Introduction to Polymer Viscoelasticity

Completely revised and updated, the fourth edition of this classic text continues to offer the reader a thorough understanding of viscoelastic behavior, essential for the proper utilization of polymers.

• Explains principles, corresponding equations, and experimental methods with supporting real-life applications
• Adds coverage of measurement techniques (nano-indentation, atomic force microscopy (AFM), and diffusing wave spectroscopy (DWS)), biopolymer viscoelasticity, and the relationship between mechanical polymer properties and viscoelastic functions
• Has two new ections to address modern areas of viscoelastic measurement: large amplitude oscillatory shear (LAOS) and microrheology
• Includes problems in the text and an Instructor’s Manual (including solutions) available for adopting professors
• 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)

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 xiii

Preface to the Third Edition xv

Preface to the Second Edition xviii

Preface to the First Edition xx

1. Introduction 1

PROBLEMS, 6

GENERAL REFERENCE TEXTS, 7

REFERENCES, 8

2. Phenomenological Treatment of Viscoelasticity 9

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 66

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 125

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 150

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 198

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 249

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 284

CHAPTER 2, 284

CHAPTER 3, 296

CHAPTER 4, 304

CHAPTER 5, 308

CHAPTER 6, 312

CHAPTER 7, 320

List of Major Symbols 324

List of Files on the Website 331

Author Index 334

Subject Index 339

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