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Molecular Characterization and Analysis of Polymers [1 ed.]
 0444530568, 9780444530561

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COMPREHENSIVE ANALYTICAL CHEMISTRY VOLUME

53

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands Linacre House, Jordan Hill, Oxford OX2 8DP, UK

First edition 2008 Copyright r 2008 Elsevier B.V. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected] Alternatively you can submit your request online by visiting the Elsevier web site at http:// www.elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-444-53056-1 ISSN: 0166-526X

For information on all Elsevier publications visit our website at books.elsevier.com

Printed and bound in Hungary 08 09 10 11 12 10 9 8 7 6 5 4 3 2 1

ADVISORY BOARD Joseph A. Caruso University of Cincinnati, Cincinnati, OH, USA Hendrik Emons Joint Research Centre, Geel, Belgium Gary Hieftje Indiana University, Bloomington, IN, USA Kiyokatsu Jinno Toyohashi University of Technology, Toyohashi, Japan Uwe Karst University of Mu¨nster, Mu¨nster, Germany Gyo¨rgy Marko-Varga AstraZeneca, Lund, Sweden Janusz Pawliszyn University of Waterloo, Waterloo, Ont., Canada Susan Richardson US Environmental Protection Agency, Athens, GA, USA

Wilson & Wilson’s

COMPREHENSIVE ANALYTICAL CHEMISTRY

Edited by ´ D. BARCELO Research Professor Department of Environmental Chemistry IIQAB-CSIC Jordi Girona 18-26 08034 Barcelona Spain

Wilson & Wilson’s

COMPREHENSIVE ANALYTICAL CHEMISTRY MOLECULAR CHARACTERIZATION AND ANALYSIS OF POLYMERS

VOLUME

53 Edited by JOHN M. CHALMERS VS Consulting, 14 Croft Hills, Tame Bridge, Stokesley TS9 5NW, UK PROF. Dr ROBERT J. MEIER Institut fu¨r Agrosphere, ICG-4, Forschungszentrum Ju¨lich GmbH, D-52425 Ju¨lich, Germany

Amsterdam  Boston  Heidelberg  London New York  Oxford  Paris  San Diego San Francisco  Singapore  Sydney  Tokyo

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CONTENT S

Contributors to Volume 53 Volumes in the Series Preface Series Editor’s Preface

xiii xv xix xxi SECTION I: INTRODUCTION

1. Introduction

3

John M. Chalmers and Robert J. Meier 1. The Analytical Competence 2. Contents and Structure 3. Practical Considerations in the Multi-Technique Approach References

2. Polymer Chemistry and Microstructure

3 6 11 12

13

Jacques Devaux and Sophie Demoustier-Champagne 1. Introduction 2. Polymer: Definitions 3. From Molecules to Macromolecules 4. Fundamentals of Polymer Chemistry 5. Polymer Degradation 6. Summary References

3. Polymeric Materials: Composition, Uses and Applications

14 15 25 34 58 62 62

65

J.P. Candlin 1. Introduction 2. Mode of Polymerisation 3. Polymer Materials: Types and Forms 4. Polymer Additives 5. Summary Bibliography

65 66 68 87 117 118

vii

viii

Contents

SECTION II: POLYMER CHAIN ANALYSIS

4. Chain Structure Characterization

123

Gregory Beaucage and Amit S. Kulkarni 1. Introduction to Structure in Synthetic Macromolecules 2. Local Structure and Its Ramifications 3. Summary References

5. Chain End Characterisation

123 134 165 166

171

Anthony T. Jackson and Duncan F. Robertson 1. 2. 3. 4.

Introduction End Groups in Free Radical Polymers End Groups in Condensation Polymers End Groups in Polymers from Ionic Polymerisation 5. Closing Remarks Acknowledgements References

6. Determination of Molecular Weights and Their Distributions

171 175 182 194 201 201 201

205

Simone Wiegand and Werner Ko¨hler 1. Introduction 2. Distribution Functions and Averages 3. Methods Based on Colligative Properties 4. Viscometry 5. Scattering Techniques 6. Liquid Chromatography 7. Analytical Ultracentrifuge 8. Other Methods 9. Practical Examples 10. Conclusion Acknowledgements References

205 208 212 218 220 228 235 237 241 247 248 248

SECTION III: POLYMER MORPHOLOGY AND STRUCTURE 7. Phase Structure and Morphology

255

Rufina G. Alamo 1. Phase Structure and Morphology 2. Supermolecular Morphology

255 274

Contents

3. Concluding Remarks Acknowledgements References

8. Characterization of Molecular Orientation

ix

286 287 287

295

Thierry Lefe`vre, Christian Pellerin and Michel Pe´zolet 1. Introduction 2. Theory 3. Birefringence 4. Infrared Linear Dichroism (IRLD) 5. Raman Spectroscopy and Microspectroscopy 6. Fluorescence Spectroscopy 7. NMR Spectroscopy 8. X-Ray Diffraction and Absorption 9. Conclusion References

9. Polymer Networks: Elastomers

295 297 301 305 313 322 325 328 333 333

337

B. Erman and J.E. Mark 1. 2. 3. 4. 5. 6. 7.

Introduction Structure of a Typical Network Elementary and More Advanced Molecular Theories Phenomenological Theories Some Relevant Simulations Swelling of Networks and Responsive Gels Enthalpic and Entropic Contributions to Rubber Elasticity: The Force–Temperature Relations 8. Multimodal Elastomers 9. Liquid–Crystalline Elastomers 10. Novel Reinforced Elastomers 11. Further Comments on Some Characterization Techniques Acknowledgement References

338 339 341 351 352 356 358 359 365 370 374 376 377

SECTION IV: POLYMER DEGRADATION 10. Polymer Degradation and Oxidation: An Introduction

387

John M. Chalmers and Robert J. Meier 1. Introduction 2. Standard Tests and Comparative Methods 3. Spectroscopic Techniques 4. Thermal Methods 5. Chromatographic Analysis 6. Closing Remarks Acknowledgement References

388 390 402 436 442 447 448 448

x

Contents

11. The Role of Oxidation in Degradation of Polymers: The Relation of Oxidation to the Light Emission from Oxidized Polymers

451

Jozef Rychly´ and Lyda Matisova´-Rychla´ 1. Introduction, Historical Overview and Terminology Associated with the Degradation and Ageing of Polymers 2. Methodology and Analytical Techniques in Polymer Stability Studies 3. Mechanisms Leading to the Light Emission from Thermally Oxidized Polymers (Chemiluminescence), Similarities and Differences within Respective Groups of Polymers 4. General Classification of Chemiluminescence from Polymers 5. Comparison of Chemiluminescence for Isothermal and Non-Isothermal Conditions with those Obtained by DSC 6. The Effect of Initial Molar Mass on Chemiluminescence Runs 7. The Effect of Temperature on Chemiluminescence Intensity; The Mutual Relation of Isothermal and Non-Isothermal Studies 8. Relaxation Experiments (Jump Changes of Concentration of Oxygen, Temperature and Humidity) and Rate Constants of Respective Elementary Reaction Steps 9. The Effect of Antioxidants and Polymer Stabilizers 10. Isothermal Kinetics of Polymers Oxidation and Its Relation to the Concentration of Oxygen in Surrounding Atmosphere 11. The Effect of Alkaline Additives on Chemiluminescence Runs: A Possible Impact 12. Conclusions and Outline of the Further Perspectives Acknowledgements References

12. ESR and ESR Imaging Methods for the Study of Oxidative Polymer Degradation

452 461

463 471 476 478 480

482 483 487 490 493 496 496

499

Shulamith Schlick and Krzysztof Krucza"a 1. 2. 3. 4.

Introduction: Polymer Degradation in the Presence of Oxygen Fundamentals of ESR and ESR Imaging ESR as a Tool for the Study of Polymer Degradation ESR Imaging: A Nondestructive Method for Spatially Resolved Polymer Degradation 5. Concluding Remarks Acknowledgements References

500 504 513 517 521 521 522

SECTION V: POLYMER PRODUCT ANALYSIS 13. Spatial Imaging/Heterogeneity

527

Peter Wilhelm and Boril Chernev 1. Introduction 2. Raman and FTIR Microscopy

527 529

Contents

3. Examples of Heterogeneous Polymers Investigated by IR and Raman Microscopy 4. Other Methods and Comparison of Methods 5. Conclusions References

14. Additive Analysis

xi

538 550 557 558

561

John Sidwell 1. Introduction 2. Analytical Techniques for Additive Analysis 3. Analysis of Specific Additives 4. Future Developments in Analytical Methodology References

15. Failure, Defect, and Contaminant Analysis

562 563 573 603 605

607

James D. Rancourt, Jennifer Brooks, Sue Mecham, Alan Sentman, Brian Starr and Jason Todd 1. Introduction 2. Case Studies 3. Summary References

607 608 673 674

16. Surface Analysis

675

John M. Chalmers and Robert J. Meier 1. Introduction 2. A Surface and Spatial Resolution 3. Adhesion 4. Polymer Degradation 5. Polymer Fracture 6. Characterizing Polymer Surfaces 7. Delamination 8. Cure 9. Closing Remark References

675 676 677 679 679 679 679 681 682 682

SECTION VI: POLYMER AND POLYMER PRODUCT DEVELOPMENT: SUPPORT TECHNIQUES 17. The Supporting Role of Molecular Modelling and Computational Chemistry in Polymer Analysis

685

John Kendrick 1. 2. 3. 4.

Introduction Methodologies Infrared and Raman Spectroscopy Photoelectron Spectroscopy and Auger Electron Spectroscopy (AES)

686 687 693 703

xii

Contents

5. Mass Spectrometry 6. X-Ray Diffraction 7. Nuclear Magnetic Resonance 8. Electron Spin Resonance 9. Summary References

18. High-Throughput Analysis

712 718 722 727 729 730

735

Robert J. Meier 1. Introduction 2. Some General Considerations on MTE and the Corresponding Analytical Needs 3. Analytical Techniques for Medium-Throughput Polymer Analysis 4. Outlook References

Subject Index See Color Plate Section at the End of This Book

735 737 740 742 743

745

CONTRIBUTORS TO VOLUME 53 Rufina G. Alamo FAMU/FSU College of Engineering, Department of Chemical and Biomedical Engineering, 2525 Pottsdamer St., Tallahassee FL 32310, USA Gregory Beaucage Department of Chemical and Materials Engineering, University of Cincinnati, Mail location 12, Cincinnati, OH, 45221-0112, USA Jennifer Brooks Polymer Solutions Incorporated, 2903C Commerce Street, Blacksburg, Virginia 24060, USA J.P. Candlin 4 Rudby Lea, Hutton Rudby, Yarm, TS15 0JZ, UK John M. Chalmers VS Consulting, 14 Croft Hills, Tame Bridge, Stokesley, TS9 5NW, UK Boril Chernev Centre for Electron Microscopy and Nanoanalysis, Steyrergasse 17, A-8010 Graz, Austria Sophie Demoustier-Champagne Universite´ catholique de Louvain, Unite´ de Chimie et de Physique des Hauts polyme`res (POLY), Croix du Sud, 1. B-1348 Louvain-la-Neuve, Belgium Jacques Devaux Universite´ catholique de Louvain, Unite´ de Chimie et de Physique des Hauts polyme`res (POLY), Croix du Sud, 1. B-1348 Louvain-la-Neuve, Belgium B. Erman Department of Chemical and Biological Engineering, Koc University, Rumeli Feneri Yolu 34450 Istanbul, Turkey Anthony T. Jackson AkzoNobel CARG, 137 Jiangtian East Road, Songjiang Industrial Estate, Shanghai 201600, P.R. China John Kendrick Institute of Pharmaceutical Innovation, Bradford University, BD7 1DP, UK Werner Ko¨hler Physikalisches Institut, Universita¨t Bayreuth, D-95440 Bayreuth, Germany Krzysztof Krucza"a Faculty of Chemistry, Jagiellonian University, 30-060 Krakow, Poland Amit S. Kulkarni Department of Chemical and Materials Engineering, University of Cincinnati, Mail location 12, Cincinnati, OH 45221-0112, USA

xiii

xiv

Contributors to Volume 53

Thierry Lefe`vre De´partement de chimie, Universite´ Laval, Que´bec, QC, G1V 0A6, Canada J.E. Mark Department of Chemistry, Crosley Tower, Martin Luther King Drive, University of Cincinnati, Cincinnati, OH 45221-0172, USA Lyda Matisova´-Rychla´ Polymer Institute, Centre of Excellence for Degradation of Biopolymers, the Slovak Academy of Sciences, 842 36 Bratislava, Slovakia Sue Mecham Polymer Solutions Incorporated, 2903C Commerce Street, Blacksburg, Virginia 24060, USA Robert J. Meier DSM Research, P.O. Box 18, 6160 MD Geleen, The Netherlands; Institut fu¨r Agrosphere, ICG-4, Forschungszentrum Ju¨lich GmbH, D-52425 Ju¨lich, Germany Christian Pellerin De´partement de chimie, Universite´ de Montre´al, Montre´al, QC, H3C 3J7, Canada Michel Pe´zolet De´partement de chimie, Pavillon Alexandre-Vachon, local 1084D, Univeriste´ Laval, Que´bec, G1V 0A6, Canada James D. Rancourt Polymer Solutions Incorporated, 2903C Commerce Street, Blacksburg, Virginia 24060, USA Duncan F. Robertson Intertek-MSG, D131, Wilton Centre, Wilton, Redcar, Cleveland, TS10 4RF, UK Jozef Rychly´ Polymer Institute, Slovak Academy of Sciences, Du´bravska´ cesta 9, 842 36 Bratislava, Slovakia. Shulamith Schlick Department of Chemistry and Biochemistry, University of Detroit Mercy, 4001 West McNichols Road, Detroit, Michigan 48221-3038, USA Alan Sentman Polymer Solutions Incorporated, 2903C Commerce Street, Blacksburg, Virginia 24060, USA John Sidwell Smithers Rapra Technology Ltd., Shawbury, Shrewsbury, Shropshire, SY4 4NR, UK Brian Starr Polymer Solutions Incorporated, 2903C Commerce Street, Blacksburg, Virginia 24060, USA Jason Todd Polymer Solutions Incorporated, 2903C Commerce Street, Blacksburg, Virginia 24060, USA Simone Wiegand Forschungszentrum Ju¨lich, IFF – Weiche Materie, Postfach 1913, 52425 Ju¨lich, Germany Peter Wilhelm Research Institute for Electron Microscopy, Graz University of Technology, Steyrergasse 17, A-8010 Graz, Austria

VOLUMES IN THE SERIES

Vol. 1A

Vol. 1B Vol. 1C Vol. 2A

Vol. 2B

Vol. 2C

Vol. 2D Vol. 3

Vol. 4

Vol. 5

Vol. 6 Vol. 7 Vol. 8

Vol. 9

Analytical Processes Gas Analysis Inorganic Qualitative Analysis Organic Qualitative Analysis Inorganic Gravimetric Analysis Inorganic Titrimetric Analysis Organic Quantitative Analysis Analytical Chemistry of the Elements Electrochemical Analysis Electrodeposition Potentiometric Titrations Conductometric Titrations High-Frequency Titrations Liquid Chromatography in Columns Gas Chromatography Ion Exchangers Distillation Paper and Thin Layer Chromatography Radiochemical Methods Nuclear Magnetic Resonance and Electron Spin Resonance Methods X-ray Spectrometry Coulometric Analysis Elemental Analysis with Minute Sample Standards and Standardization Separation by Liquid Amalgams Vacuum Fusion Analysis of Gases in Metals Electroanalysis in Molten Salts Instrumentation for Spectroscopy Atomic Absorption and Fluorescence Spectroscopy Diffuse Reflectance Spectroscopy Emission Spectroscopy Analytical Microwave Spectroscopy Analytical Applications of Electron Microscopy Analytical Infrared Spectroscopy Thermal Methods in Analytical Chemistry Substoichiometric Analytical Methods Enzyme Electrodes in Analytical Chemistry Molecular Fluorescence Spectroscopy Photometric Titrations Analytical Applications of Interferometry Ultraviolet Photoelectron and Photoion Spectroscopy Auger Electron Spectroscopy Plasma Excitation in Spectrochemical Analysis

xv

xvi

Volumes in the Series

Vol. 10 Vol. 11 Vol. 12

Vol. 13

Vol. 14 Vol. 15 Vol. 16 Vol. 17 Vol. 18 Vol. Vol. Vol. Vol. Vol.

19 20 21 22 23

Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol.

24 25 26 27 28 29 30 31 32 33 34

Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol. Vol.

