Introduction to Polymer Viscoelasticity

MONTGOMERY T. SHAW, PhD, is Emeritus Distinguished Professor of Chemical Engineering at the University of Connecticut. Among his books are the prior edition of Introduction to Polymer Viscoelasticity and Introduction to Polymer Rheology, both published by Wiley.

WILLIAM J. MACKNIGHT, PhD, is a Professor Emeritus at the University of Massachusetts Amherst, where he was formerly the co-Principal Investigator for the Center for UMass/Industry Research on Polymers (CUMIRP). He has been a co-author for each edition of Introduction to Polymer Viscoelasticity, all published by Wiley.

Preface to the Fourth Edition


Preface to the Third Edition


Preface to the Second Edition


Preface to the First Edition


1. Introduction


PROBLEMS, 6


GENERAL REFERENCE TEXTS, 7


REFERENCES, 8


2. Phenomenological Treatment of Viscoelasticity


A. ELASTIC MODULUS, 9


B. TRANSIENT EXPERIMENTS, 21


C. DYNAMIC EXPERIMENTS, 25


1. Low-Strain Measurements, 25


2. Large Amplitude Oscillatory Shear (LAOS), 30


3. Microrheology, 34


D. BOLTZMANN SUPERPOSITION PRINCIPLE, 38


E. RELATIONSHIP BETWEEN THE CREEP COMPLIANCE AND THE STRESS RELAXATION MODULUS, 43


F. RELATIONSHIP BETWEEN STATIC AND DYNAMIC PROPERTIES, 44


APPENDIX 2-1. Connecting Creep Compliance and Stress Relaxation Modulus Using Laplace Transforms, 45


APPENDIX 2-2. Borel s Theorem, 48


APPENDIX 2-3. Geometries for the Measurement of Viscoelastic Functions, 49


1. Linear Motion Geometries, 49


2. Rotational Motion Geometries, 53


PROBLEMS, 57


REFERENCES, 64


3. Viscoelastic Models


A. MECHANICAL ELEMENTS, 66


1. Maxwell Model, 68


2. Voigt Model, 74


3. Generalized Maxwell Model, 76


4. Voigt-Kelvin model, 79


B. DISTRIBUTIONS OF RELAXATION AND RETARDATION TIMES, 81


C. MOLECULAR THEORIES THE ROUSE MODEL, 84


D. APPLICATION OF FLEXIBLE-CHAIN MODELS TO SOLUTIONS, 93


E. THE ZIMM MODIFICATION, 94


F. EXTENSION TO BULK POLYMER, 96


G. REPTATION, 108


APPENDIX 3-1: MANIPULATION OF THE ROUSE MATRIX, 112


PROBLEMS, 117


REFERENCES, 123


4. Time Temperature Correspondence


A. FOUR REGIONS OF VISCOELASTIC BEHAVIOR, 125


B. TIME TEMPERATURE SUPERPOSITION, 133


C. MASTER CURVES, 136


D. THE WLF EQUATION, 136


E. MOLECULAR INTERPRETATION OF VISCOELASTIC RESPONSE, 143


PROBLEMS, 144


REFERENCES, 149


5. Transitions and Relaxation in Amorphous Polymers


A. PHENOMENOLOGY OF THE GLASS TRANSITION, 150


B. THEORIES OF THE GLASS TRANSITION, 155


1. Free-Volume Theory, 155


2. Thermodynamic Theory, 158


3. Kinetic Theories, 164


C. STRUCTURAL PARAMETERS AFFECTING THE GLASS TRANSITION, 166


D. RELAXATIONS IN THE GLASSY STATE, 172


E. RELAXATION PROCESSES IN NETWORKS, 176


1. Physical Relaxation, 176


2. Chemical Processes, 177


F. BIOPOLYMER VISCOELASTICITY, 180


1. Biopolymer Sources, 180


2. Humidity Control, 181


3. Examples of Biopolymer Viscoelastic Response, 183


PROBLEMS, 189


REFERENCES, 196


6. Elasticity of Rubbery Networks


A. THERMODYNAMIC TREATMENT, 199


B. STATISTICAL TREATMENT, 205


1. Derivation, 205


2. Energy Contribution, 216


C. PHENOMENOLOGICAL TREATMENT, 220


D. FACTORS AFFECTING RUBBER ELASTICITY, 224


1. Effect of Degree of Crosslinking, 224


2. Effect of Swelling, 226


3. Effect of Fillers, 229


4. Effect of Strain-Induced Crystallization, 232


APPENDIX 6-1. Statistics of a Polymer Chain, 234


APPENDIX 6-2. Equation of State for a Polymer Chain, 240


PROBLEMS, 242


REFERENCES, 246


7. Dielectric and NMR Methods


A. DIELECTRIC METHODS, 249


1. Phenomenology, 250


2. Molecular Interpretation of Dielectric Constant, 257


3. Interfacial Polarization, 264


4. Application to Polymers, 265


5. Experimental Methods, 268


6. Application of Dielectric Relaxation to Poly (methyl methacrylate), 272


7. Comparisons between Mechanical and Dielectric Relaxation for Polymers, 273


B. NUCLEAR MAGNETIC RESONANCE METHODS, 274


PROBLEMS, 280


REFERENCES, 282


Answers to Selected Problems


CHAPTER 2, 284


CHAPTER 3, 296


CHAPTER 4, 304


CHAPTER 5, 308


CHAPTER 6, 312


CHAPTER 7, 320


List of Major Symbols


List of Files on Website


Author Index


Subject Index

Prior edition reviews: The book is clear written and...[is] appropriate for students in introductory undergraduate courses and for others wanting introduction to the fundamentals of the subject. (CHOICE, December 2005); This book is invariably well written, logically organized and easy to follow...I highly recommend this book to anyone studying polymer viscoelasticity. (Polymer News, December 2005)