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MELT RHEOLOGY AND ITS ROLE IN PLASTICS
PROCESSING
THEORY AND APPLICATIONS
MELT RHEOLOGY AND ITS ROLE IN PLASTICS
PROCESSING
THEORY AND APPLICATIONS
MELT RHEOLOGY AND ITS ROLE IN PLASTICS
PROCESSING
THEORY AND APPLICATIONS
by
JOHN M. DEALY Department of Chemical Engineering,
McGill University, Montreal, Canada
and
KURT F. WISSBRUN Hoechst Celanese Research Division,
Summit, New Jersey
KLUWER ACADEMIC PUBLISHERS DORDRECHTI BOSTON I LONDON
MELT RHEOLOGY AND ITS ROLE IN PLASTICS
PROCESSING
THEORY AND APPLICATIONS
by
JOHN M. DEALY Department of Chemical Engineering,
McGill University, Montreal, Canada
and
KURT F. WISSBRUN Hoechst Celanese Research Division,
Summit, New Jersey
KLUWER ACADEMIC PUBLISHERS DORDRECHTI BOSTON I LONDON
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-13:978-0-7923-5886-2 DOl: 10.1007/978-94-009-2163-4
e-ISBN-13:978-94-009-2163-4
Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Sold and distributed in North, Central and South America by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed by Kluwer Academic Publishers,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
First published by Van Nostrand Reinhold 1990 Reprinted by Chapman & Hall 1995, 1996
Reprinted 1999
Printed on acid-free paper
All Rights Reserved © 1999 Kluwer Academic Publishers
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-13:978-0-7923-5886-2 DOl: 10.1007/978-94-009-2163-4
e-ISBN-13:978-94-009-2163-4
Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Sold and distributed in North, Central and South America by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed by Kluwer Academic Publishers,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
First published by Van Nostrand Reinhold 1990 Reprinted by Chapman & Hall 1995, 1996
Reprinted 1999
Printed on acid-free paper
All Rights Reserved © 1999 Kluwer Academic Publishers
No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Preface
This book is designed to fulfill a dual role. On the one hand it provides a description of the rheological behavior of molten polymers. On the other, it presents the role of rheology in melt processing operations. The account of rheology emphasises the underlying principles and presents results, but not detailed derivations of equations. The processing operations are described qualitatively, and wherever possible the role of rheology is discussed quantitatively. Little emphasis is given to non-rheological aspects of processes, for example, the design of machinery.
The audience for which the book is intended is also dual in nature. It includes scientists and engineers whose work in the plastics industry requires some knowledge of aspects of rheology. Examples are the polymer synthetic chemist who is concerned with how a change in molecular weight will affect the melt viscosity and the extrusion engineer who needs to know the effects of a change in molecular weight distribution that might result from thermal degradation.
The audience also includes post-graduate students in polymer science and engineering who wish to acquire a more extensive background in rheology and perhaps become specialists in this area. Especially for the latter audience, references are given to more detailed accounts of specialized topics, such as constitutive relations and process simulations. Thus, the book could serve as a textbook for a graduate level course in polymer rheology, and it has been used for this purpose.
The structure of the book is as follows. Chapter 1 is an introduction to rheology and to polymers for readers entering the field for the first time. The reader is assumed to be familiar with the mathematics and chemistry that are taught in undergraduate engineering and physical science programs.
Chapters 2 through 6 are a treatment of rheological behavior that includes the well established areas of steady shear and linear
v
Preface
This book is designed to fulfill a dual role. On the one hand it provides a description of the rheological behavior of molten polymers. On the other, it presents the role of rheology in melt processing operations. The account of rheology emphasises the underlying principles and presents results, but not detailed derivations of equations. The processing operations are described qualitatively, and wherever possible the role of rheology is discussed quantitatively. Little emphasis is given to non-rheological aspects of processes, for example, the design of machinery.
The audience for which the book is intended is also dual in nature. It includes scientists and engineers whose work in the plastics industry requires some knowledge of aspects of rheology. Examples are the polymer synthetic chemist who is concerned with how a change in molecular weight will affect the melt viscosity and the extrusion engineer who needs to know the effects of a change in molecular weight distribution that might result from thermal degradation.
The audience also includes post-graduate students in polymer science and engineering who wish to acquire a more extensive background in rheology and perhaps become specialists in this area. Especially for the latter audience, references are given to more detailed accounts of specialized topics, such as constitutive relations and process simulations. Thus, the book could serve as a textbook for a graduate level course in polymer rheology, and it has been used for this purpose.
The structure of the book is as follows. Chapter 1 is an introduction to rheology and to polymers for readers entering the field for the first time. The reader is assumed to be familiar with the mathematics and chemistry that are taught in undergraduate engineering and physical science programs.
Chapters 2 through 6 are a treatment of rheological behavior that includes the well established areas of steady shear and linear
v
vi PREFACE
viscoelasticity. There is, in addition, an extensive discussion of nonlinear viscoelasticity effects, which often play an important role in melt processing operations. Chapters 7 through 9 are devoted to the experimental methods used to measure the properties that have been defined, using both the traditional flows and some special types of deformation.
The dependence of the parameters of the rheological relations upon the composition and structure of the polymeric materials is the subject of Chapters 10 through 13. The description is most extensive for stable, homogeneous, isotropic molten polymers, and less so for more complex systems. Chapters 14 through 17 summarize what is known about the role of rheology in the most important melt processing operations. Finally, we close with a chapter whose aim is to provide guidelines, often by example, of how to apply the information in this book and in the literature to solve problems in applied rheology.
This volume is not an exhaustive monograph on all aspects of polymer rheology. However, we have included all the material that we believe is likely to be of direct use to those working in the plastics industry. The reference lists are not intended to be exhaustive, but all the work that we believe is central to the themes of the book has been cited.