35 36 37 38 39 40 41 42 43

Vol. 44 Vol. 45 Vol. 46

Organic Spot Tests Analysis The History of Analytical Chemistry The Application of Mathematical Statistics in Analytical Chemistry Mass Spectrometry Ion Selective Electrodes Thermal Analysis Part A. Simultaneous Thermoanalytical Examination by Means of the Derivatograph Part B. Biochemical and Clinical Application of Thermometric and Thermal Analysis Part C. Emanation Thermal Analysis and other Radiometric Emanation Methods Part D. Thermophysical Properties of Solids Part E. Pulse Method of Measuring Thermophysical Parameters Analysis of Complex Hydrocarbons Part A. Separation Methods Part B. Group Analysis and Detailed Analysis Ion-Exchangers in Analytical Chemistry Methods of Organic Analysis Chemical Microscopy Thermomicroscopy of Organic Compounds Gas and Liquid Analysers Kinetic Methods in Chemical Analysis Application of Computers in Analytical Chemistry Analytical Visible and Ultra-violet Spectrometry Photometric Methods in Inorganic Trace Analysis New Developments in Conductometric and Oscillometric Analysis Titrimetric Analysis in Organic Solvents Analytical and Biomedical Applications of Ion-Selective Field-Effect Transistors Energy Dispersive X-ray Fluorescence Analysis Preconcentration of Trace Elements Radionuclide X-ray Fluorecence Analysis Voltammetry Analysis of Substances in the Gaseous Phase Chemiluminescence Immunoassay Spectrochemical Trace Analysis for Metals and Metalloids Surfactants in Analytical Chemistry Environmental Analytical Chemistry Elemental Speciation – New Approaches for Trace Element Analysis Discrete Sample Introduction Techniques for Inductively Coupled Plasma Mass Spectrometry Modern Fourier Transform Infrared Spectroscopy Chemical Test Methods of Analysis Sampling and Sample Preparation for Field and Laboratory Countercurrent Chromatography: The Support-Free Liquid Stationary Phase Integrated Analytical Systems Analysis and Fate of Surfactants in the Aquatic Environment Sample Preparation for Trace Element Analysis Non-destructive Microanalysis of Cultural Heritage Materials Chromatographic-Mass Spectrometric Food Analysis for Trace Determination of Pesticide Residues Biosensors and Modern Biospecific Analytical Techniques Analysis and Detection by Capillary Electrophoresis Proteomics and Peptidomics: New Technology Platforms Elucidating Biology

Volumes in the Series

Vol. Vol. Vol. Vol. Vol. Vol.

47 48 49 50 51 52

Modern Instrumental Analysis Passive Sampling Techniques in Environmental Monitoring Electrochemical (Bio) Sensor Analysis Analysis, Fate and Removal of Pharmaceuticals in the Water Cycle Food Contaminants and Residue Analysis Protein Mass Spectrometry

xvii

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PREFACE

When, over three years ago, we were asked to commission a book on polymer analysis, our initial reaction was to decline, since we both believed that there was enough excellent books already published that dealt with the subject matter. However, we then contemplated that most existing books cover the subject from a technique point of view, that is, they tend to have a format in which individual chapters focus specifically on a single technique, such as mass spectrometry, nuclear magnetic resonance, vibrational spectroscopy, thermal analysis methods, chromatographic methods, etc. Occasionally, the scope is wider, if we can put it that way, but in these cases the focus is on a particular segment of the world of polymers. It was during our discussions on this viewpoint when our industrial experience kicked in, for which we recognised that the paramount desire of the ‘‘customer for polymer molecular characterization and analysis’’ is that of problem solving, not of championing a single or set of particular techniques. What these customers ideally require is a solution or information that enables them to solve or overcome a problem on a timescale that is relevant to the customers’ business needs, whether they be research-related, production-related, property-related, service-related, marketing-related, competitive product deformulation,y It was with this mindset that we agreed to try to commission a book, the result of which you have in front of you, in which each chapter addresses a particular problem or property, for example, chain structure or chain end characterization, polymer degradation, molecular orientation, product failure,y, and in which the techniques were secondary, that is ‘‘a means to an end’’ rather than ‘‘how can I solve this problem/measure this property by the technique for which I am a recognised specialist?’’ The task we set for many of our authors was therefore often a very difficult one: that of providing as balanced a viewpoint as possible of the various techniques and methods that may be used to tackle a particular problem or property characterization, and how they may optimally complement each other, and their comparative limitations and strengths. This was our ultimate aim; that is, a text from which the essential information to tackle a problem, for which polymer analysis is required, could be readily distilled from its pages, and from which the supportive, confirmatory and complementary positions of the various measurement techniques could be readily grasped.

xix

xx

Preface

Our industrial experience should have forewarned us: while it is relatively easy to find well-recognised technique specialists, it did turn out, however, to be not trivial to find authors fully comfortable with covering the issues and all techniques from a problem-solving/property-related point of view. Some chapters might, therefore, from some specialist readers and reviewers perceptions, still have some missing issues albeit relevant. In other cases, for example, polymer degradation, optimum coverage has been achieved by including multiple chapters. Nevertheless, considering all the possible topics to be covered and the complexity of the issues involved, we believe most topics are well covered by the contributing authors, and, notwithstanding, we believe the coverage is comprehensive, and provides a unique text on the molecular characterization and analysis of polymers, and approaches our ideal closely. As intimated above, reaching this point, that is publication of this book, has not been a straightforward task; the road has been sometimes rocky, with various professional and personal problems causing both the need to refine our original outline and the need along the way to commission late in the project new authors. To all our chapter authors, we are therefore truly indebted. For those whose chapters we have ‘‘sat on’’ for nearly two years, we especially thank you for your understanding and patience! For those who ‘‘stepped into the breach’’ near the end, we especially thank you for coming to our aid! We are also very thankful to the publishers, Elsevier Science B.V., for their patience too! This book is divided up into sections. The first three chapters provide a background; sections that follow contain chapters dealing with polymer chain analysis, polymer morphology and structure, polymer degradation, polymer product analysis and support techniques. These are listed in more detail in Chapter 1, which also expands more fully on our industrial perception of the requirements for competence and appreciation in all techniques and methods for polymer molecular characterization and analysis. We hope you find this book of value and its approach both unique and technically informative and useful. John Chalmers Robert J. Meier November 2008

S ER I E S E D I TOR ’ S P R E F A CE

This volume on ‘‘Molecular Characterization and Analysis of Polymers’’ has been edited by John M. Chalmers and Robert J. Meier, both of whom have considerable experience in the industrial sector. They have compiled a broad compilation of chapters on the various aspects of polymer analysis and placed a clear and useful emphasis on problem solving, rather than on the techniques used. The first three chapters layout the background; the following chapters deal with polymer chemistry and microstructure and polymeric materials, polymer chain analysis, polymer morphology and structure, polymer degradation, polymer product analysis, and polymer product development support techniques. The book contains a considerable amount of information on the techniques and methods used for polymer molecular characterization and analysis. Various techniques covered include analytical options for polymer product analysis, like size exclusion chromatography, thermal methods, nuclear magnetic resonance spectroscopy, electron spin resonance spectroscopy, mass spectrometry, infrared spectroscopy, gas chromatography-mass spectrometry and liquid chromatography-mass spectrometry. The book is a useful addition to the Comprehensive Analytical Chemistry series and it is the first on the topic of polymer analysis in the series. A tremendous effort was made by the editors to achieve this compilation and as they say in their Preface ‘‘the road has been sometimes rocky’’. Thanks to the editors and all contributing authors for their time and efforts in preparing this comprehensive compilation of research papers that will make this book on molecular characterization and analysis of polymers a unique reference in this field. D. Barcelo´ Barcelona, April 14, 2008

xxi

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SECTION I: Introduction

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CHAPT ER

1 Introduction John M. Chalmers and Robert J. Meier

Contents

1. The Analytical Competence 2. Contents and Structure 3. Practical Considerations in the Multi-Technique Approach References

3 6 11 12

1. THE ANALYTICAL COMPETENCE Polymers are around us everywhere, and their industrial production is a major activity of the chemical industry throughout the world. As a consequence, there is a significant support related R&D (research and development) activity within both academia and industry. This applies to the search for new catalysts, synthesis of new polymers, as well as attempts to produce new polymer chain architectures, formulations, and finally the processing and shaping of polymers. Few polymers are used in their pure form: additives and fillers, including fibres, are commonly added to arrive at a material with the desired lifetime use properties. Polymers can be functionalised to improve certain properties such as adhesion or to make them suitable for use in a particular application, such as an electronic component or aerospace application. To verify that the polymer chain synthesized is what was expected, or in order to relate polymer properties to the structure of the material, one needs polymer analysis and characterisation tools. Analysis can be thought of as the breaking up of anything complex; it is the contrary of synthesis, and can sometimes be referred to as such as ‘reverse engineering’. Characterisation is the determination of properties, such as form, chemical structure, colour, etc. Morphology is the science of form. The build-up of a polymeric sample in terms of amorphous and crystalline domains, threedimensional networks, spherulites or other structural units, or the presence and distribution of glass-fibres or other filler material, constitutes the morphology of the sample. Morphological characterisation thus is a key means to establish structure–property relations. Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00401-7

r 2008 Elsevier B.V. All rights reserved.

3

4

John M. Chalmers and Robert J. Meier

Traditionally, analysis and, to a lesser extent, characterisation, have been viewed from the viewpoint of expertise in an individual technique, e.g., spectroscopy of polymers (infrared (IR) and Raman spectroscopies, mass spectrometry (MS) and nuclear magnetic resonance (NMR) spectroscopy), thermal properties of polymers (differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA)), surface characterisation (e.g., secondary ion mass spectrometry (SIMS) and atomic force microscopy (AFM)), etc. However, particularly in an industrial context, problem solving is primarily what product group customers of analytical groups are interested in and the technique expertises should be considered as supporting activities. Moreover, in academic groups those that synthesize polymers based on newly developed catalysts often want to undertake their own analyses. Such groups are essentially interested in appropriate answers from polymer analysis and characterisation, not in building up expertise in individual analytical techniques. What is needed primarily for problem solving and general analytical support is an analytical/characterisation science competence. The competence in polymer analysis is the capability to analyse polymers for constituents and properties, each in relation to the questions or interests from the customer. Whereas in academic synthetic groups the customer and the analyst may be one and the same person, in industry the customer is usually a different person, often with conflicting priorities of timescale. Defined as a competence, the traditional individual expertises, e.g., microscopy, spectroscopy, thermal analysis, etc., are considered as supporting the competence. Foremost is the capability to investigate, analyse and characterise, the polymer, both effectively and efficiently. ‘‘What do we want to know about the polymer?’’ is the question that comes first, whereas the technique and therewith the required expertise comes second. This, obviously, is not meant to suggest that an expertise in a specific technique is not important; in many cases the involvement of a technique expert is vital. However, in both the industrial environment as well as in academic synthetic and materials research groups, the problem solving capability is the key issue. With which technique the problem is going to be solved is less relevant. In most real cases all that matters is whether a problem is addressed appropriately, both in terms of the solution information and its derived timescale; this might, for example, in a failure analysis, simply be identifying cause and not a detailed reason. Important components of the solution may be any one or a combination of accuracy or precision really required, overall time to obtain the results, price per analysis, etc. Accuracy is mentioned at this point because the traditional expert has the tendency to strive for results that are scientifically the best. This, however, is often not required. This requires experts who are well trained in analytical competence thinking. Precision is sometimes much more important than accuracy in a quality assurance measurement. The key appreciation here is the difference between technique expertise and analytical competence. While retaining the necessary expertise on individual techniques, understanding of the customer questions and aims (the problem setting) is paramount. Understanding of the strengths, weaknesses and

Introduction

5

limitations of different techniques is an integral part of optimal performance in a competence. The level of technique expertise required will likely vary from one situation to the other. The requirement on technique expertise does not imply that in each laboratory where an analytical competence is required, a high-level analytical expertise level is required. What is required is the set of skills to provide analyses up to the level required and appropriate to the problem, and perhaps its value of solution. Whether equipment is in-house or elsewhere does not have to matter, as long as it is available when required for problem solving. Having said this, it was felt therefore that there is a need for a book addressing analysis and characterisation of polymers from the point of view of what we wish to call the primary analytical question. Many excellent textbooks and reference works exist which address one or more individual analytical techniques, see, for example, references [1–10]. These books form the basis of the knowledge of the technique expert. They also contain many excellent and varied examples on successful applications of analytical techniques to polymer analysis and characterisation. There are also books which address the multitude of analytical techniques applied in polymer analysis, see, for example, references [11–24]. However, a synthetic chemist may wish to know the constitution of his/her polymer chain, a material scientist may want to find out the reasons why a fabricated sample had failed. What technique is best or optimal to study chain constitution will depend on the situation. Polymer failure may result from morphological features, which needs to be avoided, a contaminant, a surface property degradation, etc. When a sample has been processed, e.g., a film blown, molecular orientation may be the key parameter to be studied. A formulation scientist may wish to know why an additive from a different supplier performs differently. It is from such points of view that polymer analysis and characterisation is addressed in this book. The aim of this book is therefore to present and discuss modern approaches and strategies to polymer characterisation and analysis. As appropriate, however, space will be given to theory, practice and instrumentation. While state-of-the-art characterisation methods will feature highly, conventional use of analytical techniques will also be well covered. The emphasis however, whenever possible, will be pragmatic and problem solving and property determination led, illustrated by ‘real-world’ application examples. As suggested above, the real accuracy or precision required, the time allowed to arrive at a satisfactory result, and the monetary/manpower budget available to obtain meaningful results are all integral elements when the intention is to run an analytical competence in optima forma. Therefore, the emphasis must be on the synergistic, complementary, effective and efficient usage of characterisation techniques and tools and analytical methodology, expertise and skill; it cannot be technique led. Foremost must be the property characterisation, the problem solution and effective polymer analysis; techniques provide the means, and per se should not be the driver! The materials covered in this book will be organic polymers; biopolymer and inorganic polymer characterisations are not considered. The characterisations will focus on polymer and polymer product microstructure and

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John M. Chalmers and Robert J. Meier

composition; the discussions will not feature bulk property measurements, e.g., mechanical, electrical. The emphasis is on commercial materials and formulations. The reason is that commercial materials are rarely pure materials. A pure homopolymer is a rare species in the ‘real-world’ materials. To arrive at the desired material’s properties, either a copolymer is used, sometimes a blend or a dispersion, or additives or filler materials including rubber particles, carbon black or fibres of various type and make may be added, and are thus commonplace in commercial products. This implies a more complex constitution and morphology than expected for pure polymers. However, obviously, the methods described herein can be applied to pure, unmodified, polymers as well.

