Physical optics of dynamic phenomena and processes in macromolecular systems: Proceedings. 27th Microsymposium on Macromolecules, Prague, Czechoslovakia, July 16–19, 1984 9783111517667, 9783111149769

Table of contents :
PREFACE
CONTENTS
A. Dilute and Semidilute Solutions
HYDRODYNAMICS OF POLYMER CHAINS IN DILUTE SOLUTION
QELS FROM VERY LONG AND SEMIFLEXIBLE FILAMENTS IN SOLUTION
THEORETICAL AND EXPERIMENTAL STUDIES OF ANISOTROPY IN TRANSLATIONAL DIFFUSION WITH SPECIAL REFERENCE TO TOBACCO MOSAIC VIRUS
MOLECULAR WEIGHT AND SECOND VIRIAL COEFFICIENT INFLUENCES ON THE CONCENTRATION DEPENDENCE OF DIFFUSION COEFFICIENT OF POLYSTYRENE MOLECULES IN DILUTE SOLUTIONS
THE CONCENTRATION DEPENDENCE OF DIMENSIONS OF FLEXIBLE POLYMER MOLECULES IN SOLUTION
DIFFUSION AND RELAXATION IN POLYMER-SOLVENT SYSTEMS BY PHOTON CORRELATION SPECTROSCOPY
QUASI-ELASTIC LIGHT SCATTERING IN SEMI-DILUTE SOLUTIONS AT THE θ-TEMPERATURE
LIGHT SCATTERING OBSERVATIONS OF THE PLATEAU MODULUS IN SEMI-DILUTE THETA SOLUTIONS
DYNAMIC LIGHT SCATTERING ON SEMIDILUTE SOLUTIONS OF POLYSTYRENE AS A FUNCTION OF SOLVENT QUALITY
DYNAMIC PROPERTIES OF ENTANGLED POLYMER SOLUTIONS BY FORCED RAYLEIGH LIGHT SCATTERING
DYNAMICS OF POLYELECTROLYTES IN AQUEOUS SOLUTIONS PROBED BY ELECTRO-OPTICAL RELAXATION
DYNAMIC LIGHT SCATTERING FROM A ROD-LIKE POLYMER IN SEMIDILUTE SOLUTION
LASER LIGHT SCATTERING OF DILUTE AND SEMI-DILUTE HYDROSOLUBLE BIOPOLYMER AND SYNTHETIC POLYELECTROLYTE SOLUTIONS
B. Concentrated Systems: Gels and Solids
STATISTICAL THEORY OF STREAMING-BIREFRINGENCE IN TEMPORARY POLYMER NETWORKS
QUASI-ELASTIC LIGHT SCATTERING OF AN IRREVERSIBLE SOL-GEL TRANSITION
MICROPHASE SEPARATION IN POLY(ACRYLAMIDE-BISACRYLAMIDE) COPOLYMERIZED GELS
RAYLEIGH AND BRILLOUIN SCATTERING FROM LINEAR POLYMER DURING GELATION
QUASI-ELASTIC LIGHT SCATTERING STUDIES OF THE DIFFUSION OF COMPACT MACROMOLECULES THROUGH GELS
SLOW DIFFUSION OF LABELED MACROMOLECULES STUDIED BY A HOLOGRAPHIC GRATING TECHNIQUE
MECHANICAL INSTABILITY OF GELS UNDERGOING LARGE SWELLING
PHOTON CORRELATION SPECTRA OF AMORPHOUS LOW MOLECULAR WEIGHT POLYETHYL METHACRYLATE ABOVE THE GLASS TRANSITION TEMPERATURE
RAYLEIGH-BRILLOUIN SCATTERING OF AMORPHOUS POLYMERS
BRILLOUIN SCATTERING STUDY OP SEGMENTAL MOTIONS OF POLYALKYL METHACRYLATES (PMMA,PEMA AND PNBMA) AT LOW TEMPERATURE
TIME RESOLVED SMALL-ANGLE X-RAY SCATTERING STUDIES ON KINETICS AND MOLECULAR DYNAMICS OF ORDER-DISORDER TRANSITION OF BLOCK POLYMERS
THERMOSTIMULATED LUMINESCENCE IN THE RELAXATION REGIONS OF POLYMERS
C. Intramolecular Phenomena and Process
DYNAMIC PHENOMENA, INTERACTIONS, CONFORMATIONAL CHANGES AND CHEMICAL PROCESSES IN MACROMOLECULAR SYSTEMS AS STUDIED BY POLARIZED LUMINESCENCE
INTRAMOLECULAR EXCIMER FORMATION AND POLYMER DYNAMICS: THE COIL-GLOBULE TRANSITION
EXCIMER FORMATION IN POLYSTYRENE SOLUTIONS: EFFECT OF THE COIL-GLOBULE TRANSITION
THE INFLUENCE OP CHROMOPHORIC GROUPS ROTATION ON THE DECAY OF FLUORESCENCE OF POLYSTYRENE IN SOLUTION
SMALL-ANGLE SCATTERING OF POLYELECTROLYTE SOLUTIONS
LIGHT-INDUCED CONFORMATIONAL CHANGES OF MACROMOLECULES IN SOLUTION AS DETECTED BY FLASH PHOTOLYSIS IN CONJUNCTION WITH LIGHT SCATTERING MEASUREMENTS
PHOTON CORRELATION SPECTROSCOPY OF POLYMETHACRYLIC ACID
PHOTON CORRELATION SPECTROSCOPY OF MACROMOLECULAR SOLUTIONS UNDER HIGH PRESSURE
INTRAMOLECULAR MOTILITY IN PIG IMMUNOGLOBULIN G STUDIED BY NEUTRON SPIN ECHO TECHNIQUE
THE CONFORMATION OF A DNA-PROTEIN COMPLEX
ELECTROOPTICAL KERR EFFECT STUDIES OF HEMOGLOBIN
MOLECULAR MOBILITY IN LIQUID POLYMERS AND POLYMERIZATION PROCESS INVESTIGATED BY ACOUSTICAL METHODS
D. Intermolecular Phenomena and Processes
THEORY OF LIGHT SCATTERING FROM SYSTEMS OF INTERACTING SPHERICAL MACROMOLECULES IN SOLUTION
COOPERATIVE GROWTH OF MOLECULAR AGGREGATION IN SEMICONCENTRATED PBLG SOLUTIONS INVESTIGATED BY THE DYNAMIC ELECTRO-OPTICAL METHOD
LIGHT SCATTERING ANOMALY OBSERVED IN DILUTE SOLUTIONS OF POLY (VINYL ALCOHOL) AGED AT HIGH CONCENTRATION
LIGHT-SCATTERING FROM CARRAGEENAN SOLUTIONS
STUDIES OF PROTEIN - NUCLEIC ACID INTERACTIONS BY PHOTON CORRELATION SPECTROSCOPY. II. tRNA - BSA INTERACTIONS AT INTERMEDIATE AND HIGH IONIC STRENGTH
SOLVATION OF PROTEIN MOLECULES STUDIED BY COMBINED QELS AND SAXS INVESTIGATIONS
LIGHT SCATTERING STUDIES OF BOVINE EYE LENS aL-CRYSTALLIN AT HIGHER CONCENTRATIONS : SHORT- AND LONG-RANGE ORDER
MAGNETO-OPTICS OF COLLOIDS
CHARACTERIZATION OF INVERSE POLYACRYLAMIDE LATICES BY QUASI-ELASTIC LIGHT SCATTERING
INTERACTION BETWEEN MICELLES OF POLY(STYRENE-b-HYDROGENATED BUTADIENE-b-STYRENE) IN 1,4-DIOXANE/n-HEPTANE MIXTURES
PROPERTIES OF BLOCK COPOLYMER MICELLES NEAR THE C.M.C. and C.M.T.
LATERAL DIFFUSION OF MICELLES MEASURED BY FLUORESCENCE RECOVERY AFTER PHOTOBLEACHING
E. Theoretical and Experimental Methods
MOLECULAR DYNAMICS SIMULATION OP THE N-ALKANES ROTATOR PHASE
THE KERR EFFECT RELAXATION IN HIGH ELECTRIC FIELDS
DIELECTRIC RELAXATION OF A FLEXIBLE MOLECULE
PHOTON STATISTICS IN LIGHT SCATTERING
ATTENUATION OF A COHERENT FIELD IN A DENSE DISPERSION OF PARTICLES
DETERMINATION OF POLYDISPERSITY INDEX BY QUASIELASTIC LIGHT SCATTERING
APPLICATION OF PICOSECOND LASER PULSES IN LIGHT SCATTERING STUDIES
APPLICATION OF EXPERIMENTAL TECHNIQUES FOR OBTAINING PHOTON CORRELATION FUNCTIONS AT HIGH PRESSURE
BIMODAL ANALYSIS OF QELS DATA
APPLICATION OF SPECKLE TECHNIQUES IN MACROMOLECULAR PHYSICS
LIGHT SCATTERING SPECKLE PHOTOGRAPHY: DETERMINATION OF SLOW CORRELATION TIMES
STUDY OF POLYMER SOLUTION/SOLID INTERFACES BY EVANESCENT WAVE SPECTROSCOPY
SINGULAR VALUE DECOMPOSITION IN THE ANALYSIS OF SPECTRA
FLOW BIREFRINGENCE OF MACROMOLECULAR SOLUTIONS IN VARIOUS ELONGATIONAL FLOWS
USE OF LIGHT SCATTERING METHODS FOR THE STUDY OF DYNAMIC PROCESSES OF MACROMOLECULES COAGULATION IN HYDROCARBON MEDIUM
ASSOCIATION OF ALCOHOLS INVESTIGATED BY RAYLEIGH LIGHT SCATTERING
REFRACTOMETRIC STUDY OP PRESSURE EFFECT Oil" PREFERENTIAL SORPTION OF MIXED LIQUIDS ON GELS UNDER DYNAMIC CONDITIONS
COMPATIBILIZATION THROUGH HYDROGEN BONDING OF PAIRS OF COPOLYMERS
CONTRIBUTORS
INDEX

Citation preview

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems Proceedings 27th Microsymposium on Macromolecules Prague, Czechoslovakia, July 16-19,1984 Editor Blahoslav Sedlàcek

W G DE

Walter de Gruyter • Berlin • New York 1985

Editor Blahoslav SedldCek, PhD.,DSc. Institute of Macromolecular Chemistry Czechoslovak Academy of Sciences Heyrovsky sq. 2 CS-162 06 Prague 616 Czechoslovakia

Library of Congress Cataloging in Publication Data Prague IMPAC Microsymposium on Macromolecules (27th : 1984) Physical optics of dynamic phenomena and processes in macromolecular systems. „Under the sponsorship of the International Union of Pure and Applied Chemistry (IUPAC)"~Pref. Includes bibliographies and index. 1. Macromolecules-Analysis-Congresses. 2. Spectrum analysis-Congresses. I. Sedl&cek, B. (Blahoslav) II. International Union of Pure and Applied Chemistry. III. Title. QD380.P73 1984 547.7'046 84-28793

CIP-Kurztitelaufnahme der Deutschen

Bibliothek

Physical optics of dynamic phenomena and processes in macromolecular systems : proceedings / 27th Microsymposium on Macromolecules, Prague, Czechoslovakia, July 16-19,1984. Ed. Blahoslav Sedlàcek. Berlin ; New York : de Gruyter, 1985. ISBN 3-11-010234-X (Berlin) ISBN 0-89925-011-4 (New York) NE: Sedlàcek, Blahoslav [Hrsg.]; Microsymposium on Macromolecules

311010234 X Walter de Gruyter • Berlin • New York 0-89925-011-4 Walter de Gruyter, Inc., New York Copyright © 1985 by Walter de Gruyter& Co., Berlin 30. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form - by photoprint, microfilm or any other means nor transmitted nor translated into a machine language without written permission from the publisher. Printing: Gerike GmbH, Berlin. Binding: Dieter Mikolai, Berlin. - Printed in Germany.

PREFACE This volume includes the majority of the short special lectures and about h a l f of the poster contributions presented at the 27th IUPAC Microsymposium "Physical Optics of Dynamic Phenomena and Processes in Macromolecul a r Systems", held in Prague (Czechoslovakia) from July 16 to 19, 1984. The Prague Meetings on Macromolecules (including Microsymposia, D i s c u s s i o n Conferences and Summer Schools) have been organized, almost from t h e i r very beginning in 1967, under the sponsorship of the International of Pure and Applied Chemistry (IUPAC). Due to t h e i r s p e c i f i c ,

Union

usually

monothematic character, these meetings would seem to be in contrast to the regular IUPAC Symposia and Congresses, which have a broad, polythemat i c program: in fact, however, the micro-Symposia supplement the macroSymposia by bringing together s p e c i a l i s t s in the respective f i e l d ( s )

for

an e f f e c t i v e exchange of ideas and experience. Thus, the volume also o f fers the reader a good opportunity to inform himself about recent progress in the respective

disciplines.

This book deals with a problem area which could also be c a l l e d "Dynamics of Polymers and Biopolymers as Studied by Physico-Optical

and Related

Methods", acting in s o l u t i o n s , c o l l o i d d i s p e r s i o n s , gels and s o l i d s . The subject (macromolecules) and a tool for t h e i r study (method) are 'percolated'

to an extent which makes the papers rather complex to read,

but ' h o l o g r a p h i c a l l y '

i l l u s t r a t i v e nonetheless; at the same time, however,

t h i s makes any systematic c l a s s i f i c a t i o n of papers into sections

diffi-

c u l t or a r b i t r a r y . Therefore, only methods (and theories) not d i r e c t l y connected with the application to a given polymer are grouped together in a special

section.

The contents are divided into f i v e s e c t i o n s : Section A deals with the (hydro)dynamic behaviour of (preferably model) polymers in d i l u t e and semidilute s o l u t i o n s , followed by l i g h t s c a t t e r i n g and other physicooptical methods. In Section B s i m i l a r problems connected with concentrated systems (such as dense s o l u t i o n s and g e l s ) are discussed; a l s o , some new

VI

or l e s s well-known methods for their research are introduced. Sections C (Intramolecular Phenomena and Processes) and D (Intermolecular Phenomena and

Processes) s t r e s s processes

which occur in macromolecular systems

either i n d i v i d u a l l y or, in most cases, simultaneously. For several

papers,

no s t r i c t borderline can be drawn between the individual s e c t i o n s : the i n c l u s i o n in one or another section i s made, for the r e a d e r ' s convenience, with respect to the main emphasis and s i m i l a r i t y to subsequent papers. Section E deals with theoretical and/or experimental methods outlined or used for a general or, sometimes, special purpose. Occasionally, here and in other sections of t h i s volume, a theory, technique or application may depart somewhat from the scope of the book, but i t has been retained as i t might be of i n t e r e s t for comparison, application or as additional

in-

formation. Due to the very limited time a v a i l a b l e , pressing demands were sometimes made upon the more than 140 authors, whose e f f i c i e n t cooperation in preparing nearly seventy camera-ready papers i s highly appreciated. This form of p u b l i s h i n g has the indisputable advantage of an early publication of papers, which i s of great value, e s p e c i a l l y in the case of conference proceedings. With regard to the e d i t i n g , compromises are in some cases unavoidable in view of the 'least-change p r i n c i p l e ' barrier':

and the 'language

I hope that the papers w i l l be found at l e a s t understandable,

i f not well formulated. My thanks are a l s o due to de Gruyter Publishers and t h e i r leading coworkers for a very e f f i c i e n t and helpful approach to a l l problems which arose during our cooperation. I hope that these f r u i t f u l contacts in the Prague Meetings on Macromolecules w i l l also continue in the future. Blahoslav Sedlácek Chairman and Editor

VII

CONTENTS

Preface

A.

Dilute and Semidilute Solutions

Hydrodynamics of Polymer Chain in Dilute Solution

1

C.J.C. Edwards and R.F.T. Stepto QELS from Very Long and Semiflexible Filaments in

17

Solution S. Fujima and T. Maeda Theoretical and Experimental Studies of Anisotropy in

33

Translational Diffusion with Special Reference to Tobacco Mosaic Virus T. Maeda, S. Fujime, K. Kubota, H. Urabe and Y. Tominaga Molecular Weight and Second Virial Coefficient

37

Influences on the Concentration Dependence of Diffusion Coefficient of Polystyrene Molecules in Dilute Solution K. Witkowski, L. Wolinski, and B. Kolodziej The Concentration Dependence of Dimensions of Flexible Polymer Molecules in Solution J.S. King, W. Boyer, G.D. Wignall, and R. Ullman

43

Vili Diffusion and Relaxation in Polymer-Solvent Systems

49

by Photon Correlation Spectroscopy C. Cohen and D.H. Hwang Quasi-Elastic Light Scattering in Semi-Dilute

59

Solutions at the ©-Temperature M. Adam and M. Delsanti Light Scattering Observations of the Plateau Modulus in Semi-Dilute Theta Solutions

67

A.-M. Hecht, H. Bohidar, and E. Geissler Dynamic Light Scattering on Semidilute Solutions of

71

Polystyrene as a Function of Solvent Quality W. Brown Dynamic Properties of Entangled Polymer Solutions by

83

Forced Rayleigh Light Scattering M.F. Millet, H. Hervet, and L. Léger Dynamics of Polyelectrolytes in Aqueous Solutions

87

Probed by Electro-Optical Relaxation S. Wijmenga, F. van der Touw, and M. Mandel Dynamic Light Scattering from a Rod-Like Polymer in

107

Semidilute Solution K.H. Langley and P.S. Russo Laser Light Scattering of Dilute and Semi-Dilute Hydrosoluble Biopolymer and Synthetic Polyelectrolyte Solutions G. Muller

117

IX

B.

Concentrated Systems: Gels and Solids

Statistical Theory of Streaming Birefringence in

131

Temporary Polymer Networks E. Kröner and R. Takserman-Krozer Quasi-Elastic

Light Scattering of an Irreversible

145

Sol-Gel Transition S.J. Candau, M. Ankrim, J.P. Munch, P. Rempp, G. Hild, and R. Okasha Microphase Separation in Poly(acrylamide-

157

bisacrylamide) Copolymerized Gels E. Geissler and A.-M. Hecht Rayleigh and Brillouin Scattering from Linear

165

Polymer During Gelation T. Igarashi and S. Kondo Quasi-Elastic Light Scattering Studies of the

177

Diffusion of Compact Macromolecules through Gels D. B. Sellen Slow Diffusion of Labeled Macromolecules Studied

191

by a Holographic Grating Technique M. Antonietti, J. Coutandin, D. Ehlich, and H. Sillescu Mechanical Stability of Gels Undergoing Large Swelling Y. Hirokawa, J. Kucera, S.-T. Sun, and T. Tanaka

197

X Photon Correlation Spectra of Amorphous Low

205

Molecular Weight Polyethyl Methacrylate above the Glass Transition Temperature G. Fytas Rayleigh-Brillouin Scattering of Amorphous Polymers

217

C.H. Wang and B. Stuhn Brillouin Scattering Study of Segmental Motions of

229

Polyalkyl Methacrylates (PMMA, PEMA and PnBMA) at Low Temperature E. Kato and Y. Saji Time Resolved Small-Angle X-Ray Scattering Studies

2 33

on Kinetics and Molecular Dynamics of Order-Disorder Transition of Block Polymers T. Hashimoto Thermostimulated Luminescence in the Relaxation

245

Regions of Polymers J. Pospisil, A. Havranek and I.A. Tale

C.

Intramolecular Phenomena and Process

Dynamic Phenomena, Interactions, Conformational

251

Changes and Chemical Processes in Macromolecular Systems as Studied by Polarized Luminescence E. Anufrieva and M. Krakovyak Intramolecular Exciraer Formation and Polymer Dynamics: The Coil-Globule Transition C. Cuniberti and A. Perico

267

XI

Excimer Formation in Polystyrene Solutions:

271

Effect of the Coil-Globule Transition P. Stepänek, C. Konäk, and B. Sedläcek The Influence of Chromophoric Groups Rotation on

275

the Decay of Fluorescence of Polystyrene in Solution K. Sienicki and C. Bojarski Small-Angle Scattering of Polyelectrolyte Solutions

279

R. Koyama Light-Induced Conformational Changes of Macromolecules

287

in Solution as Detected by Flash Photolysis in Conjunction with Light-Scattering Measurements M. Irie and W. Schnabel Photon Correlation Spectroscopy of Polymethacrylic Acid

301

P. Brak and A. Persoons Photon Correlation Spectroscopy of Macromolecular

305

Solutions under High Pressure B. Nyström and J. Roots Intramolecular Motility in Pig Immunoglobulin G

317

Studied by Neutron Spin Echo Technique S. Borbely, Y.M. Ostanevich, L. Cser, B. Farago, F. Mezei, and F. Franek The Conformation of a DNA-Protein Complex

321

M.A. Scheerhagen, H. van Amerongen, M.E. Kuil, R. van Grondelle, and J. Blok Electro-Optical Kerr Effect Studies of Hemoglobin Z. Biaszczak, M. Witrh, and B. Norden

325

XII

Molecular Mobility in Liquid Polymers and

329

Polymerization Process Investigated by Acoustical Methods P. Hauptmann

D.

Intermolecular Phenomena and Processes

Theory of Light Scattering from Systems of

335

Interacting Spherical Macromolecules in Solution R. Klein, G. Nägele and W. Hess Cooperative Growth of Molecular Aggregation in

349

Semiconcentrated PBLG Solutions Investigated by the Dynamic Electro-Optical Method H. Watanabe, T. Nakano, and Y. Fukuda Light Scattering Anomaly Observed in Dilute

353

Solutions of Poly(vinyl alcohol) Aged at High Concentration L. Mrkvickovä, C. Konäk, and B. Sedläcek Light Scattering from Carrageenan Solutions

359

C. De Jonghe, H. Reynaers, K. Bloys van Treslong, and F. Varkevisser Studies of Protein-Nucleic Acid Interactions by

363

Photon Correlation Spectroscopy. II. tRNA-BSA Interactions at Intermediate and High Ionic Strength A. Patkowski and B. Chu Solvation of Protein Molecules Studied by Combined QELS and SAXS Investigations K. Gast, D. Zirwer, P. Plietz, J.J. Müller, G. Damaschun, and H. Welfle

367

XIII Light Scattering Studies of Bovine Eye Lens

371

a -Crystallin at Higher Concentrations: Short and Lt

Long-Range Order C. Andries, M. Van Laethem, and J. Clauwert Magneto-Optics of Colloids

377

R.V. Mehta Characterization of Inverse Polyacrylamide Latices

397

by Quasi-Elastic Light Scattering F. Candau, C. Holtzcherer, and S. Candau Interaction between Micelles of Poly(styrene-b-

401

hydrogenated butadiene-b-styrene) in 1,4-Dioxane/n-Heptane Mixtures C. Konak, P. Stepanek, and Z. Tuzar Properties of Block Copolymer Micelles Near the

405

C.M.C. and C.M.T. Z. Tuzar, P. Stepanek, and C. Konak Lateral Diffusion of Micelles Measured by

409

Fluorescence Recovery after Photobleaching W. Van de Sande and A. Persoons

E.