We have adhered to the Society of Rheology official nomenclature wherever possible. Also, we have used index rather than dyadic notation for tensor quantities, because we felt this would be more easily understood by readers seeing tensor notation for the first time.
JMD wishes to acknowledge the support and encouragement of McGill University for providing a working environment conducive to a major writing project. He also wishes to recognize the colleagues and research students who have played a vital role in the development of his understanding of polymer rheology and its applications. In addition, JMD wishes to express his appreciation to the University of Wisconsin, especially to R. B. Bird and A. S. Lodge, for their professional hospitality during the time when he got his part of the writing well launched.
KFW wishes to acknowledge the management of Hoechst Celanese for their permission to participate in this book. He also
vi PREFACE
viscoelasticity. There is, in addition, an extensive discussion of nonlinear viscoelasticity effects, which often play an important role in melt processing operations. Chapters 7 through 9 are devoted to the experimental methods used to measure the properties that have been defined, using both the traditional flows and some special types of deformation.
The dependence of the parameters of the rheological relations upon the composition and structure of the polymeric materials is the subject of Chapters 10 through 13. The description is most extensive for stable, homogeneous, isotropic molten polymers, and less so for more complex systems. Chapters 14 through 17 summarize what is known about the role of rheology in the most important melt processing operations. Finally, we close with a chapter whose aim is to provide guidelines, often by example, of how to apply the information in this book and in the literature to solve problems in applied rheology.
This volume is not an exhaustive monograph on all aspects of polymer rheology. However, we have included all the material that we believe is likely to be of direct use to those working in the plastics industry. The reference lists are not intended to be exhaustive, but all the work that we believe is central to the themes of the book has been cited.
We have adhered to the Society of Rheology official nomenclature wherever possible. Also, we have used index rather than dyadic notation for tensor quantities, because we felt this would be more easily understood by readers seeing tensor notation for the first time.
JMD wishes to acknowledge the support and encouragement of McGill University for providing a working environment conducive to a major writing project. He also wishes to recognize the colleagues and research students who have played a vital role in the development of his understanding of polymer rheology and its applications. In addition, JMD wishes to express his appreciation to the University of Wisconsin, especially to R. B. Bird and A. S. Lodge, for their professional hospitality during the time when he got his part of the writing well launched.
KFW wishes to acknowledge the management of Hoechst Celanese for their permission to participate in this book. He also
PREFACE vii
wishes to thank his many colleagues at Hoechst Celanese, in particular H. M. Yoon, and his colleagues at the University of Delaware, most especially A. B. Metzner, for their contributions to his experience and knowledge of the fields discussed in this book. Others to whom appreciation is due include W. W. Graessley, F. N. Cogswell, D. Pearson, M. Doi, and G. Fuller.
Several people read one or more chapters of the manuscript and made many helpful suggestions for improvement. These include H. M. Laun, J. E. L. Roovers, H. C. Booij, G. A. Campbell, S. J. Kurtz, and 1. V. Lawler. Their contributions are gratefully acknowledged. Finally, we wish to thank Hanser Publishers, particularly Dr. Edmund Immergut, for permission to reproduce some material from our chapter in the Blow Molding Handbook.
J. M. Dealy K. F. Wissbrun
PREFACE vii
wishes to thank his many colleagues at Hoechst Celanese, in particular H. M. Yoon, and his colleagues at the University of Delaware, most especially A. B. Metzner, for their contributions to his experience and knowledge of the fields discussed in this book. Others to whom appreciation is due include W. W. Graessley, F. N. Cogswell, D. Pearson, M. Doi, and G. Fuller.
Several people read one or more chapters of the manuscript and made many helpful suggestions for improvement. These include H. M. Laun, J. E. L. Roovers, H. C. Booij, G. A. Campbell, S. J. Kurtz, and 1. V. Lawler. Their contributions are gratefully acknowledged. Finally, we wish to thank Hanser Publishers, particularly Dr. Edmund Immergut, for permission to reproduce some material from our chapter in the Blow Molding Handbook.
J. M. Dealy K. F. Wissbrun
Contents
Preface
1. INTRODUCTION TO RHEOLOGY
1.1 What is Rheology? 1.2 Why Rheological Properties are Important 1.3 Stress as a Measure of Force 1.4 Strain as a Measure of Deformation
1.4.1 Strain Measures for Simple Extension 1.4.2 Shear Strain
1.5 Rheological Phenomena 1.5.1 Elasticity; Hooke's Law 1.5.2 Viscosity 1.5.3 Viscoelasticity 1.5.4 Structural Time Dependency 1.5.5 Plasticity and Yield Stress
1.6 Why Polymeric Liquids are Non-Newtonian 1.6.1 Polymer Solutions 1.6.2 Molten Plastics
1.7 A Word About Tensors 1.7.1 Vectors 1.7.2 What is a Tensor?
1.8 The Stress Tensor 1.9 A Strain Tensor for Infinitesimal Deformations 1.10 The Newtonian Fluid 1.11 The Basic Equations of Fluid Mechanics
1.11.1 The Continuity Equation 1.11.2 Cauchy's Equation 1.11.3 The Navier-Stokes Equation
References
2 .. LINEAR VISCOELASTICITY
2.1 Introduction 2.2 The Relaxation Modulus
v
1
1 3 3 6 7 9
10 10 11 13 16 18 19 19 20 22 23 23 25 31 36 37 38 39 40 41
42
42 43
ix
Contents
Preface
1. INTRODUCTION TO RHEOLOGY
1.1 What is Rheology? 1.2 Why Rheological Properties are Important 1.3 Stress as a Measure of Force 1.4 Strain as a Measure of Deformation
1.4.1 Strain Measures for Simple Extension 1.4.2 Shear Strain
1.5 Rheological Phenomena 1.5.1 Elasticity; Hooke's Law 1.5.2 Viscosity 1.5.3 Viscoelasticity 1.5.4 Structural Time Dependency 1.5.5 Plasticity and Yield Stress
