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Polymer Dynamics and Relaxation


  • Page extent: 266 pages
  • Size: 247 x 174 mm
  • Weight: 0.63 kg

Library of Congress

  • Dewey number: 547.7
  • Dewey version: 22
  • LC Classification: QD381 .B69 2007
  • LC Subject headings:
    • Polymers
    • Polymers--Structure
    • Molecular dynamics

Library of Congress Record


 (ISBN-13: 9780521814195)


Polymers exhibit a range of physical characteristics, from rubber-like elasticity to the glassy state. These particular properties are controlled at the molecular level by the mobility of the structural constituents. Remarkable changes in mobility can be witnessed with temperature, over narrow, well defined regions, termed relaxation processes. This is an important, unique phenomena controlling polymer transition behavior and is described here at an introductory level. The important types of relaxation processes from amorphous to crystalline polymers and polymeric miscible blends are covered, in conjunction with the broad spectrum of experimental methods used to study them. In-depth discussion of molecular level interpretation, including recent advances in atomistic level computer simulations and applications to molecular mechanism elucidation are discussed. The result is a self-contained, up-to-date approach to polymeric interpretation suitable for researchers and graduate students in materials science, physics and chemistry interested in the relaxation processes of polymeric systems.

RICHARD H. BOYD is a distinguished Professor Emeritus of Materials Science and Engineering and of Chemical Engineering at the University of Utah. He was awarded the Polymer Physics Prize from the American Physical Society and is the author of over 150 technical papers and book chapters.

GRANT D. SMITH is a Professor at the University of Utah. He is an NSF Career awardee and Humboldt Fellow. He is also the author of co-author of over 170 papers.


Distinguished Professor Emeritus of Materials Science and
Engineering and of Chemical Engineering, University of Utah

Professor of Materials Science and Engineering, University of Utah

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK

Published in the United States of America by Cambridge University Press, New York
Information on this title:

© R. H. Boyd and G. D. Smith 2007

This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2007

Printed in the United Kingdom at the University Press, Cambridge

A catalog record for this publication is available from the British Library

ISBN - 978-0-521-81419-5 hardback

Cambridge University Press has no responsibility for the persistence or
accuracy of URLs for external or third-party internet websites referred to
in this publication, and does not guarantee that any content on such
websites is, or will remain, accurate or appropriate.


  Preface page ix
  PART I Methodology 1
1   Mechanical relaxation 3
  1.1  Regimes of behavior 3
  1.2  Superposition principle 5
  1.3  Relaxation modulus 5
  1.4  Simple stress relaxation 6
  1.5  Dynamic modulus 7
  1.6  Interconversion of stress relaxation and dynamic modulus 9
  1.7  Representation of the relaxation function: single relaxation time (SRT) 11
  1.8  Relaxations in polymeric materials tend to be “broad” 13
  1.9  Distribution of relaxation times 14
  1.10  Relaxation spectrum from ER(t) 15
  1.11  Creep compliance 18
  1.12  Dynamic compliance 19
  1.13  Representation of the retardation function 21
  1.14  Summary of the data transformations illustrated 22
  Appendix A1 A brief summary of elasticity 23
  References 26
2   Dielectric relaxation 27
  2.1  Dielectric permittivity 27
  2.2  Measurement of dielectric permittivity 30
  2.3  Time dependence of polarization: reorientation of permanent dipoles 31
  2.4  Polarization and permittivity in time dependent electric fields 33
  2.5  Empirical representations of the dielectric permittivity 35
  References 43
3   NMR spectroscopy 44
  3.1  NMR basics 45
  3.2  The pulsed NMR method 47
  3.3  NMR relaxation measurements 49
  3.4  NMR exchange spectroscopy 54
  References 56
4   Dynamic neutron scattering 57
  4.1  Neutron scattering basics 57
  4.2  Time-of-flight (TOF) and backscattering QENS 63
  4.3  Neutron spin echo (NSE) spectroscopy 66
  References 69
5   Molecular dynamics (MD) simulations of amorphous polymers 70
  5.1  A brief history of atomistic MD simulations of amorphous polymers 70
  5.2  The mechanics of MD simulations 71
  5.3  Studying relaxation processes using atomistic MD simulations 75
  5.4  Classical atomistic force fields 76
  References 79
  Part II Amorphous polymers 81
6   The primary transition region 83
  6.1  Mechanical relaxation 83
  6.2  Dielectric relaxation 90
  6.3  Mechanical vs. dielectric relaxation 96
  6.4  NMR relaxation 104
  6.5  Neutron scattering 110
  References 118
7   Secondary (subglass) relaxations 120
  7.1  Occurrence of mechanical and dielectric secondary processes 120
  7.2  Complexity and multiplicity of secondary processes 121
  7.3  Flexible side group motion as a source of secondary relaxation 129
  7.4  NMR spectroscopy studies of flexible side group motion 138
  References 140
8   The transition from melt to glass and its molecular basis 142
  8.1  Experimental description 142
  8.2  Molecular basis 157
  References 194
  Part III Complex systems 197
9   Semi-crystalline polymers 199
  9.1  Phase assignment 200
  9.2  Effect of crystal phase presence on amorphous fraction relaxation 209
  9.3  Relaxations in semi-crystalline polymers with a crystal phase relaxation 214
  9.4  NMR insights 223
  References 226
10   Miscible polymer blends 227
  10.1  Poly(isoprene)/poly(vinyl ethylene) (PI/PVE) blends 228
  10.2  Models for miscible blend dynamics 229
  10.3  MD simulations of model miscible blends 233
  10.4  PI/PVE blends revisited 239
  The Rouse model 243
AI.1   Formulation and normal modes 244
AI.2   Establishment of Rouse parameters for a real polymer 245
AI.3   The viscoelastic response of a Rouse chain 245
AI.4   Bead displacements and the coherent single-chain structure factor 246
  References 247
  Appendix AII Site models for localized relaxation 248
AII.1   Dipolar relaxation in terms of site models 248
AII.2   Mechanical relaxation in terms of site models 251
  References 252
  Index 253