Theoretical and Experimental Methods

Molecular Dynamics Simulation of the n-Alkanes

413

Rotator Phase M.A. Mazo, E.F. Oleinik, N.K. Balabaev, L.V. Lunevskaya, and A.G. Grivtsov The Kerr Effect Relaxation in High Electric Fields H. Watanabe and A. Morita

427

XIV

Dielectric Relaxation of a Flexible Molecule

443

A. Morita and H. Watanabe Photon Statistics in Light Scattering

447

J. Perina Attenuation of a Coherent Field in a Dense

457

Dispersion of Particles C. Konäk, P. Stepanek, J. Krepelka, and J. Perina Determination of Polydispersity Index by

461

Quasi-Elastic Light Scattering P. Stepanek, Z. Tuzar, and C. Konäk Application of Picosecond Laser Pulses in Light

465

Scattering Studies B. Van Wonterghem and A. Persoons Application of Experimental Techniques for

469

Obtaining Photon Correlation Functions at High Pressure J. Roots and B. Nyström Bimodal Analysis of QELS Data

473

R. Johnsen Application of Speckle Techniques in

477

Macromolecular Physics J. Holoubek, J. Mikes, and B. Sedläcek Light Scattering Speckle Photography: Determination of Slow Correlation Times J. Holoubek

481

XV

Study of Polymer Solution/Solid Interfaces by

485

Evanescent Wave Spectroscopy H. Hervet, D. Ausserr^, and F. Rondelez Singular Value Decomposition in the Analysis of

493

Spectra W. Curtis Johnson, Jr. Flow Birefringence of Macromolecular Solutions in

507

Various Elongational Flows R. Cressely, R. Hockquart, J.-P. Decruppe, and T. Wydro Use of Light Scattering Methods for the Study of

511

Dynamic Processes of Macromolecules Coagulation in Hydrocarbon Medium G.F. Bolshakov Association of Alcohols Investigated by Rayleigh

517

Light Scattering B.M. Fechner Refractometric Study of Pressure Effect on

521

Preferential Sorption of Mixed Liquids on Gels under Dynamic Conditions T. Macko, D. Berek, and M. Chalinyova Compatibilization through Hydrogen Bonding of Pairs of Copolymers

525

0. Aouadj, A. Lassoued, and S. Djadoun

Contributors

529

Index

541

HYDRODYNAMICS OF POLYMER CHAINS IN DILUTE SOLUTION

Christopher J C Edwards and Robert F T Stepto Department of Polymer Science and Technology, U n i v e r s i t y of Manchester I n s t i t u t e of Science and Technology, Manchester M60 1QD, UK

Introduction The t r a n s l a t i o n a l

d i f f u s i o n c o e f f i c i e n t , D, of a molecule i s related to

i t s e f f e c t i v e hydrodynamic radius, r D , by the Stokes-Einstein D = kT/f = kT/6irnorD

U)

where f i s the molecular f r i c t i o n c o e f f i c i e n t and n 0 viscosity.

equation:

i s

the

solvent

The r e l a t i o n between D and the d e t a i l e d molecular

structure

of a polymer chain i s complicated, mainly because of hydrodynamic interactions

between the centres of f r i c t i o n

the equation due to Kirkwood

„

=

kT

+

kT_

represents the best

in the chain.

(1,2)

[ £ ]

(2)

analytical s o l u t i o n to the problem.

i s the segmental

Currently,

Here £ - 6-nTiQ-3

f r i c t i o n c o e f f i c i e n t with a the radius of a segment and

x the number of segments in the chain [R" 1 ] = i K r ^ 7 > where i s the mean r e c i p r o c a l

separation of segments i and j and

the angled brackets denote a c o n f i g u r a t i o n a l

average.

Eq(2) can be

w r i t t e n in a form which i s independent of solvent v i s c o s i t y

(3), namely:

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

The f i r s t term on the righthand side (rhs) of Eq(3) i s the s o - c a l l e d f r e e - d r a i n i n g term associated with the flow of solvent through the molecular domain and t h i s term becomes i n s i g n i f i c a n t as x-»-».

The

second term on the rhs of Eq(3) takes account of hydrodynamic i n t e r a c t i o n s between segments and relates to the effective impermeable d i f f u s i o n radius of the chain. The derivation of Eq(2) makes several important assumptions which have been discussed recently in d e t a i l ( 4 ) .

For example, the chain i s assumed

to d i f f u s e as a r i g i d body in a solvent continuum.

In a d d i t i o n , hydro-

dynamic interactions between segments are assumed to be weak and the i n t e r a c t i o n s are assumed not to perturb the equilibrium configurations of the chain. In the present paper, previous interpretations in terms of Eq(2) of r^ for short polymethylene (PM) (3,5), polyoxyethylene (POE) (5,6) and l i n e a r and c y c l i c poly(dimethylsiloxane) together and compared.

(PDMS) (7,8) chains are brought

For a given chain structure c i s found to vary

with solvent, temperature and chain length, and possible reasons for these v a r i a t i o n s are discussed.

In a d d i t i o n , for systems with strong

s p e c i f i c interactions Eq(2) i s shown not to apply with free-draining being of n e g l i g i b l e consequence.

F i n a l l y , the predicted errors (4) in

Eq(2) compared with the f u l l Oseen evaluation of D for high molar-mass PM chains are discussed.

A key point in t h i s comparison and in the

c o r r e l a t i o n s of r D for short chains i s the use of r e a l i s t i c chain models and Monte Carlo calculations

(4,9) to evaluate

3 Interpretation

of

experimental

data

M u l t i p l i c a t i o n of each term in Eq(3) by x^ y i e l d s :

i i i ir - = r + r^ D F E

V

(4) '

where rp, the e f f e c t i v e f r e e - d r a i n i n g r a d i u s , i s equal to x.a and rp, the e f f e c t i v e impermeable r a d i u s , i s equal to

For unperturbed

c h a i n s , x^/r D and x f y r ^ tend to the same constant value and x*/ rp tends to zero as x+». the s u m - i n - p a r a l l e l

Thus the e f f e c t i v e d i f f u s i o n r a d i u s , rp, i s

of the f r e e - d r a i n i n g r a d i u s , rp, and the e f f e c t i v e

impermeable radius rp.

Eq(4) has been used p r e v i o u s l y

(3,10,11) to

i l l u s t r a t e g r a p h i c a l l y the r e l a t i v e magnitudes of the c o n t r i b u t i o n s of rp and rp to rg.

Values of r F = X 2 / [ R _ 1 ] have been evaluated

f o r PM, POE and c y c l i c and l i n e a r PDMS using a Monte Carlo technique which employs Metropolis sampling (12) and r o t a t i o n a l - i s o m e r i c - s t a t e models of the polymer chains given by Flory £ t a i 1.

Short polymethylene chai ns.

(13).

In Figure 1 x /r^, x 2 /rp and

x=/rp are plotted versus x for short PM chains ( 3 ) .

Also shown in

Figure 1 i s the Gaussian curve, calculated by assuming that rp=3ir* /8. a

The f r e e - d r a i n i n g curve xfyrp has been calculated for

= 0.08 nm which i s a reasonable estimate of the s i z e of a - C H 2 -

segment.

(4,9)

4

Figure 1 Variation of reciprocal diffusion £adii of polymethylene at 298K with chain length (x). [R ] and 2 calculated using Hill-Stepto model (5) . a = 0.08 nm. Curves: 1. Gaussian approximation to StokesEinstein radius, 2. Stokes-Einstein radius, 3. impermeable radius and 4. free-draining radius.

Inspection of Figure 1 shows that the effects of free-draining are still significant for x = 50.

The Gaussian approximation to x ^ / r E is poor

at low x but tends with increasing chain length to the same value as the Monte Carlo curve rather faster than the effects of free-draining disappear.

Figure 2 shows the same plots with experimental

short PM chains in benzene and quinoline also included (10).

data for It is

5 apparent from Figure 2 that a constant value of the segment radius, a, will not explain the experimental

data and that, furthermore, the value

of a depends on solvent.

Figure 2 Reciprocal diffusion radii versus chain length (x) for (•) polymethylene/ quinoline/298K and (0) polymethylene/benzene/298K. Curves: 1. Freedraining radius, x*/rp with rp = x.a and a = 0.08 nm, 2. impermeable radius, x | / r E witlj r E = x ^ / [ R _ 1 ] , 3. Kirkwood-Riseman diffusion radius, x V r D = x 2 / r p + x 2 / r p , 4. and 5. calculated diffusion radius with a =.b and (4) < c b > = 0.216 and (5) < c b > = 0.121.

Previously, this increase in the apparent segment radius with increasing x has been rationalised by allowing a to vary in proportion to the effective bond length of the chain b=( generally tend

to decrease as the molar volume of the solvent and/or the solvent viscosity

increase. Table 1

Values of Ck required to give agreement between calculated and experimental S t o k e s - E i n s t e i n r a d i i for polymethylene chains in various solvents

x

b/nm

benzene 25°C c

5 6 1 8 9 10 12 14 16 18 19 20 24 28

0.228 0.247 0.263 0.277 0.289 0.300 0.318 0.331 0.343 0.352 0.356 0.359 0.371 0.380

11 cP, , V cm mol"

b

carbon tetrachloride 25°C c

b

0.267 U723U 0.221 0.218 0.217 0.215 0.204

0.287 W7ZN 0.225 0.204

0.203 0.203 0.220 0.226

0.196 0.213

0.216 0.608 88.9

0.193 0.182

tetralin 22.2°C c

b

0,.157 0..139 0,.127 -

0,.127 -

0,.105 0,.112 0..108

0.185 0.178

0..134

0.201 0.938 96.5

0..122 2.,1 Ì6

quinoline 25°C C

b

0..148 0..121 0..115 0..116 0..116 0..118 0..120 0..125 0.,136

decalin 22.2°C c

b

0,.134 0,.118 0,.104 0,.098 0,.099 0,.092 0,.092 0,.091 0,.096

0,.109 0. 121 3.,44 118

0..100 2..64 159

7 The values of in benzene and quinoline have been used to recalculate x V r p , with rp = x.b, and the curves obtained in this way are those shown dashed in Figure 2.

The agreement between the

calculated curves and the experimental data is now good except at the shortest chain lengths, where end-effects become important.

The general

decrease in with increasing molar volume and/or viscosity of solvent may be thought of as resulting from the assumption of a solvent continuum.

< % > is a measure of the effective friction experienced by

a "hydrodynamic segment" and this decreases as slippage due to voids in the solvent structure (or molar volume) increases and as the perturbation of solvent flow for a given shear gradient decreases (i.e. viscosity increases).

The constancy of , or the concomitant increase in a

with chain length is not so easily rationalised.

It may result from the

assumption of rigid-body hydrodynamics in the derivation of the Kirkwood equation^).

Given that segmental velocities depend less on chain

length than the centre-of-mass velocity, the difference between these velocities will increase with chain length giving an effective increase in

2.

The proportionality of e to b remains unexplained.

Polyoxyethylene chains.

Figure 3 shows plots according to Eq(4) for

POE in water and quinoline with x*/rp calculated for a = 0.1 nm (10). In this case the experimental data for POE in quinoline agree well with the calculated curve, x 2 /Tq, suggesting that a is independent of x. However, the reason for this behaviour, which contrasts with that found previously for PM, becomes apparent when data for methoxy terminated POE chains are considered (points shown as "+" in Figure 3).

Similar

behaviour is now observed to that found previously for PM and it is clear that quinoline molecules hydrogen-bond to the terminal

-OH groups

of the POE chain and thereby increase the effective chain length.

It is

probable that a doubly end-blocked POE chain would show an even larger increase in x^/Rq as x decreases similarly to that found previously for PM.

nm'

15

10

00

20

to

60

t

80

100

Figure 3 Reciprocal diffusion radii versus chain length (x) for (•) POE/quinoline/ 298K and (•) P0E/water/298K. The points marked (+) refer to POE terminated with one -OH and one -QMe group in quinoline at 298K. Curves: 1. Free-draining radius x^/rp, a = 0.1 nm, 2. Impermeable radius x V f p , 3. Kirkwood-Riseman diffusion radius x i / r D . The data for POE in water (5,6) l i e well below the calculated curve for x*/r D at a l l values of x.

In t h i s case water molecules are

hydrogen-bonded to the skeletal oxygen atoms as well as the terminal -OH groups, thereby increasing the e f f e c t i v e chain cross-section.

Thus

POE chains in quinoline and water provide examples of systems which show non-Kirkwood behaviour due to strong s p e c i f i c interactions between polymer and solvent. 3.

Linear and c y c l i c poly(dimethylsiloxane)

(1-PDMS and r-PDMS).

In

Figure 4 an analysis is presented for 1-PDMS in toluene and bromocyclohexane (10).

In t h i s case the data can only be reproduced by consider-

ing the f r i c t i o n centres to be fSi ( C H 3 ) u n i t s

with a = 0.25 nm.

nnf s

i

__ _ — — —

f

_

—

!

~

/

/

A

2

\

°0

10

20

30

to

50

Figure 4 Reciprocal diffusion radii versus chain length (x) for (0) 1-PDMS/toluene/ 298K and (0) l-PDMS/bromocyclohexane/301K. Curves: 1. Free-draining radius, x'/rp, a = 0.25 nm, 2. Impermeable diffusion radius x^/r^, 3. Ki rkwood-Ri seman diffusion radius x^/rn, 4. and 5. calculated with a = b and (4) < c b > = 0.509 and (5) = 0.405.

Again at low x the effective segment size varies with chain length, although this effect is less marked for 1-PDMS than for PM, possibly due to the larger segment radius of 1-PDMS.

The values of required to

reproduce the experimental data are 0.509 in toluene and 0.405 in broniocyclohexane.

Curves recalculated using those values of

are

shown dashed in Figure 4 and as for PM the agreement with the experimental data is good. shown in Figure 5.

An equivalent analysis (11) for data on r-PDMS is Since 1-PDMS and r-PDMS differ only in topology it

would be expected that the same value of a would reproduce the data for both species.

However, Figure 5 shows that this is not the case and

that for r-PDMS a = 0.4 nm as compared with the value of 0.25 nm found for 1-PDMS.

The difference between the values of «i

0.4 nm and

ca 0.25 nm for the segment radius of r-PDMS compared with 1-PDMS is consistent with less free-draining flow in the cyclic molecules as would be expected from their higher segment densities.

10

Figure 5 Reciprocal d i f f u s i o n radii v e r s u s chain length (x) for cyclic PDMS in (•) t o l u e n e at 298K and (•] b r o m o c y c l o h e x a n e at 301K. Curves: 1. and 2. free draining radius x 2 / r p w i t h rp = x.a and a = 0.25 nm and a = 0.4 nm r e s p e c t i v e l y , 3. i m p e r m e a b l e d i f f u s i o n radius x * / r E , 4. and 5. K i r k w o o d - R i s e m a n d i f f u s i o n radii w i t h (4) the sum of c u r v e s (1) and (3) ( a = 0 . 2 5 nm) and (5) t h e sum of curves (2) and (3) (a=0.4 nm). (x) c o m p l e t e e n u m e r a t i o n ( + ) Monte Carlo c a l c u l a t i o n s .

Again a g r e e m e n t w i t h the experimental

d a t a is improved

(11) if the

segment radius is a l l o w e d to vary in p r o p o r t i o n to an e f f e c t i v e length. br

bond

For c y c l i c species t h e e f f e c t i v e bond length m a y be redefined as

= (6/x)i b e c a u s e the m e a n - s q u a r e end separation

is u n d e f i n e d for such molecul es. to d e f i n e values of

Values of bp have been used in Eq(5)

> for the data in t o l u e n e and

The improvement in a g r e e m e n t w i t h the experimental

bromocyclohexane.

data at short

chain

lengths using a c o n s t a n t v a l u e of < c b > is not so m a r k e d as for 1 - P D M S , but t h e d i f f e r e n c e significant.

in v a l u e s of < c b > b e t w e e n the two solvents is still

11 4.

Characteristic values of segment radii at Infinite chain length.

use of Eq(5) to define the segmental

The

friction coefficient means that at

infinite chain length the effective segment radius tends to a constant value as the effective bond length b reaches its limiting value for the unperturbed chain, viz

= .b

(6)

with independent of chain length, and evaluated as described from data on short chains.

The parameter a ^ is useful for summarising

differences in segmental

friction for different polymer/solvent

systems

at given temperatures.

Table 2 gives the resulting values of a n for

PM, 1-PDMS and r-PDMS.

Dependences of a ^ on solvent are clearly seen

and relate to solvent viscosity and molar volume as previously discussed. The values of

a^ increase in the order PM < 1-PDMS < r-PDMS showing that

free-draining decreases in the same order. Table 2 Values of and a for 'Kirkwood-Riseman 1 systems, from experimental dafa on finite chains.

PPM/CC1 4 /298K PM/benzene/298K PM/tetralin/295K PM/quinoline/298K PM/decalin/298K o 1-PDMS/toiuene/298K 2

» 0 r-PDMS/to!uene/298K 1-PDMS/BrC,H../301K o 11 r-PDMS/BrCgH .J/301K

/So

evaluated

b

b /nm

a oo /nm

0.225 0.213 0.122 0.121 0.100

0.435

0.098 0.093 0.053 0.052 0.044

0.509

0.566

0.288

0.559

II

0.316

1.31

0.402

0.527

0.405

0.566

0.229

0.449

II

0.254

0.923

0.402

0.371

12 Oseen analysis and rat

infinite chain length

Notwithstanding the r i g i d body approximation, the Kirkwood equation known to be approximate.

For t h i s reason Edwards, Kaye and Stepto

is (4)

have recently examined for PM chains the magnitudes of the e r r o r s introduced by the assumptions of pre-averaging and weak hydrodynamic interactions.

Using a development of the equations for the

frictional

f o r c e s on a polymer chain which i s related to that o r i g i n a l l y used by Kirkwood and Riseman ( 1 ) , i t has been shown that the Kirkwood equation r e l i e s only on the assumption of weak hydrodynamic i n t e r a c t i o n s and not on the use of a pre-averaged Oseen t e n s o r .

In a d d i t i o n , ensembles of

r i g i d - b o d y c o n f i g u r a t i o n s of r o t a t i o n a l - i s o m e r i c - s t a t e model PM chains were generated using the Monte Carlo procedure described

previously.

The d i f f u s i o n tensor equations were then solved numerically for two d i f ferent c a s e s .

F i r s t l y , using the pre-averaged form of the Oseen t e n s o r :

when i i s the bond l e n g t h , r^j i s the magnitude of the distance between f r i c t i o n centres i and j and

denotes the unit m a t r i x .

the approximation of weak hydrodynamic i n t e r a c t i o n s the i n t e r a c t i o n s are pre-averaged.

In t h i s case

i s not p r e s e n t , but

Secondly, the f u l l form of the Oseen

tensor

8-irrio Ar i j has been used, where Q i j Q i j denotes the d i r e c t product of the unit vector connecting segments i and j .

This approach g i v e s the exact

Oseen s o l u t i o n for the case of a r i g i d body moving with constant and random o r i e n t a t i o n

velocity

( i . e . Brownian motion i s assumed to be

overwhelming) in a solvent continuum.

For ease of comparison of

results

from the two cases with those from the Kirkwood equation, Eq(2) can be expressed a s :

13

i

=

f

where [R

I + x

(9)

x2

] represents the sum of reciprocal

normalised to unit bond length and

K =c/6im 0 Ji

separations of segments characterises

strength of the hydrodynamic interactions between segments. previous observation that s is related to b implies that to a limiting value of x-m».

the The

< increases

The lower limit of < = 0 represents

complete free-draining. Figure 6 shows a plot for PM in benzene at 298 (K) of the percentage reduction in c/f relative to the Kirkwood _1 result, for the pre-averaged Oseen solution, as a function of x 2 .

50

J /

4

*-.x= 0.566 '*»

A • \ , • x=0.S23 2.0

x

X x

\

0.1,36

\

•

*=0.31.9

\

V

*

\ \ \ \

V '

V \

\

*=0.17i.

s * ^ V V • * CM *~r — A

o.e

Figure 6 Percentage difference between values o£ c/f for PM chains from «Oseen> and K-R treatments as a function of x - 2 . (+) percentage differences at percentage constant K , (•) percent differences derived from experimental diffusion coefficients of PM in benzene at 298K.

14 Several

values of

to the values of Eq(9).

are employed and the points marked (0) correspond

K

derived by interpreting the experimental

K

data using

It can be seen that the limiting reduction in c/f at high

molar-mass lies in the range 2-3%.

Corresponding plots

(4) are shown

in Figure 7 for the results from the full Oseen treatment with those from the Kirkwood equation. c/f as x+co is of the order of 8%.

compared

Here the limiting reduction in

The overestimate of 8% in t/f from

Eq(9) compared with the full Oseen treatment is characteristic of the PM chain in benzene at 298K.

Since

(or 5) depends on chain

K

structure, solvent and temperature, the overestimate in ?/f from Eq(9) will also depend on these variables. Figure 7 (and 6) that actual

In addition, it can be seen from

polymer/solvent systems must be used in

order to determine the values of

K

to be considered.

at present of determining < independently.

There is no way

The overestimate in 5/f

for a given value of < is the same as the overestimate in the parameter

(3,10). 10.0

50

10

5

(X *=0.566

c

o




T/T
1 , the diffusion coefficient D

v

= T

- 1 2 /q

follows the same law as

that measured by gradient concentration (10) : D c ( c m 2 / s ) • = (1.25 + 0.10)X10" 6 C; it is proportional to the concentration. At T/T„ < 1, the diffusion coefficient D = T g R The ratio

-1

/q n

2

is larger than D . " c

of the two diffusion coefficients follows the relation : D /D = 1 + 5.22X10" 2 S c

C-'-

04+0

-2

63 Discussion

The observations can be explained as follows. The diffusion coefficient D^ is proportional to the osmotic bulk modulus

K

=

C

3TT/3C

and inversely pro-

portional to the friction coefficient f per unit volume of the solvent through the polymer : D

c

= —. This relation can be directly demonstrated by f

comparison with intensity light scattering and sedimentation measurements from which it was found that (11-12) : K (dyn/cm 2 )

= (2.93 + 0.14)X10 7 C 3

and s

- 1.15X10-' 4

•96+0.04

The sedimentation coefficients, s, is related to the friction coefficient f per unit volume by s = (1-vp) C/f

(pv = 0.703 for polystyrene in cyclo-

hexane at 35°C). Following scaling laws (1-3)the reduced diffusion coefficient D /D , where c o D q is the diffusion coefficient of an isolated chain, is a function only of C/C . In Fig.4 we can see that the scaling law is fully respected.

