Polymers, Liquid Crystals, and Low-Dimensional Solids

634 Pages·1985·37.873 MB·English

by  A. Keller (auth.), Norman March, Mario Tosi (eds.)

Polymers,
Liquid Crystals,
and
Low-Dimensional
Solids
PHYSICS OF SOLIDS AND LIQUIDS
Editorial
Board: Josef T. Devreese • University of Antwerp, Belgium
Roger P. Evrard • University of Liege, Belgium
Stig Lundqvist • Chalmers University of Technology, Sweden
Gerald D. Mahan. Indiana University, Bloomington, Indiana
Norman H. March • University of Oxford, England
SUPERIONIC CONDUCTORS
Edited by Gerald D. Mahan and Walter L. Roth
HIGHLY CONDUCTING ONE-DIMENSIONAL SOLIDS
Edited by Jozef T. Devreese, Roger P. Evrard, and Victor E. van Doren
ELECTRON SPECTROSCOPY OF CRYSTALS
V. V. Nemoshkalenko and V. G. Aleshin
MANY -PARTICLE PHYSICS
Gerald D. Mahan
THE PHYSICS OF ACTINIDE COMPOUNDS
Paul Erdos and John M. Robinson
THEORY OF THE INHOMOGENEOUS ELECTRON GAS
Edited by S. Lundqvist and N. H. March
POLYMERS, LIQUID CRYSTALS, AND LOW-DIMENSIONAL SOLIDS
Edited by Norman March and Mario Tosi
A Continuation Order Plan is available for this series. A continuation order will bring delivery of
each new volume immediately upon publication. Volumes are billed only upon actual shipment. For
further information please contact the publisher.
Polymers,
Liquid Crystals,
and
Low-Dimensional
Solids
Edited by
Norman March
University of Oxford
Oxford, England
and
Mario Tosi
International Center for Theoretical Physics
Trieste, Italy
Plenum Press • New York and London
Library of Congress Cataloging in Publication Data
Main entry under title:
Polymers, liquid crystals, and low-dimensional solids.
(Physics of solids and liquids)
Bibliography: p.
Includes index.
1. Polymers and polymerization. 2. Liquid crystals. 3. Solids. I. March, Norman H.
(Norman Henry), 1927- . II. Tosi, Mario, 1932- . III. Title: Low-dimen-
sional solids. IV. Series.
QD381.P6125 1984 530.4'1 84-13445
ISBN -13: 978-1-4612-9448-1 e-ISBN-13: 978-1-4613-2367-9
DOl: 10.1007/978-1-4613-2367-9
©1984 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1985
A Division of Plenum Publishing Corporation
233 Spring Street, New York, N.Y. 10013
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording, or otherwise, without written permission from the Publisher
Contributors
S. Chandrasekhar, Raman Research Institute, Bangalore, India
G. Durand, Laboratoire de Physique des Solides, Universite de Paris-Sud,
Orsay, France
A. Keller, Physics Laboratory, University of Bristol, England
1. Ladik, Chemistry Department (and Laboratory of the National Founda
tion for Cancer Research), University of Erlangen-Niirnberg, Federal
Republic of Germany
S. Lundqvist, Theoretical Physics Department, Chalmers University of
Technology, Goteborg, Sweden
N. H. March, Theoretical Chemistry Department, University of Oxford
G. Marrucci, Istituto di Prinicipi di Ingegneria Chimica, Universita di
Napoli, Italy
M. Seel, Chemistry Department (and Laboratory of the National Founda
tion for Cancer Research), University of Erlangen-Niirnberg, Federal
Republic of Germany
F. Stern, IBM Thomas 1. Watson Research Center, Yorktown Heights,
New York, U.S.A.
R. B. Stinchcombe, Institut Laue-Langevin, Grenoble, France; and
Theoretical Physics Department, University of Oxford, England
S. Striissler, Cerberus AG, Mannedorf, Switzerland
S. Suhai, Chemistry Department (and Laboratory of the National Founda
tion for Cancer Research), University of Erlangen-Niirnberg, Federal
Republic of Germany
1. Vannimenus, Groupe de Physique des Solides, Ecole Normale
Superieure, Paris, France
P. Wyder, Research Institute for Materials, University of Nijmegen, The
Netherlands
v
Preface
This book deals with three related areas having both fundamental and
technological interest. In the first part, the objective is to provide a bird's
eye view on structure in polymeric solids. This is then complemented by a
chapter, directly technological in its emphasis, dealing with the influence of
processing on polymeric materials. In spite of the technological interest,
this leads to some of the current fundamental theory.