1.6 Why Polymeric Liquids are Non-Newtonian 1.6.1 Polymer Solutions 1.6.2 Molten Plastics
1.7 A Word About Tensors 1.7.1 Vectors 1.7.2 What is a Tensor?
1.8 The Stress Tensor 1.9 A Strain Tensor for Infinitesimal Deformations 1.10 The Newtonian Fluid 1.11 The Basic Equations of Fluid Mechanics
1.11.1 The Continuity Equation 1.11.2 Cauchy's Equation 1.11.3 The Navier-Stokes Equation
References
2 .. LINEAR VISCOELASTICITY
2.1 Introduction 2.2 The Relaxation Modulus
v
1
1 3 3 6 7 9
10 10 11 13 16 18 19 19 20 22 23 23 25 31 36 37 38 39 40 41
42
42 43
ix
x CONTENTS
2.3 The Boltzmann Superposition Principle 44 2.4 Relaxation Modulus of Molten Polymers 48 2.5 Empirical Equations for the Relaxation Modulus 51
2.5.1 The Generalized Maxwell Model 52 2.5.2 Power Laws and an Exponential Function 53
2.6 The Relaxation Spectrum 54 2.7 Creep and Creep Recovery; The Compliance 55 2.8 Small Amplitude Oscillatory Shear 60
2.8.1 The Complex Modulus and the Complex Viscosity 61
2.8.2 Complex Modulus of Typical Molten Polymers 66 2.8.3 Quantitative Relationships between G*(w) and
MWD 68 2.8.4 The Storage and Loss Compliances 69
2.9 Determination of Maxwell Model Parameters 70 2.10 Start-Up and Cessation of Steady Simple Shear and
Extension 72 2.11 Molecular Theories: Prediction of Linear Behavior 74
2.11.1 The Modified Rouse Model for Unentangled Melts 74 2.11.1.1 The Rouse Model for Dilute Solutions 74 2.11.1.2 The Bueche Modification of the Rouse
Theory 75 2.11.1.3 The Bueche-Ferry Law 79
2.11.2 Molecular Theories for Entangled Melts 79 2.11.2.1 Evidence for the Existence of
Entanglements 79 2.11.2.2 The Nature of Entanglement Coupling 80 2.11.2.3 Reptation 81 2.11.2.4 The Doi-Edwards Theory 82 2.11.2.5 The Curtiss-Bird Model 85 2.11.2.6 Limitations of Reptation Models 86
2.12 Time-Temperature Superposition 86 2.13 Linear Behavior of Several Polymers 94 References 100
3. INTRODUCTION TO NONLINEAR VISCOELASTICITY 103
3.1 Introduction 103 3.2 Nonlinear Phenomena 105
x CONTENTS
2.3 The Boltzmann Superposition Principle 44 2.4 Relaxation Modulus of Molten Polymers 48 2.5 Empirical Equations for the Relaxation Modulus 51
2.5.1 The Generalized Maxwell Model 52 2.5.2 Power Laws and an Exponential Function 53
2.6 The Relaxation Spectrum 54 2.7 Creep and Creep Recovery; The Compliance 55 2.8 Small Amplitude Oscillatory Shear 60
2.8.1 The Complex Modulus and the Complex Viscosity 61
2.8.2 Complex Modulus of Typical Molten Polymers 66 2.8.3 Quantitative Relationships between G*(w) and
MWD 68 2.8.4 The Storage and Loss Compliances 69
2.9 Determination of Maxwell Model Parameters 70 2.10 Start-Up and Cessation of Steady Simple Shear and
Extension 72 2.11 Molecular Theories: Prediction of Linear Behavior 74
2.11.1 The Modified Rouse Model for Unentangled Melts 74 2.11.1.1 The Rouse Model for Dilute Solutions 74 2.11.1.2 The Bueche Modification of the Rouse
Theory 75 2.11.1.3 The Bueche-Ferry Law 79
2.11.2 Molecular Theories for Entangled Melts 79 2.11.2.1 Evidence for the Existence of
Entanglements 79 2.11.2.2 The Nature of Entanglement Coupling 80 2.11.2.3 Reptation 81 2.11.2.4 The Doi-Edwards Theory 82 2.11.2.5 The Curtiss-Bird Model 85 2.11.2.6 Limitations of Reptation Models 86
2.12 Time-Temperature Superposition 86 2.13 Linear Behavior of Several Polymers 94 References 100
3. INTRODUCTION TO NONLINEAR VISCOELASTICITY 103
3.1 Introduction 103 3.2 Nonlinear Phenomena 105
CONTENTS xi
3.3 Theories of Nonlinear Behavior 106 3.4 Finite Measures of Strain 108
3.4.1 The Cauchy Tensor and the Finger Tensor 109 3.4.2 Strain Tensors 110 3.4.3 Reference Configurations 112 3.4.4 Scalar Invariants of the Finger Tensor 113
3.5 The Rubberlike Liquid 114 3.5.1 A Theory of Finite Linear Viscoelasticity 115 3.5.2 Lodge's Network Theory and the Convected
Maxwell Model 117 3.5.3 Behavior of the Rubberlike Liquid in Simple
Shear Flows 118 3.5.3.1 Rubberlike Liquid in Step Shear Strain 119 3.5.3.2 Rubberlike Liquid in Steady Simple
Shear 119 3.5.3.3 Rubberlike Liquid in Oscillatory Shear 121 3.5.3.4 Constrained Recoil of Rubberlike
Liquid 122 3.5.3.5 The Stress Ratio (Nt! 0') and the
Recoverable Shear 122 3.5.4 The Rubberlike Liquid in Simple Extension 123 3.5.5 Comments on the Rubberlike Liquid Model 126
3.6 The BKZ Equation 127 3.7 Wagner's Equation and the Damping Function 128