Figure 4 : Triangles are values obtained from ref.(13) : AM =1.3Xl0 5 ,VM =2X106. For the meaning of the other symbols see Fig.3, D /D values have been cal= 1.30X10-4 / K (14)^ ° culated using : D (cm 2 /s)

64 The diffusion coefficient D^ is the diffusion coefficient of the polymer pseudo-gel (7) :D^ = (K+ M)/f ,tohereM is the longitudinal elastic modulus of the pseudo-gel. Following this hypothesis D /D - 1 must be proportional £ c to M/K. From the present measurements and the measurements done inref/l'), we deduce that M (dyn/cm 2 )

= 1.53x10® c'" 9 ^. The elastic longitudinal mo-

dulus of the pseudo-gel is proportional to the volume number density of 2 entanglements (> C ). This point is in agreement with the theoretical predictions (1-3) and shear elastic modulus behaviour deduced from viscoelastic measurements (5) . The observation by quasi-elastic light scattering, in a semi-dilute 9 polymer solution, of either a liquid or pseudo-gel behaviour, depending on the experimental time scale (2,3), is possible because : M and K are of the same order of magnitude. The time t , which is independent of the momentum transfer , is a structural relaxation time and is eaual to the stress viscoelastic relaxation time T . T. as well K .L as T_ is related to the disentanglement of one chain. Figure 5 shows that the reduced relat ie . R . * xation timers does not obey a scaling law in C/C as is the case in a good solvent (4) .

Figure 5 : T R /T j as a function of C/C* where T j is the characteristic time of the first mode of a single chain in the dilute regime (C

(1984).

(1976).

1 5 9 5

(1980).

11. S t e p a n e k , P . , P e r s y n s k i , R . , D e l s a n t i , M . , A d a m , M . , M a c r o m o l e c u l e s , to a p p e a r in (1984). 12. Vidakovic, P. , A l l a i n , C. , R o n d e l e z , F. , J. P h y s i q u e 42^, L 3 2 3 13. M u n c h , J . P . , H i l d , G . , C a n d a u , S. , M a c r o m o l e c u l e s j_6, 71 14. S c h m i d t , M. , B u r c h a r d , W. , M a c r o m o l e c u l e s , J4-, 210

(1981).

(1983).

(1981).

LIGHT SCATTERING OBSERVATIONS OF THE PTATEAU MODULUS IN SEMI-DILUTE THETA SOLUTIONS § Anne-Marie Hecht, Himadri Bohidar

and Erik Geissler

Laboratoire de Spectrométrie Physique*, Université de Grenoble I, B.P. 68, 38402 St Martin d'Hères Cedex, France. Abstract Dynamic light scattering measurements are described for semi-dilute solut-

7

ions of polystyrene (M w = 2.6X10

Daltons) in cyclohexane at the theta temp-

erature. Observations as a function of scattering angle allow the effects of the shear modulus to be distinguished from those of the osmotic modulus. Introduction Theta solutions of polymers of sufficiently high molecular weight are characterized by two distinct cross-over concentrations that separate the dilute from the semi-dilute régime (Figure 1): the usual overlap concentr-0.5 ation (proportional to M

, where M is the degree of polymerization),

and a critical entanglement concentration c e (proportional to M - 1 ) .

Figure 1 Schematic diagram of the behaviour of the shear (G) and osmotic (K ) moduli as a function of concentration in theta solutions of high O S molecular weight polymers. § Present address: Department of Physics, Indian Institute of Technology, New Delhi 110016, India. * CNRS associate

laboratory

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

68 Brochard (1) has noted that in theta solutions the osmotic modulus is = K° c 3 , (1) OS OS is a constant. The polymer-solvent friction coefficient f varies K

where K

OS

(2, The shear modulus, G, however, is determined by the probability that two polymer chains encounter one another, and hence G

=

G c2. o

(3)

Brochard's suggestion is that in semi-dilute theta solutions (c* < G »

K

os

c 1 (Fig.1) except for a divergence at the highest concentrations vAiich is more pronounced the greater the value of M. The data in Fig.4 correspond to:

where the Devalues are measured values (D) corrected for solvent backflcw according to: D = Dc(1-0) and 0 is the volume fraction of polystyrene. This exponent is substantially lower than the value y = 0.75 predicted by de Gennes1. Furthermore, there is no tendency for y to increase with M. This inability of the model to describe the observed variation of D^ with C should serve as a reminder of the extent to which entanglements influence the concentration dependence and which is an aspect ignored in the simple model. "Marginal" solvent (ethyl acetate) Results for PS 950 in ethyl acetate are shewn in Fig.5. The main feature is the presence of two distinct modes of relaxation which are separable using bimodal analysis. Thus, at all but the lowest concentrations, a single exponent plus baseline gave a very poor fit (at the highest concentration it was appropriate to add a baseline term to the bimodal expression for a marginally improved fit). The slew relaxation has a slightly negative dependence on C whereas thefesthas a positive dependence given by:

This exponent is much lewer than predicted for cooperative motions of the pseudogel, and there is evidence that this may be the case in poorer solvents. However, it is not suggested that a complete separation of the two nodes has been achieved (or can be using the present irethod) and the points at low concentration in particular scatter considerably making the slope uncertain.

76

The relative intensity amplitude of the fast mode is strongly concentration dependent (Fig.5 a), the correlation function being close to single exponential at the lowest concentration and rapidly beccming a birrodal distribution as C increases. Marginal and theta solvents reveal a complexity which is not found in good solvents and bimcdal autocorrelation 12 13 functions in ethyl acetate have been noted previously ' _ Amplitude

la) 2 U q10/m-2

_ ir/qW

C % I w/w)

10

12

Fig. 5. PS 950/ethyl acetate (25°C): (a) Relative intensity airplitude of the fast mode.(b) Fast (I) and slew (0) modes derived using bimodal analysis. Cumulant data (A) (=weighted average of fast and slow modes) and D^p (•) data from classical gradient diffusion. Fig.6. PS 950/ethyl acetate (C = 3.29% w/w): (a) The relative intensity 2

anplitude of the fast node depicted in Fig. 5. (b) (q -dependence of) fast and slow components in Fig. 5. We observe that the slow relaxation decreases strongly in intensity amplitude with increasing concentration, a finding which contrasts with the exponential increase in the amplitude of a slew relaxation described by 12 Mathiez et al . This suggests, instead, the presence of local concentration inhomogeneities in their solutions particularly since their slow mode amplitude was found to decrease on standing. The amplitude of the

77

fast node should eventually decrease at even higher concentrations as constraints increase due to the greater entanglement density as shown by 10

Hwang and Cohen

. A slow node as found for good solvents should then

became evident. The angular dependence of the relaxation frequency is linearly dependent 2 on q (Fig.6) suggesting that both modes are diffusional processes. The intensity amplitude of the fast mode increases strongly with increasing angle (Fig.6a). It is presumed here that the slow relaxation describes the centre of mass translational motions while the fast corresponds to the cooperative motions of the developing pseudogel. At this intermediate molecular weight (M = 950,000) both processes are features of the autocorrelation function. This situation persists over a wide range in concentration, well in excess of C* where it is usually assumed that the transient gel motions are the only ones of importance. Valussof D c u m (= ) have an intermediate concentration dependence, reflecting the relative weighting of the two nodes. 5 Data for the low molecular weight (M = 10 ) sample are typified by single exponential (Sf.

If.

• th » «!>

• llh F i g u r e 4. A n g u l a r E l e c t r i c f i e l d of The appearance o f sity fluctuations

d i s t r i b u t i o n of I r / 2 I n i n the h o r i z o n t a l plane the i n c i d e n t l i g h t is in the v e r t i c a l d i r e c t i o n . d i r e c t i v i t y i s a s s o c i a t e d w i t h f o r m a t i o n o f denw i t h the s i z e of the wavelength of the l i g h t . 2

of intermolecular potential ( i . e . energetic e l a s t i c i t y ) .

On t h e o t h e r hand,

hydrodynamics t e l l s us t h a t damping c o e f f i c i e n t o f sound i s g i v e n by r = -J—J-i-j-n + c)|k|2

(8)

where ti i s t h e shear v i s c o s i t y and ? i s t h e volume v i s c o s i t y . The v a l u e o f aX s (=r/Vg)=0.4 observed f o r phonon ( F i g u r e 2) g i v e s t h e v a l u e o f 4 / 3 - r i + ? = 0 . 6 p o i s e a c c o r d i n g t o e q u a t i o n ( 8 ) , i f t h e v a l u e o f X i s r e g a r d e d as 3000A, 5 - 1 i . e . k = 2 x l 0 cm . T h i s v a l u e o f 0 . 6 p o i s e cannot be t h e v a l u e deduced f r o m m o t i o n o f l o n g c h a i n m o l e c u l e s i n r u b b e r y s t a t e . Phonon damping a l s o may be l e d from a n h a r m o n i c i t y o f i n t e r m o l e c u l a r

potential.

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173 ally perfect dielectric crystals under the condition w s t « 1 , 2 aA

=

2ttC y Trio V * S 3pvs2

(10)

where C y is the isochoric specific heat, T is the absolute temperature and p is the density. In gas-kinetic theory one finds the following

expression

for the thermal conductivity,!«, of solids: k = 4-CvVs2X

(11)

f

otXs, therefore, becomes

5lOO-

20

40

115

channel number

9-8 .

40

20 (a)

115

channel number

or

Ih ' OT5*

Figure 2. Correlation functions obtained from light scattered from a 7.5% polyacrylamide gel (bis/acrylamide ratio 1%) using a multibit correlator whilst scanning angles of scatter at 16s per degree. Incident light 50mw, 633nm. The broken lines are the computer baselines. a) scan from 85 to 95 . sample time 3ys. b) scan from 80 to 115 s i x times with gel in s l i g h t l y different positions (see text), sample time 0.1s, prescaling factor 128, light attenuation 170.

where de/dt is the scanning rate and 9 S p ^ ( 9 ) i s the f i r s t order normalized spatial correlation function. at N (

)

2

There is an apparent short term baseline

1 + ß{ 1 - R ) n whilst the zero time value i s N ( s

S

)2(l+e)

s sp —> 2 /Ii P Thus T and both the and the computer baseline i s Ns(. ) • 9 ( ) spati a l l y integrated total count rate and the count rate associated with the broadened component may be found from one experiment. In equation 6, r i s replaced by R. Figure 2a shows a correlation function obtained with a Polyacrylamide gel by scanning from 85° to 95°. From the zero time value relative to the computer baseline ß=0.43. I t has been found convenient with gels to work with this relatively low coherence factor in order to avoid

182 critical alignment of the system.

Distortion of the correlation function

due to systematic variation in

and g ^ ( - r ) over the angular range

is negligible, and the data is effectively valid for e=90 . to investigate g

^(e)

It is possible

by using much longer sample times, and the result

of such an experiment is shown in Figure 2b where the equivalent values of e are indicated.

The problem here is to obtain a sufficiently large sample

of the fluctuations in for the correlation function to be properly defined, without introducing systematic variations in . The correlao o tion was therefore taken over six scans between 80 and 115 , and between each scan the cylindrical sample was twisted about its axis slightly so as to change the speckle pattern.

On the assumption of Gaussian statistics

however, this correlation function contains no information about the gel. It is entirely a function of the arrangement and dimensions of the stops in the scattered light receiver system. In all work with gels the mounting of the apparatus is important.

If the

gel is set in oscillation due to external vibrations, the otherwise stationary component of the random speckle changes, and oscillations, usually at the frequency of oscillation of the gel, appear in the correlation function.

This phenomenon has been used to investigate the mechanical

properties of gels (3,4), but in the type of work being discussed here it is important to avoid these oscillations.

This may be achieved most

effectively by mounting the apparatus on a heavy base which is then placed on an air bed.

Polysaccharide Gels Agarose and calcium alginate gels have been investigated (2,5,6).

The

Rayleigh ratio of light scattered from both types of gel is some two orders of magnitude greater than that from a "clear" gel such as polyacrylamide. Nevertheless provided that the dimensions of the specimen are reduced sufficiently to avoid secondary scatter, the Debye theory is obeyed, i.e. 4 2 2 if X Rg is plotted against Sin ( e / 2 ) / A for different wavelengths, using incoherent light, a single plot is obtained, indicating that the scatter does not arise from macroscopic fluctuations in gel density.

183 10D D0

•

»

0-5-

\ nm

2-5

Figure 3. Diffusion coefficient, D, relative to that in dilute solution, D , of dextran fractions within agarose gels of various concentration, C, as a function of dextran hydrodynamic diameter, d. The plots at the various concentrations have been superimposed by displacing horizontally (C =0.7%). 0 0.3% • 0.7% v 1% A 2% X 4% Degrees of spectral broadening have been found to be very small,one percent or less, falling as low as 0.01% for a 4% agarose gel.

Correlation funct-

ions are non-exponential and relaxation times are of the order of tens of milliseconds and do not vary as [sin^(9/2)j observed.

\

much less variation being

It is not appropriate therefore to describe g ^ ( i )

scattered from these gels in terms of diffusion coefficients.

for the light However when

dextran fractions of suitable concentration are allowed to diffuse within these gels, separate relaxation times which vary as [sin^(e/2j]

^ can be

easily identified and measured, and the diffusion coefficients of the dextrans within the gels determined.

Because of the high level of unbroadened

scatter from these gels it is safe to assume that the optical beating is entirely heterodyne, so that it is not necessary in this case to know 6 in order to determine diffusion coefficients. order to determine partition coefficients.

However e must be known in

The zero time value of that part

of the correlation function associated with the diffusing marker macromolecule (after subtracting the baseline and contributions from the gel) is

184 2gN .

The partition coefficient is found by comparing the counts

per sample time associated with the diffusing macromolecule > with the count rate observed when the cell contains a solution of the diffusing macromolecule only.

A correction must be made however for attenuation of

the incident and scattered light due to the turbidity of the gel.

Figure 3 shows diffusion coefficients of dextran within agarose gel, D, relative to corresponding diffusion coefficients in water, D q , as a function of hydrodynamic diameter, D, and agarose concentration, from D q using the Stokes-Einstein equation.

d is calculated

D/D Q has been plotted against

log d for each agarose concentration and the plots displaced horizontally relative to the data at 0.7% concentration, (C Q ), to yield a single "master" plot.

The fact that this can be done shows that:

D/D q = f[g(C)d]

(8)

g(C) is a function which can be found from the displacements and f is the function generating the master curve.

A double logarithmic plot of the

displacement against gel concentration shows that: 9(C) = a C b with b = 0.5. 1 /2

(9) Since by dimensional analysis D/D

must be a function of

p-| ' d where p-j is the length of gel fibre per unit volume, and C=p-]m where m is the mean mass per unit length of fibre, b=0.5 is just the value expected if m is independent of concentration.

A plot of very similar shape was

obtained with calcium alginate gel except that values of d for given values of D/D Q were seven times smaller, indicating that the mass per unit length of gel fibre is some fifty times smaller.

The only available theory

for the function f is due to Ogston et al (7) who give the relation: D/D q = E x p ^ 1 / 2 P l 1 / 2 d / 2 ]

(10)

If plotted as a function of log d, an exponential

is similar in shape to

the curve shown in Figure 3, but the transition from the freely diffusing to the completely immobilized state takes place much more slowly.

The val-

idity of equation 10, and possible modifications to it, have already been discussed extensively(2).

It is thought that it is valid for conditions

near complete immobilization, and on this basis molecular weights per unit length of gel fibre of 25,000 and 590g.mol"^nm~^ have been calculated for agarose and calcium alginate gels respectively.

The latter figure is in

excellent agreement with the model proposed for calcium alginate gel by

185

o •

»

ö

4H

cm 10^ total intensity

\

o\ total intensity

1Ö4-*—g—*

r

broadened component

ï

3cr

90° (a)

T

T

130*

angle of scatter

-o-

J

1öl

broadened component

90°

30* (b)

130*

angle of scatter

Figure 4. Diffusion c o e f f i c i e n t s and i n t e n s i t i e s of l i g h t scattered from a 7.5% Polyacrylamide gel (bis/acrylamide ratio=l%). X indicates the gel alone, 0 indicates the gel surrounded by, a) a 4% solution of bovine plasma albumin, b) a 4% solution of a dextran f r a c t i o n of weight average molecular weight 70,000 g.mol~l. a) and b) represent d i f f e r e n t gel samples.

Morris et a l ( 8 ) . The f i g u r e f o r agarose suggests that there are of the order of f i f t y agarose chains associated together in each gel f i b r e .

Partition

c o e f f i c i e n t s determined f o r agarose are consistent with the d i f f u s i o n coeffi c i e n t s on the basis of the theory of Ogston et al for gel concentrations above 1%. At lower concentrations smaller p a r t i t i o n c o e f f i c i e n t s are found, possibly due to dextrans becoming temporarily trapped by mobile agarose chains (2).

Polyacrylamide Gels Polyacrylamide gels were made up as cylinders of 5mm in diameter using the

186 standard procedure ( 9 ) , except that 0.01M sodium azide was added during the preparation of the g e l s , which were subsequently stored in 0.01M sodium azide s o l u t i o n .

The bis/acrylamide r a t i o was 1% and gel concentrations ran-

ged from 4% to 13%. Light s c a t t e r i n g measurements were made with each sample held with i t s a x i s v e r t i c a l in the centre of a 20mm diameter c y l i n d r i c a l l i g h t s c a t t e r i n g c e l l , in which i t was surrounded by 0.01M azide s o l u t i o n , or either 4% bovine plasma albumin or 4% dextran (M w =70,000) s o l u t i o n with 0.01M azide added. Even without d i f f u s i n g macromolecules present degrees of spectral broadening up to 30% were observed and,in general, d i f f u s i o n c o e f f i c i e n t s were obtained with equation 6 by means of an appropriately weighted l e a s t squares f i t going up to the t h i r d term of the polynomial.

Usually

the scanning method (from - 5 ° to +5° of the desired angle) described above was used, although preliminary experiments were carried out in the normal manner in order to s e l e c t an appropriate sample time.

The s p a t i a l l y

integ-

rated total count rate and the count rate associated with the broadened component were found with equation 7, and these were converted to Rayleigh r a t i o s by c a l i b r a t i n g the l a s e r l i g h t s c a t t e r i n g apparatus a g a i n s t a conventional Aminco l i g h t s c a t t e r i n g apparatus which in turn had been c a l i b r a ted with Ludox.

The usual s c a t t e r i n g volume correction was applied. Small

corrections for systematic v a r i a t i o n s i n the various parameters with angle of scatter within the scanning range were made for angles below 50°.

A

Malvern Instruments 64 channel m u l t i b i t c o r r e l a t o r was used for a l l measurements with polyacrylamide g e l s . Figure 4 shows data obtained at various angles of scatter f o r a 7.5% gel and Figure 5 shows data for various gel concentrations.

Diffusion coeffic-

ients were converted to 20°C assuming a v a r i a t i o n proportional to the r a t i o of absolute temperature to the v i s c o s i t y of water. Considering f i r s t p o l y acrylamide gels in the absence of d i f f u s i n g macromolecules; calculated d i f f u s i o n c o e f f i c i e n t s were found to be independent of angle of scatter,and the deviation of the c o r r e l a t i o n function from a s i n g l e exponential was not u s u a l l y more than that expected from the fact that the optical beating i s neither completely heterodyne nor completely homodyne. The maximum value of found was 1.02.

Whereas the total Rayleigh r a t i o increased

markedly at 1 ow angles, the Rayleigh r a t i o of the s p e c t r a l l y broadened component was found to be independent of angle of s c a t t e r . Measurements of

187

Figure 5. a) Diffusion coefficients and, b) intensities of l i g h t scattered from polyacryl amide gels of various concentration. X gel alone, 0 gel surrounded by 4% bovine plasma albumin solution. In b) the upper plots are the total Rayleigh ratios at 90 angle of scatter, whilst the lower plots are the Rayleigh ratios of the spectrally broadened component which were found to be independent of angle of scatter.

the total Rayleigh ratio were also made with incoherent l i g h t in an Aminco 4 apparatus using the wavelengths 546nm and 436nm. Plots of X R, against 2

sin ( e / 2 ) A

2

yielded a single plot for the two wavelengths showing that the

stationary component in the fluctuations in gel density does not in the main arise from macroscopic causes and that there are genuine static fluctuations in polyacrylamide density at a molecular level. A double logarithmic plot of diffusion coefficient against gel concentration yielded a straight line of slope 0.8. However the concentrations indicated in Figure 5 have not been corrected for swelling and as this i s l i k e l y to increase with decreasing concentration i t is l i k e l y that 0.8 is too high. Similarly the slope of the double logarithmic plot of the Rayleigh ratio of the spectrally broadened component against concentration 0.55, i s also probably too high.

188 Laser l i g h t s c a t t e r i n g from polyacrylamide gels has already been extensively investigated by G e i s s l e r and Hecht (10,11) and the r e s u l t s discussed in terms of current t h e o r i e s .

The r e s u l t s for the gels in the absence of

d i f f u s i n g macromolecules w i l l not therefore be discussed further here. Bovine plasma albumin and dextran f r a c t i o n of molecular weight 70,000 have -7 2 - 1 -7 2 -1 d i f f u s i o n c o e f f i c i e n t s in water of 5.8x10 tively

cm s

and 3.4x10

cm s

respec-

(no buffers or s a l t s other than sodium azide were added in these

experiments). Thus they have respectively higher and lower d i f f u s i o n c o e f f i c i e n t s than that of a 7.5% polyacrylamide gel ( 4 . 4 x l 0 - 7 c m 2 s _ 1 ) and 4% s o l u t i o n s have Rayleigh r a t i o s r e s p e c t i v e l y f i v e times and twice that of the s p e c t r a l l y broadened component.

S u r p r i s i n g l y therefore, e s s e n t i a l l y

the same d i f f u s i o n c o e f f i c i e n t as that of the gel was measured after these macromolecules had been allowed to d i f f u s e in for twenty four hours, and »

there was no evidence of more than one relaxation time in the c o r r e l a t i o n functions.

There was a small increase in the magnitude of the s p e c t r a l l y

broadened component with bovine plasma albumin, but none with the dextran fraction.

The most marked effect in the case of a 7.5% gel was a f a l 1 of

some 30% in the total scattered i n t e n s i t y .

The f a l l in Rayleigh r a t i o i s

of the same order as the Rayleigh r a t i o of the s o l u t i o n s surrounding the g e l , and i t was checked by making measurements with incoherent l i g h t at two wavelengths as described above. The effect of a 4% s o l u t i o n of bovine plasma albumin on gels of various concentration i s shown in Figure 5.

The measured d i f f u s i o n c o e f f i c i e n t

f a l l s with increasing gel concentration until i t equals the d i f f u s i o n c o f f i c i e n t of the g e l , a f t e r which i t r i s e s as the d i f f u s i o n c o e f f i c i e n t of the gel. Even when the measured d i f f u s i o n c o e f f i c i e n t i s markedly d i f f erent from that of the gel at the lower gel concentrations, there was no evidence of more than one relaxation time i n the c o r r e l a t i o n f u n c t i o n s . The proportionate increase in the s p e c t r a l l y broadened component of the scattered l i g h t increases with decreasing gel concentration, w h i l s t the f a l l in the total scattered i n t e n s i t y seems to be greatest at intermediate concentrations.

