POLYMER RHEOLOGY

POLYMER RHEOLOGY

R. S. LENK Senior Lecturer in Plastics Technology,

Polytechnic of the South Bank, London, UK

APPLIED SCIENCE PUBLISHERS LTD

LONDON

APPLIED SCIENCE PUBLISHERS LTD RIPPLE ROAD, BARKING, ESSEX, ENGLAND

ISBN 978-94-010-9668-3 ISBN 978-94-010-9666-9 (eBook) DOII0.I007/978-94-010-9666-9

WITH 17 TABLES AND 214 ILLUSTRATIONS

cg APPLIED SCIENCE PUBLISHERS LTD 1978

Softcover reprint of the hardcover 1 st edition 1978

A11 rights reserved. No part ofthis publicatioll may be reproduced, stored in a retrieva1 system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recol'uing, or otherwise, without the prior writtcn permission ofthe Pllblisl1ers, Applied Science Publishers Ltd, Ripple

Road, Barking, Essex, England

navra p1'/el

(Everything Flows)

HERACLITOS

Foreword

Everything flows, so rheology is a universal science. Even if we set aside claims of such width, there can be no doubt of its importance in polymers. It joins with chemistry in the polymerisation step but polymer engineering is supreme in all the succeeding steps. This is the area concerned with the fabrication of the polymer into articles or components, with their design to meet the needs in service, and with the long and short term performance of the article or component. This is a typical area of professional engineering activity, but one as yet without its proper complement of professional engineers.

An understanding of polymer rheology is the key to effective design and material plus process selection, to efficient fabrication, and to satisfactory service, yet few engineers make adequate use of what is known and understood in polymer rheology. Its importance in the flow processes of fabrication is obvious. Less obvious, but equally important, are the rheological phenomena which determine the in-service performance. There is a gap between the polymer rheologist and the polymer engineer which is damaging to both parties and which contributes to a less than satisfactory use of polymers in our society. It is important that this gap be filled and this book makes an attempt to do so. It presents an outline of what is known in a concise and logical fashion. It does this starting from first principles and with the minimum use of complex mathematics. Nevertheless, the approach is quite rigorous and the book should rightly find its way onto any rheologist's bookshelf. There must be some complexity in describing the effects of the interaction of viscosity and elasticity so subtly present in polymers, but the treatment adopted should not be more difficult than most engineers can normally handle.

The book does not attempt to spoonfeed. Any designer or processor of polymers on reading it will gain a much better understanding of the materials he is handling, but he will rightly be left to make his own translation into the engineering aspects of design and processing. The

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bridge is there, firmly and well constructed, but the engineer must walk across. There is no assumption that he wishes to be carried over. I therefore commend it especially to all engineers in the polymer field who wish to have a solid base for their day to day activities.

A. A. L. CHALLIS

Director Polymer Engineering Directorate

Science Research Council London, UK

Preface

Since 'Plastics Rheology' was published in 1968t important further developments have created a need for a new book to serve the practitioner. The present volume is intended to fill this need whilst simultaneously promoting a fundamental understanding of the behaviour of polymer materials.

The material which was retained from the earlier English and the subsequent expanded and revised Germant books has been completely reorganised and augmented. There were nine chapters in the first and eleven in the second; this volume has twenty-two. We begin with an introduction which discusses the philosophy of rheology and the special nature of plastics in the spectrum of materials and end with a chapter which attempts to reinforce a conclusion that all properties are ultimately dependent on structural parameters on a supramolecular and molecular level.

Like Caesar's Gaul, 'Polymer Rheology' is divided into three parts, but unlike the historical model the divisions are not such as to isolate one area from the rest. If the rheology of melt processing represents one part, and the mechanical properties of manufactured components a second, then the third part is provided by the consideration in depth of the phenomena which affect flow and deformation, the interpretation of these phenomena on a structural basis and a description of the methods which are used to gain an understanding of the materials; thus the practitioner is assisted in his rational approach to processing and design problems. Portions of the third part are intercalated where the need arises, without disturbing the natural sequence of subject matter. Serving as a theoretical cement this 'third part' acts as a leaven in what might otherwise be a diet of <;trictly ad hoc problems.

In preparing this book I had the pleasure and privilege of receiving contributions from a number of distinguished colleagues who very kindly agreed to cover the subjects appropriate to their special expertise, namely

t 'Plastics Rheology', R. S. Lenk, Applied Science Publishers, London, 1968. t 'Rheologie der Kunststoffe', R. S. Lenk, Carl Hanser Verlag, Munich, 1972.

