, 2, 3, 4, 10, 12, 13, 14, 16, 25, 86, 87, 112, 132, 148 internal heat capacity, 12, 25 irreversibility thermodynamics, 2 irreversible, vii, 1, 2, 4, 5, 6, 10, 12, 13, 14, 15, 16, 17, 25 irreversible heat, vii, 1, 2, 5, 6, 14, 15, 16, 17, 25 irreversible heat capacity, vii, 1, 2, 5, 6, 14, 15, 16, 17, 25 isotherm, 44, 49

K kinetics, 56, 72, 136

165 measurement(s), ix, 3, 23, 25, 30, 31, 53, 54, 58, 60, 67, 69, 99, 107, 108 melt, 56, 67, 69 melting, 56, 64, 65, 67, 69, 98, 154, 159 melts, 55, 59, 65, 67 methodology, 12, 59, 60 methyldiethanolamine, ix, 28, 50, 51, 52, 78, 79 micro reaction calorimeter, 30, 49 mixing, viii, 2, 38 molar heat capacities, viii, 28, 29, 33, 35, 38, 41, 43, 50, 51, 52, 76 molar heat capacity, excess molar heat capacity, amines, blends, v, vii, viii, ix, 27, 28, 29, 33, 38, 40, 41, 44, 49, 51, 67, 75, 76, 77, 78, 80, 108, 118, 123, 149, 154, 156, 157, 159 molar volume, 76, 154, 157, 158, 159 mole, 32, 33, 35, 43, 77, 79, 132, 148 molecular gas, 7, 23 molecules, ix, 7, 8, 19, 65, 76, 99, 102, 105, 114, 160, 161 monoethanolamine, v, vii, viii, 27, 30, 49, 50, 51

N L

liquids, 29, 55, 67, 68, 69, 70, 71, 72, 73, 82, 86, 107, 113

M magnitude, viii, 2, 3, 6, 16, 17, 69, 155, 159 mass, 30, 56, 82, 148 materials, 3, 4, 6, 54, 55, 97, 98, 99, 100, 109, 129, 130, 134, 137, 140, 147, 149, 157 matter, 4, 114, 128, 129, 148 maximal entropy, viii, 2, 16, 25

nanocomposites, 114, 115, 119, 120 negative, 12, 14, 36, 38, 43, 44, 49, 78

O operations, 9, 16, 55 oscillation, 8, 103, 106 oscillators, 100, 101, 103, 104, 107, 123, 127, 128 oxygen, 28, 99, 138

166

Index P

physics, 97, 98, 99, 101, 104, 149, 150 piperazine, v, vii, viii, 27, 28, 30, 35, 49, 50, 52 polymer(s), 55, 69, 72, 99, 115, 119 pressure-heat capacity relationship, 2 principles, viii, 2, 81, 150 probability, 17, 101, 105 pyridine, 78, 79

specific heat, ix, 53, 54, 55, 57, 58, 59, 60, 64, 65, 66, 68, 72, 76, 77, 78, 83, 139 specific heat capacity, ix, 53, 54, 57, 58, 59, 60, 63, 64, 65, 66, 68, 72, 81, 83, 139 state(s), 3, 4, 5, 11, 18, 22, 23, 54, 68, 72, 85, 97, 98, 100, 101, 104, 105, 114, 132, 135, 138, 140, 148, 161 structure, ix, 71, 76, 80, 98, 99, 114, 115, 119, 120, 136, 155, 161

T Q quaternary ammonium salts, ix, 54, 58, 73

R radiation, 86, 109, 112, 139, 140, 150 reactions, 55, 69, 82, 99, 113, 133 ribonuclease A, 161 room temperature, 35, 55, 161 Royal Society, 70, 86, 107 Russia, 153, 155, 156, 158, 160, 161

S salts, ix, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 70, 73, 108, 137 sapphire, 58, 59, 60 scanning calorimetry, ix, 54, 72, 108, 161 science, 55, 82, 100, 109, 124, 139, 140, 147, 149 simulation, 83, 84, 108, 157 solid state, 18, 56, 73, 97, 136, 154, 158 solubility, 28, 35, 81, 83 solution, 28, 30, 33, 36, 44, 57, 67, 68, 102, 105, 110 solvents, 29, 49, 50, 77, 78 species, ix, 54, 62, 67, 68

techniques, viii, 2, 54, 68, 85, 102, 105, 108, 138 technology/technologies, 28, 55, 85, 103, 107, 138 temperature, viii, ix, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 28, 30, 32, 33, 35, 36, 38, 42, 43, 44, 49, 54, 55, 56, 58, 59, 60, 63, 64, 65, 66, 67, 68, 100, 110, 113, 136, 139, 148, 149, 155, 156, 157, 159, 161 temperature dependence, 2, 42, 97, 113, 148, 155, 156, 157, 159 temperature dependence of H, 16 tertiary amine, 40, 57, 62, 68 TGA, ix, 54, 56, 57, 58, 63, 64, 65, 72 thermal analysis, 56, 61, 99, 100 thermal expansion, 154, 156, 157, 159 thermal stability, 62, 67, 72 thermodynamic equilibrium, viii, 2, 25 thermodynamic parameters, 55, 159 thermodynamic properties, vii, ix, 29, 53, 68, 85, 154, 157, 158 thermodynamics, vii, 1, 2, 10, 12, 54, 82, 83, 84, 85, 87, 109, 110, 111, 112, 113, 131, 132, 150, 158 thermograms, 64, 67, 160 thermo-gravimetric analysis, ix, 54 thermophysical analysis, viii, 2 transformation, 3, 14, 25, 71, 126

Index treatment, 7, 70, 100, 124 trial, 19, 20, 24 tunneling, 102, 106, 126

U United States (USA), 71, 83, 111, 113

V vapor, viii, 2, 8, 18, 19, 21, 22, 23, 25

167 variables, 10, 11, 148 vibration, 7, 102, 105 volume, internal, 12

W water, vii, ix, 29, 30, 31, 33, 35, 44, 50, 51, 52, 57, 67, 72, 73, 75, 76, 77, 78, 79, 80, 81, 133, 149, 161 water structure, vii, ix, 75, 76 work, internal, 12