2. CONTENTS AND STRUCTURE In contrast to a book describing contributions of individual techniques, there is undoubtedly not a single way to structure the approach to be dealt with in this book. The approach taken is as follows. A polymer material consists of individual polymer chains, and all together these make the material and its morphology, which in turn relate to the material’s properties. A cluster of chapters addressing the individual chain characteristics was therefore thought appropriate, followed by another cluster on morphology. As mentioned before, as most polymeric materials for practical use are not pure polymers, a third cluster was formed dealing with analysis of the product, which includes issues such as additives and surface characteristics. Consequently, this book comprises six sections. The first section serves as an Introduction, it includes this chapter and the next two chapters, which deal with the basics of polymer chemistry and microstructure (Chapter 2) and polymeric materials and their composition, uses and application (Chapter 3). The next section (Polymer Chain Analysis: Chapters 4–6) relates to polymer chain analysis (chain structure characterisation, chain end characterisation and molecular weight and distribution). The third section (Polymer Morphology and Structure) that deals with polymer morphology and structure is subdivided into phase structure and morphology (Chapter 7), molecular orientation (Chapter 8) and polymer networks (Chapter 9). Chapters 10–12, the fourth section (Polymer Degradation), cover approaches to study and investigate polymer degradation. The next section, Polymer Product Analysis, covers spatial imaging and heterogeneity (Chapter 13), analysis of additives (Chapter 14), failure, defect and contaminant analysis (Chapter 15) and concludes with a short chapter on surface analysis (Chapter 16). The final section, which we have called Polymer and Polymer Product Development: Support Techniques, considers the role of computational chemistry and molecular modelling in supporting polymer analysis (Chapter 17), and high-throughput analysis (Chapter 18). The polymer characteristics addressed within these clusters are presented below in Table 1. Table 1 presents an overview of the many analytical/ characterisation techniques and methods used for the molecular characterisation

Introduction

7

Table 1 (a) Summary of the techniques used for molecular analysis and characterisation of polymers. The techniques and methods listed have been mostly picked from those mentioned in the chapters within this book; the order in which they appear is random, and does not reflect their relative importance or their order of most common use, particularly since they are most frequently used in synergistic, confirmatory and/or complementary combinations. (b) Abbreviation and acronym definitions for techniques cited in Table 1(a). (a): Polymer

Property to be analysed/ characterised

Suitable/primary techniques/methods

monomer, comonomer type and composition degree of polymerisation (dp) conformation (e.g., transgauche), isomerism (e.g., cis-trans) tacticity, stereoregularity chain lengths (persistence, Kuhn unit) branching (e.g., shortchain, long-chain, hyper-, star, ladder, brushes) unsaturation copolymer sequencing end-group analysis

NMR, IR, Raman

Polymer chain structure:

cross-linking

molecular weight, molecular weight distribution

NMR NMR, IR, Raman

NMR, IR SANS SEC, GPC, NMR, rheology, SANS, SAXS NMR, Raman, IR NMR, IR NMR, MS, MALDI-MS, IR, Raman, chemical titration indirect techniques, including s-NMR, gelpoint determination, rheology, LC-MS techniques can in part be applied GPC/SEC, MALDI-MS, membrane osmometry, vapour pressure osmometry, viscometry, light scattering, TDFRS, SAXS, SANS, SECHPLC, SEC-MS, SEC-IR, FFF, ultracentrifugation, MALDI-TOF-MS, NMR, capillary electrophoresis

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John M. Chalmers and Robert J. Meier

Table 1 (Continued ) (a): Polymer

Property to be analysed/ characterised

Suitable/primary techniques/methods

crystallinity, amorphous content, phase analysis

WAXS, WAXD, SAXS, SALLS, density, DSC, IR, Raman, s-NMR, AFM, optical microscopy, SEM, TEM WAXD, s-NMR, IR, Raman, fluorescence spectroscopy, birefringence CL, ESR, ESRI, IR/IR microscopy, Raman/ Raman-microscopy, GC-IR, EGA-IR, Py-IR, Py-GC-IR, UV, visible spectroscopy, fluorescence/ phosphorescence, MS, MALDI-TOF-MS, GC-MS, Py-MS, Py-GCMS, GPC, SEC, GPC-MS, GPC-IR, s-NMR, NMR, TA, DSC, TGA, oxidative-induction time (DSC), DPC, TGA-IR, TGA-MS, GC, IGC, LC, LC-CC, HPLC, LC-IR, LC-MS, XPS, SIMS, optical microscopy, oxygen uptake, carbonyl index (IR), iodometric test, titration, staining, MFI

Polymer material/product characterisation:

molecular orientation

degradation, oxidation

Product analysis: polymer network

s-NMR, gelation, swelling, birefringence, IR, NMR, STM, SANS, Brillouin scattering, pulsepropagation

Introduction

Table 1 (Continued ) (a): Polymer

Property to be analysed/ characterised

Suitable/primary techniques/methods

surface analysis

optical microscopy, XPS (ESCA), IR-ATR, Raman, AFM, SIMS, LEIS, IR optical microscopy, IR-microscopy, Ramanmicroscopy, TOF-SIMS, NIR-imaging, SNOM, MRI, ESRI, mXRF, PES, LEIS, RIS AAS, GC, GC-MS, IR, HPLC, LC-MS, ICP-AES, SEM, TGA, XRF, NMR optical microscopy, IR, Raman, XRF, DSC, TGA, NMR, SEM, SEM-EDS, XPS, SIMS, GPC/SEC, ICP-MS, GC-MS, LC-MS, AFM

spatial heterogeneity

additive analysis

failure, defect, contaminant analysis

(b)

AAS AFM ATR CL DPC DSC EDS EGA ESCA ESR ESRI FFF GC GPC HPLC IGC ICP-AES ICP-MS IR LC LC-CC

Atomic absorption spectrometry Atomic force microscopy Attenuated total reflection Chemiluminescence Differential photocalorimetry Differential scanning calorimetry Energy dispersive spectroscopy Evolved gas analysis Electron spectroscopy for chemical analysis Electron spin resonance spectroscopy Electron spin resonance imaging Field-flow fractionation Gas chromatography Gel permeation chromatography High-performance liquid chromtography Inverse gas chromatography Inductively coupled plasma atomic emission spectroscopy Inductively coupled plasma mass spectrometry Infrared Liquid chromatography Liquid chromatography under critical conditions

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John M. Chalmers and Robert J. Meier

Table 1 (Continued ) (b)

LEIS MALDI-TOF-MS MFI MRI MS NIR NMR PES Py RIS SALLS SANS SAXS SEC SEM SIMS s-NMR SNOM STM TA TDFRS TEM TGA ToF WAXD WAXS XPS XRF mXRF

Laser enhanced ionisation spectroscopy Matrix-assisted laser desorption time-of-flight mass spectrometry Melt flow index (Nuclear) magnetic resonance imaging Mass spectrometry Near-infrared spectroscopy Nuclear magnetic resonance spectroscopy Photoelectron spectroscopy Pyrolysis Resonance ionisation spectroscopy Small-angle laser light scattering Small-angle neutron scattering Small-angle X-ray scattering Size exclusion chromatography Scanning electron microscopy Secondary ion mass spectroscopy Solid state nuclear magnetic resonance spectroscopy Scanning near-field optical microscopy Scanning tunnelling microscopy Thermal analysis Thermal diffusion forced Rayleigh scattering Transmission electron microscopy Thermogravimetric analysis Time-of-flight Wide-angle X-ray diffraction Wide-angle X-ray scattering X-ray photoelectron spectroscopy X-ray fluorescence spectroscopy micro-X-ray fluorescence spectroscopy

and analysis of polymers and polymer formulations and products. While one or two techniques/methods may be dominant in a particular area, it can be readily seen that several to many can be applied depending on the information required and the depth of problem solving and understanding that is needed, along with the suitable or most common analytical techniques. The requirement and need for a multi-technique attack on a problem or study is probably most exemplified in the chapter on polymer failure (Chapter 15) and polymer degradation (see Chapter 10); in the latter many of the references cited used five or more analytical/characterisation tools in the investigation. The need for a multitechnique approach is an even more prominent need in the study of polymer morphology, although perhaps less often practised in single studies. A key

Introduction

11

feature here obviously is the various length scales involved, from single chain conformation and configuration (as they co-determine the possibility of certain larger structures to be formed) to crystalline lamellae, shperulites, etc. Key issues when polymer chain analysis or polymeric materials characterisation is applied is the choice of property to analyse, and when selected, which is the most suitable technique given the question to be addressed and circumstances, e.g., business pressure (availability, price, accuracy, speed).

3. PRACTICAL CONSIDERATIONS IN THE MULTI-TECHNIQUE APPROACH Whereas several techniques may thus be used to study a certain characteristic of a polymer sample, for instance IR and Raman spectroscopy and X-ray diffraction as well as NMR may be used to determine or infer the crystallinity level of a sample, different techniques work differently and therefore usually do not measure the same. What this means is that crystallinity levels obtained from the same sample may differ when a different technique is applied, see, for example, ref. [23] and chapter 7 and references therein. However, these differences do not necessarily imply one technique being better than another. In fact these differences may contain useful information on the sample (see, for example, ref. [25]). This brings us to the point of considering the suitability of a technique with respect to a certain analysis, particularly from an industrialist’s or contract laboratory viewpoint. This is a very important consideration, as this is not a priori straightforward. There are a number of factors influencing the choice. We will mention just a few of these in arbitrary order: (i)

(ii) (iii) (iv) (v) (vi) (vii) (viii)

When, for whatever reason, one does not wish to be involved in further method development but just apply a technique, this means that the technique must have been applied to the problem of interest before, or it must be essentially a trivial translation from a previously demonstrated application. Example: IR spectrum of an unknown, NMR can do the job; X-ray crystallinity. Does the technique need to be applied on a lab-scale or in-process? Does the technique have to be applied off-, at-, in- or on-line? Is cost of analysis relevant? What is the accuracy/precision required? Is concentration/composition to be measured? Is speed important? Do you have the equipment available (in-house or otherwise readily available)? If such as a failure analysis, is it just satisfactory to identify the cause, or does reason matter too?

The chapters following in this book should, we hope, enable one to obtain an objective assessment and comparison of the most appropriate polymer molecular

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John M. Chalmers and Robert J. Meier

characterisation or analysis tool according to the problem solving circumstances. The reader will be able to obtain experts’ overviews of the range of tools, and their strengths, convenience of use and limitations, necessary to characterise or analyse the molecular structure, composition and properties of polymers and their formulated products.

REFERENCES 1 I. Ando and T. Asakura, Solid State NMR of Polymers, Elsevier, Amsterdam, 1998. 2 F. Bovey and P. Mirau, NMR of Polymers, Elsevier, Amsterdam, 1996. 3 J.M. Chalmers and P.R. Griffiths (Eds.), Handbook of Vibrational Spectroscopy, Vol. 4, Wiley, Chichester, 2002. 4 N.J. Everall, J.M. Chalmers and P.R. Griffiths (Eds.), Vibrational Spectroscopy of Polymers: Principles and Practice, Wiley, Chichester, 2007. 5 P. Worsfold, A. Townshend and C. Poole (Eds.), Encyclopedia of Analytical Science, 2nd ed., Academic Press, London, 2004. 6 D. Briggs, Surface Analysis of Polymers by XPS and Static SIMS, Cambridge University Press, Cambridge, 1998. 7 S. Schlick (Ed.), Advanced ESR Methods in Polymer Research, Wiley, Chichester, 2006. 8 W.M. Groenewoud (Ed.), Characterisation of Polymers by Thermal Analysis, Elsevier, Amsterdam, 2001. 9 I. Wilson, C. Poole and M. Cooke (Eds.), Encyclopedia of Separation Science, Academic Press, London, 2000. 10 G. Montaudo and R.P. Lattimer, Mass Spectrometry of Polymers, CRC Press, Boca Raton, 2001. 11 B.J. Hunt and M.I. James (Eds.), Polymer Characterisation, Blackie Academic & Professional, Glasgow, 1993. 12 J.L. Koenig, Spectroscopy of Polymers, 2nd ed., Elsevier Science, New York, 1999. 13 J.I. Kroschwitz (Ed.), Polymers: Polymer Characterization and Analysis, Wiley, New York, 1990. 14 J.I. Kroschwitz, Concise Encyclopedia of Polymer Science and Engineering, Wiley, New York, 1998. 15 Polymers and Rubbers. In: R.A. Meyers (Ed.), Encyclopedia of Analytical Chemistry, Wiley, Chichester, 2002. 16 H.F. Mark (Ed.), Encyclopedia of Polymer Science and Technology, 3rd ed., Wiley-VCH, Weinheim, 2004. 17 J.C.J. Bart, Additives in Polymers: Industrial Analysis and Applications, Wiley, Chichester, 2005. 18 J. Scheirs, Compositional and Failure Analysis of Polymers: A Practical Approach, Wiley, Chichester, 2000. 19 J. Haslam, H.A. Willis and D.C.M. Squirrell, Identification and Analysis of Plastics, 2nd ed., Buterworth, London, 1972. 20 J.I. Kroschwitz (Ed.), Concise Encyclopedia of Polymer Science and Engineering, Wiley, Chichester, 1998. 21 R.A. Pethrick and J.V. Dawkins (Eds.), Modern Techniques for Polymer Characterisation, Wiley, Chichester, 1999. 22 M. Bolgar, J. Hubbal, J. Groger and S. Meronek, Handbook for the Chemical Analysis of Plastic and Polymer Additives, CRC Press, Boca Raton, 2007. 23 D. Campbell, R.A. Pethrick and J.R. White, Polymer Characterization: Physical Techniques, 2nd ed., CRC Press, Boca Raton, 2000. 24 R.A. Prethrick, Polymer Structure Characterization from Nano to Macro Organization, RSC Publishing, Cambridge, 2007. 25 R.J. Lehnert, P.J. Hendra, N. Everall and N.J. Clayden, Comparative quantitative study on the crystallinity of poly(tetrafluoroethylene) including Raman, infra-red and F nuclear magnetic resonance spectroscopy, Polymer, 38(7) (1997) 1521–1535.

CHAPT ER

2 Polymer Chemistry and Microstructure Jacques Devaux and Sophie Demoustier-Champagne

Contents

1. Introduction 2. Polymer: Definitions 2.1 Monomers, chain length, length distribution 2.2 Thermoplastics and thermosets 2.3 Thermal transitions and properties 2.4 Microstructure 3. From Molecules to Macromolecules 3.1 Chain length and entanglements 3.2 End groups 3.3 Chain substituents 3.4 Spatial arrangements 4. Fundamentals of Polymer Chemistry 4.1 Chain polymerisation vs. step polymerisation 4.2 Types of chain polymerisations and polymers synthesized — keypoints of mechanisms, kinetics 4.3 Radical chain polymerisations 4.4 Ionic polymerisations — active species 4.5 Olefin polymerisation processes 4.6 Processes for polyolefin syntheses 4.7 Copolymers 4.8 Types of step polymerisations and polymers synthesized — keypoints of mechanisms, kinetics 5. Polymer Degradation 6. Summary References

Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00402-9

14 15 15 17 17 21 25 27 27 28 28 34 34 35 35 42 45 48 50 53 58 62 62

r 2008 Elsevier B.V. All rights reserved.

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Jacques Devaux and Sophie Demoustier-Champagne

1. INTRODUCTION ‘‘A material is a solid used by man to produce items that constitute the support for his living environment’’ [1]. Such a definition, although restrictive as it excludes liquids, is simple enough. It might imply however, on the one hand, that materials as such only existed from the beginning of mankind, moreover, on the other hand, that the usual three classes of ‘‘materials’’ — ceramics, metals and polymers — have always coexisted. Indeed, most of the earth’s terrestrial crust is made of minerals, the majority of which are considered to be ceramics, that is, ‘‘resulting from the combination of a limited number of metallic elements (Si, Ca, Mg, Al, Ti, etc.) with non-metallic elements, most commonly oxygen’’ [1]. Ceramic materials marked the so-called ‘‘Stone Ages’’, the earliest stages of civilisation. A few pure (native) metals have existed as materials from the first ages of mankind, namely those that have a high oxido-reduction potential, which protects against oxidation by atmospheric oxygen (e.g., gold, platinum, silver,y). Their bright colour and inalterability led humans to use them in jewellery. However, geological science tells us that huge amounts of natural metals exist in the earth’s nucleus (e.g., Si, Al, Fe, Ni, etc.), which constitute the main part of the earth’s mass. Being oxidised through reaction with oxygen, landmarks in civilisation’s progress (bronze age, iron age) are labelled by mankind’s mastering of more and more complex metal productions (reduction). Natural polymers are far more complex materials, being exclusively ‘‘organic’’, that is, products of life (cellulose, proteins, DNA,y). Nevertheless, as nature seems to have formed (size, weight, hardness, etc.) several natural polymers (wood, bones, ivory, etc.) in such a way as to be almost immediately usable by our ancestors, they were most probably the bases of the first human tools. The commonly widespread conception that polymers are the youngest ‘‘materials’’ in the historical world is not true, but, strictly speaking, only applies to synthetic polymers, which were discovered about 100 years ago, early in the XXth century. Polymers are undoubtedly ‘‘materials’’. Knowledge and understanding of their properties belongs to the so-called field of ‘‘Materials Science’’. Study and understanding of their formation, properties and performance characteristics involves chemistry, physico-chemistry and physics, the latter including mechanics, optics, electricity, etc. Material’s knowledge is not limited to the aforementioned fields of science, but includes also technological properties, which are most often used for their classification: strength, hardness, transparency, conductivity, etc. Materials science is thus built on complex interrelationships between such fields, see Figure 1. Few properties, if any, depend directly and only on the chemistry. Indeed, as shown in Figure 1, the ‘‘route’’ implies that it is chemistry that influences (micro-) structure, which, in turn, governs properties. Processing, which is not often classified as a ‘‘science’’ but as ‘‘engineering’’, has to find its place in the picture, since it is the normal way to go from a macromolecule to a product with the desired properties.

Polymer Chemistry and Microstructure

15

Processing Synthesis

Characterisation

Microstructure

Properties

Figure 1 Polymers in materials science: Interrelationships between synthesis, processing, microstructure, properties and characterisation.

Characterisation covers a wide field of science and technology and interacts from the synthesis stage through the analysis of structure to the determination of properties. Characterisation allows one to observe, control and model (including ‘‘closed-loop’’ backward interaction) all the complex interrelationships of materials science.