At gel concentrations where no change i n d i f f u s i o n c o e f f -

i c i e n t was measured, evidence that the protein had a c t u a l l y permeated the gel i s provided by the fact that there was a marked effect on the total

189

scattered intensity.

This was however confirmed by dyeing the protein

within the gel with aniline blue.

Discussion and Conclusion I t i s obvious that polysaccharide gels and polyacrylamide gels are quite different as regards both the dynamics of their structure, and the mechanisms by which compact macromolecules diffuse within them.

In the case of

polysaccharide gels the picture we have i s one of an almost stationary fibrous structure, in which compact macromolecules can diffuse subject to being impeded by the geometry of the structure, but with well defined d i f f usion coefficients which can be clearly identified and measured by quasie l a s t i c light scattering.

In the case of polyacrylamide gels we have a

highly mobile structure, which i t s e l f has a diffusion coefficient corresponding to the diffusion of fluctuations in the density of the gelling material.

I t appears that whereas diffusing compact macromolecules are impe-

ded by the gel structure their diffusion coefficient does not fall below that of the gel i t s e l f and that at higher gel concentrations the diffusing macromolecules are carried along by the diffusion fluctuations in the density of the gelling material, presumably following the migration of the less dense regions, provided of course that they are small enough to enter the gel in the f i r s t instance.

Thus the diffusion processes are not indep-

endent and i t is not possible to assign a well defined diffusion coefficient to the diffusing macromolecules. Thus partition coefficients cannot be determined by quasi-elastic light scattering. The fact that the diffusing macromolecules actually give r i s e to a marked fall in the overall scattered intensity, but not the broadened component, indicates that they show a preference for the regions of the gel which are permanently less dense, so rendering the system more homogeneous.

Further studies of diffusion within

polyacrylamide gels are in progress.

Acknowledgements The author wishes to thank Mr S. Hunter of the Astbury Department of

190 Biophysics at Leeds, who prepared the polyacryalmide gels and c a r r i e d out the protein dyeing experiments.

The photon c o r r e l a t i o n equipment was

obtained with a grant from the Science and Engineering Research Council.

References 1.

Tanaka, T . , Hocker, 0 . , Benedeck, G.B.: J.Chem.Phys.

59, 5151-5159

(1973), and many subsequent p u b l i c a t i o n s by these and other authors. 2.

Key, P.Y., S e l l e n , D.B.: J.Polym.Sci.Polym.Phys.Ed. 20, 659-679 (1982).

3.

Brenner, S . L . , Gelman, R.A., Nossal, R.: Macromolecules 11 , 202-212 (1978).

4.

Gelman, R.A., Nossal, R.: Macromolecules

311-316 (1979).

5.

Mackie, W., S e l l e n , D.B., S u t c l i f f e , J . : P o l y m e r ] ^ , 9-16 (1978).

6.

S e l l e n , D.B.; Polymer Jj), 1110 (1978).

7.

Ogston, A.G., Preston, B.N., Wells, J . D . ; Proc.R.Soc. London A333, 297-316 (1973).

8.

M o r r i s , E.R., Rees, D.A., Thom, D., Boyd, J . : Carbohydrate Research 66, 145-154 (1978).

9.

Shapiro, A . L . , Vinuela, E . , Maizel, J . V . : Biochem.Biophys.Res.Comm. 28, 815-820 (1967).

10. Hecht, A.M., G e i s s l e r , E.: Journal de Physique 39, 631-638 (1978). 11. G e i s s l e r , E . , Hecht, A.M.: Macromolecules J 4 , 185-188 (1981).

SLOW DIFFUSION OF LABELED MACROMOLECULES STUDIED BY A HOLOGRAPHIC GRATING TECHNIQUE

Markus Antonietti, Jochen Coutandin, Dietmar Ehlich, Hans S i l l e s c u I n s t i t u t für Physikalische Chemie der Universität Mainz Jakob-Welder-Weg 15, D-6500 Mainz

Introduction Experimental methods for investigating slow translational diffusion are subject to limits given by the Einstein relation D = ^ r ( t ) 2 ^

r

/6 t where

( t ) 2 ^ is the mean square average displacement of the diffusant in the

time interval t. Most techniques imply an interface between two parts of the sample one containing the diffusant at the beginning of the experiment. Examples are the radioactive tracer (1), the IR-scanning (2), and the Rutherford backscattering (3) techniques. Although i t has been possible to prepare thin polymer films of thickness down to a few um the d i f f i c u l t i e s of obtaining a well defined interface are considerable and have so far limited most applications to diffusion coefficients D ^ 1 0 ^

cm^s

The

NMR pulsed gradient techniques (4) are applicable to homogeneous samples, however, are limited by the requirement that the diffusion time t must be shorter than the longest spin relaxation time which again yields a limit of D 2>10" 1 0 cm^s~*. This limitation can be overcome by the holographic grating technique in which, by interference of two coherent beams, a grating is induced in a sample where the diffusant molecules are labeled with a photosensitive dye. The diffusive decay of this grating i s monitored by measuring the intensity of forced Rayleigh scattering (FRS) from the sample. The f i r s t application of this technique to polymer diffusion was an investigation of labeled polystyrene (PS) in solution (5). We have used a similar experimental setup for measuring self diffusion coefficients in molten PS (6, 7, 8). In order to extend the range of accessible D values we are using photolabels having a

lifetime of some days with respect to

thermal decay. Furthermore, we have increased the angular range of the two

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

192

intersecting beams to 9 ~ 90° thus reducing the grid spacing d = X/ 2 sin(9/2)

to ~ 300 nm for X = 458 nm. Since the FRS intensity is 2

2

roughly (cf.ref.7) proportional to exp(- 8ir Dt/d ) i t decays to 1% of i t s -14 2 -1 i n i t i a l value in t < 1 h for D £ 10

cm s

. Thus, diffusion of macro-

molecules in polymer melts can easily be investigated within acceptable diffusion times. The present contribution provides experimental data for testing de Gennes1 reptation model (10) of polymer chain diffusion.

Experimental The fluorescein label used in our previous applications (6-8) gives r i s e to secondary reactions that may influence the FRS decay curves (7,11). Furthermore, i t exists as a dimer in PS, and affects the diffusion of labeled PS in the region of

low

molecular weights (7,8). Thus, we have

prepared a stilbene label by the following procedure (12,13). p-Tolunitrile is treated with a 3:1 mixture (by volume) of H 2 S0 4 (98%) and HN03 (65%) at T < 30°C. Condensation of the resultant o - n i t r o - p - t o l u n i t r i l e with an equimolar quantity of p-dimethylamino-benzaldehyde occurs within 2 h at 120-130°C in a mixture containing ~ 5% piperidine as catalyst. One obtains a black s o l i d , 2-nitro-4-cyano-4'-dimethylamino-stilbene, which is recrystallized from acetic acid (m.p. 178°C). The n i t r i l e is hydrolysed by refluxing over night in a water-ethanol-K0H mixture. The Cs salt of the product is reacted with the chloromethyl end group of PS as described in ref. (7). The main label reaction

193

PS—0— c

occurs in two steps where the first photochemical step leads to a colourless intermediate which reacts thermally to the blue final product. The thermal step is very rapid above ~ 150°C, and very slow below«50°C. In between, it occurs on the same time scale as the diffusion process which can, however, easily be separated since the FRS decay by diffusion depends upon the grid spacing d. Crosslinked PS was obtained by a Friedel-Crafts reaction with p-dichloroxylylene in C ? H.C1 solution (14):

The soft gel obtained from a 20% solution was passed through a fine sieve, treated with THF/HC1, precipitated from CH 3 0H, and dried at 175°C in order to obtain particles of crosslinked PS having a size of

~ 100 um (14).

194 These particles were mechanically mixed with 2-5% of a fine powder of labeled linear PS, pressed to a 0.3 mm thick pellet, and annealed in vacuo for 4 days at 180°C. During this annealing period the labeled chains diffuse into the particles and form a solution in the crosslinked PS matrix. For details see ref.(14). The diffusion coefficients could be determined as described for linear PS in ref.(7).

Results and Discussion The molecular weight dependence of polymer chain diffusion is usually discussed in terms of a power law D = D o (T)M" a

(1)

where a = 2 is predicted by the reptation model. In order to test this prediction, we have measured D values of 9 samples of linear PS labeled with fluorescein having a number average degree of polymerization P R between 177 and 1 550 (18 000 6

£ 161 000; M w /M n 5 1.02). Except for the

highest P n values of 1 100 and 1 550, we have dissolved the labeled PS in a PS matrix having M

= 110 000. At temperatures between 135 and 208°C, -14 -10 2 -1 the D values ranging between 2 x 10 and 3 x 10 cm s could be fitted by the WLF equation 0 = 0^ exp [ - CjCg In 10/(c2 + T - T )]

(2)

where T^ = 104°C is the glass transition temperature of the matrix and D^, c^, c2 are fit parameters that depend upon M n - The values c^ and c 2 (8) are approximately constant for P n £

400 and similar to those found for the

zero shear gradient viscosities. At higher P n > our c 2 values increase in a manner that cannot be understood in terms of the usual free volume assumptions. In a plot of log D versus log P n we find straight lines for Pn

Z 300. A least square fit of the power law, Eq.(l), yields a slope a

that varies from 2.0 at 208°C to values above 2.4 at temperatures below 167°C. We have checked whether this behavior originates from a label influence by doing some experiments using the stilbene label described above. For short chains, P n = 177, we find D values increased by 20-50% in comparison with fluorescein labeled PS. However, for P n > 300 the differences become smaller, and the label influence upon D can safely be neglected. At

195

present, we have no explanation for the unexpected temperature dependence of a. The fact that a approaches the reptation value of 2 at the highest temperature confirms the reptation model for diffusion of s u f f i c i e n t l y flexible chains in an entangled polymer melt. Polymer chain diffusion can be forced to curvilinear motion along the chain contour by chemical crosslinking of the surrounding matrix. In particular, the diameter of the "tube" defined in the reptation model (10) can be varied by changing the average number N c of monomer units between crosslinks. I f one assumes about 200 monomer units between entanglements in molten linear polymers (10,15) a choice of N c < 200 provides a test of whether the reptative motion depends c r i t i c a l l y upon a tube diameter defined by the root mean square distance between entanglements. Since entanglements are largely eliminated in dilute solutions one can prepare networks without physical entanglements by performing the crosslinking reaction in dilute solution as described above. In our experiments (14) we have varied N c between 16 and 400, and we have measured D values of PS chains having chain lengths P n between 177 and 572 at temperatures of 177, 185 and 194°C. The D values were found reduced with respect to diffusion in uncrosslinked PS by factors less than 4. The reduction is smaller in the microgel systems prepared from dilute solution. Apparently, the fixation of physical entanglements by crosslinking in concentrated entangled polymer solutions leads to networks where reptative motion is more d i f f i c u l t . The measured D values in a net-1 8 work with N c = 50 were proportional to P~ "

at a l l 3 temperatures. The

main result of our study is the remarkably small decrease of D in crosslinked as compared with linear molten PS which provides strong support of the reptation model.

References 1.

Bueche, F.: J. Chem. Phys. 48, 1410 (1968)and references cited therein.

2.

Klein, J . : Nature 271, 143 (1978).

3.

Kramer, E.J., Green, P., Palmstrom, Ch.J.: Polymer 25, 473 (1984).

4.

von Meerwall, E.D.: Adv. Polym. S c i . 54, 1 (1983).

5.

Hervet, H., Leger, L., Rondelez, F.: Phys. Rev. Lett. 42, 1681 (1979).

196 6.

Coutandin, J . , S i l l e s c u , H., Voelkel, R.: Makromol. Chem. Rapid Commun. 3, 649 (1982).

7.

A n t o n i e t t i , M., Coutandin, J . , S i l l e s c u , H.: Macromolecules 17, 798 (1984).

8.

A n t o n i e t t i , M., Coutandin, J . , S i l l e s c u , H.: Makromol. Chem. Rapid Commun., in press.

9.

E h l i c h , D.: Diplomarbeit, Mainz 1984.

10.

de Gennes, P.G.: " S c a l i n g Concepts in Polymer P h y s i c s " , Cornell Univ e r s i t y P r e s s , Ithaca 1979.

11.

Coutandin, J . : PhD-thesis, Mainz 1984.

12.

P f e i f f e r , P.; Ber. 48, 1777, 1808 (1915).

13.

S p l i t t e r , J . S . , C a l v i n , M.: J. org. Chem. 20, 1086 (1955).

14.

A n t o n i e t t i , M., S i l l e s c u , H.: submitted f o r p u b l i c a t i o n . rd Ferry, J . D . : V i s c o e l a s t i c Properties of Polymers, 3 Ed., Wiley, New York 1981.

15.

MECHANICAL INSTABILITY OF GELS UNDERGOING LARGE SWELLING Yoshitsugu Hirokawa*, John Kucera, Shao-Tang Sun§ and Toyoichi Tanaka Massachusetts

Institute of Technology, Cambridge, MA

02139,

USA *Permanent Address: Research and Development Center, Nippon Zeon Company, Kawasaki, Japan ^Hercules Company, Wilmington, Delaware, USA

Abstract When

an

ionic

polymer

gel

undergoes

extensive

swelling,

a regular buckling pattern temporarily appears on its surface due to a mechanical instability. scale

of

the pattern

comparable

to

disappears

leaving the gel exactly

shape.

the

The characteristic

increases with

overall

size

of

length

time until it becomes the

gel

and

then

it

similar to its original

In this paper we demonstrate a method

for creating

the buckling pattern in equilibrium and study its dependence on gel size and osmotic pressure.

I.

Introduction

The kinetics of swelling and shrinking gels is an important scientific and technological problem which is not yet fully understood. gel

It was

expansion

can

demonstrated be

described

process of a polymer network diffusion the

of

previous,

a

polymer but

(1).

network

incorrect,

that, as

a

for

small

swelling,

collective

diffusion

The concept of collective is

idea

totally that

different

the

gel

from

swelling

and shrinking is caused by the diffusion of solvent molecules. The new point of view on the kinetics of gel swelling was supported by the quantitative agreement between the collective

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

198 diffusion laser

coefficient

light

scattering

experiments ments

(1,2).

two

a

polymer

network

spectroscopy

determined

and macroscopic

2

3(±0.5)xl0" cm /s

orders

of

7

and

magnitude

experi-

2

3.2xl0" cm /s

smaller

than

by-

swelling

T h e v a l u e s o b t a i n e d by i n d e p e n d e n t 7

were

were

of

which

that

of

water

c o m p a r e d to the o r i g i n a l v o l u m e the

linear

molecules. For

large

kinetic

swelling

theory

no

behavior

emerges

surface.

First

gels,

this

thin

slabs

We

describe

seen

applies. form

as

now

to

how

of

Interesting,

mechanical

a transitory

has

affixed

here

and osmotic Gel

the

buckling

in

II.

longer

in

a

base

the

phenomenon

been

produced

by

(crosslink 240

pi

and

4 0mg

0.133

molecule)

of

initiate

7.5cm

on

film.

thickness

grams and

were

of

(main

ammonium

the

0-0.64

grams

dissolved

a

to

hour

in

in

glass 2mm

persulfate

gelation. a

glass

in

of 100

sodium

bulbs

4cm

were

glass

and

was

allowed

made

plates

in

pouring

with

set

for

Slabs pre-gel

spacers

and

added

to

immediately

Spherical

diameter.

by

water.

(accelerator) were

then

to

atmosphere.

acrylate

ml of p u r e

(initiator)

solution

mold

nitrogen

thick

square

The

constitu-

N,N'-methylenebisacrylamide

N,N,N',N'-tetramethylethylenediamine of

transferred

to

treated

copolymerization

5.00 g r a m s of a c r y l a m i d e

molecule)

(ionizable

0.2

spherical

Preparation

molecule),

cast

the

equilibrium

depends

S a m p l e s of g e l s w e r e p r e p a r e d in free r a d i c a l

one

on

pressure.

at room temperature. ent

in

in

chemically

instability

non-linear

buckling

at

least

gels

were

gel

from

solution

of

onto

covering

with

®

commercially

available

onto

acrylic

square

treated backings.

film The

(GelBond film

PAG)

glued

chemically

bonds

to t h e g e l d u r i n g g e l a t i o n , p r e v e n t i n g t h a t side from when

immersed

immersed reach

in

in

pure

equilibrium.

solvent. water

and

After kept

for

curing, 24

the

hours

to

swelling

gels 3

were

days

to

199 III. K i n e t i c Figure in

Experiments

1 s h o w s the t i m e e v o l u t i o n of a s p h e r i c a l gel

pure

water.

glossy.

Initially

Immediately

regular

pattern

similar

of

pattern

increased

the

day

a

single

the

original

engrossed Growth

pattern radius

the

the

gel

until

diameter

that and

of

gel. gel

became

The

gel

swells

pressure

of

Na

Immediately osmotic it

a

a

regular

layer

of

while

pattern

decreasing

the

P a t t e r n F o u n d in

Slab

gels

of

into

This with

to

an

shows

acrylic some

of Shape

of

is

its

growth

the

osmotic

remain

causes

layer.

fixed limited

osmotically

square

until

As

buckling

scale

The

the

from

solvent.

length

as

acrylate.

released

layers

gradient

thicknesses

f o r m e d w i t h one as

gels

similarity

but

root

finally

of the

disappears.

after

same

sodium

acrylate

face m e c h a n i c a l l y

previously

to e q u i l i b r i u m in p u r e w a t e r . remains.

times the

Equilibrium

square these

sphere.

the

shear a

thickens

expansion

various

concentration were

to

pattern

sodium

gel b e c o m e s h o m o g e n e o u s a g a i n a n d the b u c k l i n g IV.

size

the

of

the

deeper

expanded

diffusively

one

glossy four

30%

surface

out

stress.

the

by

its

"diffuses"

shear

in

size

disappeared.

introduced

expands,

thickness

released time

it

a

extent because

immersion,

and

large

forms

the

ions

after

diffuses,

by

+

stress

creating which

to s u c h a large

The after

about

to

and fine,

until

Eventually, again

a

glass.

comparable

20%

o c c u r r i n g a f t e r the b u c k l i n g h a d

smooth

appeared

deeper

became

about

was

there frosted

forming

the

with

surface

became

element of

gel

immersion

to

entire

continued

original

the

after

immersed

they

described. were

anchored Figure

allowed

to

W i t h one side f i x e d the

is n o t m a i n t a i n e d

between

2

swell pattern initial

200

Figure 1: Swelling of a spherical gel. Swelling time 0 min, (b) 0 min, (c) 3 min, (d) 11 min, (e) 30 min, 90 min, (g) 26 hours, (h) 3 days.

(a) (f)

201

d

e

icm

j.cm

Figure 2: Swelling of slab gels with different thicknesses and same concentration of sodium acrylate (0.15g/100ml water). Thickness of gels: (a) 2.00mm, (b) 1.65mm, (c) 1.33mm, (d) 1.01mm, (e) 0.83mm, (f) 0.66mm, (g) 0.50mm, (h) 0.32mm. Note scale difference for (e), (f), (g) and (h).

202

1.0

d0 (mm) Figure 3: Relation between initial thickness of gel.

and final states. size

with

characteristic

wavelength

and

One can clearly see the increase in pattern

increasing

thickness.

The

characteristic

length

scale ( A) , obtained by taking the square root of the average area per cell, is plotted in Figure 3 as a function of the original thickness (dQ).

The length scale is linearly related

to original thickness in this instance with slope 1.95 (±0.04) and intercept 0.19 (±0.03).

203

a >

h

Figure 4: Swelling of slab gels with same thickness (2.00mm) and different concentrations of sodium acrylate. Concentrations (g/lOOml water): (a) 0.12, (b) 0.10, (c) 0.09, (d) 0.08, (e) 0.07, (f) 0.06, (g) 0.05, (h) 0.04.

204

Figure

4 shows

sodium

acrylate.

The

sodium

acrylate

(high

buckling

and

effect

large

concentrations less

the

gels

having

swelling

Those

varying

osmotic

(low osmotic

swelling.

of

the concentration of

high

concentrations

pressure)

whereas

the

pressure)

intermediate

show gels

swelling

higher

and

osmotic

the

pressure.

values of osmotic between

depth

of

the

There

of

regular

having

low

show no buckling and

show

the

of buckling but with an irregular pattern. of

a

stages

Both the amount

buckling

seems

early

to

increases

be

two

with

critical

stress one of which defines the boundary

linear and non-linear behavior, and the other which

determines

if

the

pattern

is

regular.

Further

study

is

necessary to understand this phenomenon.

References 1.

Tanaka, T, (1979) .

Fillmore,

D.J.:

J.

2.

Tanaka, T., Hocker, L. , Benedek, G.B.: J. Chem. 59, 5151 (1973)

Chem.

Phys.

7_0,

1214 Phys.

PHOTON CORRELATION SPECTRA OF AMORPHOUS LOW MOLECULAR WEIGHT POLYETHYL METHACRYLATE ABOVE THE GLASS TRANSITION TEMPERATURE

George F y t a s * M a x - P l a n c k - I n s t i t u t f ü r Polymerforschung Mainz c/o I n s t i t u t f ü r P h y s i k a l i s c h e Chemie der U n i v e r s i t ä t Mainz Postfach 3980, D-6500 Mainz, FRG

Abstract

The photon c o r r e l a t i o n f u n c t i o n s o f the p o l a r i z e d component o f the s c a t poly(ethyl methacrylate) (PEMA) of 4 4 weight average molecular weight M 1 . 6 x 10 and 7 . 3 x 10 were measured t e r e d l i g h t from two f r a c t i o n s o f

A

i n the temperature range from 70 t o 107 C and a t pressure from 1 to 1000 b a r . An a n a l y s i s o f the data using o n l y one r e l a x a t i o n a-process y i e l d s an unexpected t e m p e r a t u r e , pressure and Mw dependent d i s t r i b u t i o n o f l a x a t i o n t i m e s . I n c o n t r a s t to t h i s , a double r e l a x a t i o n process

re-

repre-

s e n t a t i o n o f the experimental time c o r r e l a t i o n f u n c t i o n s leads to

relax-

a t i o n parameters which have p h y s i c a l l y meaningful values f o r both PEMA f r a c t i o n s . The c h a r a c t e r i s t i c time o f the two processes approach each o t h e r a t high t e m p e r a t u r e s , low pressures and hence the s e p a r a t i o n

is

l a r g e r f o r the higher Mw PEMA f r a c t i o n . The present r e s u l t s are i n agreement w i t h the f i n d i n g s o f d i e l e c t r i c and mechanical experimental

•Permanent address: Department o f Chemistry, U n i v e r s i t y o f C r e t e , I r a k i i o n , Greece

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

methods.

