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Introduction to Polymer Rheology

ISBN: 978-1-118-30494-5
March 2012
Introduction to Polymer Rheology (1118304942) cover image
An introduction to the rheology of polymers, with simple math

Designed for practicing scientists and engineers interested in polymer rheology science, education, consulting, or research and development, Introduction to Polymer Rheology is a comprehensive yet accessible guide to the study of the deformation and flow of matter under applied stress. Often considered a complicated topic for beginners, the book makes grasping the fundamentals of polymer rheology easy by presenting information in an approachable way and limiting the use of complex mathematics. By doing so, this introductory overview provides readers with easy access to the key concepts underlying the flow behavior of polymer melts, solutions, and suspensions. Incorporating sample problems that are worked through and explained on the page, as well as numerous practice problems to gauge learning comprehension, the book prepares new students and practitioners for moving on to more advanced concepts.

Comprising twelve chapters, the book covers stress, velocity and rate of deformation, the relationship between stress and rate of deformation (Newtonian fluid), generalized Newtonian fluids, normal stresses and elastic behavior, experimental methods, small and large strain, the molecular origins of rheological behavior, elementary polymer processing concepts, quality control in rheology, and the flow of modified polymers and those with supermolecular structure.

The essential reference for accurately interpreting polymer rheology data, Introduction to Polymer Rheology provides readers with an elementary understanding of the key issues and modern approaches to resolving problems in the field.

An Instructor’s Guide with answers to select problems in the text, 60 new problems with full solutions, hints for effective presentation of the material in the text, and an errata listing is available for professors using the book as a course textbook.
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1. INTRODUCTION

A. Polymers and the importance of rheology

B. Rheology in its simplest form

Problems

Suggested references, with commentary

2. STRESS

A. Stress and pressure

B. Organization of the stress components

C. Coping with subscripts

D. Typical stress tensors

Appendix 2-1: Compilation of equations of motion (ssc)

Appendix 2-2: Equations of motion—curvilinear quick list (ssc)

Problems

References

3. VELOCITY, VELOCITY GRADIENT AND RATE OF DEFORMATION

A. Why velocity is simpler than location—Speedometers vs. GPS

B. Velocity gradients

C. Rate of deformation

Appendix 3-1: Components of the rate-of-deformation tensor

Appendix 3-2: Components of the continuity equation

Appendix 3-3: Nomenclature and sign conventions used in popular rheology texts

Problems

References

4. RELATIONSHIP BETWEEN STRESS AND RATE OF DEFORMATION: THE NEWTONIAN FLUID

A Material idealizations in rheology

B. The Newtonian fluid

Problems

References

5. GENERALIZED NEWTONIAN FLUIDS — A SMALL BUT IMPORTANT STEP TOWARD A DESCRIPTION OF REAL BEHAVIOR FOR POLYMERS

A. Reasons for inventing generalized Newtonian fluids — behavior of polymer melts

B. Generalizing the GNF to three dimensions

C. Inventing relationships for viscosity vs. shear rate

D. Short primer on finding GNF parameters from data

E. Summary of GNF characteristics

Appendix 5-1: Fitting data with Excel

Problems

References

6. NORMAL STRESSES—ORDINARY BEHAVIOR FOR POLYMERS

A. Introduction

B. What are normal stresses

C. Origin of normal stresses in simple shear

D. The second normal-stress difference

E. Normal-stress coefficients and empirical findings

F. Transient rheological functions

D. Temperature effects and superposition of steady-flow data

Problems

References

7. EXPERIMENTAL METHODS

A. Measurement of viscosity

B. Normal stresses from shearing flows

C. Extensional rheology

D. Specialized geometries

E. Flow visualization and other rheo-optical methods

F. Micro and nano rheology

Appendix 7-1: Numerical derivatives

Appendix 7-2: Velocity-profile correction for non-Newtonian fluids

Appendix 7-3: Incorporation of slip into the velocity-profile correction— the Mooney correction

Appendix 7-4: Normal stresses using the cone-and-plate geometry

Appendix 7-5: Desktop rheo-optical experiment

Problems

References

8. STRAIN, SMALL AND LARGE

A. Displacement

B. Infinitesimal strain

C. Hookean solids

D. Finite strain

E. The Lodge elastic fluid and variants

F. The Cauchy strain measure

G. Fixing up integral equations based on C and C-1

Appendix 8-1: The relaxation function

Appendix 8-2: Constant-rate extension of the LEF

Problems

References

9. MOLECULAR ORIGINS OF RHEOLOGICAL BEHAVIOR

A. Description of polymer molecules

B. The Rouse chain—a limited description of polymer behavior

C. Other chain-like models

D. Dealing with entanglements

E. Summary of predictions of molecular theory

Problems

References

10. ELEMENTARY POLYMER PROCESSING CONCEPTS

A. Simple laboratory processing methods

B. Elementary extrusion concepts

C. A downstream process—spinning

D. Summary

Appendix 10-1: Densities of melts at elevated temperatures

Problems

References

11. QUALITY-CONTROL RHEOLOGY

A. Examples of methods used by various industries

B. Test precision

Appendix 11-1: ASTM tests methods for rheological characterization

Problems

References

12. FLOW OF MODIFIED POLYMERS AND POLYMERS WITH SUPERMOLECULAR STRUCTURE

A. Polymers filled with particulates

B. Liquid crystallinity and rheology

C. Polymers with microphase separation in melts or solutions

D. Covalent crosslinking of polymers

Appendix 12-1: Van 't Hoff equation applied to gelation

Problems

References

ANSWERS TO SELECTED PROBLEMS

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Montgomery T. Shaw, PhD, is the DiBenedetto Distinguished Professor Emeritus at the University of Connecticut in Storrs, Connecticut. He is a coauthor of Introduction to Polymer Viscoelasticity, Third Edition, also published by Wiley.
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“The book is written in a relaxed style and targeted at students which do not yet have a background in transport phenomena, linear algebra, differential equations and numerical analysis, thus bridging a gap to mathematically much more demanding text books on rheology which e.g. use short hand tensor notation.”  (Applied Rheology, 1 October 2013)

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