2. POLYMER: DEFINITIONS 2.1 Monomers, chain length, length distribution The word ‘‘polymer’’ (first proposed by Berzelius in 1833) is made of ‘‘poly’’ from the ancient Greek word ‘‘poluB’’ meaning ‘‘many’’ and ‘‘meroB’’ meaning ‘‘part’’. Polymers are molecules built up from numerous identical chemical ‘‘units’’ spatially repeated to form a chain. From the early times and still nowadays, a distinction is often made between ‘‘natural’’ and ‘‘synthetic’’ polymers, but it is somewhat artificial as natural polymers can now sometimes be synthesized (e.g., synthetic ‘‘natural rubber’’) and some synthetic polymers, which are never found in nature, can be synthesized by natural ways (enzymatic syntheses). Nevertheless, synthetic polymers are most often made from monomers (from ancient Greek ‘‘monoB’’ meaning single), which are precursor molecules of a polymer chain. When only a few monomers are joined to form a chain, they are called oligomers (from ‘‘oligoB’’ a few, in ancient Greek). Despite this distinction between oligomers and polymers is rather ill defined, one generally conceives that polymer chains exhibit high molecular masses ranging from 104 to about 107, the masses of oligomers being conventionally limited to below about 104. Polymer is also a word the use of which is restricted to chemical compounds based on covalent links, chemically stable at ambient conditions. Most often polymers are made from carbon and hydrogen or hydrocarbon derivatives (with oxygen, nitrogen, sulfur, halogens,y) (Table 1). But, they are sometimes based on inorganic backbone atoms (silicon, nitrogen and phosphorous,y). From the above considerations, it appears that chain length is a main characteristic of polymers. Natural macromolecules, particularly in living bodies, can exhibit exact lengths, thus exact molecular masses. For instance haemoglobin molecular mass is known to within one dalton. However, a synthetic polymer

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Jacques Devaux and Sophie Demoustier-Champagne

Table 1

Examples of some ‘‘natural’’ and ‘‘synthetic’’ polymers

Name of polymer

Formula

Polyethylene

Approximate date of invention

1935

C C H2 H2 n

Polypropylene (isotactic)

1954

C CH H2 n CH3

Poly(methyl methacrylate) (PMMA)

O

C

O

1935

CH3

C C H2 n CH3

Poly(vinyl chloride) (PVC)

1872

C CH H2 n Cl

Polystyrene

1925 C CH H2 n

Poly(ethylene terephthalate) (PET)

Poly(hexamethylene adipamide) (Nylon 66)

1941 H

O

C C O H2 H2

C

C

O

O

H

N H

Cellulose

O

C N C H2 6 H

H2 C OH O H HO H H H

OH

1938

O

O

OH n

C OH C H2 4 n

H O

HO H

Natural polymer

OH H H

O C OH H2

n

Polymer Chemistry and Microstructure

17

sample contains chains having a wide distribution of chain length. The breadth of the molecular mass1 distribution depends on the synthesis process. Therefore, it is necessary to define average molecular masses to characterize a polymer sample. The simplest method — the number average molecular mass or Mn — is an arithmetic average based on the total mass of a sample divided by the total number of molecules in this sample. For correlation with most physical properties (mechanical strength, optical scattering), mass average molecular mass of a polymer ‘‘Mw ’’ appears more satisfactory. Higher-power averages like z-average molecular mass ‘‘Mz ’’ seem to better correlate with rheological properties. Expressions of Mn ; Mw and Mz are P P 2 P 3 ni mi

i Mn ¼ P n

i

ni mi

i Mw ¼ P nm

i

i

i

i

ni mi

i Mz ¼ P n m2 i

i

i

where ni and mi are the number and the molecular mass of molecules containing i units, respectively. A measure of the breadth of the molecular mass distribution is given by the ratios of molecular mass averages. The most commonly used ratio Mw =Mn ¼ H, is called the polydispersity index. Wiegand and Ko¨hler discuss the determination of molecular masses (weights) and their distributions in Chapter 6.

2.2 Thermoplastics and thermosets Thousands of polymers have been synthesized and more are likely to be produced in the future. Fortunately, all polymers can be divided into two major groups based on their thermal processing behaviour. Some polymers behave as (viscous) liquids upon heating and can be re-processed, almost indefinitely. These are classified as ‘‘thermoplastics’’ (from the ancient Greek prefix ‘‘yermo’’ for ‘‘heat’’). Some major commercial examples are polystyrene (PS), polyethylene, polypropylene and poly(vinyl chloride) (PVC). Other polymers keep their (definitive) shape after a first heating step during synthesis or subsequent treatment. These are called ‘‘thermosets’’. Once formed the crosslinked networks resist heat and solvent attack. Such properties make thermosets suitable materials for composites, coatings and many adhesive applications. Major examples of thermosets include epoxy resins, phenol-formaldehyde resins, urea/melamine formaldehyde resins and unsaturated polyesters.

2.3 Thermal transitions and properties 2.3.1 Glass transition Matter is made from atoms or molecules, for which the spatial arrangements depend on cohesion (energy from interaction forces) and thermal energy, which is proportional to temperature. Weak cohesion and/or high temperatures lead to 1

The notation M is used here for molecular masses, while X is used for chain lengths (or ‘‘degrees of polymerization’’). M ¼ XMO with MO, the molecular mass of one unit in the polymer chain.

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Jacques Devaux and Sophie Demoustier-Champagne

gases, while, in contrast, high cohesion and/or low temperatures yields solids, with liquids as an intermediate state. There are rather limited differences between liquid and solid states as specific masses of solids are usually only about 15% higher than those of corresponding liquids. Inside liquids, due to the rather low level of empty volume (the so-called ‘‘free volume’’), molecules can move due to ‘‘concerted’’ movements of the neighbouring molecules. Upon cooling down a liquid, the ratio between the thermal and the cohesion energy decreases, molecules become closer to each other and the free volume decreases. Thermal energy, which leads to molecular mobility, becomes lower, and attraction and repulsion forces between molecules begin to play a more significant role. When these latter forces predominate over thermal energy, an equilibrium is usually reached between them leading to ordered (crystalline) structures. However, this is only the case when the time needed for molecular movement (the so-called ‘‘characteristic time’’) is lower than that of cooling. When no extended ordering can occur and/or if molecular movements are extremely slow (very big and/or branched molecules) and/or if the cooling is very fast, ordering remains limited to rather small ‘‘domains’’ of molecules. The solid is said to be ‘‘amorphous’’ and retains in the solid state, the rather disordered microstructure (including the free volume) of a liquid. Figure 2 shows how atomic organisation changes with temperature. The temperature at which a liquid (highly viscous, or even rubbery for very high molecular masses) becomes an amorphous solid (rigid, stiff, often brittle) on cooling (or vice versa an amorphous solid becomes liquid on heating) is called the glass transition and noted Tg (Figure 3). In the glassy state, thus below Tg, very few molecular movements (group rotations, vibrations) are allowed. Above Tg, large-scale motions involving the whole macromolecule (translations, repetations) become possible. It has to be noticed that no isothermal volume contraction on cooling or volume expansion on heating is associated with Tg, contrary to crystallisation or melting. The latter is a true first-order transition exhibiting a discontinuity in

Figure 2 Evolution of atomic organisation with increasing temperature. Reproduced from Mercier, Zambelli and Kurz [1], Elsevier (2002) with permission of Elsevier. Copyright Elsevier 2002.

Polymer Chemistry and Microstructure

19

Figure 3 Curves of specific volumes vs. temperature for poly(vinyl acetate) measured on cooling. Equilibrium values measured 0.02 h and 100 h after cooling, as indicated. Tgu and T g are glass transitions respectively at fast and slow cooling rate. Reproduced from Ref. [2] with permission of John Wiley & Sons, Inc.

thermodynamic variables. Despite the discontinuity occurring only in the first derivative of thermodynamic variables, Tg is not a true ‘‘second-order’’ transition as it also depends on kinetics. Figure 3 also shows how Tg moves with cooling rate for a sample of poly(vinyl acetate). Tg is said to be a ‘‘kinetic transition’’.

2.3.2 Crystallisation-melting temperature The commonest state of the solid matter is the crystal. A crystalline solid is made of a periodic arrangement of atoms (or small molecules) in the three dimensions of space. A (single) crystal is a very ordered state formed by the juxtaposition of numerous identical ‘‘unit cells’’ (parallelepipedic volume containing one atom or one small molecule). A crystal structure is characterised by its symmetry [1]. Due to the length of the macromolecules, the existence of single crystals of polymers has remained a controversy for a long time. Soon after World War II, microscopic polymer ‘‘single crystals’’ were obtained by very slow cooling from

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Jacques Devaux and Sophie Demoustier-Champagne

Figure 4 Scheme of chain folding in polymer crystals.

dilute solutions. Upon cooling from the liquid state at a suitable rate, polymers whose chain segments (including a few repeat units) exhibit symmetry elements of high enough order, can thus crystallise. Such a crystallisation goes along with long-range ordering. The determination of the ‘‘unit cell’’ led to the conclusion that, within such a single crystal, one macromolecule encompasses many ‘‘unit cells’’, which, itself, includes only one or a few ‘‘repeat units’’. Moreover, upon examination by electron diffraction, it appeared also that in these ‘‘single crystals’’, the chain axis was perpendicular to the largest faces, thus, that the chains are oriented in the ‘‘thickness’’ direction. However, as such thicknesses are much smaller than extended-chain lengths, a model of ‘‘chain folding’’ was established for forming such polymer crystals (Figure 4). As a consequence of chain folding, besides the inclusion of chain ends, these ‘‘single crystals’’ exhibit at a minimum a certain amount of defects at their surface. This is a reason why polymers are never 100% crystalline. In polymers crystallised from the melt, lamellae were observed by electron microscopy, whose thickness are of the same order of magnitude as ‘‘single crystals’’ obtained from solution (Figure 5). Crystal ‘‘unit cells’’ within these lamellae are comparable to those of single crystals and the chains are also oriented in the thickness direction. Therefore, the same model of chain folding was applied to melt-crystallised polymers. However, lamellae are, by far, less perfect structures than ‘‘single crystals’’ and each individual polymer chain gives rise to only a limited number of ‘‘folds’’, its remaining part (the so-called ‘‘tie’’) protrudes from the lamella and remains in an amorphous phase. By this way, the crystallinity of melt-crystallised polymers lie within a range extending from 85% to 90% for very regular and flexible polyethylene chains down to about 30–40% maximum for most other crystallisable polymers. Polymers are often said to be ‘‘semi-crystalline’’, whereas ‘‘partly crystalline’’ should be more correct. By optical microscopy (OM), birefringent structures are observed in semicrystalline polymers, characterized by ‘‘Maltese-crosses’’ under crossed polars as seen in Figure 6. As these structures grow symmetrically in three dimensions

Polymer Chemistry and Microstructure

21

Figure 5 Electron micrograph of a portion of melt crystallised polyethylene spherulite by transmission electron microscopy (TEM) showing lamellae. Reproduced from Ref. [3] with permission of John Wiley & Sons, Inc.

from a nucleus, they are called ‘‘spherulites’’. Upon examination, they appear to be formed of ‘‘fibrils’’ growing from the nucleus. These fibrils include several lamellae most often linked by tie-molecules going from one lamella to its neighbour. In semi-crystalline polymers, ordered structures appear at different dimensional levels 1. 2. 3. 4.

the the the the

crystal cell lamella fibril spherulite.

Such a complex microstructure is illustrated in Figure 7.

2.4 Microstructure 2.4.1 Linear and branched homopolymers Polymers that are built from the repetition of identical ‘‘repeat units’’ are called ‘‘homopolymers’’ (from ancient Greek ‘‘o`moB’’ ¼ same).2 Linear homopolymer chains are obtained upon linking chemically identical units exclusively at both ends. However, repeat units are not always symmetrical in the chain direction. Depending on the orientation of the repeat unit, different microstructural 2

Copolymers that are made from the repetition of two (or a very few) different units will be the subject of a later paragraph.

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Jacques Devaux and Sophie Demoustier-Champagne

Figure 6 Spherulites of isotactic poly-1-butene (a, during growth) and of polyethylene (b, after completion) by optical microscopy (OM) under crossed polars. Reproduced from Ref. [3] with permission of John Wiley & Sons, Inc.

Growth

Intercrystalline tie chain (amorphous)

Crystalline lamellae

Amorphous phase

Nucleating seed

Figure 7 Scheme of the internal structure of a spherulite. Reproduced from Mercier, Zambelli and Kurz [1], Elsevier (2002) with permission of Elsevier. Copyright Elsevier 2002.

Polymer Chemistry and Microstructure

CH3 CH3

CH3 C H2

C H

C H2

C H

A

C H B

CH3 C H2

C H2 C

C H

23

CH3 C H2

C H

A

Figure 8 Schemes of (A) ‘‘head–tail’’, (B) ‘‘head–head’’ and (C) ‘‘tail–tail’’ microstructural arrangements in polypropylene.

SCB

LCB

Dendrimer

Hyperbranched

Figure 9 Examples of branching in polymers LCB (long-chain branched, e.g., LDPE) and SCB (short-chain branched, e.g., LLDPE), dendrimer and hyperbranched.

arrangements — ‘‘head–head’’, ‘‘head–tail’’ or ‘‘tail–tail’’ — can occur (1D microstructure); these are called positional isomers (Figure 8). Due to either accidental or intentional events during the synthesis, branching points can occur along the chain (2D microstructure). Although this needs the presence at the branching point of, stricto sensu, a ‘‘non-identical’’ unit, these macromolecules remain classified as homopolymers. Branching can also give rise to either the so-called ‘‘long-chain branching’’ (LCB) or ‘‘short-chain branching’’ (SCB), see Figure 9. Such terms are of importance particularly for polyethylene as they describe the only3 small ‘‘chemical’’ difference between technologically highly different low-density (LDPE) and linear lowdensity (LLDPE) polyethylenes. Except for polyethylene, the distinction between LCB and SCB is somewhat controversial as it can depend on several characteristics or even on the capacity of the characterisation method itself. From the branching point three or more chains can arise. This depends on the so-called ‘‘functionality’’ of the ‘‘monomer’’ at the branching point (the ‘‘branching unit’’). This functionality can be defined as the number of molecules (monomers, branches) actually linked to one branching unit. This definition can be extended to monomers purposely inserted into a chain to create branching. In this case the definition of functionality is generalized to the number of monomers that can link to the considered unit. ‘‘Normal’’ monomers have thus a functionality of 2. Branching units can exhibit functionalities of 3, 4 or more.

3

End groups are not taken into account here.

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Jacques Devaux and Sophie Demoustier-Champagne

2.4.2 Dendrimers and hyperbranched polymers Highly non-linear homopolymers can even be synthesized exclusively from monomers of functionality higher than 2. Dendrimers (from ancient Greek ‘‘dendron’’ ¼ tree) are obtained when all the reaction sites of each branch links to another one and when all branches exhibit the same length. Whereas, hyperbranched (HB) polymers result from incomplete reaction of each multifunctional monomer, see Figure 9.

2.4.3 Crosslinked homopolymers As the number of branching points per chain increases, (when it becomes W2) an almost infinite network of covalent bonds can be created. Strictly all the system belongs to only one giant macromolecule. The polymer becomes insoluble and infusible; it is said to be ‘‘crosslinked’’. Even if, formally, an infinite network of covalent bonds can give rise to a 2D infinite structure (when grown onto a surface, for instance), crosslinked polymers are generally considered as 3D structures. Such crosslinked structures can be made either by using monomers exhibiting functionalities higher than 2 (thermosets like polyepoxides, phenolics), or by inducing a reaction of preformed linear chains with ‘‘bridging’’ molecules (e.g., vulcanisation of natural rubber) (Figure 10). Crosslinked 3D networks are normally amorphous,4 infusible and insoluble. Solvents can only swell networks. However, polymers resulting from polymerisation of molecules of functionality higher than 2 can remain soluble during the course of synthesis, below a certain ‘‘critical conversion value’’. Above this state, ‘‘gelation’’ occurs. Even in this state, the system remains partially soluble. It can be separated by solvent extraction into two phases: the soluble phase is called the ‘‘sol’’ and the insoluble phase the ‘‘gel’’. As the monomer conversion proceeds, the amount of ‘‘sol’’ decreases, while the amount of ‘‘gel’’ increases. The behaviour of crosslinkable amorphous systems during their synthesis can be described in the so-called time–temperature transformation or ‘‘TTT diagram’’ (Figure 11). It has to be noticed that such a TTT diagram can only be used in the direction of increasing time (transformation). A particular characterisation of a crosslinked system is the determination of the crosslink density. Access to the measurement of such crosslink densities is possible through models requiring determining the swelling of these systems.