206 Introduction

During the last few years, photon correlation spectroscopy (PCS) has been extensively applied to study bulk polymer dynamics above the glass transition temperature T g (1). Several general features emerge from these studies, which indicate universality of the dynamics of the relaxation process probed by PCS. 1. A main glass-rubber relaxation, also known as primary or a-mode from dielectric relaxation measurements (which has a tremendous effect on the mechanical

properties), dominates the time corre-

lation function of the polarized scattered Intensity arising from slow density fluctuations. 2. The experimental correlation functions have a highly non-exponential shape and can be,represented well by the empirical W i l H a m s - W a t t s function (2) ( e x p ( - t / T Q ) ^ ) with distribution parameter B

0.4 for all studied polymers except poly(alkyl methacrylates). 3. The T0

.

mean relaxation time t(= - y r(B

1

) with r being the gamma function) con-

forms to the VFT or the equivalent WLF temperature equation which describe well mechanical shift factors (3). While the shape of the time correlation functions is insensitive to pressure (B is constant), the relaxation time t exhibits a strong pressure dependence and the activation volume corresponds to the volume of few monomer units (4). For poly (propylene glycol), t

f and B are found to be independent of molecular weight and of the probing wavelength (5). These findings suggest that localized segmental motions of the polymer chain grossly affect the density fluctuations in undiluted polymers near T . For poly(alkyl methacrylates), however, where two relaxation processes have been observed in dielectric and mechanical measurements (3,6) the light scattering results do not conform to the previous scheme (8-10). The relatively low value of B (^ 0.2), which is found to be temperature and pressure dependent distorts significantly the mean time T . One could fit, of course, a very broad distribution with two less distributed functions; however, the solution should be unique and physically meaningful

results

should be obtained. Since we do not yet have a theoretical model

describ-

ing the measured correlation spectra of bulk polymers near T , a significant contribution to this problem can be achieved by selecting suitable experimental conditions i.e. temperature, pressure and molecular weight,

207 and by comparison with other methods. In poly(butyl methacrylate)

(PBMA)

(10) we have shown that the most appropriate analysis of the data near T g and at ambient pressure involves two distinct relaxation

processes.

In this paper we attempt to explore the applicability of PCS on broad distributions in amorphous polymers and report a photon correlation study of the polarized scattered light from two fractions of poly(ethyl (PEMA) of weight average molecular weight (M w ) 1 . 6 x 1 0

4

methacrylate)

(T g =47°C) and

7 . 3 x 1 0 4 (Tg=65°C) in the temperature range from 70°C to 107°C and at a pressure from 1 to 1000 bar. It is known, mainly from dielectric measurements ( 6 ) , that the separation on the time scale of the two processes varies rapidly with temperature and pressure. Since similar response is also expected by changing T , the present pressure,temperature and molecular weight dependent study is further justified.

Theoretical

Background

The quantity measured in PCS is the auto correlation function o f the scattered electric field g(q,t)=/ where q 1s the

scattering wave vector and the angular brackets denote an ensemble average. The function g(q,t) depends on the polarization of the scattered light relative to the incident beam. In the VV-geometry, the scattered Includes both isotropic

Intensity

and anisotropic Iy^ contributions (V and H

denote perpendicular and parallel polarization to the scattering phase respectively). For weakly anisotropic scatterers, which 1s the case for poly(alkyl methacrylates), the VV intensity is almost equal to the Isotropic component. This arises m a i n l y from density fluctuations in undiluted polymers and has the correlation

function:

g(q.t) = < M q , t ) S p * ( q , o ) > / < | 6 p ( q , o ) | 2 >

(1)

where 6p(q,t) is the q th mode o f the density fluctuations. Equation (1) can also be written in the form (5): fl(q.t) = J m , n i,j where

(2)

is the position of the center of mass of scattering unit j of

208 polymer n at time t. Only the segment center of mass motion affects the isotropic scattering component in eq.(2). However, due to the intra- and interchain Interactions in bulk polymers, there is no rigorous calculation of the general expression entering in eq.(2). The normalized first order correlation function g(t) is related to the directly measured single clipped intensity correlation function G ^ t ) in an homodyne experiment through the equation: G k (t) = A|l+b|g(t)| 2 |

(3)

where A is the baseline and b is an unknown parameter used in the fitting procedure which depends on the relaxation strength i.e. the fraction of the - fi

scattered intensity associated with the slow (t>10" s) density fluctuations.

Experimental Photon correlation functions at different temperatures (70-107°C) and pressures (1-1000 bar) were obtained at a scattering angle of 6=90° with the apparatus described elsewhere (4). The light source was an argon ion laser operating at A=514.5 nm and power up to 300 mW. The incident beam was polarized perpendicular to the scattering plane and since there was very little depolarized intensity, no polarizer was used in the scattered light. The single-clipped photocount auto-correlation function G ^ t ) was measured by means of a 96-channel Malvern correlator. The method of matching the sections with different delay time AT to construct the composite correlation function over 6 decades in time was described in ref.(5). The two samples used in this study (kindly provided by Dr.W.Wunderlich, Rohm & Haas GmbH Darmstadt, W.Germany) were poly(ethyl methacrylate) (PEMA) 4 4 having M w =1.6x10

and 7.3x10

respectively. The ratio

M w / M n for both sam-

ples amounts to 2.36. The glass transition temperature determined from DTA data amount to 48

and 65°C for the low and high molecular weight fraction

respectively. We have prepared clear, optically homogeneous, dust free and strain free samples using the procedure described elsewhere (10). A strong confirmation of the suitability of the bulk PEMA samples for photon correlation measurements was provided by the low value of the Landau-Plazcek intensity ratio

(11).

209 Data analysis

The highly

nonexponential

time correlation functions of PEMA can be re-

presented by the Williams-Watts function (2): g(t) = exp ( - t / T 0 ) 6

(4)

however, the distribution parameter 3 is found to decrease with decreasing temperature (T) at constant pressure (P) and with increasing P

at

constant

T. For given P,T,B is smaller for the higher molecular weight PEMA fraction and varies systematically in the range 0.17-0.4. For the other bulk polymers investigated so far, 3 is found to be

0.4 insensitive to T and P

provided that a single relaxation mechanism dominates g(t). The present results mirror those obtained for poly(methyl methacrylate) (PMMA) (9) and indicate the presence of at least two relaxation processes, as is the case of PBMA (10). Moreover, we know from dielectric and mechanical studies of poly(alkyl methacrylate) that the separation on the time scale of the two processes is larger 1n PEMA than in PBMA at given P,T. For these reasons we performed a double-relaxation process fit of the equation: B B 1/9 1 ? ( ( G k ( t ) - A ) / A ) 1 / Z = ^ e x p i - t / T , ) 1 + b 2 exp(-t/T 2 ) L

(5)

to the experimental time correlation functions as described elsewhere (10). The numerical subscripts are used to denote the relaxation parameters of the fast (1) and slow (2) component respectively. A further support for the present type of data analysis is provided by the internal

consistency

of the obtained relaxation parameters for the two PEMA fractions.

Results and Discussion

1. Molecular weight dependence First

we consider the time correlation functions of the two PEMA frac-

tions as a function of temperature at atmospheric pressure. Flg.1

shows

two normalized correlation functions g(t) at 85.5°C for PEMA.It Is apparent, that g(t) of the higher M -fraction (hereafter referred as II) w

210

lines represent f i t s of eq.(4) and eq.(5) to the experimental functions for the low and high molecular weight fractions respectively. The experimental points (340 for the low and 430 for the high molecular weight) are within the thickness of the lines. i s shifted to long delay times and shows a broader shape as compared to PEMA-I (low Mw f r a c t i o n ) . Whilst the former effect should be expected because of the higher T g value of PEMA-II, the change of the relaxation time d i s t r i b u t i o n can be ascribed to the double relaxation d i s t r i b u t i o n feature of g ( t ) . For polystyrene (12), where one relaxation process dominates the slow density fluctuations, the shape of g ( t ) i s indeed insensitive to the molecular weight and the correlation functions are therefore superposable. The mean r e l a x a t i o n times T^ and

obtained from the f i t of eq.(5) to the

experimental correlation functions at atmospheric pressure, are plotted vs 1/T in F i g . ( 2 ) . Up to about 80°C for sample I and 100°C for sample I I the deviation plot of the f i t to eq.(4) shows a systematic error and the data have consequently been represented by eq.(5). In t h i s temperature

211

range, the d i s t r i b u t i o n parameters 3j and ¿ 2

are

equal to 0.36+0.2 and

0.34+0.2 for the fast and slow process respectively and the ratio b^/bg amounts to 0.43+0.04. At higher temperatures the relaxation time t^ i s close to t 2 ( F i g . ( 2 ) ) , so that the s i n g l e Williams-Watts equation (4) represents the experimental functions yielding the slow relaxation time x 2 (10).

The slow time x 2 for the two PEMA fractions exhibit a large temperature dependence typical for a - d i e l e c t r i c times and mechanical s h i f t factors of amorphous polymers near and above T . Hence in these systems t 2 conforms to the WLF equation (3): t2 g

C,(T-TJ 2

g

where C< and C 0 are the WLF constants and t_ i s the mean relaxation time 1 2 g at T . For PEMA the superposition of dynamic shear compliance data y i e l d s 0 ^ 1 8 and C 2 =65K for T g =335K (3). Using the measured values for T g (321 and 338K for PEMA I and I I respectively) and molecular weight Independent C 2 (= 65K) (12,13) we obtain C,, =21 .4+0.4 from the f i t of eq.(6) to the times t 2 of Fig.2. This finding suggests that the difference between t 2 for the two PEMA fractions i s mainly due to the difference in the fractional

free

volume. Concerning the temperature dependence of t 2 , there i s a f a i r agreement between the results derived from l i g h t scattering and mechanical relaxation data. As for the absolute value of t 2 > one has to compare the photon correlation functions g(t) with compressional compliance measurements (14). A new pertinent aspect of the relaxation times in Fig.2 i s the invarlance, within experimental uncertainty, of the fast relaxation time t ^ , on the molecular weight and hence on T . We feel therefore j u s t i f i e d 1n f i t t i n g an Arrhenius temperature dependence to the times t^. The obtained activation energy amounts to 22+5kcal/mol, which l i e s in the reported range of the activation energy for the B-d1electric process. On the grounds of t h i s agreement we ascribe the fast l i g h t scattering mode to the 3-relaxation. For poly(alkyl methacrylates),the B - d i e l e c t r i c mode i s assigned to the hindered rotation of the -COOR side group around the bond l i n k i n g 1t to the main chain (6,15). The slow and fast relaxation processes in Fig.2 seem to merge at high temperatures where the shape of the experimentalcorrela-

212

110

90 i

i

PEMA OM^^-IO4 AM^I^-IO*

1 x/s

T/°C

/

/

10-

10"-

y

70 i

/

/

/ 1

I T

•

27

1000. ~T~ K

2.9

F i q . 2 : Temperature dependence o f the mean r e l a x a t i o n time o f the slow process (o,A) and the f a s t process ( s o l i d symbols) i n PEMA. t i o n f u n c t i o n become narrower.

Finally,

the d i f f e r e n c e between B f o r the

two PEMA functions and the strong temperature dependence o f 6 as well strong evidence o f the a d d i t i o n a l

is

f a s t mode.

2. Pressure dependence

While the h y d r o s t a t i c pressure has a pronounced e f f e c t on the mean ar e l a x a t l o n time f o r poly(ethyl acrylate) (PEA) ( 4 ) , PS (1 6), poly(methyl acrylate)

(PMA) (17) and poly(phenylmethylsiloxane)

(18) the shape o f

the time c o r r e l a t i o n functions i s e s s e n t i a l l y i n s e n s i t i v e to, pressure (B i s c o n s t a n t ) .

For PEMA however, the shape o f g ( t )

i s changed with

pressure i n a s i m i l a r manner as with decreasing temperature. illustrates

Fig. 3

t h i s s i t u a t i o n f o r PEMA-II at 100°C, 1 bar and 800 bar,

213

Fig.3: Normalized composite correlation functions for PEMA at 373K at two different pressures. The thick lines represent fits of eq.(5) to the experimental functions. The 340 and 430 experimental points at 1 and 800 bar respectively are within the thickness of the lines. which is a further support for the double relaxation distribution 1n the experimental correlation functions for PEMA. We have consequently fitted eq.(5) to the experimental data and the obtained values of times t^ and t 2 at 373K are plotted vs pressure in Fig.4. If we consider the relaxation process as an activated process, the slope of the lines in Fig.4 is proportional to the activation volume AV (»2.303 RT(81ogx/3P)j), which represents the difference between the molar volume of the transition state and the molar volume of the initial state. M & for the fast relaxation process is much smaller then A V 2

We see that AV^

for the slow process in both PEMA fractions. The relaxation time x 2 exhibits a strong pressure dependence, which resembles strongly the results obtained for the glass-rubber (a) relaxation In bulk polymers above T . a 3 " b S a t 373K amounts to 204 and 234 cm /mo1 for PEMA-I and II respectively. This small difference is due to the decrease of the cooperativity 1n the

214

F i g . 4 : Pressure dependence of the mean r e l a x a t i o n time of the slow process (o,A) and the f a s t process ( s o l i d symbols) in PEMA. high molecular weight f r a c t i o n g r o s s l y r e p r e s e n t e d by T / ( C , + T - T J ( 4 ) . The 9 u value of AV2 corresponds to the molar volume of aifewimonomer r e p e a t u n i t s ( t h e monomer volume i s 103 cm^/mol a t 20°C). Thus, the slow (a)mode can be understood on a molecular b a s i s as a process involving i s o m e r i z a t i o n of the main chain r e s t r i c t e d to only a small number of monomer r e p e a t u n i t s ( 5 , 1 9 ) . A l t e r n a t i v e l y , the weak p r e s s u r e dependence of the f a s t r e l a x a t i o n time

in Fig.4 i s in accord with the physical p i c t u r e of the hindered

s i d e group r o t a t i o n . F i n a l l y , the a n a l y s i s o u t l i n e d above has y i e l d e d unique values f o r the r e l a x a t i o n parameters of the two processes and hence led to an adequate d e s c r i p t i o n of the slow d e n s i t y f l u c t u a t i o n s in amorphous PEMA above T .

215

Acknowlegement This work i s based on the experimental data obtained in the Department of Chemistry at the University of Bielefeld, West Germany. The financial support from the Max-Planck-Gesellschaft I s gratefully acknowledged. Thanks are due to Dr.I.G.Voigt-Martin for reading the manuscript and to Mrs. I . S c h i l l e r for typing i t .

References 1. Patterson, G.D.: Adv.Polym.Sei.: 48, 125 (1983). 2. Williams, G., Watts, D.C.: Trans.Faraday Soc. 66, 80 (1970). 3. Ferry, J.D.: Viscoelastic Properties of Polymers, John Wiley & Sons, New York 1980. 4. Fytas, G., Patkowski, A., Meier, G., Dorfmüller, Th.: Macromolecules 870 (1982). 5. Wang, C.H., Fytas, G., L i l g e , D., Dorfmüller, Th.: Macromolecules 1_4, 1363 (1981 ). 6. Mc Crum, N.G., Read, B.E., Williams, G.: Anelastic Properties and Dielectric Effects in Polymeric S o l i d s , John Wiley & Sons, New York 1967. 8. Patterson, G.D., Stevens, J.R..Lindsey, C.P.: J.Macromol.Sei., Phys. B18, 641 (1980). 9. Patterson, G.D., Carrol, P.J., Stevens, J.R.: J.Polym.Sci., Polym.Phys. Ed. 21_, 613 (1983). 10. Meier,G., Fytas,G., Dorfmüller, Th.: Macromolecules 1_7, 957 (1984). 11. Fytas, G., L i , B.Y., Wang, C.H.: to be published. 12. Mittag, U.

Diplomarbeit, Universität Bielefeld (1 983).

13. Plazek, D.J., 0'Rourke, V.M.: J.Polym.Sci. A-2, 9, 209 (1971 ). 14. Fytas, G., Wang, C.H., Fischer, E.W., Meier, G., to be published 15. Heijboer, J.: Intern.J.Polymeric Mat. 6, 11 (1 977). 16. Patterson, G.D., Caroll, P.J., Stevens, J.R.: J.Polym.Sci., Polym.Phys. Ed. 21_, 605 (1983). 17. Fytas, G., Patkowski, A., Meier, G., Dorfmüller, Th.: J.Chem.Phys. 80, 2214 (1984). 18. Fytas, G., Dorfmüller, Th., Chu, B.: J.Polym.Sci., Polym.Phys.Ed. 22, 000 (1984). 19. Hall, C.K., Helfand, E.: J.Chem.Phys. 77, 3275 (1982).

RAYLEIGH-BRILLOUIN SCATTERING OF AMORPHOUS POLYMERS

C.H.Wang Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 / USA

B. Stuhn

*

Institut für Physikalische Chemie der Universität Mainz, 6500 Mainz, FRG

* present address: Chemische Werke Hüls, Marl, FRG

Abstract The technique of determining the longitudinal stress modulus over a wide dynamic range using Rayleigh-Brillouin

scatter-

ing has been studied. A correct relation between the RayleighBrillouin spectrum owing to density fluctuations and the mechanical relaxation spectrum of linear viscoelastic

polymer

is provided. The method of computing the longitudinal modulus and the compliance spectra from the time correlation of density fluctuations of PPG, as determined by the photon correlation spectroscopic technique, is illustrated.

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

218 Introduction Rayleigh-Brillouin

s c a t t e r i n g in bulk p o l y m e r s

o c c u r s as a

r e s u l t of f l u c t u a t i o n s of local d e n s i t y a n d o r i e n t a t i o n c h a i n s e g m e n t s . The d y n a m i c s o f the long w a v e l e n g t h a t i o n s in the f r e q u e n c y range of 0.1 - 1 0 ^

Hz can be

i n v e s t i g a t e d by the d y n a m i c l i g h t s c a t t e r i n g t e c h n i q u e Fabry-Perot interferometry and optical mixing At the 90° s c a t t e r i n g a n g l e ,

of

fluctuusing

spectroscopy.

the s c a t t e r e d l i g h t o b s e r v e d

in

the VV s c a t t e r i n g c o n f i g u r a t i o n is a s u p e r p o s i t i o n of the density fluctuation and orientational

fluctuation

w h e r e a s the s c a t t e r e d l i g h t o b s e r v e d in the VH c o n f i g u r a t i o n s is due

to o r i e n t a t i o n a l

by m e a s u r i n g b o t h the VV a n d VH s p e c t r a ,

components,

scattering

fluctuations.

Thus,

it is p o s s i b l e

o b t a i n the c o m p o n e n t o w i n g to d e n s i t y f l u c t u a t i o n s . the R a y l e i g h - B r i l l o u i n s p e c t r u m o w i n g to d e n s i t y

to

To study

fluctuations

is e q u i v a l e n t to s t u d y i n g the F o u r i e r t r a n s f o r m of

C(q,t)

g i v e n by C ( q j t) = < 6 p ( q , t ) 6 p * ( q ) >

where

6p(q,t)

(1)

is the s p a t i a l F o u r i e r t r a n s f o r m of the

f l u c t u a t i o n of the n u m b e r d e n s i t y f r o m the e q u i l i b r i u m w i t h i n s c a t t e r i n g v o l u m e V. T h e q u a n t i t y q is the

value

scattering

v e c t o r a n d its a m p l i t u d e is r e l a t e d to the s c a t t e r i n g a n g l e 9 by B r a g g r e l a t i o n : q = 4im s i n ( 6 / 2 ) / A , w h e r e

A

is

the

w a v e l e n g t h of the i n c i d e n t l i g h t in v a c u u m , a n d n is the r e f r a c t i v e index of the s c a t t e r i n g m e d i u m . In the

amorphous

p o l y m e r s y s t e m the l i g h t s c a t t e r i n g s p e c t r u m d e p e n d s only

on

the a m p l i t u d e of the s c a t t e r i n g v e c t o r a n d not on its d i r e c t i o n . In the l i g h t s c a t t e r i n g e x p e r i m e n t u s i n g 5 -1 l i g h t , q is of the o r d e r o f 10

cm

visible

; thus, in an

a m o r p h o u s m e d i u m the f l u c t u a t i o n w a v e l e n g t h of

density

f l u c t u a t i o n s g i v e n by A„ = 2ir/q is long c o m p a r e d w i t h

the

219

intermolecular distance. This permits using the method of continuum mechanics to calculate C(q,t), the time correlation 1-4 function of density fluctuactions.In our previous work we were mainly interested in the interpretation of the Rayleigh-Brillouin spectrum in terms of the longitudinal modulus. In this paper we consider the reverse problem and we hope to extract information about the longitudinal modulus spectrum in the 0.1 to 10^ Hz frequency range from the time correlation function of density fluctuations, a quantity which can be measured by the photon correlation

technique.

Although our theoretical result is valid above and below the glass transition temperature, we argue that above T O the longitudinal modulus as determined by the photon correlation technique mainly reflects the bulk modulus, due to the fact that above T g the shear modulus is smaller than the bulk modulus by one to two orders of magnitude. Since the bulk modulus is difficult to measure by the usual mechanical technique, light scattering provides an effective method for determining the bulk modulus. In this paper we shall first provide the relationship between the imaginary part of the longitudinal modulus M"

and the Rayleigh-Brillouin

spectrum

using the method of continuum mechanics. Computation of M" from the dynamic light scattering spectrum is illustrated by the photon correlation function data of poly(propylene c glycol) above T g published previously . Longitudinal Modulus and the Dynamic Light Scattering Spectrum The most general constitutive equation describing the stressstrain relation of an amorphous linear viscoelastic system is given w by 6 (2) t

a.,(t)=-P • Pjlr)

1

i ' O

'l

4.

\

ft. t't, junction point

segmental distribution

)

Figure 1. Molecular mechanism of order-disorder t r a n s i t i o n . and the spatial d i s t r i b u t i o n of the chemical junction points h(r) becomes broader with time as shown in Figure 1(b). by a random stochastic process.

This process may be described

As the reptation takes place the segments

loose t h e i r memories with respect to t h e i r position and orientation, resulting in mixing of the unlike segments, increased i n t e r f a c i a l

thick-

ness and eventually in a e s s e n t i a l l y uniform segmental density d i s t r i b u tion c h a r a c t e r i s t i c for the disordered mixture as shown in Figure 1(c). We further simplify our treatment by assuming that the temperature T i s raised s u f f i c i e n t l y high above T^,, so that the thermodynamic interaction between A and B polymers does not s i g n i f i c a n t l y affect the d i f f u s i o n of polymers. Under these conditions, the change of the segmental density p r o f i l e with time P K ( r , t ) should be simply given by Fickian (9) 3p K (r, t)/3t

=

D c V2 p K ( r , t ) ,

K = A or B

(2)

where D c i s the s e l f - d i f f u s i v i t y f o r the block polymer as a whole which

236 should be a function of the self-diffusivity of the constituent polymers Dc

In case when T i s not sufficiently high above T , eq. 2 should be

modified to take into account an effect of f i n i t e value of x(T).