3.7.1 Strain Dependent Memory Function 128 3.7.2 Determination of the Damping Function 131 3.7.3 Separable Stress Relaxation Behavior 132 3.7.4 Damping Function Equations for Polymeric
Liquids 134 3.7.4.1 Damping Function for Shear Flows 134 3.7.4.2 Damping Function for Simple Extension 138 3.7.4.3 Universal Damping Functions 139
3.7.5 Interpretation of the Damping Function in Terms of Entanglements 141 3.7.5.1 The Irreversibility Assumption 142
3.7.6 Comments on the Use of the Damping Function 144 3.8 Molecular Models for Nonlinear Viscoelasticity 146
3.8.1 The Doi-Edwards Constitutive Equation 148 3.9 Strong Flows; The Tendency to Stretch and Align
Molecules 150 References 151
CONTENTS xi
3.3 Theories of Nonlinear Behavior 106 3.4 Finite Measures of Strain 108
3.4.1 The Cauchy Tensor and the Finger Tensor 109 3.4.2 Strain Tensors 110 3.4.3 Reference Configurations 112 3.4.4 Scalar Invariants of the Finger Tensor 113
3.5 The Rubberlike Liquid 114 3.5.1 A Theory of Finite Linear Viscoelasticity 115 3.5.2 Lodge's Network Theory and the Convected
Maxwell Model 117 3.5.3 Behavior of the Rubberlike Liquid in Simple
Shear Flows 118 3.5.3.1 Rubberlike Liquid in Step Shear Strain 119 3.5.3.2 Rubberlike Liquid in Steady Simple
Shear 119 3.5.3.3 Rubberlike Liquid in Oscillatory Shear 121 3.5.3.4 Constrained Recoil of Rubberlike
Liquid 122 3.5.3.5 The Stress Ratio (Nt! 0') and the
Recoverable Shear 122 3.5.4 The Rubberlike Liquid in Simple Extension 123 3.5.5 Comments on the Rubberlike Liquid Model 126
3.6 The BKZ Equation 127 3.7 Wagner's Equation and the Damping Function 128
3.7.1 Strain Dependent Memory Function 128 3.7.2 Determination of the Damping Function 131 3.7.3 Separable Stress Relaxation Behavior 132 3.7.4 Damping Function Equations for Polymeric
Liquids 134 3.7.4.1 Damping Function for Shear Flows 134 3.7.4.2 Damping Function for Simple Extension 138 3.7.4.3 Universal Damping Functions 139
3.7.5 Interpretation of the Damping Function in Terms of Entanglements 141 3.7.5.1 The Irreversibility Assumption 142
3.7.6 Comments on the Use of the Damping Function 144 3.8 Molecular Models for Nonlinear Viscoelasticity 146
3.8.1 The Doi-Edwards Constitutive Equation 148 3.9 Strong Flows; The Tendency to Stretch and Align
Molecules 150 References 151
xii CONTENTS
4. STEADY SIMPLE SHEAR FLOW AND THE VISCOMETRIC FUNCTIONS 153
4.1 Introduction 153 4.2 Steady Simple Shear Flow 153 4.3 Viscometric Flow 155 4.4 Wall Slip and Edge Effects 158 4.5 The Viscosity of Molten Polymers 158
4.5.1 Dependence of Viscosity on Shear Rate 159 4.5.2 Dependence of Viscosity on Temperature 169
4.6 The First Normal Stress Difference 170 4.7 Empirical Relationships Involving Viscometric
Functions 173 4.7.1 The Cox-Merz Rules 173 4.7.2 The Gleissle Mirror Relations 175 4.7.3 Other Relationships 176
References 176
5. TRANSIENT SHEAR FWWS USED TO STUDY NONLINEAR VISCOELASTICITY 179
5.1 Introduction 179 5.2 Step Shear Strain 181
5.2.1 Finite Rise Time 181 5.2.2 The Nonlinear Shear Stress Relaxation Modulus 183 5.2.3 Time-Temperature Superposition 188 5.2.4 Strain-Dependent Spectrum and Maxwell
Parameters 188 5.2.5 Normal Stress Differences for Single-Step Shear
~~ 100 5.2.6 Multistep Strain Tests 191
5.3 Flows Involving Steady Simple Shear 194 5.3.1 Start-Up Flow 194 5.3.2 Cessation of Steady Simple Shear 199 5.3.3 Interrupted Shear 203 5.3.4 Reduction in Shear Rate 205
5.4 Nonlinear Creep 206 5.4.1 Time-Temperature Superposition of Creep Data 209
5.5 Recoil and Recoverable Shear 210 5.5.1 Creep Recovery 210
5.5.1.1 Time-Temperature Superposition; Creep Recovery 213
xii CONTENTS
4. STEADY SIMPLE SHEAR FLOW AND THE VISCOMETRIC FUNCTIONS 153
4.1 Introduction 153 4.2 Steady Simple Shear Flow 153 4.3 Viscometric Flow 155 4.4 Wall Slip and Edge Effects 158 4.5 The Viscosity of Molten Polymers 158
4.5.1 Dependence of Viscosity on Shear Rate 159 4.5.2 Dependence of Viscosity on Temperature 169
4.6 The First Normal Stress Difference 170 4.7 Empirical Relationships Involving Viscometric
Functions 173 4.7.1 The Cox-Merz Rules 173 4.7.2 The Gleissle Mirror Relations 175 4.7.3 Other Relationships 176
References 176
5. TRANSIENT SHEAR FWWS USED TO STUDY NONLINEAR VISCOELASTICITY 179
5.1 Introduction 179 5.2 Step Shear Strain 181
5.2.1 Finite Rise Time 181 5.2.2 The Nonlinear Shear Stress Relaxation Modulus 183 5.2.3 Time-Temperature Superposition 188 5.2.4 Strain-Dependent Spectrum and Maxwell