2.4.4 Linear and branched copolymers Copolymers are built from the repetition of two (or more) ‘‘repeat units’’. Depending on the spatial arrangement of those units (e.g., A and B) along the chain (sequencing), various types of copolymers can be made: alternating, block, random (or statistical), branched, crosslinked (see Figure 12). More sophisticated microstructures are sometimes synthesized, but the highly complex chain sequencing encountered in natural copolymers, like proteins or 4

Depending on the mobility of chain segments, some crystallisation can occur in crosslinked systems.

25

Polymer Chemistry and Microstructure

C CH C C H2 H2 H

C CH H2

Cross-link C C H2 H

A

C CH H2

CH C H2

C CH C C H2 H2 H

C H2

CH3 CH

C

C H

C H2

S

B

S C C H2 H

C

C H

CH3

Figure 10 Examples of crosslinked polymers (A, polyfunctional; B, vulcanised).

enzymes, are still not accessible to chemical synthesis at the beginning of the third millennium. Several physical properties of copolymers are directly or indirectly dependent upon the distribution of sequences. The phase behaviour (microphase separation) in block copolymers is linked to the mutual insolubility/ solubility of the sequences. This will be discussed further.

3. FROM MOLECULES TO MACROMOLECULES As mentioned previously, chemistry and physico-chemistry play major roles in polymer microstructure, and, as a consequence, on polymer properties. The characterisation of several chemical parameters of polymer chains is thus of paramount importance for controlling the final properties of polymer materials  Chain length or molecular masses J Entanglement J Concentration and type of end groups  Nature of chain substituents

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Jacques Devaux and Sophie Demoustier-Champagne

UNGELLED GLASS GELLED GLASS GELATION

TIME TO GELATION AND VITRIFICATION

GLASS

VITRIFICATION

RUBBER LIQUID

GELATION

Tgg

Tg∞

CURE TEMPERATURE, TCURE

Figure 11 Example of time–temperature transformation (TTT) diagram. (Increasing time in vertical direction). Reprinted from Roller and Gillham [4], published by the Federation of Societies for Coatings Technology, with permission of publisher.

A A B A A B B B A B B A

Random

B

A B

A B

A B

A A A A A B

B

A B

A B

A

Alternate

B

B

B

Block or sequenced

B

B

A A A A A A A A A A A A B

B

B

B

B

Figure 12 Examples of microstructures of copolymers.

Branched

Polymer Chemistry and Microstructure

27

 Spatial arrangement J Cis–trans isomerism J Chain configuration J Chain conformation The chain structure (length, entanglement, branching, tacticity,y) of polymers is discussed further in the next chapter (Chapter 4) by Beaucage and Kulkarni.

3.1 Chain length and entanglements An important chemical characteristic of a polymer is the chain length. Chain length strongly influences the thermal properties as illustrated in Table 2 for several aliphatic compounds of different lengths. Detailed studies have been published on the influence of chain length on melting temperatures of various polymers [5] or on Tg and Tm (melting temperature) of aromatic polymers [6]. Above a characteristic chain length polymer chains may (depending on the rigidity of the polymer backbone and/or on processing (stretching)) undergo the formation of entanglements. These entanglements mainly govern rheological properties and several mechanical (viscoelastic) properties. A less known, and indirect, effect of such entanglements is a lowering of ‘‘pure’’ thermal stability of polymers as compared with corresponding lower mass compounds (non-entangled). As an example, in absence of oxygen, linear polyethylene starts degrading at about 3001C, while hexadecane can resist up to 5001C [7].

3.2 End groups A useful relationship can be written between molecular mass and end group concentration for linear polymers. Indeed, as there are exactly two end groups Table 2

Influence of chain length on melting point, T, of aliphatic compounds H–(CH2)n–H

n

Name

Melting T (1C)

1 2 3 4 5 6 8 10 12 18 30 EN

Methane Ethane Propane Butane Pentane Hexane Octane Decane Dodecane Octadecane Triacontane Polyethylene

182.4 182.8 189,9 138.3 129.7 95.0 56.5 29.7 9.6 28.0 65.5 110–135

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Jacques Devaux and Sophie Demoustier-Champagne

per chain (of n units), their concentration [EG] can be written as: ½EG ¼

2 Mn

End group quantification is thus a useful method for number average molecular mass determination. Also, if the end group concentration is higher than the value calculated from an independent Mn determination, chain branching can be deduced and quantified. Jackson and Robertson consider the molecular structure characterisation and analysis of polymer end groups in Chapter 5.

3.3 Chain substituents The nature of the chain substituents strongly influence the properties of the resulting polymer. For instance, the influence of the nature of chain substituents on Tg is illustrated in Table 3 for a series of vinyl polymers.

3.4 Spatial arrangements In addition to the type, number and sequential arrangement of monomers along the chain, the spatial arrangement of substituent groups plays also an important role in determining the polymer properties. Table 3

Influence of chemical nature of substituents on Tg

Structure

C C H2 H2

Glass transition (Tg)1C

Polyethylene

B100

Polypropylene

15

Polyvinyl chloride

+80

Polystyrene

+100

n

C CH H2 n CH3

C CH H2 n Cl

C CH H2

Name

n

Polymer Chemistry and Microstructure

29

CH3 C H2

C

C H2

CH3 CH3 H2 H2 H2 C C C C C C C C C C H H H2 H2 H

CH3 H C C

CH3 H2 H2 H C C C C C C C C C H2 H H2 H2 CH3

Gutta percha

Natural rubber

Figure 13 Chemical structures of trans and cis isomers of 1,4 polyisoprene (gutta-percha and natural rubber, respectively).

3.4.1 Cis–trans isomerism For polymers with double bonds in the backbone, a first arrangement to consider is the cis–trans isomerism. A well-known example of the influence of this isomerism is found in the natural resins from the saps of hevea (‘‘natural rubber’’) and of sapotacea (‘‘gutta-percha’’). The chemical structures of these materials are, respectively, cis-1,4 polyisoprene for natural rubber and trans-1,4 polyisoprene for gutta-percha (Figure 13). From their properties, mainly that of the chain symmetry allowing the trans isomer to crystallise more easily than the cis isomer, natural rubber achieved its huge commercial exploitation, while uses of gutta-percha remained limited mainly until the end of XIXth century to textile impregnation, and nowadays to golf balls and to dental filling.

3.4.2 Configuration — tacticity Chirality (from ‘‘weir‘‘, hand in ancient Greek) is a property of organic molecules containing at least one carbon atom (or a silicon) with four different substituents. When there is only one asymmetric centre in the molecule, two stereoisomers can be drawn. Along a long chain (considering both sides of the chain as different) carbons (or silicons) bearing two different substituents are considered as asymmetric and two structures (R or S) that would not superimpose can be drawn (Figure 14A). Upon laying out such units along a polymer chain, successive units can be either identical (R,R or S,S) or different (R,S or S,R), giving rise to different stereochemical arrangements of atoms, called configurations. Unlike the conformation, the configuration of a polymer chain cannot be altered without breaking chemical bonds. The general term for the stereoregular configurations is the tacticity of the chain. When all successive asymmetric units exhibit the same configuration, the polymer is said to be ‘‘isotactic’’, when the configurations alternate, the polymer is said to be ‘‘syndiotactic’’; it is ‘‘atactic’’5 when the configurations are randomly distributed along the chain. As illustrated in Figure 14A, three different placements 5

‘‘Heterotactic’’ is sometimes used.

30

Jacques Devaux and Sophie Demoustier-Champagne

H3C

Polypropylene

Poly(methyl-phenyl)silane

A

B

H3C C

C

C C

C

φ

H3C

H3C

H3C

Si

C C

Si

Isotactic

CH3 H3C C

C C

CH3 C

C

C C

φ

H3C

Si

C

CH3 H3C C

C

CH3 C

C

φ

C C

φ H3C

φ

φ

H3C

φ

Si

Si φ CH H3C 3

φ Si

Si

CH3 φ

CH3 H3C

Si

φ

H3C

Si

CH3 φ

CH3

Si Si

φ H3C

Si

Si Atactic

SI

Si

Syndiotactic

φ

H3C

Si

H3C

φ CH3

φ

H3C

Si H3C

H3C

φ

H3C

φ

CH3 φ

Si Si φ H3C

CH3 Si

Si φ

Figure 14 Tacticity of (A) polypropylene and (B) poly(methyl-phenyl) silane.

of the substituents (in the example, H, CH3) are possible. As the vinyl polymers contain only one stereogenic centre every two carbon atoms, the asymmetric carbons are separated by one methylene group. Therefore in an isotactic vinyl polymer, all (identical) substituents are situated on the same side of the plane formed by the extended-chain backbone, whereas they alternate in the case of a syndiotactic vinyl polymer. When each backbone atom is a stereogenic centre, the situation is exactly the opposite, substituents alternating on both sides of the chain plane form an isotactic polymer and non-alternating substituents give rise to a syndiotactic polymer (e.g., Figure 14B is the tacticity of an asymmetric polysilane [8]).

3.4.3 Conformations 3.4.3.1 Definitions. From basic knowledge of chemical bonding, a rather satisfactory representation of the backbone of a hydrocarbon polymer chain is given in Figure 15A. Carbon–carbon bond angles are about 1091 while the ˚. average bond length is 1.52 A However, this representation, while giving a good idea of the linearity of the chain, and of bond lengths and angles, remains limited to the particular situation where all the backbone atoms are located in the plane of the paper (the so-called ‘‘extended chain’’ or ‘‘planar zig-zag’’ situation). Indeed, while maintaining lengths and angles internal rotations around single bonds allows one to

Polymer Chemistry and Microstructure

H2 C

A

C H2

H2 C C H2

H2 C C H2

Energy

H3C

H2 C C H2

H2 C C H2

H2 C C H2

H2 C C H2

H2 C C H2

31

H2 C C H2

H2 C C H2 CH3

Gauche

Gauche

B Eclipsed

Eclipsed Trans = "zig-zag"



180°

360° Angle

Figure 15 (A) Polyethylene chain in planar zig-zag conformation. (B) Energy diagram of n-butane as a function of ‘‘chain’’ rotation.

realise a large number of different geometrical arrangements, which are called ‘‘conformations’’. Conformations are defined as ‘‘non-identical arrangements produced by the rotation of backbone atoms around one or more single bonds’’. The different conformations are easily understood by reference to simple molecules like ethane or butane for a rotation around the central carbon–carbon single bond. ‘‘Eclipsed’’ and ‘‘staggered’’ conformations refer to the situations where two identical substituents on both central carbon atoms are aligned, or non-aligned (rotation of 601), respectively. Of course, depending on the size and shape of the substituents, all conformations are characterised by a slight energy difference. The lowest energy conformation of a linear molecule with more than four backbone atoms is always the planar or ‘‘trans’’ conformation (like the example in Figure 15A). Two other low-energy conformations are obtained by a clockwise or counter-clockwise rotation of the central bond of 1201 (Figure 15B). The two staggered conformations are said to be ‘‘gauche’’ and are skewed and non-planar. Energy differences between conformations remain, however low and, in most cases, less than the thermal energy, allowing almost free rotation around carbon–carbon single bonds at room temperature, hence, the average conformation of a polymer chain in a liquid (melt or solution) or amorphous state is a ‘‘random coil’’ (or ‘‘statistical coil’’).

3.4.3.2 Ordered conformations. As explained above, the mean conformation of a polymer chain in the amorphous state is near to being a random coil. Situations where an isolated molecule displays a highly ordered arrangement are rather uncommon. It can however result from intramolecular bonding and strong interactions. An example can be found in p-phenylene polyamides (see, e.g., Figure 16) where the phenyl groups are planar and therefore rotation around the C–N bond is restricted due to electron delocalisation. Such molecules are

32

Jacques Devaux and Sophie Demoustier-Champagne

O

O

C

C

N

N

N

H

H

H

O

O

C

C

O

O

C

C

N

N

N

H

H

H

O

O

C

C

Figure 16 Chain structure of poly(p-phenylene terephthalamide) (Kevlars).

consequently asymmetric and are best visualised as long thin rods, explaining why they often behave as liquid crystals in solution. An increase in rod-like arrangement of the macromolecules can also arise by stretching a polymer either in its solid state, either in the melt or even in solution (for polymers leading to lyotropic liquid crystals such as aromatic polyamides). This is the basis of the development of synthetic fibres including high modulus polyethylene Dyneemas, polyamide Nylonss and Kevlars, polyester Tergals or Dacrons fibres. Stretching a polymer in two perpendicular directions, either successively or by blowing a bubble of molten material, leads to its biaxial orientation, which strongly improves mechanical properties in the stretching directions and/or gas permeability (e.g., biaxial orientation of polypropylene leads to BOPP (for biaxially oriented polypropylene) or biaxial orientation of poly(ethylene terephthalate) gives CO2-impermeable bottles for carbonated beverages.) (Characterisation methods for determining molecular orientation are considered in Chapter 8.) The most important way of ordering linear molecules remains however crystallisation (Section 2.3.2). In crystals, the most common conformations are those that minimize energy, for instance planar zig-zag in polyethylene. Usual intermolecular forces (van der Waals interactions, hydrogen bridges, dipole–dipole interactions) can be responsible for polymers maintaining preferred chain conformations more or less ordered as quasi-linear extended chains in crystal lattices. Hydrogen bridges occur in both the crystal phase and the amorphous (or liquid) phase of polyamides like Nylonss and are responsible for their high-melting enthalpy, hence high-melting point. They are responsible for the higher thermal properties of polyamides compared to the corresponding polyesters. Hydrogen bridges also play a prominent role in celluloses and in proteins by maintaining preferred arrangements able, for instance, to catalyse biological reactions (enzymes). In hydrocarbons like polyethylene, interactions in the crystal phase are weaker and of the van der Waals type. Dipole interactions are important in PVC as a consequence of the C–Cl bonds. In some cases, planar chain structures become impossible when replacing a hydrogen atom on the backbone of a macromolecule by a bulky group. Packing problems arise due to steric hindrance if the trans orientation of each bond is

Polymer Chemistry and Microstructure

33

: CH3 :C :H

Figure 17 Helical structure of isotactic polypropylene. (See Color Plate Section at the end of this book.)

maintained, which becomes eventually less energetically favourable than the gauche conformation. Hence, other rotational angles or a succession of rotational angles must be adapted as, for instance, in a helix (x/y)6 conformation, which, in the general case, is realised by the repetition of a trans-gauche sequence. The same gauche angle must always occur. As there are two possibilities, righthanded and/or left-handed helices can form. Examples are isotactic polypropylene (a 3/1 helix) (Figure 17), polytetrafluoroethylene (e.g., Teflons) where a 13/1 helix is found, or polyisobutylene arranged in a 8/5 helix. Helices can be included in crystal lattices.

6

An x/y helix is a helix with x repeat units in y turns.

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Jacques Devaux and Sophie Demoustier-Champagne

4. FUNDAMENTALS OF POLYMER CHEMISTRY 4.1 Chain polymerisation vs. step polymerisation It is not the purpose of this chapter to describe in detail the synthetic chemistry of polymers. From the early ‘‘Principles of polymer chemistry’’ book of Flory, the first edition of which dates from 1953 [9], numerous other books have been written on the subject, among which a few examples are referenced [3,10,11]. In addition to biological reactions, there are two main mechanisms of building synthetic polymers from their monomers: addition (or chain) polymerisation and step polymerisation. Schematically, synthesizing a polymer can be compared to playing dominos. On the one hand, it can be done by aligning a long series of them on their smallest face, then, by a small push on the first one (initiation), inducing a concerted falling down (propagation). On the other hand, dominos can be arranged in long series by associating corresponding ends step by step, like functional molecules by reacting corresponding functions. A major difference between both kind of syntheses lies in polymerisation kinetics: in the former case there is a chain mechanism (initiation, propagation, termination), in the latter case there is no chain reaction and each step is equiprobable. Main comparison points are highlighted in Table 4 [9]. For both types of polymerisation mechanisms, different polymerisation processes can be used ranging from simple bulk and solution polymerisation processes to more sophisticated ones such as suspension, emulsion, interfacial, plasma,y polymerisation processes.

