THE PHYSICS OF GLASSY POLYMERS MATERIALS SCIENCE SERIES Advisory Editors LESLIE HOLLIDAY, Visiting Professor, Brunei University, Uxbridge, Middlesex, Great Britain A. KELLY, Sc.D., Deputy Director, National Physical Laboratory, Teddington, Middlesex, Great Britain THE PHYSICS OF GLASSY POLYMERS Edited by R. N. HAWARD Professor of Industrial Chemistry Department of Chemistry, University of Birmingham APPLIED SCIENCE PUBLISHERS LTD LONDON APPLIED SCIENCE PUBLISHERS LTD RIPPLE ROAD, BARKING, ESSEX, ENGLAND WITH 28 TABLES AND 269 ILLUSTRATIONS © APPLIED SCIENCE PUBLISHERS LTD 1973 ISBN-13: 978-94-010-2357-3 e-ISBN-13: 978-94-010-2355-9 DOl: 10.1007/978-94-010-2355-9 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publishers, Applied Science Publishers Ltd, Ripple Road, Barking, Essex, England LIST OF CONTRIBUTORS E. H. ANDREWS Department of Materials, Queen Mary College, University of London, Mile End Road, London El 4NS, England W.BORCHARD Physikalisch-Chemisches Institut Technischen Hochschule Clausthal, 3392 Clausthal-Zellerfeld, Adolf-Romer-Strasse 2A, West Germany P. BOWDEN Department of Metallurgy and Materials Science, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, England B. ELLIS Department of Glass Technology, University of Sheffield, Elmfield, Northumberland Road, Sheffield S10 2TZ, England J. R. FITZPATRICK Research & Engineering Laboratories, Thorn Lighting Limited, Melton Road, Leicester LE4 7PD, England M. J. FOLKES University of Bristol, H. H. Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 1T L, England R. N. HAWARD Plastic Materials Laboratory, Centre for Materials Science, The University of Birmingham, PO Box 363, Birmingham B15 2TT, England v VI LIST OF CONTRIBUTORS H. B. HOPFENBERG Department oj Chemical Engineering, North Carolina State University, Raleigh, North Carolina, USA A. KELLER University oj Bristol, H. H. Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 1T L, England J. MANN Shell Research Limited, Carrington Plastics Laboratory, Urmston, Near Manchester, England G. REHAGE Physikalisch-Chemisches Institut Technischen Hochschule Clausthal, 3392 Clausthal-ZellerJeld, Adolf-Romer-Strasse 2A, West Germany G. E. ROBERTS Department ojP olymer and Fibre Science, The University ojM anchester Institute oj Science and Technology, PO Box No. 88, Sackville Street, Manchester 1, England V. STANNETT Department oj Chemical Engineering, North Carolina State University, Raleigh, North Carolina, USA S. TURNER ICI Limited, Plastics Division, PO Box No.6, Bessemer Road, Welwyn Garden City, Hertfordshire, England E. F. T. WHITE Department ojP olymer and Fibre Science, The University ojM anchester Institute oj Science and Technology, PO Box No. 88, Sackville Street, Manchester 1, England G. R. WILLIAMSON Shell Research Limited, Carrington Plastics Laboratory, Urmston, Near Manchester, England PREFACE This work sets out to provide an up-to-date account of the physical properties and structure of polymers in the glassy state. Properties measured above the glass transition temperature are therefore included only in so far as is necessary for the treatment of the glass transition process. This approach to the subject therefore excludes any detailed account of rubber elasticity or melt rheology or of the structure and conformation of the long chain molecule in solution, although knowledge derived from this field is assumed where required. Major emphasis is placed on structural and mechanical properties, although a number of other physical properties are included. Naturally the different authors contributing to the book write mainly from their own particular points of view and where there are several widely accepted theoretical approaches to a subject, these are sometimes provided in different chapters which will necessarily overlap to a significant extent. For example, the main theoretical presentation on the subject of glass