I f the

i n i t i a l segment density profile is given by a periodic function with a repeat distance 21, having domain size 2a and 2£-2a for the A and B domains, respectively, and the domain boundary thickness as characterized by the characteristic

inter facial

thickness

(1, 10) Ttn aQ as shown in

Figure 1(c) (lamellar mi crodomain), i . e . , P A (x,t=0)

= p A (x,t=0)/p Ao

•f+ £ *

00 2 2 a 2 y ( m tt o \ 1 L " exp( 72~ — J I T m=l v

s i.„ n

( mira \ „ „ „ ( mirx \ b H c o s J

(3)

where p Ao i s the number density of the A segment in the homopolymer A, then the reduced segment density profile p A ( x , t ) at time t i s given by (from eqs. 2 and 3 (9)) 9 00 a . 2 v 1 7 ^ m=l

~ i pA{x>t]

"FT

sin

(—A—J

/ J J„„„ / m it (" — 2

exP

cos

o

+ 2D t c 2

—i—J

(4)

= pA(x,t=0,ao=0)*h(x,t)

(5)

where h(x, t ) represents the spatial distribution of the chemical junctions at time t and is a solution of eq.2 with the i n i t i a l condition of h(x, t = 0)

= (2mJ 0 2 )" 1 / 2 exp(-x2/2ao2)

(6)

for the spatial distribution of junctions (Gaussian approximation).

h(x,

t ) is given by (9) h(x,t)

= [2w(a Q 2 + a 1 2 )]" 1 / 2 exp[-x 2 /2(a o 2 + a / ) ]

(7)

where a

2

1

= 2D t c

Similar equation for p B (x, t ) is obtained by replacing x by x-2a.

(8) Now

knowing the segmental density profile P K (X, t ) , one can calculate the

237 scattering contrast for X-ray and therefore the change of the scattering intensity with time I(q, t), I(q, t)

=

I(q, t = 0) exp[-2R(q)t]

R(q)

=

q2Dc

q

(4TT/A)

(9)

where

=

(10) sin

9

(11)

where X and 26 are the wavelength of X-ray and the scattering angle, respectively.

Based on eqs. 9 to 11, one can study kinetics of the order-

disorder transition by the time-resolved SAXS technique.

Equilibrium Aspects of Order-Disorder Transitions

Effects of the order-disorder transition on the SAXS profiles were investigated by Roe et al (5) and Hashimoto et al- (6).

Strong scattering maxima

in the ordered state arises from a long-range spatial order of the microdomains and the spacing calculated from the maximum generally decreases with increasing T and decreasing p, polymer volume fraction in neutrally good solvents, due to decreasing segregation power (6), D

~

(p/T)1/3

(in ordered state)

(12)

A weak scattering maximum is observed even for block polymers in bulk and concentrated solution in disordered state (5, 6) and is interpreted as the maximum arising from correlation

hole effect

as predicted by deiGennes (11)

and Leibler (3) based on the random phase approximation (RPA) and recently by Benoit and Benmouna (12).

The scattering formula presented by Leibler (3) for the bulk disordered block polymers may be rewritten as follows (6) I_1(q) —

{F(x)/N - 2A} - 2B/T

if one can write x as A + (B/T).

(13)

We applied eq. 13 to the block polymer

solutions with neutral solvents by replacing x for bulk by x (eV)

0 .9 0.7

< s> (Hz)

io21 io20

dilat. + DTA + +

T x(l are excluded vofume exponents, is the solvent viscosity,w =l/n and, (x) is the Riemann zeta function. We have shown(6) eq.2 to hold also in case of randomly distributed chromophores of long lifetime at low w by studying dilute solutions of pyrenyl-labeled polyvinyl acetate with w=0.01. At fixed molecular weight,

269 the solvent dependence of K was given at T^ © by k — T/1^0^ (3) To the purpose of studying the behavior below 6, two features of the pyrenyl excimers method are important :(a)the spectroscopic characteristics of the pyrenyl moieties affording the use of very dilute polymer solutions,(b)the inverse proportionality of Jc to the volume swelling factor providing a sensitive probe of any departure from the coil behavior. Results and discussion The results here presented refer to two samples of the same pyrenyl-labeled polyvinyl acetate (PVA-PBA) used in the investigation of the dynamics above 0 (MWl=l.08x10 ,MW2=6.2xl05). The relevant properties of PVA-PBA solutions in the three solvents employed are listed in Table 1( T is the light scattering phase separation point of lxlO -4 g/dl lolutions,TE is the point that separates diffusion from equilibrium controlled regime in the F £ /F m VS. T diagram, T m a x IS the maximum temperature value at which the k were calculated in each solvent).Mixtures of MOH-EOH and MOH-POH at 20°C were used as well.The 6-temperature of solvents and solvents: mixtures were obtained by the turbidimetric method(7),the viscosities measured by capillary viscometry and fluorescence spectra obtained with a Perkin-Elmer MPF44 spectrofluorimeter. The temperature and solvent dependence of the proportionality constant in eq.3 result negligible in respect of the friction and swelling effects.A reduced average relaxation time t X> re( j = =(K r e d ) - 1 =2.46(F e /F m ) C^/T)10~12seconds,is obtained taking at reference T//r\o for MOH at 6°C(0). Figure 1 shows t , relative to its value at 9 plotted against the reduced temperature. Two regions with very distindt behaviors are evident. Table 1.Characterization of PVA-PBA solutions in single solvents Solvent Methanol(MOH) Ethanol (EOH) Propanol(POH)

e CC) 6 57 81

a

T p C C) T E 1.08xÌ0b 6.2xl05 ("C) T-j where x . is the time of energy localization on the phenyl group. We have shown recently C5) that in case of PS, x• J is of order of picoseconds. Therefore rotation of the phenyl groups at room temperature has a secondary meaning in the description of PS monomer fluorescence decay and the factor deciding about the character of decay is the E,1 process leading to the formation of excimers. Figure 1b shows the time dependence of InCi-gCt)) computed from 8q. (5) at a fixed energy transport rate and concen_2 tration of F3S (q = 1.72x10 ) . As one can see, in this case too, the rotation of chromophoric groups only negligibly modifies the excimer fluorescence decay. The especially characteristic feature (.Pig. 1b) is the shift of

278

maximum of ijj(t) to shorter times with increasing rotation rate. Similar changes of ijjrt) were shown recently by Predrickson and Prank (3) on the basis of a model utilising the t-matrix approximation in solving the problem of energy transport in a macromolecule. Prom the fitting of Eq. (.4) to the fluorescence decay of poly (1-vinylnaphthalene) and poly (2-vinylnaphthalene) we have determined values of PES which are equal to 6.26x10"^ and 8.02x10 ^ , respectively.

This work was carried out under Research Project MR.1-5.

References 1. Papers presented at this Conference. 2. Anufrieva, E.V., Gotlib, Y.Y.: Adv. Polym. Sci. 40 , 1 11981). — 3. Predrickson, G.H., Pranck, C.W.: Macromolecules 16 , 572577 (1983). — 4. Itagaki, H., Horie,K., Mita, I.: Macromolecules 16 , 1395-1397 (1983). — 5. Sienicki, K., Bojarski, C. in preparation. 6. Soutar, I., Phillips, D., Roberts, A.J., Rumbles, G.: J. Polym. Sci., Polym. 3d. 20 , 1759-1770 (1982) . 7. Sienicki, K., Bojarski, 0.: Polym. Photochem., 4 , 000 (1984) . ~ 8. Friedrich, C., Laupretre, P., Noel, C., Monnerie, L.: Macromolecules , 1119-1125 (.1981) . 9. Gelles, R., Pranck, C.W. : Macromolecules , 741-748

SMALL-ANGLE SCATTERING OF POLYELECTROLYTE SOLUTIONS

Ryuzo Koyama College of General Education, Kyoto University Kyoto 606, Japan

Introduction The small-angle neutron and X-ray scattering curves of polyelectrolyte solutions have various characteristic forms according to the physical conditions(1 — 5). tions without added salts

In the solu-

the scattering intensity I(q) has —2 —1 —1

a broad peak in the region 10" ~ 10

A

, where q is the

absolute value of the scattering vector q q = (WA)sin(6/2) (A is the

wavelength

(1)

and 6 is the scattering angle).

But when some salts are added to the solution, I(q) increases at small q, and becomes monotonically decreasing with q at sufficiently high concentration of the salts.

These scatt-

ering curves have been calculated in a previous paper(6), assuming a strong electrostatic repulsion between rodlike segments in a random coil molecule.

The following calcula-

tion derives these by a more realistic chain polymer model(7).

Calculation of Scattering Intensity In this calculation we neglect the internal structure of the monomer unit, and regard it as a point scatterer of the radiation.

The scattering intensity per unit volume of the

polymer solution can be written as the Fourier transform of the radial distribution function of the monomers g(R) ,

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

280 r

I(q) = C-j. n [ 1 + n

(g(R) - l ) e x p ( - i q . R ) d R ]

(2)

where C^ is a constant and n is the average number of monomers in unit volume.

Since

ng(R) gives the probability of find-

ing a monomer at the distance R from another monomer at the origin, this is the sum of the probability of finding a monomer of the same polymer with that at origin

ng^(R)

and that

of finding a monomer of different polymer from that at origin n g 2 (R) , i.e. g(R) =

gl(R)

+ g 2 (R)

(3)

When using the normalized intramolecular distribution function f..(R) of the i-th and j-th monomers in the polymer, ng-^(R) can be written as N N £ E f..(R), (i + J) (1) J i j Therefore the Fourier transform of g-^(R) can be given by the ng (R) = N

molecular scattering factor of the polymer P(q) g]_(q) = n _ 1 ( N P(q) - 1 ) _

P

N

(5)

N

P(q) = N

E E fM(q) J i j where f..(q) is the Fourier transform of f..(R). ij ij 5 do not contain the special terms with i = j f 1 ± ( R ) = 6(R), but eq 6 includes them.

f

ii(q) =

1

(6) Eqs 4 and

(i = 1J 2..,N)

(7)

Here 6(R) is the 6 function.

Next, considering the strong electrostatic repulsion between the polyelectrolyte chains, we assume that the probability of finding two monomers from two different polymer molecules within a distance R q is negligible, but beyond this distance this probability is almost constant.

Then if a

monomer of a polymer A is somewhere in a spherical region of radius R , any monomer from polymers other than A is scarcely

281 f o u n d at the c e n t e r of this ical region.

Therefore,

spherafter

i n t r o d u c i n g the o r i g i n of a c o o r dinate s y s t e m at the i - t h m o n o m e r of p o l y m e r A, one can w r i t e x i m a t e l y the p r o b a b i l i t y

appro-

of not

f i n d i n g the m o n o m e r of the

other

p o l y m e r s at R as (cf. P i g . l )

Fig. 1

C where i

o

(8)

f. .(R + S) d S ij " ~ (S(S) = G o exp(-S 2 /R o 2 ) , Using eqs 6 — 1 3 »

(12)

Gq = 1

(13)

one can calculate the Fourier transform of

- p(R) = g 2 (R) - 1 as - p(q) = n _ 1 N h (q) P(q) h

=

TT3/2C

G

n l? R

o o

(14)

2

(15)

*-o o

0(q) = exp(-X 2 /4),

X = Roq

(16)

By eqs 3 and 11, I(q) of eq 2 can be given by 1 + n(g^(q) - p(q)). Therefore using eqs 5 and 14, we obtain the equation for I(q) I(q) = C I n N P(q) [ 1 - h (q) ]

(17)

For the particular case q = 0 we have P(0) = (J>(0) = 1 (from eqs 6, 7 and 16), and eq 17 becomes 1(0) = C I n N [ 1 - h ]

(18)

This 1(0) should not be negative, hence h < 1

(19)

For various polymer models, P(q) is generally a decreasing function of q, but l-(q) is a monotonically increasing function converging to unity at large q.

Therefore for

very small h ( > 1)

w h e r e L can be g i v e n by (22)

L = N ec Kql/Cjn N

I(q)/CT n N H=.8B

Fig. 2

284

When this P(q) is introduced into eq 17, we obtain an approximate equation valid for large L q I (q) = tt C I n HQ R q [ 1 - h exp(-X 2 /4) ] /X

(23)

The maximum point X m (h) as a function of h of this I(q) can be determined numerically X (h) = R Mq m o m

/0,,n (24)

where R q is given by eq 15 R

o

= ir~3/1,v(h/C G d n)1/2 o 0K0

(25)

Therefore from eqs 2 3 ~ 2 5 , the maximum point q m and the maximum intensity I(q ) can be written as •"m q

m

=

7T3 / \„C „ G_ g, ) 1 / 2 n 1 / 2 h " 1 / 2 X o o o

(h)

I(q m )/no« R q [ 1 - h e x p ( - X m ( h ) 2 / ^ ) ] /X m (h)

(26] (2?)

Particularly for h = l, the numerical calculation gives X

(1)

=

2.2118..

(28)

Since C , G and 1 are constants, in this case we have from o' o o ' eqs 25 ~ 27, the qualitative results n"1/2

Rq

q

m

~n

(29)

1 / 2

(30)

I(q m )/n - n " 1 / 2

(31)

In ordinary polymers with single carbon bonds in the main chain

the monomer length is Qq - 2.5 A.

and eq 28

Using this value

in eq 26, and also assuming C Q = G

= 1 , Q M for h = l

becomes q m = 8.36 n 1 / 2 X" 1

(32)

These results are compared with the experimental results of small-angle neutron scattering of deuterated sodium poly(styrenesulfonate) solutions without added salts by Nierlich and others(l).

In Figures 4 and 5 the straight lines show the

285 I(qm)/n

(A_1)

q

.1

, 01

-I L. 10

10 Fig. 4

10

k

n

5

3

(T )

10,-5

10 - 3

10 n

Fig-.5

c a l c u l a t e d v a l u e s by eqs 32 a n d 31 r e s p e c t i v e l y , a n d the dots show the e x p e r i m e n t a l

small

values.

Results F i g u r e 4 shows that eqs 30 a n d 32 a g r e e experimental results.

w e l l w i t h the

The f o r m e r q u a l i t a t i v e

result

has

b e e n o b t a i n e d by H a y t e r and o t h e r s ( 9 ) , b u t eq 32 g i v e s a n a b solute

value.

In p o l y e l e c t r o l y t e

solutions without added salts,

the

e l e c t r o s t a t i c r e p u l s i o n b e t w e e n p o l y m e r chains is s t r o n g , Rq

can be a s s u m e d v e r y large c o m p a r e d w i t h

polymer solutions. assume h s 1

Therefore

irrespectively

o b t a i n e d in the c a l c u l a t i o n .

nonelectrolyte

f r o m eqs 15 a n d 19 we

reases R

can

of n, a n d I(q) has a m a x i m u m as However

it is

considered

that the a d d e d salts ions s c r e e n the e l e c t r o s t a t i c between polyelectrolyte

and

forces

c h a i n s , a n d this e f f e c t p r o b a b l y

So in the s o l u t i o n s w i t h a d d e d salts we

dec-

can

o a s s u m e a s m a l l e r v a l u e of h by eq 15. that as h d e c r e a s e s I(q) i n c r e a s e s at m u m d i s a p p e a r s at h = 0 . 8 5 . I(q) is m o n o t o n i c a l l y

Figure

2 a n d 3 show

s m a l l aq, a n d the

maxi-

A n d for h s m a l l e r t h a n t h i s ,

d e c r e a s i n g w i t h q.

Therefore

c a l c u l a t i o n c a n e x p l a i n the e x p e r i m e n t a l r e s u l t

this

(1~4).

286

The assumption h ~ 1 for very strong interaction means that I(q) has a very small value at q ~ 0

(eq 18).

Thermo-

dynamically 1(0) is related to the osmotic compressibility of the solution K = n-"*" ( 9n/3ir 1(0) oc k B T n 2 k

(33)

where IT is the osmotic pressure, T is the absolute temperature and k_ is the Boltmann constant. Consequently this assumpB tion agrees with the known fact that k of polyelectrolyte solutions without added salt

is very small compared with that

for nonelectrolyte polymer solutions(10).

References 1.

Nierlich, M.,Williams, C.E., Boue, P., Cotton, J.P., Daoud , M., Parnoux, B., Jannink, G., Picot, C., Moan, M., Wolf, C., Rinaudo, M., de Gennes, P.G.rJ. Phys.(Paris) 40, 701704 (1979).

2.

Plestil, J., Mikes, J., Dusek, L.: Acta Polym. 30, 29-32 (1979)•

3.

Ise, N., Okubo, T., Yamamoto, K., Kawai, H., Hashimoto, T. , Fujimura, M., Hiragi, Y.,: J. Am. Chem. Soc. 102, 79017906 ( 1 9 8 0 ) . Patokowsky, A., Gulari, E., Chu, B.: J. Chem. Phys. 73, 4178-4184 (1980).

4. 5. 6.

Benmouna, M., Weill, G., Benoit, H., Akcasu, A.Z.: J. Phys. (Paris) 43, 1679-1685 (1982). Koyama, R.,: Physica B 120, 418-421 (1983).

7.

Koyama, R.,: Macromolecules (to be published 1984).

8.

Koyama, R.,: J. Phys. Soc. Jpn. 34, 1029-1038 (1973), 36, 1409-1417 (1974).

9.

Hayter, J., Jannink, G., Brochard-Wyart, F., de Gennes, P. G.: J. Phys.(Paris), Lett. 41, L-451-454 (1980).

10. Lifson, S., Katchalsky, A.: J. Polym. Sei. 13, 43-55 (195 4).

LIGHT-INDUCED CONFORMATIONAL CHANGES OF MACROMOLECULES IN SOLUTION AS DETECTED BY FLASH PHOTOLYSIS IN CONJUNCTION WITH LIGHT SCATTERING MEASUREMENTS

Masahiro Irie Institute of Scientific and Industrial Research, Osaka University, Osaka, Japan Wolfram Schnabel Hahn-Meitner-Institut für Kernforschung Berlin, Bereich Strahlenchemie, D-1000 Berlin 39, Federal Republic of Germany

Introduction Recently, flash photolysis in conjunction with the light scattering detection method has been applied for investigations concerning the dynamics of macromolecules in solution. The dynamics of disentanglement diffusion were studied by measuring the rate of the change of the light scattering intensity (LSI) after very fast main-chain scission. In this case the diminution of the average molecular weight gave rise to a decrease of the LSI after irradiation of the polymer solution with a 20 ns flash [1] . Flash photolysis in conjunction with the LS-detection method is also applicable to measure the rate of conformational changes of macromolecules at constant chain length. As can be seen from the Debye equation (1) [2] —

l s 2 > s i n 2 ( V 2 ) + 2A 2

= j- + 3A

0

M

(1)

w

the light scattering intensity R^ (Rayleigh ratio) is correlated to the weight average molecular weight M w , the mean square radius of gyration and the second virial coeffi-

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

288 cient A 2 - Here, K = U n ^ n ^ / N ^ )

(dn/dc) 2 , c is the polymer

concentration, n^ is the refractive index of the solvent, dn/dc is the specific refractive index increment, Ag is the wavelength of the incident light and N a is Avogadro's number. 2 Expansion of the polymer chain leads to an increase in and A, which causes a decrease in the LSI, whereas upon 2 shrinkage of the chain, leading to a decrease in and A the LSI increases. Advantage was taken of this behavior by measuring the rate of the photo-induced conformational change of a polyamide having backbone azobenzene groups [3]: COOH NH

~ O ^ "

N=

N

~ 0 ~

N H

_

c o

C

(I)

°""

COOHJn

Upon irradiation with UV light (350 nm < A
mnm'

J J trans, extended stable

The reverse cis

J

J

U k

R

,

(2)

cts. compact Instable

trans reaction can be achieved either by

heating or by irradiation with light of A

> 470 nm. It causes

unfolding of the compact chain as indicated by a decrease of the light scattering intensity due to an increase of the radius of gyration. The rate of unfolding of polyamide I (M = 3 7x10 ) was measured after pretreatment by UV irradiation for trans ->• cis isomerization. In these experiments, dilute polymer solutions

(0.3 g/1) in various solvents were irradiated

with 15 ns flashes of 530 nm light at 22°C. The halflife of the decrease of the LSI in N,N-dimethylformamide (DMF) was -4 5.7x10 s. Additional data are given in Table 1.

289

Table 1

Conformational Relaxation of Polyamide Chains Subsequent to cis -»• trans isomerization of Azobenzene Groups in the Backbone

Solvent N,N-dimethylacetamide

5.8x10

N,N-dimethylformamide (DMF)

5.7x10

4:1 b) DMF-ethanol

7.2x10

3:.2b) DMF-ethanol

11.0x10

4:1

b)

DMF-water

8.8x10

-4 -4 -4 -4 -4

Halflives of the decrease of the light scattering intensity at 514 nm and 22°C. Volume ratio. From the results obtained with mixtures of DMF and ethanol it was concluded that upon worsening

the solvent quality the

rate of unfolding was retarded. In the following a new experiment concerning light-induced coil contraction of macromolecules containing pendant azobenzene groups will be presented. Moreover, an experiment concerning coil expansion of a polyelectrolyte due to a light-induced pH jump will be described. Results 1) Coil contraction of polystyrene having pendant azobenzene groups.

Coil contraction due to trans -»- cis isomerization was

studied recently [4] with copolymers containing pendant azogroups: These copolymers,consisting of styrene and 4-(methacryloylamino) azobenzene

(see Table 2 ) ,

290

were found to precipitate in dilute cyclohexane solution at temperatures above the critical miscibility temperature upon irradiation by UV light [5] . Because the optical absorption spectra of the two isomers differ appreciably (^ m a x of the Table 2.

Sample

Characterization of copolymers of styrene and 4-(methylacryloylamino)azobenzene Content of Azobenzene Groups (mol %)

m Nw

a

>

PS-A-2. 2

2.2

3.1x104

PS-A-4. 3

4.3

2.7x104

PS-A-5. 6 PS-A-6. 5

5.6 6.5

2.0x104 1.8x104

Estimated from GPC using a calibration curve for polystyrene. trans form: 353 nm. \ of the cis form: 440 nm) the trans ' max cis isomerization induced by a 15 ns flash of 347 nm light could readily be detected by absorption measurements. It occurred during the flash, i.e. with a rate constant greater 8

— 1

than 10 s

. From the very fast trans •*• cis isomerization of

pendant azo groups it was inferred that neighbouring phenyl groups did not interact strongly with trans azobenzene groups. Light scattering measurements revealed the following: With all copolymers except PS-A-2.2, an increase of the LSI after the flash with halflives of several hundred us was observed. A typical oscillogram demonstrating the LSI change is shown in Fig. 1, trace (a). It can be seen that the LSI decreased initially. This decrease is due to the concurrent increase of the optical absorption at 514 nm (see oscillogram (b) ) and of the decrease of dn/dc as a consequence of trans •*• cis isomerization. The refractive index increment was measured with copolymer PS-A-2.2 in cyclohexane solution at 28°C and 546 nm: dn/dc = 0.125 ml/g before and dn/dc = 0.100 ml/g after trans •*• cis isomerization. Due to the low content of azo-

291

a

L.S.

2mV 200jus U0'-168mV b

Fig.1. Oscillograms illustrating the increase in the light scattering intensity (a) and in the optical absorption (b) both at 514 nm after irradiation of copolymer PS-A-4.3 in cyclohexane solution (0.13 g/1) with a 15 ns flash of 347 nm light at 25°C.

0. A.

H

H

200>JS

J.