Table 4

Comparison between addition and step polymerization

Chain polymerisation (addition polymerisation)

Step polymerisation (polycondensation)

Only growing species add units one at a time Monomer concentration decreases steadily throughout reaction Long chains formed at once Molecular mass changes little throughout reaction The longer the reaction time, the higher the yield Reaction mixture contains:  monomer  high polymer  E104 part of active species

Any two molecules can react Monomer almost disappears early during reaction Molecular mass increases all along reaction The longer the reaction time, the higher the molecular mass Distribution of all species can be calculated all along the reaction

Polymer Chemistry and Microstructure

35

4.2 Types of chain polymerisations and polymers synthesized — keypoints of mechanisms, kinetics Addition polymerisation is mainly characterised by the existence of a chain mechanism. This means that the process of building the chain is always based on the sequence: initiation - propagation - termination. A long chain (high) polymer is only obtained if the propagation step is much faster than the initiation and/or termination7 reactions. Therefore, during the synthesis, a very limited amount (or number) of active species can actually react at a given instant. Moreover, the lifetime of these active species is often shorter than the total duration time of the reaction. Long terminated (non-reactive) chains thus coexist with monomer molecules throughout the reaction. Disregarding the actual chemical mechanism of each monomer reaction, a good example of polymers made by chain reactions are the vinyl polymers (by definition, polymer made from monomers having the vinyl group: CH2QCH–, as the reactive group). Formulae of some typical vinyl polymers were reported in Table 1. Chain polymerisations are often classified on the basis of their elemental reaction type as:  Radical chain polymerisation  Ionic chain polymerisation  Transition metal insertion polymerisation. Each of these leads to particular characteristics of the polymer chain. Each will be briefly discussed in the following sections, with a special focus on the viewpoint of characterisation.

4.3 Radical chain polymerisations 4.3.1 Free radical polymerisation A schematic representation of the principal steps (initiation, propagation and termination) of a radical chain polymerisation is presented in Figure 18.

4.3.1.1 Initiation. Initiation in radical polymerisation consists of two steps: the dissociation of the initiator to form two radical species, followed by addition of a single molecule to the initiating radical (Figure 18). Initiators include any organic compound with a labile group, such as an azo (–NQN–), disulfide (–S–S–) or peroxide (–O–O–) compound. The labile bond can be broken by various ways like heat, UV light, g-irradiation or by a redox reaction. 4.3.1.2 Propagation: head-tail. As usually considered, a propagation reaction leads to the addition of a monomer molecule, with the same linear orientation as

7

When there is a termination reaction.

36

Jacques Devaux and Sophie Demoustier-Champagne

I R

2R +

H H2C C

H R C CH C C H2 H2 n

R

+

H C C H2

Initiation

H H2C C

H R C CH C C H2 H2 n+1

Propagation

H R C CH C C H2 H2 n

+

C C C C R H H2 H H2 n

R C CH C CH C C C C R H2 H2 H H2 H H2 n n

by addition

by disproportionation

Termination

R

H C CH C C H2 H n

+

C C C C R H2 H2 H H2 n

Figure 18 Mechanism of radical chain polymerisation of styrene.

the previous unit to the growing radical (head-to-tail addition). The main reasons invoked to justify this behaviour are:  head-to-head addition would lead to less stable radicals (case of PS),  head-to-head addition is unfavourable due to steric hindrance (case of poly(vinyl acetate)),  the polarity of the substituent of the vinyl moiety orients the addition to headto-tail (case of PVC).

Polymer Chemistry and Microstructure

37

Monomer addition under radical propagation conditions leads to mainly an atactic configuration. As a consequence, radical polymerisations of asymmetric vinyl polymers usually lead to amorphous materials. However, if the substituent is small enough to enter into the crystal cell, atactic vinyl polymers can crystallise (an example is poly(vinyl fluoride)).

4.3.1.3 Kinetics of radical chain polymerisation. Kinetics calculations on radical chain polymerisation are based on the three steps mechanism with notations as shown in Figure 19. Two main hypotheses are made on radicals to simplify the calculations. 1st hypothesis: Equi-reactivity. The radical reactivity remains independent on the nature or size of the radical. 2nd hypothesis: Steady state. Radical concentration instantaneously reaches and keeps its steady-state value throughout the reaction. The rate of radical formation (rate of initiation, Ri) equals the rate of radical disappearance (rate of termination Rt). d½M  ¼ 2Ri  2Rt ¼ 2kd ½I  2kt ½M 2 ¼ 0 (1) dt  where [I] is the concentration of initiator, [M ] the concentration of radicals, kd the rate constant of dissociation and kt the rate constant of termination. Using these two hypotheses, the overall rate of polymerisation is simply the rate of chain propagation (Rp).   d½M kd 1=2 1=2  ¼ kp ½M ½M ¼ kp f Rp ¼  ½I ½M (2) dt kt where [M] is the concentration of monomer, f the fraction of primary radicals initiating a polymer chain and kp the rate constant of propagation. Equation (2) shows that the rate of radical chain polymerisation is proportional to the monomer concentration and to the square root of initiator concentration.

I M

R

+

Mn

+ M

Mm + Mn

kd ka kp

kt

2R M

Mn+1

Mn+m Mn + Mm

Figure 19 Mechanisms of radical chain polymerisation with kinetic notations.

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Jacques Devaux and Sophie Demoustier-Champagne

S + Mn S

+ M

I + Mn R

ktrS

M ktrI

+ M

M + Mn M + M

Mn + S

Mn + R M

ktrM

Mn + M M

Figure 20 Transfer reactions in radical chain polymerisation.

4.3.1.4 Chain transfer reactions 4.3.1.4.1 Kinetic vs. material chain. Kinetically, a chain reaction exists throughout the ‘‘life’’ of the radical, that is, from the initiation of a radical up to its termination by recombination or by disproportionation. The lifetime of a radical determines the so-called kinetic chain length Lk defined as the number of monomers consumed per initiating radical. Lk, by definition, can be calculated from the ratio between the propagation rate Rp to the initiation rate Ri, or, using steady-state hypothesis (Equation (1)), from the ratio between propagation rate to the termination rate Rt (Equation (3)). 2

2

kp ½M Rp kp ½M ½M kp ½M Lk ¼ ¼ ¼  ¼  2 2k Rt ½M  2kt Rp 2kt ½M  t

(3)

During the course of radical chain propagation, several types of transfer reaction can occur, leading to the interruption of the ‘‘material’’ chain, while allowing the ‘‘kinetic’’ chain to continue. ‘‘Different’’ end groups can appear as a result of such transfer reactions (Figure 20). In the absence of any transfer, only the type of termination reaction has to be taken into account to obtain the number average degree of polymerisation (or chain length) Xn . Indeed, if the reaction terminates by addition, two radicals give one chain, while if the reaction terminates by disproportionation, one radical generates one chain. Using 0.5oxo1, one obtains Xn ¼

2 2 Lk kp ½M ¼ x 2xkt Rp

(4)

Equation (4) clearly shows that the number average degree of polymerisation Xn is inversely proportional to the reaction rate Rp, meaning that, in radical chain polymerisation high reaction rates are linked to low molecular masses and vice versa. One way to avoid this dilemma is to use emulsion polymerisation where the lifetime of a radical (i.e., the ‘‘kinetic’’ chain length) is independent of

Polymer Chemistry and Microstructure

39

‘‘overall’’ monomer or radical concentrations, but only depends on the number of micelles and on the percentage of time they are ‘‘active’’ (statistically 50%).8 If transfer reactions occur, they terminate ‘‘material chains’’, thus decreasing Xn , without affecting the ‘‘kinetic’’ chain length Lk. Thus Rp P Xn ¼ (5) xRt þ Rtr P with Rtr the sum of all transfer reaction rates. Equation (5) denotes that a control of Xn can be obtained by controlling transfer reactions, that is, by adding calculated amounts of molecules able to transfer a radical thus creating new end groups. 4.3.1.4.2 The low-density polyethylene and polypropylene cases. In the course of the radical chain polymerisation of ethylene two kinds of transfer on the polymer play a major role, giving rise to LCB or SCB. These are illustrated in Figure 21. Due to both kinds of branching leading to chain irregularities, the crystallisation of radical chain-polymerised polyethylene is strongly hindered. Its maximum degree of crystallinity is limited to about 50%, its melting temperature ranges from 801C to 1151C and its density remains low (B0.92). From this latter property, it received the name of low-density polyethylene (LDPE). In radical chain polymerisation of allylic monomers (containing the chemical allyl group CH2QCR–CH3, like propylene, isobutylene,y), a transfer on the monomer can occur leading to a very stable allyl radical unable to propagate the chain. Thus radical chain polymerisation of such monomers, especially propylene is not feasible, as a competition exists between the propagation rate and the high rate of transfer on the monomer (see, Figure 22). 4.3.1.4.3 Termination reactions 4.3.1.4.3.1 LOW VISCOSITY (LOW CONCENTRATION SYSTEMS). Radicals are species that normally have short lifetimes (102 s to 10 s). In the course of a chain growth mechanism (see Figure 18) they terminate by finding a second non-paired electron to build a chemical link made of an electron pair. This requires that two radicals meet, either to pair their electrons and combine (addition) or to exchange a hydrogen, leading to the formation of one saturated bond and one double bond (disproportionation). 4.3.1.4.3.2 GEL OR TROMMSDORF EFFECT, VITRIFICATION AND LIVING RADICALS. When the initial monomer concentration is high (X40%), the viscosity of a system increases upon increase of the conversion. This increase is linked to progressive interpenetration of coiled macromolecules, leading to entanglement. Due to this viscosity increase, the mobility of the molecules, mainly the longer ones (growing radicals) decreases and the kinetics may be affected by slower diffusion. This effect is first noticeable for reactions involving two large reactive molecules, that are the termination reactions. Therefore, as the initiation reaction is less affected, the steady-state hypothesis is no more valid and the radical lifetime increases, 8

Due to the very small (nanometric) size of a micelle, only one radical at a time can exist inside.

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Jacques Devaux and Sophie Demoustier-Champagne

Long Chain branching

CH

+

CH2

C H2

n H 2C

+

H2 C

CH2

CH

+

CH3

H 2C

H 2C

H2 C

CH 2

LCB

CH C H2 H 2C

H 2C

Short Chain branching

H2 C

CH

H H2C

H2 C

H2 C C H

CH2 CH2

H 3C

H2 C

H2 C

H2 C

C H

CH2

CH 2 CH 2

CH2 H 3C

+

n H 2C

CH2

H2 C

CH

H2 C

H2 C C H2

C H2

(CH2)3 CH3

SCB

Figure 21 Transfer reactions in radical chain polymerisation of ethylene.

together with their concentration (Equation (1)), leading to an auto-acceleration of the overall polymerisation reaction. As this phenomenon is due to entanglement of coiled chains and a large increase of viscosity, it is called, somewhat improperly, the ‘‘gel effect’’ (even if there is no true ‘‘gel’’ because there is no crosslinking). It is also sometimes named the ‘‘Trommsdorf effect’’ [3]. Such effects are especially observable when polymerisation occurs in the bulk (mass polymerisation). In this case, another effect can be observed at high

Polymer Chemistry and Microstructure

R

+

R

C C H2 H

H2 C

C H

CH3

CH3

+

H 2C

R

C H

C C H2 H

CH3

R

C C CH3 H 2 H2

41

CH3

R

C CH C C H2 H2 H CH3

CH3

H 2C

C H

CH2

H 2C

C H

CH2

+

stable allyl radical unable to propagate

Figure 22

Transfer reactions inhibiting propylene radical polymerisation.

conversion. If the final synthesized polymer is characterized by a Tg higher than the actual temperature at which the polymerisation reaction is carried out, it happens that the Tg of the system, which increases with the conversion degree, reaches the reaction temperature. At this point, the whole reaction medium vitrifies and the molecular mobility vanishes, stopping the reaction without termination, at a monomer conversion below 100%.

4.3.2 Controlled/Living radical polymerisation Recently, controlled/living systems based on radical mechanism have been reported [12,13]. The new concept for controlling chain growth processes relies on forming an equilibrium between active species (radicals) and various types of dormant species. Very small amounts of the active species equilibrate with the dormant species, slowing down the rate of polymerisation and allowing tolerance to impurities. There are three approaches to the exchange process. Two of them are based on the persistent radical effect and are spontaneous (nitroxide-mediated polymerisation, NMP) or catalysed (atom transfer radical polymerisation, ATRP). The third approach uses a degenerative transfer mechanism with either alkyl iodides or dithioesters (reversible addition fragmentation transfer, RAFT) as transfer agents [12]. These new synthetic polymerisation processes provide efficient routes to precisely control molar mass and its distribution, macromolecular architecture as well as microstructure (tacticity and sequencing). Controlled/living radical polymerisation (CRP) is currently a fast developing area in polymer synthesis and it allows preparation of many advanced polymeric materials, including thermoplastic elastomers, surfactants, gels, coatings, biomaterials, materials for electronics and many others.

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Jacques Devaux and Sophie Demoustier-Champagne

4.4 Ionic polymerisations — active species Ionic chain polymerisations refer to chain mechanisms in the course of which the propagation step consists of the insertion of a monomer into an ionic bond. The strength of this ionic bond can vary, depending on the nature of the species, the temperature and the polarity of the solvent, between a closed ionic pair in contact up to free ions (see Figure 23). Final polymer microstructure (configuration,y) and molecular mass distribution depend on the actual nature of the active ionic species. Ionic chain polymerisations follow the same basic steps as radical chain polymerisation and are said to be either cationic or anionic depending on the nature of the ion formed in the initiation step. Schemes of the insertion during the propagation step in cationic and anionic chain polymerisations are shown in Figure 24. Polymerisation of vinyl monomers with electron-donating substituents can proceed by a cationic mechanism, while monomers with electron-withdrawing group can polymerise by an anionic pathway.

4.4.1 Cationic polymerisation A cationic polymerisation mechanism is illustrated in Figure 25 for the most industrially important example of polyisobutylene. Unlike radical chain polymerisation, initiation in cationic polymerisation uses a true catalyst that is recovered at the end of the polymerisation and is not incorporated at one end of the growing chain. Catalysts for cationic chain polymerisation are molecules able to withdraw electrons, mainly Bro¨nsted (H2SO4, H3PO4) and Lewis acids (BF3, AlCl3, SnCl4). The choice of solvent for cationic polymerisation is also important because it plays a major role in the association between cation and counter ion. A too tight association will prevent monomer insertion during the propagation step. However, the use of ‘‘stabilized’’ A

B

n

n A

Aδ(+)

B

Bδ(−)

aggregate

A+B−

A+//B−

ion pair solvated ion pair

A+ + B− free ions

Figure 23 Active species in ionic polymerisations. cationic A

H2 + C CH C CH B− H2 n R R

+

H2C

CHR

A

+

H2C

CHR

B

H2 + C CH C CH H2 n+1 R R

B−

anionic B

H2 − C CH A+ C CH H2 R n R

Figure 24 Schemes of propagation steps in ionic polymerisations.

H2 − C CH C CH A+ H2 n+1 R R

43

Polymer Chemistry and Microstructure

CH3 F3BOH OH +

Initiation

+ H2C

C

CH3

ki

H 3C

CH3

CH3 CH3 H2 C C + F3BOH C C H2 n CH3 CH3 CH3

CH3

Propagation

H3C

C

CH3

- + HC 2

H 3C

kp

CH3 CH3 H2 C C + F3BOH C C H2 n CH3 CH3 CH3

C

-

CH3 H 3C

CH3 CH3 H2 C C + F3BOH C C H2 n CH3 CH3 CH3

kt

C

Transfer to monomer

CH3 CH3 H2 C C + F3BOH C C H2 n+1 CH3 CH3 CH3

C

CH3 CH3 H2 C C OH C C H2 n CH3 CH3 CH3

C

C

+

BF3

ktr

CH3

CH2 CH3 H2 C C C C H2 n CH3 CH3 CH3

C

-

CH3

H 3C

CH3

CH3

H 3C

-

CH3

H 3C

CH3

- + HC 2

F3BOH

CH3

CH3

CH3

Termination

C

C+

+

H 3C

C+

F3BOH

-

CH3

Figure 25 Overall cationic chain polymerisation mechanism of isobutylene.

carbocation sites allows the cationic chain polymerisation to be undertaken under ‘‘living’’ conditions at low temperatures, where termination and transfer reactions are almost suppressed [13]. Typical termination can occur by deactivation of the cationic species from the growing chain, possibly leading to a functional end group (Figure 25). Transfer reaction to the monomer, leading to the insertion of an unsaturated end group, is an important reaction in cationic chain polymerisation. As the activation energies of both termination and transfer reactions are higher than that of the propagation step, cationic chain polymerisation can only lead to high molecular masses when undertaken at low temperatures, typically 1001C. Commercial polyisobutylene is often copolymerised with a few percentage of isoprene in order to allow for crosslinking (butyl rubber).