Part II, concerned with liquid crystals, starts with a discussion of the
physics of the various types of material, and concludes with a treatment of
optical applications. Again, aspects of the theory are stressed though this
part is basically phenomenological in character.
In Part III, an account is given first of the use of chemical-bonding
arguments in understanding the electronic structure of low-dimensional
solids, followed by a comprehensive treatment of the influence of dimen
sionality on phase transitions. A brief summary of dielectric screening in
low-dimensional solids follows. Space-charge layers are then treated,
including semiconductor inversion layers. Effects of limited dimensionality
on superconductivity are also emphasized.
Part IV concludes the volume with two specialized topics: electronic
structure of biopolymers, and topological defects and disordered systems.
The Editors wish to acknowledge that this book had its origins in the
material presented at a course organized by the International Centre for
Theoretical Physics, Trieste.
N. H. March
M. P. Tosi
vii
Contents
I. POLYMERS
I. Introduction to Polymeric Structure and Polymers ................. 3
A. Keller
1.1. Classification.............. ... ....... ................ ................ ................. ..... 3
1.1.1. Linear Chains and Networks ......................................... 3
1.1.2. Periodic and Aperiodic Polymers .................................. 5
1.1.3. Homopolymers and Copolymers ................................... 7
1.1.4. Single-Component Polymers ....... .................................. 8
1.2. Main Types of Polymerization Reaction ................................. 10
1.2.1. Condensation Polymerization ...................................... 10
1.2.2. Addition Polymerization ........ .... ....... .......................... 11
1.3. Imperfection Types in a Linear Homopolymer Chain ............ 12
1.3.1. End Groups ................................................................. 12
1.3.2. Molecular Length (Weight) Distribution ..................... 13
1.3.3. Isomerism .................................................................... 14
1.4. Formulas of Some Important Polymers .................................. 18
1.4.1. Condensation Polymers .................. ............................. 19
1.4.2. Addition Polymers ...................... ................................. 20
1.5. Melting Range of Polymers; Specialty Materials .................... 23
1.5.1. Conventional Polymers ............... ................................. 23
1.5.2. Specialty Materials ...................................................... 24
1.6. The Physical State ................................................................... 26
1.6.1. Resume of the Amorphous State ................................ 27
1.6.2. The Usefulness of Polymers in Terms of Their
Physical State ............................................................... 30
ix
x Contents
2. Crystallinity and Kinetics of Crystallization ......................... 33
A. Keller
2.1. Basic Classifications ................................................................. 33
2.1.1. Generalities ................................................................. 33
2.1.2. Sources of Lattice Imperfections in Polymers ............. 36
2.1.3. Modes of Crystallization .............................................. 37
2.2. Crystal Structure .............................. ..... ...... ................. ....... ..... 38
2.2.1. The Unit Cell .............................................................. 38
2.2.2. Chain Conformations .................................................. 39
2.2.3. Chain Packing .... ........... ............. .................................. 43
2.2.4. Crystal Structure Determination .... ............. ............ .... 47
2.3. Degree of Crystallinity.. ........... ........ .............. ................... ...... 49
2.3.1. The Principle of the Determination ............................ 49
2.3.2. Methods of Determination .......................................... 50
2.3.3. An Appreciation of the Different Methods ................ 51
2.4. Kinetics of Crystallization ......... ........ ...... ........... ................. .... 52
2.4.1. Rates of Crystallization ............................................... 52
2.4.2. The Xc vs t Curves ...................................................... 54
2.4.3. Morphological vs True Crystallinity............................ 55
2.4.4. Primary and Secondary Crystallization .... ......... .... ...... 56
2.4.5. Textures ....................................................................... 57
2.4.6. Analytical Treatment of Crystallization Kinetics ..... ... 59
2.5. Spherulites ............................................................................... 62
2.5.1. Optical Properties of Spherulites ................................ 64
2.5.2. Morphology of Spherulites .......................................... 66
2.5.3. The Fine Structure of Spherulites ............................... 68
3. The Basic Crystal Unit .......................................................... 71
A. Keller
3.1. Single-Crystal Lamella ............................................................. 71
3.1.1. Discovery and Description .......................................... 71
3.1.2. The Chain-Folding Model ........................................... 74
3.1.3. Fold Length I ............................................................... 75
3.2. Theories of Chain Folding ....................................................... 81
3.2.1. Framework of the Kinetic Theories ............................ 81
3.2.2. Further Developments and Problems ... ... ...... ...... .... .... 88
3.2.3. Growth Rates .............................................................. 91