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x Preface

Neil Cogswell (Chapter 12), Ian Barrie (Chapter 13), Juergen Pohrt (Chapters 17, 18 and 19) and Frigyes Thamm (Chapter 21).

It is good to see Euro-cooperation which brings research workers in industry and academe together in a joint enterprise. To the guest writers, their companies and institutions, thanks.

As regards the inevitable problem of mathematics: derivations are given only when they serve to illustrate a method, are needed to stimulate a quantitative approach; or when an essential relationship is to be established which the enquiring mind would prefer to emerge from basic principles rather than out oflimbo. With the one possible exception of Chapter 5, the treatment does not transcend the standard techniques with which every scientist and technologist is familiar.

The principal problem was that of reconciling simplicity of presentation and clarity of the emerging concepts with the practicalities of process and component design based upon the scientific analysis of the parameters which determine polymer behaviour. The book must be judged by the extent to which this problem has been solved.

R. S. LENK

Polytechnic of the South Bank London, UK

Contents

Foreword

Preface

Introduction

I. The Characterisation of Viscous Flow. Viscosity, Shear Rate and Shear Stress

2. The Time Dependence of Viscous Flow. Thixotropy and

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Rheopexy 15

3. The Temperature Dependence of Viscous Flow. Free Volume 21

4. The Influence of Pressure on the Viscosity of Polymer Melts. Viscosity and Molecular Weight . 31

5. Vectors and Tensors. Fundamental Equations 41

6. The Analysis of Steady-State Flow in Rectangular and Cylindrical Channels . 61

7. The Hagen-Poiseuille Equation and the Rabinowitsch Correction. The Pressure Drop in Tapered Channels . 75

8. Pressure Drop in Wire Coating Dies. Two-Dimensional Flow in Extruder Screws 87

9. Coextrusion 95

10. The Effect of Melt Elasticity on Extrusion and Other Melt Processing Operations 101

II. The Rheology of Calendering 113

12. Stretching flows by F. N. COGSWELL 123 xi

xii Contents

13. The Rheology of Injection Moulding by I. T. BARRIE 141

14. Deformation in the Solid State-Small Strains 165

IS. Deformation in the Solid State-Large Strains 193

16. Deformation in the Solid State-Cyclic Strains 219

17. Critical Strain by J. POHRT . 241

18. Critical Strain: The Effect of Processing History and Associated Factors by J. POHRT 255

19. Critical Strain: An Engineer's View of the Energy Balance During Deformation by J. POHRT 279

20. Rheo-Optics 307

21. Rheo-Optical Techniques by F. THAMM 317

22. Rheology and Morphology 351

Index 369

Introduction

Rheology has been defined as 'a branch of physics which concerns itself with the mechanism of deformable bodies'. Deformation is a phenomenon which is of necessity associated with volume elements. The pioneers of modern rheology concerned themselves principally with the bulk mechanical manifestations of the deformational effects of stresses applied to bodies in the liquid state. However, it has become increasingly apparent that rheology cannot be encompassed within such arbitrary confines for the following reasons:

I. The definition of the 'liquid state' is rather arbitrary. A liquid, ideally, is a body which deforms irreversibly as a result offlow. But we know that bodies such as metals-which are indisputably solids-do flow and so deform irreversibly if a force of sufficient magnitude is allowed to act upon them for a sufficient length of time. Flow in solids is known as 'creep', Structural engineers are well aware of the problems which creep presents. They attempt to cope by designing their structures in such a way as to limit the freedom of relative displacement of the material constituents. They endeavour to 'rigidify' a structure by locking the volume elements so that the design load is insufficient to cause a significant change in the existing spatial arrangement.

The fact that under certain conditions such a change is possible implies that at ordinary temperatures there still exists an irreversible flow potential even in such materials as metals. Since the energy required to produce such flow is irrecoverable it must be dissipated as heat. It is true, of course, that an overwhelming proportion of the energy used to deform a piece of metal is instantaneously recovered upon removal of the stress, but it is equally true that some small (and sometimes significant) amount of energy is lost in creep or irreversible flow. The actual percentage of this energy loss depends upon the case with which the constituent parts of the stressed body can be made to alter their positions in space relative to one another, to slip over one another, to flow.

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The resistance of a material to irreversible positional change of its constituent volume elements and the concomitant conversion of mechanical energy into heat is denoted by a parameter known as the 'viscosity'. The term viscosity immediately conjures up the concept of a liquid rather than a solid. In order that metals could continue to be regarded as solids, the viscosity of solids is often referred to as the 'internal' or 'frictional' viscosity, as if it were a special kind of viscosity. This devious expertise is both misleading and unnecessary. There is no need for a qualitative dividing line between solids and liquids, although the transition from one to the other usually involves a quantitative viscosity change which may cover many decades within possibly very close limits of changes in environmental conditions.