4.4.2 Anionic polymerisation Anionic polymerisation mechanism is illustrated in Figure 26 with the example of styrene polymerisation. The active species in anionic chain polymerisations are anionic growing chain ends. The main characteristic of such a process is the almost total absence of termination and transfer reactions. For this reason, anionic polymerisation is often called ‘‘living polymerisation’’.

44

Jacques Devaux and Sophie Demoustier-Champagne

Initiation C4H9-

+ Li

+

H 2C

H C

C4 H9

- + C CH Li H2

Propagation

H2 C CH C H2

-+

CH n-1

Li

+

H2 C

H C

H2C CH C H2

-+

CH Li n

NO TERMINATION

Figure 26 Overall anionic chain polymerisation mechanism of styrene initiated by n-butyllithium.

Initiators are species able to transfer either an electron or an electron pair to the monomer: Bro¨nsted or Lewis bases, or, most often, organometallic derivatives like alkyllithium (very strong bases) are used. Note that in this case the initiating species (e.g., the n-butyl group) is incorporated as an end group in the polymer chain. When the initiation step is very fast (almost instantaneous), the absence of termination during living polymerisation can lead to a very narrow molecular mass distribution. Therefore, anionic chain polymerisation is often used to synthesize monodispersed samples used as standards for size exclusion chromatography (SEC) (see Chapter 6 for discussion of SEC). In the absence of termination reactions each monomer has an equal probability of fixing to an anion site. Therefore, the number averaged degree of polymerisation is simply equal to the ratio of initial monomer concentration to initial initiator concentration. In anionic polymerisation the molecular mass increases linearly with the conversion of the monomer [14]. During the propagation step, depending on the nature of the active ionic species, a limited control on the tacticity of the final polymer is possible. Ion pairs can, indeed, require the insertion of the monomer under a defined orientation, while free ions are unable to orient the insertion. If the starting reagents are pure and if oxygen and traces of water are excluded from the reaction, propagation can proceed indefinitely or until all the monomer is consumed. However, introducing selected additives to react with active anionic end groups allows one to either functionalize the chain end, or to start a new polymerisation of the same or of another monomer, leading to building of block copolymers. Typical functionalisation of end groups are listed in Table 5.

45

Polymer Chemistry and Microstructure

Table 5

Typical end-functionalisation reactions in anionic chain polymerisation

End-functionalisation reaction

Functional end group

C

+ O2

C

O

C

+ CO2

C

C

O

O O

C

+

H2C

CH2

C

O

C H2

C

+ H2O

C

H

C

+

C

H

RH

H2 C

O

+ OH

+ R

4.5 Olefin polymerisation processes With the exception of LDPE, polyolefins like other polyethylenes and polypropylene, which represent the largest amount of vinyl-type polymers produced in the world, are neither synthesized by radical nor by classical ionic polymerisation processes. Different types of polymerisation catalysts are in use for these purposes. The Cr-based Phillips catalyst, Ziegler–Natta type catalysts, metallocene or other more recently discovered catalysts, including late transition metal catalysts, are all characterized by their propagation step where the olefin monomer inserts into a carbon-transition metal link.

4.5.1 Phillips process The Phillips process can be used for the synthesis of polyethylene only. It makes use of a Cr-based heterogeneous catalyst on the surface of which the chain grows on metallic atoms of low oxidation level (CrII). Termination and transfer reactions in the Philips process both lead to unsaturated end groups, which results in chains having one saturated and one unsaturated end group (Figure 27).

46

Jacques Devaux and Sophie Demoustier-Champagne

Figure 27 Propagation, termination and transfer reactions in ethylene polymerisation by the Phillips process.

A major characteristic of the Phillips process chain polymerisation of ethylene is that it leads to very limited branching. The resulting polymer is thus highly linear and can reach high levels of crystallinity, hence high densities approaching 0.96–0.97. Such a polyethylene is known as HDPE for ‘‘High-density polyethylene’’.

4.5.2 Ziegler–Natta process The naming ‘‘Ziegler–Natta’’ given to processes for polyolefin syntheses originates from the use of Ziegler-type catalysts and in their use by Natta for isotactic propylene synthesis. They are based on heterogeneous catalysts made from complexes of group I–III organometallic compounds (or hydrides) and compounds of a group IV–VIII transition metal. Typical initiators of Ziegler– Natta polymerisation process are listed in Table 6. A common catalyst is the complex a-TiCl3–AlR3. The chain grows by insertion of the olefin molecule into the Ti–C link. The main characteristics of most of these heterogeneous catalysts is that, due to the size and shape of the complex, the insertion is only possible for one particular spatial orientation of the monomer, which, in the case of an asymmetric monomer like propylene, leads to a good control of tacticity. While use of Ti-based catalyst can lead to isotactic polypropylene, syndiotactic polypropylene is obtained using V-based catalysts. Ziegler–Natta catalysts were also designed to synthesize polyethylene (HDPE) and copolymers of ethylene with longer chain a-olefins (n-butene,

Polymer Chemistry and Microstructure

Table 6

47

Examples of typical components of Ziegler–Natta initiators

Group I–III metal

Group IV–VIII transition metal

(C2H5)3Al (C2H5)2AlCl (C2H5)AlCl2 (C2H5)2Be C4H9Li C5H11Na

TiCl3 TiCl4 TiBr3 VCl4 Ti(OC4H9)4 ZrCl4

Figure 28 Hydrogen transfer reaction in propylene polymerisation by the Ziegler–Natta process.

n-hexene, n-octene,y), to introduce controlled amounts of SCB and a limited crystallinity. These polymers are known as linear-low density polyethylene or LLDPE. The importance of Ziegler–Natta processes result from their broad synthesis range possibilities.    

Isotactic polypropylene9 HDPE and LLDPE Ethylene — propylene copolymer (ethylene–propylene rubber or EPR) Polybutadiene (PB) and polyisoprene with cis–trans controlled microstructure (synthesis of ‘‘natural rubber’’).

The termination of Ziegler–Natta synthesis is obtained by neutralisation of the catalytic site using, for instance, alcohol. The reaction can also simply be stopped (with no clear termination) by embedding of the catalyst into the polymer. Industrially, the control of final molecular mass is often accomplished by a hydrogen transfer reaction (see Figure 28).

4.5.3 Metallocenes and others Based on an early process discovered by Natta in the 1950s, soluble transition metal catalysts like metallocenes were developed mainly in the 1950s as initiators for polyolefin syntheses. Others are still now under investigation, like the so-called LTM (for ‘‘late transition metal’’) catalysts. Metallocenes seem 9

This result led to Ziegler and Natta jointly receiving the Nobel Prize for Chemistry in 1963.

48

Jacques Devaux and Sophie Demoustier-Champagne

Typical metallocenes:

Proposed MAO structures:

CH3

H3C Al

O

Al

CH3 O

CH3

H3C Al

Al

O

Al

CH3 O

Al

CH3

H3C

m

n O

Figure 29 Structures of typical metallocenes and proposed structure of methylaluminoxane (MAO).

potentially even more versatile than Ziegler–Natta catalysts as they retain their internal chiral site due to their ‘‘sandwich’’ structure. There are numerous available molecular structures of metallocenes on the basis of Ti, Zr, Hf, Yb and other transition metals. To act as a polyolefins’ synthesis catalyst, they need to be activated by a co-catalyst, for example, by methylaluminoxane (MAO), which is used in high excess by comparison with the metallocene. Typical structures of a few metallocenes and of MAO are reported in Figure 29. Polyolefins obtainable through the use of metallocene catalysis include isotactic, syndiotactic, and atactic polypropylenes, polyethylenes and copolymers including polar comonomers. A characteristic of polyolefins synthesized with metallocene catalysts is their significantly lower polydispersity compared to one obtained by using heterogeneous Ziegler–Natta catalysts. Such narrower molecular mass distributions can lead to different mechanical properties of the resulting material.

4.6 Processes for polyolefin syntheses Table 7 shows synthesis processes and microstructures of available polyethylenes together with several of their properties.

Table 7 Synthesis processes and microstructures of polyethylenes with characteristic properties Structure data

HDPE Phillips (Ziegler–Natta) 0.96–0.94(0.95) 94 (80–87) 128–135 1.3 (4) 1.2 (0.6)

LLDPE Ziegler–Natta 0.915–0.93 46–60 120

LDPE Radical chain polymerisation 0.915 – 0.93 46–60 110 25 0.6

Polymer Chemistry and Microstructure

Abbreviation Synthesis Typical density Percentage crystallinity range Melting range (1C) –CH3/1,000 carbons –vinyl/1,000 carbons

49

50

Jacques Devaux and Sophie Demoustier-Champagne

4.7 Copolymers 4.7.1 Linear copolymers On the basis of the kinetic characteristics of chain polymerisation reactions, it is possible to predict the final microstructures available by a so-called random process from a simple mixture of two comonomers. Indeed, the global mechanism of copolymerisation can be illustrated as presented in Figure 30. From this kinetic scheme, two characteristic parameters can be defined, r1 and r2  r1 is a measure of the ratio between the rate of addition of monomer 1 to the rate of addition of monomer 2 on a growing radical terminated by monomer 1, while r2 is the ratio between the rate of addition of monomer 2 to the rate of addition of monomer 1 on a growing radical terminated by monomer 2. r1 ¼

k11 k12

r2 ¼

k22 k21

The composition of the copolymers as a function of the composition of the mixture of monomers can be best understood from the practical example of styrene and methyl methacrylate (MMA) as shown in Figure 31. For radical chain copolymerisation of styrene and MMA, r1Er2o1. The copolymer content in styrene is not very different from the monomer kd

I

2R

ka1

R + M1

ka2

R + M2

M2

k11

M1 + M1

k12

M1 + M2

k21

M2 + M1

k22

M2 + M2

M1 +

M1

M1 +

M2

M2 +

M2

Initiation

M1

kt11 kt12 kt22

M1

+ M1

M1

+ M2

M2

+ M1

M2

+ M2

Propagation

copolymer

copolymer

Termination

copolymer

Figure 30 Mechanism of ‘‘random’’ chain copolymerisation of two comonomers (M1 and M2).

Polymer Chemistry and Microstructure

51

Copolymer: fraction of styrene

1

Cationic

0.8

0.6 Radical

0.4

0.2 Anionic 0 0

0.2

0.4

0.6

0.8

1

Monomer mixture : fraction of styrene

Figure 31 Copolymer composition as a function of monomer mixture composition in the case of styrene methyl methacrylate mixtures. Reproduced from Mercier and Mare´chal [15], Reproduit avec l’autorisation de l’e´diteur. Tous droits re´serve´s.

composition and does not change a lot during the course of the copolymerisation, nevertheless the slight difference between r1 and r2 prevents the composition following a straight line (diagonal if r1 ¼ r2 ¼ 1). In the case of cationic copolymerisation of styrene and MMA, r1  r26¼1 and r1W1 and r2o1. As it adds faster, the styrene content in the copolymer is always higher than in the monomer mixture, where it decreases throughout the reaction. The styrene content in the copolymer decreases thus also throughout the reaction. However, in the anionic copolymerisation of styrene and MMA, r1  r26¼1 and r1o1 and r2W1. As it adds slower, the styrene content in the copolymer is always lower than in the monomer mixture. In summary, the copolymer composition depends on the monomer ratio in the monomer mixture and on r1 and r2 reactivity ratios.

4.7.2 Graft copolymers An important class of copolymers copolymers, synthesized in order to of a rubber phase. Examples are the for High-Impact PolyStyrene and Both are synthesized in two steps.

made by chain copolymerisation is graft toughen brittle materials through inclusion cases of styrenic copolymers called ‘‘HIPS’’ ABS for Acrylonitrile–Butadiene–Styrene.

 First step: radical polymerisation of butadiene in the presence of a chain transfer agent to control its molecular mass.  Second step: polymerisation of styrene (to get HIPS) or styrene and acrylonitrile (to get ABS) with partial grafting of PS or SAN (styrene/ acrylonitrile) sequences onto the PB chains.

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Jacques Devaux and Sophie Demoustier-Champagne

Addition ("grafting to")

Mn

M n• or

+

C C H2 H

C H

C C H2 H or

C H2

• C H

C H2

• C CH C H2 H R

R•

C H2

Transfer & grafting ("grafting from")

Mn • or

MnΗ +

C C H2 H

R•

C H

C H2

C C H2 H or

or

C H



• C H

C H

C H

• C H

• C H

C H2



Mn + nM

C H

Figure 32 Grafting mechanisms in styrenic graft copolymers.

Figure 32 shows the mechanism of grafting involved, including the grafting (addition) of growing chains onto the butadiene double bonds (sometimes referred to as ‘‘grafting to’’) and transfer of the radical to the butadiene followed by the growing of a new chain from this transferred radical (sometimes referred to as ‘‘grafting from’’). The succession of both mechanisms may lead to crosslinking.

4.7.3 Block copolymers Another important class of copolymers synthesized by chain polymerisation are block (or sequenced) copolymers; diblock and triblock copolymers being the most important ones. They are very useful as compatibilisers (emulsifiers) in immiscible polymer blends. Another major use is as thermoplastic elastomers. Both uses are best explained through the example of butadiene–styrene block copolymers.  PS and PB homopolymers are immiscible. Any added PB–PS block copolymer in a PS–PB blend will have one sequence miscible in PS and one sequence miscible in PB, hence they will localise at the interface. As a consequence, the interfacial energy will decrease, greatly helping dispersion and providing phase adhesion, thus a transfer of mechanical properties.  In a pure PB–PS block copolymer, both sequences are immiscible and the microstructure will be diphasic (at a supramolecular or nanoscopic level). If the ratio is such that PS particles are dispersed into a matrix of PB, below the Tg of PS, the system behaves like crosslinked PB, hence as an elastomer. However, above the Tg of PS, the system becomes viscous and can be processed like a thermoplastic.

Polymer Chemistry and Microstructure

A Spheres

A Cylinders

AB Lamellae

B Cylinders

53

B Spheres

Figure 33 Available morphologies in biphasic sequenced copolymers.

Synthesis of vinyl block copolymers is accomplished by living polymerisation, mostly by anionic polymerisation. Several strategies can be used, illustrated here by the example of the Styrene–Butadiene–Styrene (or SBS) triblock copolymer.  Synthesis of a PB sequence with two living ends, using a difunctional initiator, followed by the addition of styrene to build two sequences of PS (two steps).  Synthesis of a PS sequence with one living end, adding and polymerising butadiene, while keeping its living end, then adding a new amount of styrene to build the third sequence (three steps).  Sequential synthesis of a diblock styrene–butadiene copolymer, while keeping the living end onto the butadiene end. Then coupling the living end groups by a suitable bifunctional agent (e.g., COCl2) (three steps).  Making use of the higher reactivity of butadiene in anionic polymerisation (r1o1, r2 W1) to get the triblock SBS copolymer in two steps. The first step is the synthesis of a PS sequence with a living end, then, upon addition of a mixture of styrene and butadiene, butadiene will add first, building a ‘‘pure’’ PB sequence, and styrene will finally build the third sequence (two steps).

4.7.4 Links with microstructure (phase diagrams) Copolymers (graft or block) made of immiscible sequences give rise to biphasic morphologies depending on the ratio of immiscible sequences (or of their lengths). Such possible microstructures are reported in Figure 33. A minor phase can be dispersed as nodules (spheres) or filaments (cylinders) while, when concentrations of both phases get similar, lamellar (interpenetrated) structures can appear. It should be noted that rather similar morphologies could also be found in (compatibilised) polymer blends.

4.8 Types of step polymerisations and polymers synthesized — keypoints of mechanisms, kinetics 4.8.1 Step polymerisation vs. polycondensations The most important difference between chain and step polymerisations is the absence of a kinetic chain in the latter. Among the different chemical reactions usable to synthesize polymeric materials by step polymerisation are esterification, amidation, nucleophilic aromatic substitution and urethane (carbamate) formation. Polymerisation

54

Jacques Devaux and Sophie Demoustier-Champagne

usually proceeds by the reactions between two different functional groups, for instance, hydroxyl and carboxyl (to get esters), amino and carboxyl (to get amides), hydroxyl and halogen (to get ethers) or isocyanate and hydroxyl groups (to get carbamates or urethanes). The type of reactions involved also leads to use (sometimes improperly) of the terms polycondensation and polycondensates for step polymerisation and polymers made by them, despite there not always being a condensable small molecule among the by-products.