5mV T

Uo*230mV benzene groups copolymer PS-A-2.2 did not precipitate after irradiation. The relative slow increase in the LSI is considered to reflect the conformational change involving a decrease in both the radius of gyration of the coils and the second virial coefficient [6,7]. The halflives of the LSI increase for the various copolymers are compiled in Table 3. The fact that no increase in the LSI after the laser flash was observed with copolymer PS-A-2.2 is consistent with a result obtained by stationary irradiations: precipitation did not occur when the content of azobenzene units was less than 3 mol %[5]. Table 3. Sample PS-A-2.2 PS-A-4.3 PS-A-5.6 PS-A-6.5

Conformational Relaxation of Polystyrene with Pendant Azobenzene Groups -1/2

a>

(s)

—

-4 2.1x10 4.0x10 -4 8.5x10 -4

Halflives of the increase in the light scattering intensity at 514 nm and 2 5°C.

292 It is interesting to note that the halflives of coil contraction of polystyrene with pendant azobenzene groups are of the same order of magnitude as the halflives of coil expansion measured for coil expansion of polyamides having azobenzene groups in the main chains. However, it is to early to arrive at general conclusions at this stage of the studies. Quantitative parameter studies are planned in order to measure the rate of conformational changes as a function of chain length, content of azobenzene groups etc. Preliminary experiments have shown that the halflife coil contraction decreases with increasing temperature. Experiments carried out with PS-A-4.3 at three different polymer concentrations (0.11, 0.076 and 0.055 g/1) yielded the same halflife of LSI change. This result is clear evidence that the process observed in the range of several hundred us is

an

intramolecular reaction. The fact that the

isomerization of only a few azobenzene groups per chain induces significant conformational changes is attributed to a severe perturbation of the balance of polymer-solvent and polymer-polymer interaction by trans

cis isomerization of

pendant azobenzene groups. In a former paper [5], it was pointed out that the dipole moment increases from 0.5 to 3.1 D upon trans

cis isomerization of the azo groups. It

is feasible, therefore, that cis-azobenzene groups are more prone to interact with styrene base units than trans-azobenzene groups because of dipole-induced interactions. The phenomena observed with the copolymers dissolved in cyclohexane can be, then, interpreted as follows: trans-azobenzene groups interact more favorably with solvent molecules than with styrene base units, whereas the reverse situation is true for cis-azobenzene groups which interact less strongly with solvent molecules than with styrene base units. The enhanced capability of cis-azobenzene groups of interacting with other segments of the chain is considered to give rise to a shrinkage of the polymer chain in the initial stage

293

after the trans •*• cis isomerization, i.e. at a time when this interaction is purely intramolecular (in very dilute solution). When different macromolecules collide at a later stage, intermolecular interaction will also become operative. As a consequence, the polymer chains will aggregate and precipitation will be observed. These processes are schematically illustrated in Fig. 2. This model is substantiated by the fact that the increase in the LSI after the flash was not inhibited by low molecular weight azobenzene compounds that were added to the polymer solution. The idea that interaction between cis-azo groups causes coil contraction can be discarded, therefore. Intramolecular Interaction

Fig.2.

Schematic illustration of chain contraction and precipitation of polystyrene with pendant azobenzene groups.

Experiments with solutions of copolymer PS-A-4.3 in different solvents yielded results that are in accordance with this model. With decahydronaphthalene solutions similar effects were observed as with cyclohexane solutions. With benzene and methylene chloride solutions, on the other hand, no slow change in the LSI (in the y,s range) was observed, although the trans -+• cis isomerization proceeded to the same extent and at the same rate as in cyclohexane solution and caused a very rapid decrease in the LSI during the flash. This result correlates very well with the findings that photo-stimulated precipitation occurred in cyclohexane and decahydronaphthalene but not in benzene and methylene chloride solutions [53.

294

Actually, these results were expected because benzene and methylene chloride are envisaged to interact with polar cis azobenzene groups. Therefore, this kind of interaction will predominate over the interaction of styrene base units with cis-azobenzene groups in this case. On the other hand, decahydronaphthalene cannot be polarized and will not interfere with the interaction between styrene base units and cis-azo groups. 2) Coil expansion of poly(methacrylic acid) induced by rapid neutralization^]. The method employed to measure the rate of coil expansion of polyelectrolytes is based on a rapid change in the degree of ionization induced by a pH-jump which is achieved by flash photolysis of triphenylmethane leuco hydroxide derivates

1. Upon irradiation of 1 with a 20 ns laser

flash of ultraviolet light, hydroxide ions can be produced "instantaneously", i.e., within the duration of the flash according to reaction (3)

^•""O-J^O-"'

V

} ( d ,

d j

. )

(5)

Since g. .(r) = 0 for r < d. . , eq. (4) together with (5) determines c - . for IJ 'J 'J r < d.. and, more important, g. . and h. . for r > d. .. From the solution of the system (4) and (5) one gets the partial structure factors by S i j ( k ) = 61d where h ^ k )

+

(n^)*

i s the Fourier transform of

hij(k) .(r).

(6)

338 The S.jj(k) determine the i n t e n s i t y I ( k ) of scattered l i g h t , x-rays or neutrons through

I(k) -

m 1/ I (N.N ) 7 2 f (k) f . ( k ) S. (k) 1 J 1 J 1J i,j=l

(7)

where N^ i s the total number of p a r t i c l e s of species i , and f.(k) = f.(0) b ^ k )

(8)

denotes the s c a t t e r i n g amplitude of a p a r t i c l e of species i . The form factor b.j(k) for a homogeneous spherical p a r t i c l e i s 3j (kd./2) b

where j

i(k)=

(9)

kdi/2

i s the f i r s t spherical Bessel

function.

The procedure t o ^ o l v e the equations (4) and (5) in MSA follows e a r l i e r work by Blum [7], Blum and Hoye [8] and Hiroike

[9] and w i l l be published

elsewhere together with a systematic representation of the r e s u l t s . Here, some of them w i l l be presented and discussed.

(a) Influence of the f i n i t e s i z e of the small ions S.jj(k) and 9-jj( r )

are

calculated from a three-component PM. The f i r s t spe-

cies are the macroions of valency z^, number concentration sphere diameter d . The counterions

and hard-

and the ions of an additional

1-1

e l e c t r o l y t e form the other two components. We assume for s i m p l i c i t y that a l l small ions have the same diameter d„sm N(which i s varied in the c a l c u l a t i o n ) and that they carry one elementary charge ( \ z 2 \ = |z | =1). F i r s t we consider the case without s a l t . Fiq. 1 shows the g . . ( r ) for a s i tuation which might be typical f o r a m i c e l l a r system. The c o r r e l a t i o n s between the macroions are given by g

and the

counterion

distribution

around a central macroion i s described by j 3g12 . Due to the a t t r a c t i v e teraction the counterions

in-

accumulate in the extreme neighborhood of the

central macroion, the maximum of g 1 2 being at r/dj = 0.55 as expected i f

339

Fig. 1. Macroion-macroion ( g u ) > macroion-counterion (g x ) and counterioncounterion ( g 2 2 ) radial distribution functions of a two-component PM with number concentration n, = 4.6xl0 1 8 cnf 3 , valency z i = - 20 and hard-sphere diameter dj = 50 A of the macroions. The counterions diameter d is set equal to 5 A. sm ^ d s m = 5 % . A shallow minimum of g J 2 appears at the position of a " s h e l l " of nearest neighbor macroions, which is followed by a smaller maximum a r i sing from the correlations between the macroions. In Fig. 2 the structure factor S n ( k ) and the radial distribution function g n ( i " ) of the macroions are shown for point-like d $m = 5 % . As expected, S

and g

n

counterions and for

exhibit somewhat stronger structure

for dsm = 5 since f i n i t e size small ions are not as effective in screening the interaction among macroions as point-like ions. This excluded volume effect is less pronounced at smaller number densities n

of the macro-

ions. The influence of the f i n i t e size of the small ions is of particular importance i f one adds s a l t . At the rather large total volume concentrations of the systems in Figs. 1 and 2 the hard-core part of the interaction more and more determines S,, and 3g,, . Fig. 3 shows the effect of added s a l t re3 11 il lative to the s a l t - f r e e case. The structure in S ^ t k ) is being reduced and the increase at k=0 reflects the increased osmotic compressibility with

340

Fig. 2. Macroion-macroion structure factor S ^ k ) and radial distribution function 9 u ( r ) of a two component PM. The macroion species parameters are the same as in Fiq. 1. 1( ) d = 5 X; 1( — ) d = 0 A. 3 ' sm ' sm increasina salt content.

(b) Binary mixtures of macroions So far the scattered radiation was assumed to arise from a single species of macroions (denoted by the index 1). It is an advantage of the multicomponent primitive model to generalize easily to the case of several species of macroions scattering radiation with different scattering powers f

.

The measured structure factor is of the form of eq. (7) and can be defined as S M (k) = ^ L y Nf 2 a B

(N N J l 2 ;

f f Q S Q (k) a 6 '

(10) '

v

where LI N —r a f = -

I L

a

fa 2

(11)

Na

M The normalization in (10) is chosen such that S (k) = 1 for noninteracting particles. For the case of pure scattering polydispersity one assumes that all macroions behave identically with regard to their structural properties but that there are two types of particles differing in their scattering power (fx \ f 2 ). Then g a o = g for all a and 3 and (10) reduces to

341

Fig. 3. Structure factor S n ( k ) of the macroions for a three-component PM, which models a system with added s a l t . n : = 5.0xl0 1 8 cm~ 3 , z 1 = - 2 0 , dj = 50 A and d s m = 5 A . n, i s the cation respectively anion number concentration of the added 1-1 electrolyte. ( ) n 3 /nj = 0, that i s without added s a l t ; ( — ) n 3 /n t = 50; ( - • - ) n 3 /nj = 100.

S M (k) = y S i d ( k ) + (1-y) = S D ( k )

(12)

y = f2 / ¥

(13)

where

S^k)

and

f = (J N f )/(£ N ) a a

in (12) denotes the structure factor of an effective one-component

system. Whereas the simple result (12) is exact for pure scattering polydispersity i t has been proposed to use i t also as an approximation for size polydispersity [10] . The usefulness of this decoupling approximation for charged systems i s now being tested. In the following we r e s t r i c t ourselves to a binary mixture and assume both species to have equal refractive indices. As long as to the wavelength of l i g h t we have f„ = const x d„

d. i s small compared with the same constant

342 f o r both species (a = 1,2). Defining the r a t i o of diameters X = d 1 /d 2 with d

d 2 and x. = N / ( N x + N 2 ) , the quantity y ( x 2 ) i n eq. (13) has i t s mini-

mum at the concentration x* = X 3 / ( l + X 3 ) , where i t has the value y ( x 2 * ) s y * = 4X 3 /(1+X 3 ) . The r a t i o of incoherent to coherent s t a t i c s c a t t e r i n g i s given from eq. (12) as I i n c / I c o h = R/sid(k)

(14)

with R = ( l - y ) / y . Therefore, R has i t s maximum at the concentration x * 1 - x * , so that the r a t i o ^ n c / l c 0 h

1S

=

l a r g e s t at x * .

We have used X = 0.8, so that x * = 0.339, y * = 0.896 and R = 0.116. The expression (10) i s then calculated for the following three-component systems: n

= 3xl018cm"3, d

= 40 ft, d 2 = 50 8, z

= z 2 = - 15 f o r the compositions

n /n 2 = 1; 0.3 and 0.05. In addition there are corresponding numbers of 0 univalent counterions with d = 4 A. These r e s u l t s are compared with sm n id S ( k ) , eq. (12), where S (k) i s the structure factor S (k) of a two-component system, which c o n s i s t s of macroions of number concentration ( n 1 + n 2 ) , valency z = - 15 and a volume f r a c t i o n equal to the volume f r a c t i o n of the 3

3

two species of macroions in the real system, that i s n = ^ ( n ^ +n 2 d 2 )/6. The diameter d of the macroions in the e f f e c t i v e system i s then given by _ 3

(n +n 2 )d

3

=

(n d

3

+n 2 d 2 ). The second component of the e f f e c t i v e system con-

s i s t s of n e u t r a l i z i n g 3

counterions

with d„

= 4 %.

sm

I t i s found that S D ( k ) i s a very good approximation to S M ( k ) near the main maximum of the structure f a c t o r . But near k=0 large discrepancies are found in p a r t i c u l a r at higher r e l a t i v e concentrations n 2 /nj> S^(0) overestimates the true structure factor S ^ ( 0 ) . F i g . 4 shows the r e s u l t s for n

2

=

V

decoupling approximation at small wavevectors

has already been noticed by V r i j [ l l ] and by Pusey, Fijnaut and V r i j

[12]

within the Percus-Yevick approximation for hard-core systems. We have i n cluded the corresponding hard-sphere r e s u l t s in F i g . 4, since in t h i s case the MSA treatment i s identical to the Percus-Yevick approximation. I t i s seen that the s l i g h t difference between S D ( k ) and S M ( k ) for the hard-core system near k m a x i s reduced by charging up the p a r t i c l e s . For the i n v e s t i g a t i o n of charge p o l y d i s p e r s i t y e f f e c t s we have taken

343

F i g . 4. Structure factors S (k) and S (k) of a binary mixture of macroions of composition n . / n ^ l , together with the corresponding functions of the equivalent uncharged system. The parameters are n,= 3 x l 0 1 8 cm" 3 , d.= 40 A, d = 50 A, z =z 2 = - 15 and d = 4 A. ( — ) S M ( k ) ; (•••) S " ( k ) of the equivalent uncharged system; ( — ) S u ( k ) ; ( — ) S&(k) of the equivalent uncharged system.

n

i p2 , z

= - 15, a f i x e d diameter r a t i o A = 0.8 and have varied the

charge r a t i o from z 2 /z

= 0.66 to 1.33 and have compared the r e s u l t s f o r

S M ( k ) and S D ( k ) for e f f e c t i v e systems with z = (z +z )/2. I t i s found that S^(k) for k values near k m a x i s s t i l l

an acceptable approximation to S M ( k )

within the chosen parameter i n t e r v a l s . With regard to the long-wavelength M region the gross discrepancy remains; in addition S (0) changes from 0.075 to 0.030 in varying z 2 /z

within the above i n t e r v a l , whereas S ^ ( 0 ) = 0 . 1 1

for a l l charges z .

I I I . Results for Dynamical

Properties

Photon c o r r e l a t i o n experiments on polystyrene spheres [13,14,15] detect f l u c t u a t i o n s o f the system on the scale which i s of the same order as the average distance between macroions. Therefore, the s c a t t e r i n g experiments probe the system on the length scale of i t s short-range structure and de-

344 tect the temporal changes of this structure. For this reason it cannot be expected that macroscopic hydrodynamic equations of motion are sufficient for a theoretical description of the dynamical behavior of macromolecular suspensions as seen in light and neutron scattering. The basic transport equation, appropriate for N interacting Brownian particles, is the Fokker-Planck equation for the distribution function f(F;t) i f ^ , . . .

,...

of the momenta^- and coordinates r^ >

i=l,...,N of the macroions ^

f(r;t) = Q f(r;t)

(15)

where the Fokker-Planck operator is given by

5

"

£i -3F7 + li

+

?

'(kgT 4

+

^

£i )

'

(16)

Here, F. is the force acting on particle i by all other macromolecules and Ç q is the one-particle friction coefficient of the macroions. Hydrodynamic interactions can be neglected for the highly charged and rather dilute systems of polystyrene spheres. This is not justified for more concentrated and less charged systems. Various collective and one-particle properties have been calculated on the basis of eq. (15) by Hess and Klein [16]. Here, we will only mention some of the results, which are of particular importance for dynamic light scattering. The dynamic structure factor S(k,t)orits Laplace transform S(k,z) can be calculated with the help of the projection operator formalism of Mori and Zwanzig [17] . In the experimentally accessible time regime of the correlator one obtains S(k,z) =

^

c T (k)k m z + - - — C(k.z)

(17)

Here, S(k) = S(k,t=0) is the static structure factor, Cy (k) = kgT/m S(k) and ç(k,z) is a generalized dynamic friction function, which generalizes the friction coefficient ç

of a single macroion to a frequency and wave-

345 vector dependent function ç ( k , z ) . This quantity i s found to c o n s i s t of two p a r t s , namely the one-particle f r i c t i o n due to the presence of the solvent and a dynamical part which a r i s e s from the direct i n t e r a c t i o n s between the moving macroions: (18) Here, c i s the concentration of macroions and n ( k , z ) i s the Laplace t r a n s form of the longitudinal dynamic v i s c o s i t y of the i n t e r a c t i n g macroions. One of the most i n t e r e s t i n g r e s u l t s of the above mentioned l i g h t s c a t t e r i n g experiments on nearly monodisperse samples i s the fact that outside the extreme forward d i r e c t i o n the dynamic structure factor S ( k , t ) cannot be r e presented by a s i n g l e exponential function of time. From our general res u l t (17) i t i s evident that t h i s behavior i s due to the z-dependence of C(k,z) ; the deviations of S ( k , t ) from a s i n g l e exponential therefore a r i se from the v i s c o e l a s t i c properties of the suspension. This has been checked by c a l c u l a t i n g the dynamic longitudinal

viscosity

function n ( k , t ) . The Mori-Zwanzig formalism provides an expression for n ( k , t ) in the form of a time-dependent c o r r e l a t i o n function. This function has been evaluated [16] by using the mode-coupling approximation [17]. The result is 2 n(k,t) =

( 2tt )

1 /d 3 k' T [ S ( k ' )] S ( i k+k 1 , t ) S ( i k - k ' , t )

(19)

Here, * y [ S ( k ) ] i s a known function of the s t a t i c structure factor and S ( k , t ) i s the dynamic structure f a c t o r , whose Laplace transform i s expressed in terms of ri(k,z) in eq. (17) and eq. (18). Therefore, eqs. (17) to (19) form a closed set of equations which was solved numerically, where one takes S ( k ) either from a s t a t i c l i g h t s c a t t e r i n g experiment or from a theory of the type described in the f i r s t part of t h i s paper. For a comparison with experiment we have proceeded in the following way: From the experimentally determined S ( k , t ) one can define a mean-relaxation time through

346 T ( k ) =

S?W/S(k,t)dt 1 ' o

(20)

2

If y (k) = D Q k /S(k) denotes the first cumulant of S(k,t), where D q is the diffusion coefficient of a non interacting particle, then A(k) = (y (k) - - r ' ^ k ^ / y ^ k ) is an appropriate measure of the deviation of S(k,t) from a single exponential in time. On the other hand, from eqs. (17), (18) and (20)

t(k) can also be expressed as T(k) = [co + | n(k) k 2 ]/(c T 2 (k) k 2 )

where CO

n(k)

=

/ n(k,t) dt o

is the (k dependent) longitudinal viscosity. Using the numerical solution of the self-consistent set of eqs. (17) and (19), one obtains a theoretical result for A(k). The agreement with the light scattering data of Grliner and Lehmann [15] is within 20 % , see ref. [16] . It should be noted that this agreement is obtained without the fitting of an adjustable parameter. From this discussion it becomes clear why the measured correlation functions in QELS are non-exponential at finite k. The concentration fluctuations, which give rise to light scattering, are coupled to stress fluctuations of the highly correlated system of macroions. The stress fluctuations reflect the non-trivial viscoelastic behavior of the system, as described by n(k,t). If S(k,t) were a single exponential, x(k) would be equal to the inverse of the first cumulant and A(k) would vanish. The fact that the suspension exhibits viscoelasticity, leads to elastic behavior, if the system is probed on a sufficiently short time scale. The corresponding "high frequency elastic constants" have been calculated [18]. It is found that the longitudinal constant varies as the square of the concentration c, whereas the shear elastic constants increases with c / 3 . Finally it is pointed out that various other physical properties characterizing the dynamical behavior of suspensions of charged spherical macromolecules have been calculated on the same basis (16,18,19,20).

347 IV. Conclusion The aim of t h i s paper has been to demonstrate that structural and dynamical properties of suspensions of charged spherical macromolecules can be d e scribed and understood on a microscopic b a s i s . I t has been shown that in f a i r l y concentrated suspensions l i k e micellar systems the role of the small ions should be taken into account for the c a l c u l a t i o n of S ( k ) . Furthermore, various p o l y d i s p e r s i t y e f f e c t s have been investigated for s t a t i c propert i e s of charged hard spheres. With regard to the dynamical structure factor i t was found that even a monodisperse system of charged hard spheres can in general not be described by a s i n g l e exponential function, since at f i n i t e s c a t t e r i n g vectors the v i s c o e l a s t i c s t r e s s f l u c t u a t i o n s give r i s e to a more complicated behavior.

References 1.

Pusey, P.N., Tough, R.J.A., i n : Dynamic Light Scattering and V e l o c i metry: Applications of Photon Correlation Spectroscopy, R. Pecora, ed., Plenum, New York 1984.

2.

Hayter, J . B . , Penfold, J . , J. Chem. Soc. Faraday Trans. 1, 77,1851 (1981).

3.

Kalus, J . , Hoffmann, H., R e i z l e i n , K., U l b r i c h t , W., I b e l , K., Ber. Bunsenges. Phys. Chem. 86, 37 (1982).

4.

Cebula, D.J., Goodwin, J.W., J e f f r e y , G.C., O t t e w i l l , R.H., Parentich, A., Richardson, R.A., Faraday Disc. No. 76, 37 (1983).

5.

Hayter, J . B . , Penfold, J . , Mol. Phys. 42, 109 (1981).

6.

Hansen, J . P . , Hayter, J . B . , Mol. Phys. 46, 651 (1982).

7.

Blum, L . , Mol. Phys. 30, 1529 (1975).

8.

Blum, L . , Hoye, J . S . , J. Phys. Chem. 81, 1311 (1977).

9.

H i r o i k e , K., Mol. Phys. 33, 1195 (1977).

10. See the contribution by Pusey, P.N., in Faraday D i s . No. 76, 93 (1983). 11. V r i j , A . , J. Chem. Phys. 69, 1742 (1978). 12. Pusey, P.N., F i j n a u t , H.M., V r i j , A., J. Chem. Phys. 77, 4270 (1982). 13. Brown, J . C . , Pusey, P.N., Goodwin, J.W., O t t e w i l l , R.H., J. Phys. A 8, 664 (1975). 14. Dahlberg, P . S . , Boe, A . , Strand, K.A., Sikkeland, T., J. Chem. Phys. 69, 5473 (1978).

348 15. Grüner, F., Lehmann, W., J. Phys. A 12, L 303 (1979); 15, 2847 (1982). 16. Hess, W., Klein, R., Adv. Phys. 32, 173 (1983). 17. See, for instance, Boon, J.P., Yip, S., Molecular Hydrodynamics, McGraw Hill, New York, 1980. 18. Klein, R., Hess. W., Faraday Disc. No. 76, 137 (1983). 19. Hess, W., Klein, R., J. Phys. A 15, L 669 (1982). 20. Klein, R., Hess, W., in: Ionic Liquids, Molten Salts and Polyelectrolytes, K.H. Bennemann, F. Brouers, D. Quitmann, eds., Lecture Notes in Physics, vol. 172, Springer-Verlag, Berlin, 1982.