The same reasoning can be applied to the gas/liquid transition, since a gas is merely a fluid of particularly low viscosity when compared with a liquid. It is therefore logical to regard the gaseous, liquid and solid states as special aspects of one generalised continuous and universal fluid state, with the primary transitions occurring fairly sharply in some materials and less sharply in others. The unifying principle of the universal fluid state lies precisely in the fact that the principal attribute of the liquid state, namely viscosity, exists (obviously) in the gaseous state and (less obviously, but nevertheless demonstrably) in the solid state.

2. By inverting the argument, it is also easily seen that materials which are indisputably liquids do not necessarily dissipate all the deformational energy. Some of the energy is recoverable and since this is so the liquid has some of the principal attribute of the solid state, namely elasticity. Of course, in a typical liquid the magnitude of the viscous response mechanism to an applied stress may be overwhelmingly greater than any manifestation of reversible (recoverable, elastic) deformation.

This can be demonstrated when a high speed cine film of the impact of a drop of water on a glass plate is examined frame by frame. It is then seen that the drop actually bounces like a ball and returns stored energy (a) by rebounding, and (b) by recovering its spherical shape after impact instead of maintaining the squat deformed shape which the contact with the glass surface has momentarily imparted to it. We are not immediately concerned with the nature of the internal or interfacial forces which manifest themselves by forcing an elastic response. Suffice it to say that liquids have not only viscosity but possess some of the main attributes of solid state behaviour, in the same way as solids are not only elastic but possess some of the main attributes of the liquid state.

The best way to describe real materials is to regard them as viscoelastic.

Introduction xv

Some people use two terms (viscoelastic and elasticoviscous) in order to emphasise the predominance of the viscous or elastic response respectively, but the writer feels that this distinction is somewhat pedantic.

3. Rheology should not be restricted to bulk mechanical deformation. Since volume elements are involved in all deformations, whatever the force field, there is no reason why the mathematical equations developed to describe mechanical deformations should not equally apply to deformations induced by an electrical, magnetic or any other force field. Volume elements will be different in each case, to be sure; in a plastic under tension or in melt flow, viscosity manifests itself by the spatial rearrangement of polymer chain segments which constitute quite large volume elements. An electric field acting on polar plastics will cause energy dissipation as frictional heat when the dipoles do work against their environment in their endeavour to conform to the polarity of the applied field. The volume element is smaller, but the same argument applies.

Again, excitation by light rays (visible or otherwise) will cause deformations, some of which will be irreversible. In the infra-red the volume elements involved are specific atomic bond conformations and the energy dissipation is implicit in the frictional heat generated when these bonds are partially constrained in their vibrational and rotational evolutions. The volume elements are perfectly real, although they require a highly specific mode of excitation before they can manifest themselves.

Similar arguments can be applied to nuclear magnetic and electron-spin resonance where the volume elements are subatomic but no less real for that. Hence rheology is not just 'a branch of physics'. It is far more than that. It is the key to the understanding of the behaviour of materials when subjected to any kind offorce field. Indeed, far from being 'a branch' of any science, rheology emerges as the central science with such branches as chemistry, physics, engineering or biology.

Having considered the scope of rheology in general, let us now look at the rheology of polymers in particular. What has made polymer rheology particularly fascinating is the fact that plastics exhibit a spectrum of deformational responses to stresses which concerns itself in particular with the border region between the 'solid' and 'liquid' states and uses this platform as a springboard for the further penetration of the more typical regions of these two states. In addition, industry has discovered the fundamental importance of studying plastics by methods which had to be specially developed, since the methods which were acceptable for traditional materials proved to be totally inadequate if a full understanding

xvi Introduction

of the formulation, tailoring, compounding, processing, design and functional performance of plastics is to be gained. What is more, this realisation has caused the polymer chemist, physicist, technologist and engineer to concern themselves with rheology. It has enabled them to enhance their own efficiency and with it the research, development, production and applications performance of their industry.

Rheology has made important contributions to advances in food technology, medicine, paint and printing-ink technology, building and structural engineering, adhesives, cosmetics, oilwell drilling operations, and elsewhere. But it cannot be denied that it is due to its tremendous scope in the polymer field that rheology has now been recognised as a major scientific discipline affording (i) deep fundamental insights, and (ii) immediate practical rewards when the new understanding gained is applied to process and product design.