3.2.4. Melting Behavior as a Function of I ..... ...... .............. ... 92
3.2.5. Comparison of Crystallization from Solution and Melt 93
3.2.6. Some New Perspectives in Crystallization Theories .... 95
Contents xi
3.3. Morphology of Chain-Folded Crystals .................................... 97
3.3.1. Monolayer Crystals ...................................................... 97
3.3.2. Multilayer Crystals ...................................................... 99
3.4. Fold Structure - Nature of Amorphous Material................ 105
3.4.1. The Issues .................................................................. 105
3.4.2: Experimentation in Aid of the Fold-Surface Problem 107
3.4.3. Outcome of the Enquiries ............... .......................... 108
3.5. Neutron Scattering Experiments: The Chain Trajectory...... 109
3.5.1. Technique and Potential ............................................ 109
3.5.2. Angular Ranges ......................................................... 110
3.5.3. Some Results ............................................................. 111
3.6. Alternative Morphologies ............................ ........... ............... 112
3.6.1. Extended-Chain-Type Crystals .................................. 112
3.6.2. Micellar Crystals (Crystal Gels) ................................. 114
4. Other Classes of Crystallization .......................................... 117
A. Keller
4.1. Crystallization Concurrent with Polymerization
(Nascent Polymers) ................................................................ 117
4.2. Orientation-Induced Crystallization ...................................... 119
4.2.1. General ...................................................................... 119
4.2.2. Morphological Background ........ ..... .......................... 120
4.2.3. Mode of Chain Extension ......................................... 121
4.2.4. Structure of Shish-Kebabs ......................................... 124
4.2.5. Properties of Shish-Kebabs ....................................... 126
4.2.6. Some Practical Consequences ................................... 127
5. Hierarchical Nature of Macromolecular Structure 131
A. Keller
5.1. Introduction ........................................................................... 131
5.1.1. Crystalline Constituents ............................................. 131
5.1.2. Amorphous Constituents ........................................... 132
5.2. Crystal Defects ...................................................................... 132
5.2.1. Defects Within the Crystal Lattice ............................ 132
5.2.2. Defects Beyond the Level of the Lattice .......... ........ 133
5.3. Thermal Behavior .................................................................. 134
5.3.1. Amorphous Material ................................................. 134
5.3.2. Crystal Lattice ........................................................... 135
5.3.3. Melting Range ........................................................... 135
5.4. Deformation .......................................................................... 137
5.4.1. Polymers as Self-Structured Composites ................... 137
xii Contents
6. Influence of Processing on Polymeric Materials .................. 143
G. Marrucci
6.1.. Polymeric Processing ............................................................. 144
6.2. General Comments on Influence of Flow . .... ........ ..... ........... 148
6.3. Dumbbell Model ........ ........ ..... ... ...................... ............... ... ... 150
6.3.1. Shear Flow ................................................................. 154
6.3.2. Elongational Flow ..................................................... 155
6.3.3. Other Flows ............................................................... 157
6.4. Multiplicity of Friction Points: Rouse-Zimm Model............ 158
6.5. Concentrated Systems ........................................................... 162
6.6. Effects of Flow on Crystallization ............. ..... ...... ........... ...... 170
6.7. Recent Developments ............................................................ 174
References and Bibliography for Part I .................................. 175
II. LIQUID CRYSTALS
7. Structural Classification of Thermotropic Liquid Crystals . 181
S. Chandrasekhar
7.1. Introduction ........................................................................... 181
7.2. Rod-Like Molecules .............................................................. 182
7.2.1. Effect of Pressure on Polymorphism ......................... 184
7.2.2. The Reentrant Phenomenon ..................................... 184
7.3. Disk-Like Molecules .............................................................. 187
~. Nematic Liquid Crystals 189
S. Chandrasekhar
8.1. Elastic Properties ................................................................... 189
8.1.1. Basic Equations .......................................................... 189
8.1.2. Determination of the Elastic Constants:
The Freedericksz Effect ............................................. 190
8.1.3. Orientational Fluctuations and Light Scattering ....... 192
8.1.4. Disclinations .............................................................. 194
8.2. Viscous Properties ............ ..... ................................................ 199
8.2.1. Experimental Determination of the Viscosity
Coefficients ................................................................ 199
8.2.2. Viscous Torques ...... .................. ................................ 201
8.2.3. Orientational Relaxation .............................. ...... ....... 203
8.3. Nematic-Isotropic Transition ................................................. 204