transition is given in Chapter 1. This is supplemented by accounts of the free volume theory in Chapter 3 and in the Introduction, and a short account of the work of Gibbs and DiMarzio, also in Chapter 3. Similarly, there is material on solvent cracking in Chapters 7 and 9, though the two workers approach the subject from opposite directions. Every effort has therefore been made to encourage cross-referencing between different chapters. The work has been carried out in a period when most scientists are changing over to SI units of measurement and these have been generally employed in the text. Difficulties have, however, arisen where a large vii viii PREFACE number of diagrams have been quoted from other workers and many results from the literature have had to be presented in CGS or Imperial units. To help the reader we have therefore included a conversion table as an Appendix. Finally, I would like to thank the authors for their courtesy and co operation and also my secretary, Miss C. A. Jones, for her sustained support without which it would not have been possible to meet the date of publication. University of Birmingham R. N. HAWARD CONTENTS List of Contributors v Preface vii INTRODUCTION (The Nature of Polymer Glasses, Their Packing Density and Mechanical Behaviour)-R. N. HA WARD The Nature of Polymeric Glasses 1 The common glassy polymers . 1 The softening of polymer glasses 4 Polymer melts and rubbers 8 The crystallisation of polymers 9 Amorphous isotactic polymers. 12 The morphology of amorphous polymers 15 Packing Volume in the Glassy State . 25 The expansion volume of amorphous polymers 28 Free volume concepts derived from viscosity theories . 33 Viscosity and free volume in polymers 36 Geometrical factors affecting the possible value of the free volume d~ ~ Bernal's random close packed volume 39 The Rigidity of Polymer Glasses 41 Large Deformations and Fracture 48 References 51 Chapter 1 THE THERMODYNAMICS OF THE GLASSY STATE -G. REHAGE and W. BORCHARD 1.1 Introductory Thermodynamic Considerations 54 1.2 Glassy Solidification and Transition Phenomena • • 65 1.2.1 General considerations and transitions of different order 65 1.2.2 Glassy solidification with one or several internal parameters . 69 ix x CONTENTS 1.2.3 Experimental results 74 1.2.4 Position of the equilibrium curve below the glass temperature 80 1.2.5 Zero point volume of a polymer 84 1.3 Results of the Thermodynamic Theory of Linear Relaxation Phenomena 85 1.4 Glassy Mixed Phases 90 1.4.1 The glassy solidification of polymer solutions 90 1.4.2 The glassy solidification of cross-linked systems. The coexistence of glassy phases with phases in internal equilibrium 93 1.5 The Mobility and Structure of Glassy Phases 97 References 104 Chapter 2 X-RAY DIFFRACTION STUDIES OF THE STRUCTURE OF AMORPHOUS POLYMERS -J. R. FITZPATRICK and B. ELLIS 2.1 Introduction 108 2.2 The Interaction of X-rays With Matter 111 2.2.1 Scattering by a free electron 112 2.2.2 Interference among scattered waves 113 2.2.3 Atomic scattering factor . 114 2.2.4 Compton scattering 115 2.3 Order and Orientation in Polymers 116 2.3.1 Order 116 2.3.2 Orientation 119 2.4 Diffraction of X-rays by Amorphous Materials 120 2.5 Small Angle X-ray Scattering 125 2.5.1 Introduction . 125 2.5.2 Experimental requirements for SAXS 126 2.5.3 Outline of the theory of SAXS 128 2.5.4 Some applications of SAXS 130 2.6 The Radial Distribution Function for Amorphous Polymers . 138 References 147 Chapter 3 RELAXATION PROCESSES IN AMORPHOUS POLYMERS -G.E.ROBERTSandRF ~ WHITE 3.1 Introduction 153 3.2 Molecular Motion in Polymeric Melts and Glasses 154 3.2.1 General description of relaxational processes 154 3.2.2 Relaxational processes at the crystal melt temperature 159 3.2.3 Relaxations in the amorphous state above Tg and below Tm 162 3.2.4 Relaxational processes at the glass transition 168 3.2.5 Relaxations in the glassy state . 179