Parameters 188 5.2.5 Normal Stress Differences for Single-Step Shear
~~ 100 5.2.6 Multistep Strain Tests 191
5.3 Flows Involving Steady Simple Shear 194 5.3.1 Start-Up Flow 194 5.3.2 Cessation of Steady Simple Shear 199 5.3.3 Interrupted Shear 203 5.3.4 Reduction in Shear Rate 205
5.4 Nonlinear Creep 206 5.4.1 Time-Temperature Superposition of Creep Data 209
5.5 Recoil and Recoverable Shear 210 5.5.1 Creep Recovery 210
5.5.1.1 Time-Temperature Superposition; Creep Recovery 213
CONTENTS xiii
5.5.2 Recoil During Start-Up Flow 214 5.5.3 Recoverable Shear Following Steady Simple
Shear 215 5.6 Superposed Deformations 217
5.6.1 Superposed Steady and Oscillatory Shear 218 5.6.2 Step Strain with Superposed Deformations 219
5.7 Large Amplitude Oscillatory Shear 219 5.8 Exponential Shear; A Strong Flow 225 5.9 Usefulness of Transient Shear Tests 228 References 228
6. EXTENSIONAL FLOW PROPERTIES AND THEIR MEASUREMENT 231
6.1 Introduction 231 6.2 Extensional Flows 232 6.3 Simple Extension 237
6.3.1 Material Functions for Simple Extension 238 6.3.2 Experimental Methods 241 6.3.3 Experimental Observations for LDPE 249 6.3.4 Experimental Observations for Linear Polymers 258
6.4 Biaxial Extension 260 6.5 Planar Extension 263 6.6 Other Extensional Flows 265 References 266
7. ROTATIONAL AND SLIDING SURFACE RHEOMETERS 269
7.1 Introduction 269 7.2 Sources of Error for Drag Flow Rheometers 270
7.2.1 Instrument Compliance 270 7.2.2 Viscous Heating 274 7.2.3 End and Edge Effects 275 7.2.4 Shear Wave Propagation 275
7.3 Cone-Plate Flow Rheometers 277 7.3.1 Basic Equations for Cone-Plate Rheometers 278 7.3.2 Sources of Error for Cone-Plate Rheometers 279 7.3.3 Measurement of the First Normal Stress
Difference 281 7.4 Parallel Disk Rheometers 283 7.5 Eccentric Rotating Disks 284
CONTENTS xiii
5.5.2 Recoil During Start-Up Flow 214 5.5.3 Recoverable Shear Following Steady Simple
Shear 215 5.6 Superposed Deformations 217
5.6.1 Superposed Steady and Oscillatory Shear 218 5.6.2 Step Strain with Superposed Deformations 219
5.7 Large Amplitude Oscillatory Shear 219 5.8 Exponential Shear; A Strong Flow 225 5.9 Usefulness of Transient Shear Tests 228 References 228
6. EXTENSIONAL FLOW PROPERTIES AND THEIR MEASUREMENT 231
6.1 Introduction 231 6.2 Extensional Flows 232 6.3 Simple Extension 237
6.3.1 Material Functions for Simple Extension 238 6.3.2 Experimental Methods 241 6.3.3 Experimental Observations for LDPE 249 6.3.4 Experimental Observations for Linear Polymers 258
6.4 Biaxial Extension 260 6.5 Planar Extension 263 6.6 Other Extensional Flows 265 References 266
7. ROTATIONAL AND SLIDING SURFACE RHEOMETERS 269
7.1 Introduction 269 7.2 Sources of Error for Drag Flow Rheometers 270
7.2.1 Instrument Compliance 270 7.2.2 Viscous Heating 274 7.2.3 End and Edge Effects 275 7.2.4 Shear Wave Propagation 275
7.3 Cone-Plate Flow Rheometers 277 7.3.1 Basic Equations for Cone-Plate Rheometers 278 7.3.2 Sources of Error for Cone-Plate Rheometers 279 7.3.3 Measurement of the First Normal Stress
Difference 281 7.4 Parallel Disk Rheometers 283 7.5 Eccentric Rotating Disks 284
xiv CONTENTS
7.6 Concentric Cylinder Rheometers 285 7.7 Controlled Stress Rotational Rheometers 286 7.8 Torque Rheometers 287 7.9 Sliding Plate Rheometers 287
7.9.1 Basic Equations for Sliding Plate Rheometers 288 7.9.2 End and Edge Effects for Sliding Plate
Rheometers 289 7.9.3 Sliding Plate Melt Rheometers 290 7.9.4 The Shear Stress Transducer 292
7.10 Sliding Cylinder Rheometers 294 References 294
8. FLOW IN CAPILLARIES, SLITS AND DIES 298
8.1 Introduction 298 8.2 Flow in a Round Tube 298
8.2.1 Shear Stress Distribution 298 8.2.2 Shear Rate for a Newtonian Fluid 299 8.2.3 Shear Rate for a Power Law Fluid 301 8.2.4 The Rabinowitch Correction 303 8.2.5 The Schiimmer Approximation 304 8.2.6 Wall Slip in Capillary Flow 305
8.3 Flow in a Slit 307 8.3.1 Basic Equations for Shear Stress and Shear Rate 307 8.3.2 Use of a Slit Rheometer to Determine N J 309
8.3.2.1 Determination of N J from the Hole Pressure 310
8.3.2.2 Determination of N J from the Exit Pressure 313
8.4 Pressure Drop in Irregular Cross Sections 317 8.5 Entrance Effects 317
8.5.1 Experimental Observations 318 8.5.2 Entrance Pressure Drop-the Bagley End
Correction 319 8.5.3 Rheological Significance of the Entrance
Pressure Drop 323 8.6 Capillary Rheometers 324 8.7 Flow in Converging Channels 329