Polymers have become widely used materials because they exhibit an enormous range of behaviors and properties. They are most often processed or shaped as viscous melts. They can be used as stiff solid materials in the glassy or semicrystalline state. The rubbery or elastomeric state, obtained by cross-linking melts, is characterized by very high reversible extensibility and is unique to polymeric molecular organization. In addition, many applications are dependent upon the exhibition of behavior intermediate between that of the viscous melt and that of the relatively rigid glassy state. That is, the degree of rigidity is time dependent. In the solid state, major changes in physical properties can occur with changing temperature. Thus the same polymer can be a melt or, if cross-linked, an elastomer, or a somewhat rigid glass, or a quite rigid glass depending on the time and temperature of use. Further, these changes of properties occur in regions of time and temperature that are well defined. That is, the regions can be characterized by a variety of experimental techniques that probe the relaxation of the response following an applied perturbation such as mechanical stress or an electric field. Most polymers exhibit several such relaxation regions.

All of this rich manifold of behavior has its foundation in the ability of polymer molecules to locally change the details of the shape or conformation of the molecular chain and to accumulate these changes so that global changes in molecular shape can result. These local changes usually involve rotations about the constituent bonds and attendant responses of nearby bonds and surrounding chains. Energy barriers are involved and thus thermally activated responses result. This then leads to the time and temperature dependent character of a relaxation process. If relaxation processes are to be fully understood, then these molecular scale events have to be understood as well.

Four experimental methods are considered. Historically, perhaps the greatest early interest in relaxation phenomena centered on mechanical response as ex- emplified by creep and stress relaxation experiments. Concurrently, however, and probably because mechanical experiments have often been considered difficult to carry out over broad ranges of time or frequency, dielectric response measurements where the short time, high frequency region is more conveniently accessed became popular. A very large literature has developed around both the mechanical and dielectric response methods. Somewhat later it was found that the decay of polarization of nuclear spins associated with the nuclear magnetic resonance (NMR) method was sensitive to motional processes and could be invoked as a tool for relaxation studies. The specificity to certain atoms in particular bonding environments is an advantage. That and the development of pulse techniques that allow wide ranges of time to be explored have led to increasingly important applications to polymer relaxations. Several scattering processes, including Rayleigh and Brillouin scattering of light and neutron scattering, are also sensitive to motional processes. But, of these, only neutron diffraction is considered here.

Experiments rarely give direct insight into the details of the molecular motions underlying relaxation processes. However, by rationalizing the results from several experimental techniques applied to groups of structurally similar but distinct polymers a reasonable mechanism can often be formulated. The process of molecular mechanism elucidation has been significantly aided by the advent of computer assisted detailed atomistic molecular modeling. Particularly valuable is the molecular dynamics method which gives the positions of every atom as a function of time. From this information time autocorrelation functions (ACF) can be constructed utilizing linear response theory that can be compared with experimental data for various techniques. The use of simulation as a tool in molecular interpretation is heavily stressed.

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