COOPERATIVE GROWTH OF MOLECULAR CONCENTRATED PBLG SOLUTIONS ELECTRO-OPTICAL

Hiroshi

University

of T o k y o ,

molecular

solutions methods.

was

used

solution

investigated

and 2 8 . 0 ) x l 0 0 0 0

College

SEMIDYNAMIC

weights

(sample

I,

and Y o u j i r o

of A r t s

of P B L G

in

dynamic

Sciences,

liquid

crystalline

electro-optical are

II,

IV) and

and

applied pulsed range

are

and b e n z e n e (very poor).

rectangular

sine w a v e s available

with

in

pulses

with

amplitude

this

(2.1,

10.3,

the

Electric

amplitude

4 KV(p-p).

experiment

was

from

semi-concentrated

are m - c r e s o 1 ( g o o d ) , 1 , 2 - d i c h l o r o e thane (fairly

dioxane(poor),

JAPAN

transition

of P B L G u s e d III,

FUKUDA

Tokyo,

of

to a l y o t r o p i c

by

and

Meguroku,

the m e c h a n i s m

aggregation

Molecular

NAKANO,

Komaba,

to e l u c i d a t e

semi—concentrated phase,

Tatsuo

of C h e m i s t r y ,

In o r d e r

IN

BY THE

METHOD

WATANABE,

Department

AGGREGATION

INVESTIGATED

solvents good),

fields

up

The

18. G,

to 2 0 K V

and

frequency

from 2 0 0 H z

to

20

KHz. For quency

the D C

AC

fields,

oscillates frequency tude

of

fields

with of

field.

the o s c i l l a t i n g dipole

component

of

to n e g a t i v e of

electric

a frequency

the A C

permanent

value

the

(rectangular

the

increasing

signals

signal

increase

s ignals i n c r e a s e s on

of

the

sign

changes and

increasing

fre-

of

from the

value

and

angular ampli-

as e x p e c t e d

the

the«/,

low

the at , the

decreases

However,

the

is p o s i t i v e

of 2 ui w h e r e ui is On

orientation.

further

and

birefringence

the b i r e f r i n g e n c e on

pulse)

in

the

the

static

positive absolute oiUJ.

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

A

350 typical

example

Fig.1,

in w h i c h

amplitude

of

the A a r e

the

appears

the

tive

of

depends

weight

the

reported

posi-

in

semi-

et

al(l)

which

relaxation

after

the

plate, and

to c h e c k

signals.

its

the

of

observed

in h i g h

region

is

shown

in F i g . 2 a .

signal

is

positive

AC p u l s e

but

negative

and

state. tion

Just of

for

goes

first

An EB s i g n a l

decomposition

into

after

to

a

to

steady

annihilathe

and

signal

then

and

its

and

decay

(b)

positive

components.

the

frequency

the

2 0 KHz AC p u l s e ,

negative

The

down s l o w l y

reaches after

in

the

frequency

just

a high

t h e AC p u l s e ,

down s h o o t s Fig.2.

of

of

axis

birefringence

signal

application

removal

analyzer

sign

weak

enabled

in-between

the

A typical

DC ( A )

optical

was p l a c e d

the p o l a r i z e r order

dependencies

by u s i n g

field

direction,

Angular of

f 1Hz)

1

1.5

frequency AC C O )

components

and

of

EB.

been

high

birefringent

Fig.1.

solutions

already

by M o r i

we a p p l i e d

log

birefrin-

PBLG has

3.5

Such

from the

the n e g a t i v e

in m - c r e s o l

and

solvents.

of

concentrated

free

critical

which

signals to

values.

some

the m o l e c u l a r

aninversion

the and

birefringence

concentration

gence

in

o are

static

beyond

the n a t u r e

shown

oscillation

The n e g a t i v e

on

is

its and

us

fields.

In

to o b s e r v e

the p u l s e d parallel

to

this

work

the

field

fields.

A

the

field

351 gradually presents

decays. how

The

the

complicated

c a n be

interpreted

signal

and a s l o w

The the al

of

birefringence w h e r e So i s

Fig.3a.

phase

is

and £

positive

the

The

decay

annihilation

of

the

values

o f u> a r e the

These

at

AC

is

formed orient

between

t=0,are

is

It

is

in

Fig.2a

clear

the

the

and

with

negative

a

the

the

•

ones

of

in

sudden

oscillating

that

8/So

abnormal

AC f i e l d s by

in

remov-

signal.

for

In

several

relaxation

is

to.

of

that

a sort

semi-concentrated the

the

retardation

compared

of

of

birefringence

suggest

under

after

normal

obtained

a peak

the v a l u e

strongly

aggregates

in

positive

birefringence

relaxation

positive

compared.

fast

negative

DC and 200 c / s

at

of

Fig.2b

signal

a

normalized

field

field

larger

results

aggregation the

for

of

relaxation

free

the

for

relaxations

faster

as

the

slow

field

value

the

of

difference

birefringence

Fig.3b

the

The

slow.

birefringence

a very

expressed

the

very

signal.

feature is

AC f i e l d .

is

a superposition

negative

frequency

the

light

as

remarkable

high

relaxation

high

of

large

solutions

frequency

AC

and

field.

I i

V\ ^

. 5

.5

\

0

••.'••"••«.^•pfiW.

3 0

50

100

0

5

10

Tims)

Fig.3.

Normalized

solution. denoted others is

on e a c h are

part

Inset of

curves

of

Frequencies

curve.

positive.

different.

initial

decay

c=70g/dm3.

EB i s

Note in

negative

is

EB by

the

fast

in

PBLG(IV)/EDC

AC f i e l d

for

time

a close a

EB

the

negative

that

Ca)

the of

20 KHz

scale

in

observation sampling.

and DC and

the

(a)

and

of

the

are

(b)

352 The o r i e n t a t i o n the

direction

field,

as

mechanism

of

the

suggested

perpendicular measurement dichroism

is

the

of

the m i d d l e

chain benzyl

group,

is

absolute

value

however,

indicating

side

chains

negative

of

the

at

is

electric

dichroism

t h e movement free with

of

the low

the

is

very

respect

of

side The

small, groups

to

the

sign

frequency

AC f i e l d s . benzyl

and

The

band of

t h e DC and

frequency

that

is,

absorption

at

to

type

c o n f i r m e d by

That

high

relatively

is

of

moment

perpendicular

PBLG h e l i x

257nm,

positive

dipole

birefringence.

dichroism.

at but

is

the n e g a t i v e

electric

AC f i e l d s

induced

orientation by

orientation

of

of

on

the b a c k

the bone

helix. The n e g a t i v e obeys

the K e r r ' s

birefringence law

in

the

in h i g h

range

of

concentration

dependence

of

birefringence

for

IV/m—cresol

estimate

the

threshold

polymer-solvent negative

sample

concentration

system

is

birefringence

The

results

the K e r r

about

suggest

solutions,

consequently

relevant

from the K e r r the

induced

dicular

to

the

region

and

the

moment w h i c h

field

of

this

From the

we

the

negative

could

specific

beyond growth

of

that

the

direction

for

different

of

the

from

aggregates

and p o s s i b l e

orients will

be

the

lyotropic

is

decay

of

semi-concentrated

a new m e c h a n i s m The v o l u m e

constant

dipole

of

solutions

14g/dm3

f o r m a t i o n which

explanations.

constant

a cooperative

in p r e - t r a n s i t i o n phase

observation.

region

appears.

aggregates crystalline

frequency

liquid the estimated

origins

the h e l i x discussed

PBLG

elsewhere.

Re f e f e n c e s

1.

Mori,

Y. , O o k u b o ,

Sci.,

Polym.

Phys.

N. , H a y a k a w a , Ed.,

20,

2111

R. , Wada, (1982)

of

perpen-

Y. : J .

Polym.

LIGHT SCATTERING ANOMALY OBSERVED IN DILUTE SOLUTIONS OF POLY (VINYL ALCOHOL) AGED AT HIGH CONCENTRATION

Libuse Mrkvickova, Cestmlr Konak, Blahoslav

Sedlacek

Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 162 06 Prague 6, Czechoslovakia

Introduction When studying the ageing of poly(vinyl alcohol) by integral light scattering

(ILS) we observed an anomaly consisting in a

strong decrease in ILS intensity at lower angles. This phenomenon was first reported by Doty and Steiner

(1). It was re-

cognized to be characteristic of the strict "liquid-like type" structure

(2). Under such conditions, the effect is caused by

ordering of particles

(leading to a considerably

large excluded

volume) and not by the aggregation itself - this would

indicate

an opposite effect. Therefore, we decided to try to elucidate this problem by using also other LS methods.

Experimental Samples. After dissolution alcohol), PVA

(5 hours at 80°C) of poly(vinyl

(BHD Chemical LTD., England; M ^ = 2 2 300), sol-

utions of concentrations c = 1 . 6 ,

6.4, 10, 16% w/v were left to

age at 25°C. Before measurements the samples were diluted considerably

(< 1%w/v). Aqueous 0.1 N K C 1 was used as solvent.

Methods. ILS measurements were performed with a Fica 40 000 apparatus A =546.1

(vertically polarized primary beam of wavelength nm, angle interval 30-150°). For quasielastic

scattering

light

(QELS) measurements a homodyne spectrometer with

96 channel correlator

(He-Ne laser, A = 632.8 nm, interval

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

18-

354

105°) was used. Turbidity was measured with a Perkin-ElmerHitachi UV-VIS spectrometer 340 (A = 435. 8, 546. 1 , 684,3 nm) . For the characterization of supermolecular particles (SMP), both integral (ITR) and differential (DTR) turbidity ratio methods were applied (3). The solution were purified with a Beckman L8-55 ultracentrifuge (rotor SW.1, 15 000 r.p.m., 1 hour).

Results and Discussion The minimum on the reciprocal particle scattering function (9) was observed by ILS if the solution was aged at a higher -2 -3 concentration than the critical one, c = 3.3x10 gem , i.e.,

P

when the space was filled with molecularly dispersed PVA (4). The magnitude and position of this extreme are practically stable in time and depend on the given concentration after dilution (

dn

l

(3)

380

The intensity and degree of polarization of the scattered light are given by I = Trc^

(4)

P = 1 - 4k S |/Tr]

(21)

and (C

sca>S = ^

[e

2S2

+ L

1(X

+ Y)]

(22)

2. Rayleigh-Gans Particles When the colloidal particles satisfy the conditions for R-G scattering (54) all the above parameters can be modified by incorporating a suitable form factor R(0,(|>) . This factor will be different for 'T' and 'L' configurations. Thus ( ^ „ ' J r = R(6,$) T ' L (^) T ' L o U'R_G o U,dipole

(23)

Similarly one can define other parameters. It is straightforward to show that the relation (14) will be satisfied in this case while the equation (19) will not be obeyed (46).

383

3. Small Conducting Spheroids When particles are metalic and are much smaller then the wavelength of light the scattering may not be pure electric dipole scattering. In the limit when m = 00, the scattering consists of electric and magnetic dipole radiation (54). In this case it has been shown that (20) i = ei (C

ext>i "

(C

ext»r

L = l " o =

or in the concentration c: Dc /D o =1 + k_< DtY> = 1 + k' D c, ' where Do is the diffusion coefficient at infinite dilution, k D and k^ are interaction parameters; k D = k]i)/v, v being the partial specific volume of the particles. The simplest model system for theoretical calculation of k D is a dispersion of hard spheres. Two types of interactions are considered in the calculation of k D : static ones, proportional to the second virial coefficient, A2, and hydrodynamic ones, which are responsible for the scatter of calculated k D values (cited, e.g., in (1)) ranging from -6 to +3. Most of the model systems for experimental testing (lattices, colloid dispersions of metals, etc.) are unsuitable due to electrostatic interactions. For silica particles with hydrocarbon chains on their surfaces (so far the best approximation of hard spheres) in cyclohexane, k Q = 1.3 + 0.2 (2) . In this study, block copolymer micelles, for which geometrical and hydrodynamical dimensions coincide (3), were used as an experimental model for hard spheres. A2 and k Q were measured by integral and quasielastic light scattering and compared with theoretical values.

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

402

Experimental Micellar system: Spherical micelles with aliphatic cores and polystyrene shells of three-block copolymer Kraton G-1650 (Shell product) in mixtures 1 ,4-dioxane/0-30 vol.-% n-heptane. Methods: Quasielastic light scattering (QELS), Ar laser A = = 514.5 nm, 0= 90', 96 channel digital correlator. D c values were evaluated from autocorrelation functions (in all cases by the perfect single-exponential fit, indicating that micelles were practically monodisperse). Hydrodynamic radius, R H , was calculated from the Stokes formula R H = kT/67rriDc, where n is the solvent viscosity. Integral light scattering (ILS): Sofica instrument, X = 546 nm, 6 = 30°- 150'. M from K'c/R o = 1/M w + 2A_c, where K 2 R is the Rayleigh ratio at 0->O.

1

and A„ were evaluated w 2 is the optical constant and r

Results QELS and ILS data on block copolymer micelles (Figs. 1 a and 1b) provide values of basic parameters like relative micellar mass, MW . hydrodynamic radius, R„, and interaction parameters, AZ0 N and k

(Table 1).

Table 1: Light scattering data for Kraton micelles in 1,4-dioxane/n-heptane mixtures at 26°C. For the definitions of measured and calculated quantities see text. n-Heptane

Calculated values

Measured values Mw x10~6

A 2 x10 6 3

vo1.— %

RH

-2

nm

2. 1

19.5 22.3

cm g mol

0

4.80

10

4.44

4.2

20

4. 20

7.5

30

3.77

12.7

K ' D

AHSX1Q6

2 cm3 g _J mol

KD

3.07

1 .09

6.63

5.66

1

7.54

7.19

1 .01 1.15

4.02

23 . 2 24.9 1 1 .95

10.97

.05

403

c.W 2 [g cm 3 ]

Fig. 1. Concentration dependences of D C

(1a) and KC/R q

(1b)

for Kraton micelles in 1,4-dioxane/n-heptane solvent mixtures at 26"C. Curves are labelled by vol.-% of n-heptane.

404

1,4-Dioxane is a better solvent for polystyrene, while n-heptane is a better solvent for hydrogenated polybutadiene. Although solvent mixtures used (i.e., up to 30 vol.-% n-heptane) are good solvents for polystyrene and poor ones for the aliphatic blocks, an increase of the n-heptane content improves the thermodynamic quality of a solvent mixture towards micellar aliphatic cores and deteriorates that for the polystyrene shell. As a consequence, M^ decreases with n-heptane content. The increase of R^ means that the effect of swelling of micellar aliphatic cores prevails over that of deswelling of polystyrene shells. A2 values for the hard sphere model system is given (4) by Aip = 4N A V/M^ , where Nft is the Avogadro number o and V = 4ttR^/3 is the volume of a spherical particle. Since the HS

values of A2 from ILS (Fig.1a) and A2

obtained using experi-

mental R H values are similar, the assumption that the block copolymer micelles under study behave like hard spheres seems to be correct. The calculated values of k_ L)(= k'N,, D A V/MW ) in Table 1 (1.01-1.15) are smaller than that for modified silica particles (2). No effect of solvent composition exceeding the experimental error (i.e., solvent quality) has been observed.

References 1.

Stepinek, P., Konak, C.: Adv. Colloid Interface Sci. to be published.

2.

Kops-Werkhoven, M.M., Fijnaut, H.M.: J. Chem. Phys. 74, 1618 (1981).

3.

Tuzar, Z., Plestil, J., Konak, C., Hlavatd, D., Sikora, A.: Makromol. Chem. 184, 2111 (1983).

4.

Yamakawa, H.: Modern Theory of Polymer Solutions, Harper and Row, New York 1980.

PROPERTIES OF BLOCK COPOLYMER MICELLES NEAR THE C.M.C. and C.M.T.

Zdenek Tuzar, Petr Stepinek, Cestmir Konak Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 162 06 Prague 6, Czechoslovakia

Introduction Micellization of block copolymers in selective solvents (i.e. good solvents for one block, which are poor solvents for the other block) obeys the model of closed association (1). This model is characterized by an equilibrium between unimer (molecularly dissolved copolymer) and spherical micelles (having a core formed of the insoluble blocks and a shell containing the soluble blocks), with a sharp mass and size distribution. Closed association model also assumes the existence of a critical micelle concentration (c.m.c.), below which only unimer and above which also micelles can be detected by a given method. In analogy to c.m.c., a critical micelle temperature (c.m.t.) can be defined, above which, at a given copolymer concentration, no micelles would be present. The objective of this study has been to detect and describe block copolymer micelles near c.m.c. and c.m.t. by light scattering methods.

Experimental Copolymer: Fraction of a three block copolymer poly(styreneb-hydrogenated butadiene-b-styrene) (Kraton G-1650, Shell 4 product), free of homopolystyrene (M = 7x10 , 29 wt.-% w styrene). In selective solvents used, 1,4-dioxane and 1,4dioxane/30 vol.-% n-heptane mixture, micelles are formed with aliphatic core and polystyrene shell (2).

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

406 Methods. Quasielastic light scattering

(QELS): homodyne spec-

trometer, 96 channel digital correlator, Ar laser (X = 514 nm), 0 = 90*. Collective diffusion coefficient, D c , was evaluated from the autocorrelation function G(t) = A e - ^ + B, where 2 r = 2 D C K r K being the scattering vector, t time delay and A,B constants. - Integral light scattering

(ILS): Sofica

goniometer, X = 546 nm, © = 30°-150°. Processed data provide J.-L. -I ,, (av) ,, (m) (m) ,„ (u) (u) , . the average molar mass M = M w + M w , w being w w ' the mass fraction, (m) and (u) pertain to micelles and unimer, respectively. Results Micelles near c.m.c. C.m.c. for any block copolymer micelles can be expected much smaller than for, e.g., soap micelles; this has not been determined by light scattering yet. Assuming the closed association model, the ILS data should follow the idealized plot on Fig.1

(1). 1

Fig.1. Schematic plot 1 / M ( a v ) = f(c) for w closed association.

,(ov) M'

cm c Experimental data (Fig.2) show a different behavior of micelles at low c. Both QELS and ILS failed to record c.m.c. The perfect single exponential fit in QELS measurements indicates practically monodisperse micelles even at the lowest measured and 1/M^ a V ' with c w — —3 dilution, a decrease of both values below c = 1x10 g cm is concentration. Instead of an increase of D

407

Q..10P (cm2s

\o

^ctflgcm3)30 Fig. 2. Concentration dependences of D c and 1/M^ aV ' for micellar system Kraton/1,4-dioxane at 26°C.

i 7

(m)

i

i

i

(u-m)

!

(u)

D{u)

-

0

dt'-l

3

c

1 25

i 35

• •

-

|

:

cmt i -—45

i 55

T (*C)

65

Fig. 3. Temperature dependence of D for Kraton solution c - 3 - 3 (c = 5x10 g cm ) in 1,4-dioxane/30 vol.-% n-heptane. For explanation of symbols see text.

408 observed, implicating an increase of micellar size and mass. This finding resembles a similar effect described in the literature (cf. 3). There is no conclusive explanation of this effect. Micelles near c.m.t. Three temperature regions can be seen in Fig.3. D c values in the two outer regions corresponding to unimer and micelles (•) were evaluated from QELS data by a perfect single exponential fit. In the central region, contributions of unimer and micelles to the scattered light intensity are comparable. D ^ 3 ^ values (o) are based on the forced single exponential fit of poor quality. D ^ a p p ' values, evaluated by the four-parameter two-exponential fit (•) using extrapolated values (*) for the unimer contribution, must not be identified with DUpp)

£

;

D 0n) ^ Un f or tunately, above 46 °C in the vicinity of

the c.m.t. micelles contribute to the total intensity of scattered light so little that

cannot be evaluated. The

complex problem of the evaluation of D ( u ) and D ( m ) in the central region is the object of a further study.

References 1. Elias, H.-G., in: "Light Scattering from Polymer Solutions", Huglin, M.B., ed., Academic Press, London 1972 2. Tuzar, Z., Plestil, J., Konäk, C., Hlavatd, D., Sikora, A.: Makromol.Chem. 184, 2111 (1983) 3. Lally, T.P., Price, C.: Polymer 15, 325 (1974) 4. Berne, B.J., Pecora, R.: Dynamic Light Scattering, J.Wiley and Sons, New York 1976, p.41

LATERAL DIFFUSION OF MICELLES MEASURED BY FLUORESCENCE RECOVERY AFTER PHOTOBLEACHING Preliminary results on micelles labeled with a solubilized fluorescent dye

Werner Van De Sande (°), André Persoons Laboratory for Chemical and Biological Dynamics University of Leuven, Celestijnenlaan 200 D, B-3030

Leuven

Introduction Fluorescence Recovery After Photobleaching (FRAP) is a well established technique to measure the lateral diffusion of fluorescent molecules and macromolecules labeled with a fluorophore (1,2,3). Our preliminary results show that the FRAP technique is also applicable to micellar solutions. The labeling of the micelles is achieved by solubilizing a fluorescent dye.

Materials and Methods We used the cationic surfactant N,N-dimethyldodecylammonium chloride (DDAC). The preparation and purification is discribed in (4). The fluorescent dye was an N (10)-alkylated acridine orange derivative ( 3,6-bis(dimethylamino)-10dodecyl acridinium bromide, Fig. 1 ). The preparation is discribed in (5). A new and simple purification method yielded a purity of 99% (to be compared to 93% obtained earlier (6)). The dye is very slightly soluble in water. Solutions were prepared by mixing aqueous solutions of the three components (surfactant, NaCl and dye).

Physical Optics of Dynamic Phenomena and Processes in Macromolecular Systems © 1985 Walter de Gruyter & Co., Berlin • New York - Printed in Germany

410

Fig.l.

The fluorescent dye 3,6-bis(dimethylamino)-10-dodecyl acridinium bromide

[ xxxx CHj) N

I R

( \ m = v = 4 92 nm ).

Br N(CH1))

R = (CH 2 ) 11 CH 3

The main features of the FRAP apparatus were as follows. An argon-ion laser was operated at 488 nm. The laser intensity of the bleaching pulse was about 200 mW. To monitor the fluorescence recovery this intensity was optically attenuated by 4 a factor 10 . Typical bleaching times were 5 ms The radius of the uniform circular beam, focussed through a microscope objective, was 6 ym.

Theory and Data Analysis The experimental curve F(t) was normalized in the form of the fractional fluorescence recovery curve f(t): =

F (t) - F(0) F - F (0)

U

'

The fractional recovery curve was fitted to the exact closed formula (7): f(t) = exp(-x) x { I Q (x) + I 1 (x) } IQ and

(2)

are modified Bessel functions, x = 2x D /t,

t d = u^/4D, oj is the radius of the circular beam, D is the diffusion coefficient. The value of the intensity F(0), immediately after bleaching, was obtained by fitting the initial part of F(t) to a poly-

nomial of second degree. The initial points after the bleaching pulse

were omitted.

The value of the intensity F(