8.7.1 The Lubrication Approximation 329 8.7.2 Industrial Die Design 332
8.8 Extrudate Swell 332 8.9 Extrudate Distortion 336
xiv CONTENTS
7.6 Concentric Cylinder Rheometers 285 7.7 Controlled Stress Rotational Rheometers 286 7.8 Torque Rheometers 287 7.9 Sliding Plate Rheometers 287
7.9.1 Basic Equations for Sliding Plate Rheometers 288 7.9.2 End and Edge Effects for Sliding Plate
Rheometers 289 7.9.3 Sliding Plate Melt Rheometers 290 7.9.4 The Shear Stress Transducer 292
7.10 Sliding Cylinder Rheometers 294 References 294
8. FLOW IN CAPILLARIES, SLITS AND DIES 298
8.1 Introduction 298 8.2 Flow in a Round Tube 298
8.2.1 Shear Stress Distribution 298 8.2.2 Shear Rate for a Newtonian Fluid 299 8.2.3 Shear Rate for a Power Law Fluid 301 8.2.4 The Rabinowitch Correction 303 8.2.5 The Schiimmer Approximation 304 8.2.6 Wall Slip in Capillary Flow 305
8.3 Flow in a Slit 307 8.3.1 Basic Equations for Shear Stress and Shear Rate 307 8.3.2 Use of a Slit Rheometer to Determine N J 309
8.3.2.1 Determination of N J from the Hole Pressure 310
8.3.2.2 Determination of N J from the Exit Pressure 313
8.4 Pressure Drop in Irregular Cross Sections 317 8.5 Entrance Effects 317
8.5.1 Experimental Observations 318 8.5.2 Entrance Pressure Drop-the Bagley End
Correction 319 8.5.3 Rheological Significance of the Entrance
Pressure Drop 323 8.6 Capillary Rheometers 324 8.7 Flow in Converging Channels 329
8.7.1 The Lubrication Approximation 329 8.7.2 Industrial Die Design 332
8.8 Extrudate Swell 332 8.9 Extrudate Distortion 336
CONTENTS xv
8.9.1 Surface Melt Fracture-Sharkskin 337 8.9.2 Oscillatory Flow in Linear Polymers 338 8.9.3 Gross Melt Fracture 339 8.9.4 Role of Slip in Melt Fracture 340 8.9.5 Gross Melt Fracture Without Oscillations 341
References 341
9. RHEO-OPTICS AND MOLECULAR ORIENTATION 345
9.1 Basic Concepts-Interaction of Light and Matter 345 9.1.1 Refractive Index and Polarization 346 9.1.2 Absorption and Scatterip.g 347 9.1.3 Anisotropic Media; Birefringence and Dichroism 349
9.2 Measurement of Birefringence 353 9.3 Birefringence and Stress 358
9.3.1 Stress-Optical Relation 358 9.3.2 Application of Birefringence Measurements 362
References 363
10. EFFECTS OF MOLECULAR STRUCTURE 365
10.1 Introduction and Qualitative Overview of Molecular Theory 365
10.2 Molecular Weight Dependence of Zero Shear Viscosity 368 10.3 Compliance and First Normal Stress Difference 370 10.4 Shear Rate Dependence of Viscosity 374 10.5 Temperature and Pressure Dependence 381
10.5.1 Temperature Dependence of Viscosity 381 10.5.2 Pressure Dependence of Viscosity 384
10.6 Effects of Long Chain Branching 386 References 389
11. RHEOWGY OF MULTIPHASE SYSTEMS 390
11.1 Introduction 390 11.2 Effect of Rigid Fillers 390
11.2.1 Viscosity 392 11.2.2 Elasticity 400
11.3 Deformable Multiphase Systems (Blends, Block Polymers) 401 11.3.1 Deformation of Disperse Phases and Relation to
Morphology 403
CONTENTS xv
8.9.1 Surface Melt Fracture-Sharkskin 337 8.9.2 Oscillatory Flow in Linear Polymers 338 8.9.3 Gross Melt Fracture 339 8.9.4 Role of Slip in Melt Fracture 340 8.9.5 Gross Melt Fracture Without Oscillations 341
References 341
9. RHEO-OPTICS AND MOLECULAR ORIENTATION 345
9.1 Basic Concepts-Interaction of Light and Matter 345 9.1.1 Refractive Index and Polarization 346 9.1.2 Absorption and Scatterip.g 347 9.1.3 Anisotropic Media; Birefringence and Dichroism 349
9.2 Measurement of Birefringence 353 9.3 Birefringence and Stress 358
9.3.1 Stress-Optical Relation 358 9.3.2 Application of Birefringence Measurements 362
References 363
10. EFFECTS OF MOLECULAR STRUCTURE 365
10.1 Introduction and Qualitative Overview of Molecular Theory 365
10.2 Molecular Weight Dependence of Zero Shear Viscosity 368 10.3 Compliance and First Normal Stress Difference 370 10.4 Shear Rate Dependence of Viscosity 374 10.5 Temperature and Pressure Dependence 381
10.5.1 Temperature Dependence of Viscosity 381 10.5.2 Pressure Dependence of Viscosity 384
10.6 Effects of Long Chain Branching 386 References 389
11. RHEOWGY OF MULTIPHASE SYSTEMS 390
11.1 Introduction 390 11.2 Effect of Rigid Fillers 390
11.2.1 Viscosity 392 11.2.2 Elasticity 400
11.3 Deformable Multiphase Systems (Blends, Block Polymers) 401 11.3.1 Deformation of Disperse Phases and Relation to
Morphology 403
xvi CONTENTS
11.3.2 Rheology of Immiscible Polymer Blends 406 11.3.3 Phase-Separated Block and Graft Copolymers 407
References 408
12. CHEMORHEOLOGY OF REACI'ING SYSTEMS 410
12.1 Introduction 410 12.2 Nature of the Curing Reaction 411 12.3 Experimental Methods for Monitoring Curing Reactions 413
12.3.1 Dielectric Analysis 417 12.4 Viscosity of the Pre-gel Liquid 418 12.5 The Gel Point and Beyond 419
References 421
13. RHEOWGY OF THERMOTROPIC LIQUID CRYSTAL POLYMERS 424
13.1 Introduction 424 13.2 Rheology of Low Molecular Weight Liquid Crystals 426 13.3 Rheology of Aromatic Thermotropic Polyesters 431 13.4 Relation of Rheology to Processing of Liquid Crystal
Polymers 437 References 439
14. ROLE OF RHEOLOGY IN EXTRUSION 441
14.1 Introduction 441 14.1.1 Functions of Extruders 442 14.1.2 Types of Extruders 443 14.1.3 Screw Extruder Zones 444
14.2 Analysis of Single Screw Extruder Operation 446 14.2.1 Approximate Analysis of Melt Conveying Zone 446 14.2.2 Coupling Melt Conveying to Die Flow 454 14.2.3 Effects of Simplifying Approximations 459
14.2.3.1 Geometric Factors 459 14.2.3.2 Leakage Flow 460 14.2.3.3 Non-Newtonian Viscosity 462 14.2.3.4 Non-Isothermal Flow 467
14.2.4 Solids Conveying and Melting Zones 470 14.2.4.1 Feeding and Solids Conveying 470 14.2.4.2 Melting Zone 472
14.2.5 Scale-Up and Simulation 476
xvi CONTENTS
11.3.2 Rheology of Immiscible Polymer Blends 406 11.3.3 Phase-Separated Block and Graft Copolymers 407
References 408
12. CHEMORHEOLOGY OF REACI'ING SYSTEMS 410
12.1 Introduction 410 12.2 Nature of the Curing Reaction 411 12.3 Experimental Methods for Monitoring Curing Reactions 413
12.3.1 Dielectric Analysis 417 12.4 Viscosity of the Pre-gel Liquid 418 12.5 The Gel Point and Beyond 419
References 421
13. RHEOWGY OF THERMOTROPIC LIQUID CRYSTAL POLYMERS 424
13.1 Introduction 424 13.2 Rheology of Low Molecular Weight Liquid Crystals 426 13.3 Rheology of Aromatic Thermotropic Polyesters 431 13.4 Relation of Rheology to Processing of Liquid Crystal
Polymers 437 References 439
14. ROLE OF RHEOLOGY IN EXTRUSION 441
14.1 Introduction 441 14.1.1 Functions of Extruders 442 14.1.2 Types of Extruders 443 14.1.3 Screw Extruder Zones 444
14.2 Analysis of Single Screw Extruder Operation 446 14.2.1 Approximate Analysis of Melt Conveying Zone 446 14.2.2 Coupling Melt Conveying to Die Flow 454 14.2.3 Effects of Simplifying Approximations 459
14.2.3.1 Geometric Factors 459 14.2.3.2 Leakage Flow 460 14.2.3.3 Non-Newtonian Viscosity 462 14.2.3.4 Non-Isothermal Flow 467
14.2.4 Solids Conveying and Melting Zones 470 14.2.4.1 Feeding and Solids Conveying 470 14.2.4.2 Melting Zone 472
14.2.5 Scale-Up and Simulation 476
CONTENTS xvii
14.2.5.1 Scale-Up 476 14.2.5.2 Simulation 477
14.3 Mixing, Devolatilization and Twin Screw Extruders 480 14.3.1 Mixing 480 14.3.2 Devolatilization 484 14.3.3 Twin Screw Extruders 485
References 489
15. ROLE OF RHEOLOGY IN INJECTION MOLDING 490
15.1 Introduction 491 15.2 Melt Flow in Runners and Gates 492 15.3 Flow in the Mold Cavity 494 15.4 Laboratory Evaluation of Molding Resins 500
15.4.1 Physical Property Measurement 501 15.4.2 Moldability Tests 502
15.5 Formulation and Selection of Molding Resins 506 References 507
16. ROLE OF RHEOLOGY IN BLOW MOLDING 509
16.1 Introduction 509 16.2 Flow in the Die 510 16.3 Parison Swell 512 16.4 Parison Sag 519
16.4.1 Pleating 521 16.5 Parison Inflation 521 16.6 Blow Molding of Engineering Resins 522 16.7 Stretch Blow Molding 523 16.8 Measurement of Resin Processability 524
16.8.1 Resin Selection Tests 524 16.8.2 Quality Control Tests 528
References 529
17. ROLE OF RHEOLOGY IN FILM BLOWING AND SHEET EXTRUSION 530
17.1 The Film Blowing Process 531 17.1.1 Description of the Process 531 17.1.2 Criteria for Successful Processing 533 17.1.3 Principal Problems Arising in Film Blowing 534 17.1.4 Resins Used for Blown Film 534
CONTENTS xvii
14.2.5.1 Scale-Up 476 14.2.5.2 Simulation 477
14.3 Mixing, Devolatilization and Twin Screw Extruders 480 14.3.1 Mixing 480 14.3.2 Devolatilization 484 14.3.3 Twin Screw Extruders 485
References 489
15. ROLE OF RHEOLOGY IN INJECTION MOLDING 490
15.1 Introduction 491 15.2 Melt Flow in Runners and Gates 492 15.3 Flow in the Mold Cavity 494 15.4 Laboratory Evaluation of Molding Resins 500
15.4.1 Physical Property Measurement 501 15.4.2 Moldability Tests 502
15.5 Formulation and Selection of Molding Resins 506 References 507
16. ROLE OF RHEOLOGY IN BLOW MOLDING 509
16.1 Introduction 509 16.2 Flow in the Die 510 16.3 Parison Swell 512 16.4 Parison Sag 519
16.4.1 Pleating 521 16.5 Parison Inflation 521 16.6 Blow Molding of Engineering Resins 522 16.7 Stretch Blow Molding 523 16.8 Measurement of Resin Processability 524
16.8.1 Resin Selection Tests 524 16.8.2 Quality Control Tests 528
References 529
17. ROLE OF RHEOLOGY IN FILM BLOWING AND SHEET EXTRUSION 530
17.1 The Film Blowing Process 531 17.1.1 Description of the Process 531 17.1.2 Criteria for Successful Processing 533 17.1.3 Principal Problems Arising in Film Blowing 534 17.1.4 Resins Used for Blown Film 534
xviii CONTENTS
17.2 Flow in the Extruder and Die; Extrudate Swell 536 17.3 Melt Flow in the Bubble 540
17.3.1 Forces Acting on the Bubble 541 17.3.1.1 Viscous Stress in the Molten Region of
the Bubble 543 17.3.1.2 Aerodynamic Forces 544
17.3.2 Bubble Shape 547 17.3.3 Drawability 549
17.4 BubbIe Stability 550 17.5 Sheet Extrusion 552
References 555
18. ON-LINE MEASUREMENT OF RHEOLOGICAL PROPERTIES 551
18.1 Introduction 557 18.2 Types of On-Line Rheometers for Melts 558
18.2.1 On-Line Capillary Rheometers for Melts 558 18.2.2 Rotational On-Line Rheometers for Melts 560 18.2.3 In-Line Melt Rheometers 562
18.3 Specific Applications of Process Rheometers 563 References 565
19. INDUSTRIAL USE OF RHEOMETERS 561
19.1 Factors Affecting Test and Instrument Selection 567 19.1.1 Purposes of Rheological Testing 568 19.1.2 Material Limitations on Test Selection 569 19.1.3 Instruments 571
19.2 Screening and Characterization 573 19.2.1 Advantages and Disadvantages of Rheological
Tests 573 19.2.2 Other Information Useful for Screening 574 19.2.3 Stability 577
19.2.3.1 Stability Measurement 578 19.2.3.2 Use of Stability Data 580
19.2.4 Temperature and Frequency Dependence 582 19.2.4.1 Measurement Tactics 582 19.2.4.2 Interpretation of Results 583
19.3 Resin Selection and Optimization and Process Problem Solving 585
xviii CONTENTS
17.2 Flow in the Extruder and Die; Extrudate Swell 536 17.3 Melt Flow in the Bubble 540
17.3.1 Forces Acting on the Bubble 541 17.3.1.1 Viscous Stress in the Molten Region of
the Bubble 543 17.3.1.2 Aerodynamic Forces 544
17.3.2 Bubble Shape 547 17.3.3 Drawability 549
17.4 BubbIe Stability 550 17.5 Sheet Extrusion 552
References 555
18. ON-LINE MEASUREMENT OF RHEOLOGICAL PROPERTIES 551
18.1 Introduction 557 18.2 Types of On-Line Rheometers for Melts 558
18.2.1 On-Line Capillary Rheometers for Melts 558 18.2.2 Rotational On-Line Rheometers for Melts 560 18.2.3 In-Line Melt Rheometers 562
18.3 Specific Applications of Process Rheometers 563 References 565
19. INDUSTRIAL USE OF RHEOMETERS 561
19.1 Factors Affecting Test and Instrument Selection 567 19.1.1 Purposes of Rheological Testing 568 19.1.2 Material Limitations on Test Selection 569 19.1.3 Instruments 571
19.2 Screening and Characterization 573 19.2.1 Advantages and Disadvantages of Rheological
Tests 573 19.2.2 Other Information Useful for Screening 574 19.2.3 Stability 577
19.2.3.1 Stability Measurement 578 19.2.3.2 Use of Stability Data 580
19.2.4 Temperature and Frequency Dependence 582 19.2.4.1 Measurement Tactics 582 19.2.4.2 Interpretation of Results 583
19.3 Resin Selection and Optimization and Process Problem Solving 585
CONTENTS xix
19.4 Rheological Quality Control Tests References
APPENDIX A: MEASURES OF STRAIN FOR LARGE
595 599
DEFORMATIONS 601
APPENDIX B: MOLECULAR WEIGHT DISTRIBUTION AND DETERMINATION OF MOLECULAR WEIGHT AVERAGES 607
APPENDIX C: THE INTRINSIC VISCOSITY AND THE INHERENT VISCOSITY 613
APPENDIX D: THE GLASS TRANSITION TEMPERATURE 617
APPENDIX E: MANUFACTURERS OF MELT RHEOMETERS AND RELATED EQUIPMENT 622
NOMENCLATURE 630
AUTHOR INDEX 639
SUBJECT INDEX 649
CONTENTS xix
19.4 Rheological Quality Control Tests References
APPENDIX A: MEASURES OF STRAIN FOR LARGE
595 599
DEFORMATIONS 601
APPENDIX B: MOLECULAR WEIGHT DISTRIBUTION AND DETERMINATION OF MOLECULAR WEIGHT AVERAGES 607
APPENDIX C: THE INTRINSIC VISCOSITY AND THE INHERENT VISCOSITY 613
APPENDIX D: THE GLASS TRANSITION TEMPERATURE 617
APPENDIX E: MANUFACTURERS OF MELT RHEOMETERS AND RELATED EQUIPMENT 622
NOMENCLATURE 630
AUTHOR INDEX 639
SUBJECT INDEX 649
MELT RHEOLOGY AND ITS ROLE IN PLASTICS
PROCESSING
THEORY AND APPLICATIONS
MELT RHEOLOGY AND ITS ROLE IN PLASTICS
PROCESSING
THEORY AND APPLICATIONS