4.8.2 Monomers — ‘‘repeat’’ vs. ‘‘structural’’ units Step polymerizations of linear chains can involve either two different bifunctional monomers in which each monomer possesses only one type of functional group (commonly represented by X–X or Y–Y), or a single monomer containing both types of functional groups (common representation X–Y). However, whatever the monomer type, a linear polymer molecule contains, on average, one functional group of each species per chain (molecule). In order to unify most calculations in step polymerisation a notation, which will be used throughout this section, was introduced by Odian [10], the first step of which is the clear distinction between two definitions. A repeat unit is the sequence of atoms that is repeated to build a polymer chain. This definition, although very simple, distinguishes between X–Y and X–XY–Y units. For instance, the repeat units of polyamide 6 and polyamide 6610 are: O N

C C C C C C H2 H2 H2 H2 H2

H

POLYAMIDE 6 (repeat unit) n

structural unit N H

C C C C C C N H2 H2 H2 H2 H2 H2 H

structural unit

O

O

C

C C C C C H2 H2 H2 H2

POLYAMIDE 66 (repeat unit) n

structural unit

A structural unit or monomer can be defined as the residue from each monomer molecule, whatever its chemical species. In the case of X–Y monomers, a structural unit is identical to a repeat unit (e.g., in polyamide 6), while in the case of X–X, Y–Y monomers, there are two structural units per repeat unit (e.g., in polyamide 66). In the latter case, the mass of a structural unit is obtained by averaging the masses of the two different chemical species. For polyamide 6 and polyamide 66 the masses of structural units are thus 113 in both cases. 10

Polyamides are conventionally named from their number of carbon atoms in structural units with one figure only for X–Y type and two figures (first one for the amine residue, second one for the acid residue) for X–YX–Y type.

Polymer Chemistry and Microstructure

55

A last definition is needed for N (N0 at time 0), which is the total number of molecules present in the system at any time. With the above definitions, N0 initial molecules correspond to N0 monomers and N0 structural units whatever be the chemical species. Each molecule contains on the average one functional group of each kind. Calculations are thus easier and will preferably be performed using structural units.

4.8.3 Carothers equation Assuming p is the conversion ratio equal to the ratio between the actual number of one type of functional group to its initial number N0  N p¼ N0 As there is one functional group of each type per chain, one can write for Xn (number average chain length or degree of polymerisation) Xn ¼

N0 N

Xn ¼

N0 1 ¼ N 0 ð1  pÞ 1  p

or

p¼1

1 Xn

The last equation commonly named the Carothers equation is of general use in step polymerisation. From this equation it can first be deduced that the successful synthesis of high polymers by step polymerisation (i.e., polymers exhibiting molecular mass sufficiently high to be useful for technological application) requires very high conversion levels. A common characteristic to all the chemical reactions involved in step polymerisation that should be emphasised is that they are most often equilibrated reactions. For instance, the polyesterification reaction is based on the esterification/hydrolysis equilibrium K COOH

+

OH

COO

+

H2O

4.8.4 Control of molecular mass The molecular mass in step polymerisation can be controlled by  Controlling the duration of the reaction (kinetic control).  Controlling the water concentration (thermodynamic equilibrium control).  Controlling the stoichiometry by adding either difunctional monomers or a monofunctional reactant.  Performing what is known as post-condensation. Most step polymerisations are exothermic and, consequently, the equilibrium constant K decreases with increasing temperature. Hence, one way to increase the molecular mass would be to decrease the polymerisation temperature, but kinetics prohibits using a too low temperature as it will lead to an excessively long residence time in the reactor and/or too high viscosities. Thus, in order to reach very high molecular

56

Jacques Devaux and Sophie Demoustier-Champagne

masses, a second step of reaction is sometimes performed under high vacuum for long periods of time in the solid state at a temperature where K is more favourable (post-condensation). Such a process finds industrial use for bottlegrade PET. It can be demonstrated that in step polymerisation, the polydispersity index H ¼ Mw/Mn ¼ 1+p. Consequently, the equilibrium polydispersity of step-grown polymers is often close to 2.

4.8.5 Livingness of the step polymers A consequence of the nature of step reactions is that macromolecules exhibit a ‘‘living’’ character, as their functional end groups are always able to react. As most of the reactions involved in step polymerisation are equilibrated, interchange reactions can occur. Interchange mechanisms can involve reactions between the terminal functional group of one polymer molecule with the internal repeating linkage of another macromolecule. Alcoholysis, acidolysis and aminolysis are other examples of reactions involved in the process. Interchange is also said to occur between internal links of two different macromolecules (through ester or amide interchange for instance). Most interchange reactions involve breaking and building of links of exactly the same nature. These reactions are thus most often athermal being only entropy driven. An example of such interchange equilibrium can be given for a polyester: O CHAIN#1

CHAIN#1

C O

+ CHAIN#2

O

CHAIN#2

C O O

CHAIN#1

CHAIN#2

C O

+ CHAIN#2

O

CHAIN#1

C O

The consequence of such interchanges are important and numerous  Polymerisation — depolymerisation (hydrolysis for instance) equilibrium.  Equilibrium molecular mass distribution in step polymers.  Decrease of molecular masses upon end capping, due to re-equilibration.

Polymer Chemistry and Microstructure

57

 Randomisation in miscible polymer blends (formation of random copolymers).  Instability of block copolymers due to randomisation.  Equilibrium formation-opening of cyclic oligomers.

4.8.6 Functionality — gelation — crosslinked macromolecules — networks The previous sub-sections of Section 4 were devoted to linear polymers made from monomers which were assumed to be bifunctional, or able to link to two other ones (Section 2.4). Vinyl (or similar) monomers used in chain polymerisation are bifunctional when they contain one vinyl (or similar) group per molecule. Monomers used in step polymerisation were so far assumed to contain two functional groups, being thus bifunctional. Crosslinked macromolecules can be formed from bifunctional monomers by first polymerising them, then by performing coupling reactions onto existing chains. The latter mechanism is often called vulcanisation.11 Several chemical routes can be followed to accomplish vulcanisation, depending on the functions available on polymer chains. In the section following monomers with more than two functional groups (fZ2) and polymers made thereof, defined as thermosets, will be discussed from a chemical viewpoint.

4.8.7 Crosslinking in chain polymerisation – polydienes Structures of monomers able to crosslink by chain mechanism can be rather different, but the majority of them are of the diene type, with two equivalent vinyl groups per monomer.12 A crosslinked system, including units of the diene type, can be considered as formed by linear chains (the initial chains) linked by randomly distributed bridging links. The bridging density r is defined as: n r¼ N0 where N0 is the total number of structural units and n the number of structural units belonging to a bridging link. It can be calculated [16] that the critical bridging density rc, at which a 3D network will appear is given by 1 1  rc ¼  yw yw  1 where yw is the mass average degree of polymerisation of initial chains.

11

Historically, the first crosslinking of macromolecules (natural rubber) was performed with sulfur thus given the name of Vulcanus, Roman god of volcanoes from where sulfur was extracted.

12

Conjugation phenomena, which can modify the reactivity of the second vinyl group, will not be considered here.

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Jacques Devaux and Sophie Demoustier-Champagne

A bridging index can be defined as: X ny ry  P d¼ ¼ ryn ny where ny is the number of initial chains of degree of polymerisation y and yn the number average degree of polymerisation of initial chains. The critical bridging index is y 1 d c ¼ rc y n ¼ n ¼ yw H The critical bridging index is thus the reciprocal of the heterogeneity factor H of the initial chains.

4.8.8 Crosslinking in step polymerisation-modified Carothers equation At the critical conversion value, the conversion p, the functionality f and the degree of polymerisation are linked. The simplest calculation model is due to Carothers. It is based on the hypothesis that the degree of polymerisation reaches infinity at the critical conversion, meaning that all the system is made of only one macromolecule. If N0 and N are the numbers of molecules at the beginning and during the reaction, fN0 is the total number of functional groups. Providing there is no intramolecular ring formation, the amount of functional groups disappearing during the reaction is 2(N0N). Therefore, p¼ which transforms as: p¼

2ð N 0  N Þ N0 f

    2 N 2 1 1 1 ¼ f N0 f Xn

The latter equation is a modification of the Carothers equation and can be used to approximate the critical conversion value at the gelation. Indeed, when Xn goes to infinity the above equation leads to 2 p¼ f This critical value is, however, only an approximation leading often to an overestimation of the critical conversion value. The main reason to this failure is that gelation actually occurs, at least for some molecules, at a finite degree of polymerisation. Equations based on a statistical approach can provide better results in the estimation of gel point.

5. POLYMER DEGRADATION Similarly to polymer synthesis, there are essentially two main mechanisms of degradation of synthetic polymers involving main chain links and leading to

59

Polymer Chemistry and Microstructure

decrease of molecular mass: chain depolymerisation or unzipping and random (or statistical) degradation. Comparable distinctions can be made between the two mechanisms of chain and step polymerisations and degradations (see Table 8). Representative examples of such degradation mechanisms can be respectively found in radical depolymerisation of poly(methyl methacrylate) (PMMA), Figure 34, and in random thermolysis of poly(butylene terephthalate) (PBT), Figure 35. In random degradation molecular mass decreases early, while in chain degradation the molecular mass of the polymer remains almost constant. Characterisation methods for molecular mass are thus very sensitive methods to follow random degradation. In contrast, as monomer is produced in chain depolymerisation, weight loss measurement techniques are the best methods to follow this kind of degradation. (Chapters 10–12, in Section IV, of this book focus on the methods used in the molecular characterisation and analysis of polymer degradation and polymer degradation mechanisms.)

Table 8 Comparison between chain degardation (depolymerisation — unzipping) and step degradation (random degradation) Chain degradation

Step degradation

Needs initiation Monomer concentration increases steadily throughout the reaction High molecular masses remain all the along reaction The longer the reaction time, the higher the yield in monomer Reaction mixture contains:  monomer  high polymer  E104 part of active species

Any bond can break at any time Almost no monomer produced except at the end of the reaction Molecular mass decreases rapidly

Depolymerisation (‘‘unzipping’’)

Random degradation

The longer the reaction time, the lower the molecular mass Distribution of all species can be calculated all along the reaction

CH3

CH3

CH3

CH3

CH3

O

O

O

O

O

C

O

C

C C C C H2 H2 CH3 CH3

C

O C H2

C CH3

O

C

O

C

C C C C H2 H2 CH3 CH3

CH3 C

O + H2 C

O

C CH3

Figure 34 Example of propagation step in chain depolymerisation mechanism (unzipping) of polymethylmethacrylate (PMMA).

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Jacques Devaux and Sophie Demoustier-Champagne

O

O C

C O



H

H2 CH C

O C H2

O

C

C

C O H2

C

H C

+ OH

O O

O C

O

O

H2 C

H2 C

O C C O H2

C

O O

Figure 35 Example of random degradation mechanism: thermolysis mechanism of poly(butylene terephthalate) (PBT).

It has also to be emphasised that polymers synthesized by chain polymerisation can undergo random degradation (as polypropylene for instance), while certain polymers synthesized by step polymerisation can depolymerise (e.g., polyamide 6). In the case of random degradation, the molecular mass drop due to chemical reaction with a contaminant (e.g., H2O, alcohol, acid, for a polyester) can easily be calculated. Consider the example of hydrolysis of a step polymer. There are two end groups on a linear polymer chain. Thus, their molar fraction is 2 X n0 where the subscript (0) indicates the beginning of the reaction. The molar fraction of new end groups due to hydrolysis is just the difference between the molar fractions before and after hydrolysis. As there are two end groups created by each water molecule, the molar fraction of new end groups is also twice the molar fraction of water. This can be written as: 2 2 2nH2 O  ¼ N0 X n X n0 where nH2 O is the number of water moles and N0 the total number of structural units (moles) in the polymer. Multiplying both denominators by M0, which is the (mean) molecular mass of a structural unit, and dividing each member by 2 gives 1 1 nH2 O  ¼ M n M n0 N 0 M 0 The denominator on the right side is the total mass of the polymer. Thus, multiplying the numerator and the denominator of the right-hand term by the molecular mass of water (18) leads to ½H2 Ow=w 1 1  ¼ 18 M n M n0 where ½H2 Ow=w holds for weight concentration of water.

Table 9 Summary of structure — property relationships of polymers Molecular structure

Double-bond (vinyl) monomers or bifunctional monomers





Plurifunctional monomers or bifunctional monomers+ crosslinking

Network ¼ giant macromolecule



Linear chains Branched or grafted chains

Homopolymers  Copolymers

Glass transition

Order-crystallinity

WRoom temperature

Solubility

Effect of T1

Good

WoroRoom temperature

Disordered (amorphous) Amorphous thermoplastic (Partly) ordered ¼ (partly) Semi-crystalline crystalline thermoplastic

Softening to (viscous) liquid Softening+ melting

WRoom temperature

Usually disordered (amorphous)

Thermoset (crosslinked)

Insoluble (swells)

Non-meltable

Elastomer

Swellable but insoluble

Non-meltable

oRoom temperature

Type of material

Difficult

Notes: Within amorphous thermoplastics some are, due to asymmetry, non crystallisable while others are usually amorphous because they are too slow to crystallise during normal processing.

Polymer Chemistry and Microstructure

Monomers

61

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Jacques Devaux and Sophie Demoustier-Champagne

This expression is particularly simple and useful for predicting the molecular weight after hydrolysis. It can be easily extrapolated for random degradations by reaction with any little molecule (‘‘contaminant’’) other than water.

6. SUMMARY As a summary to this chapter focusing on polymer chemistry and microstructure, major characteristics of polymers are reported in Table 9, classified under  The type of monomers  The (chemical) microstructure of the macromolecule  The physico-chemical microstructural features leading to common classification J Glass transition J Order (crystallinity)  Basic properties J Solubility J Thermal behaviour. As stated in the beginning of this chapter, few properties, depend directly and only on the chemistry. Table 9 summarises how chemistry influences (micro-) structure, which, in turn, governs properties. In this chapter, the ways synthesis’ processes influence the (chemical) microstructure were discussed. Processing methods, by providing the material its (physical) microstructure, also influence its properties. It is therefore the role of characterisation to gain insight into and control all the stages from chemical synthesis to the building of microstructure as well as the final polymer properties. The composition, uses and applications of commercial polymers are discussed in the next chapter (Chapter 3).

REFERENCES 1 2 3 4 5

6

7 8 9 10 11

J.P. Mercier, G. Zambelli and W. Kurz, Introduction to Materials Science, Elsevier, Paris, 2002. A.J. Kovacs, J. Polym. Sci., 30 (1958) 131. F.W. Billmeyer, Textbook of Polymer Science, Wiley, New York, 1962. M.B. Roller and J.D. Gillham, J. Coat. Technol., 50(636) (1978) 57. J. Carlier, R.L. Devaux and P.T. McGrail, Percentage of Rigid Chain Length, a new concept for predicting glass transition temperatures and melting points of poly(aryl ether ketones) and poly(aryl ether sulphones), Macromolecules, 25 (1992) 6646. V. Carlier, J. Devaux, R. Legras and D.J. Blundell, Extrapolation of short chain oligomers melting temperatures at infinite molecular weight, J. Poly. Sci., Part B: Poly. Phys., 36 (1998) 2563–2571. N. Grassie and G. Scott, Polymer Degradation and Stability, Cambridge University press, New York, 1985. B. Jambe, Ph.D. Thesis: Thermal Behavior of Poly(methyl n-alkyl silane)s (Prom. J. Devaux) Louvain-laNeuve (1997). P.J. Flory, Principles of Polymer Chemistry, Cornell, New York, 1953. G. Odian, Principles of Polymerization, Wiley, New York, 1981. J.R. Fried, Polymer Science and Technology, Prentice Hall PTR, USA, 1995.

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63

K. Matyjaszewski, Prog. Polym. Sci., 30 (2005) 858. K. Matyjaszewski and P. Sigwalt, Polym. Int., 35 (1994) 1. G. L’Abbe and G. Smets, J. Polym. Sci., A-1, (5) (1967) 1359. J.P. Mercier and E. Mare´chal, Chimie des polyme`res in ‘‘Traite´ des mate´riaux vol 13’’, Presses polytechniques Universitaires Romandes, 1993, pp. 107–108. 16 J.P. Mercier and E. Mare´chal, Chimie des polyme`res in ‘‘Traite´ des mate´riaux vol 13’’, Presses polytechniques Universitaires Romandes, 1993, pp. 137–142.

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CHAPT ER

3 Polymeric Materials: Composition, Uses and Applications J.P. Candlin

Contents

1. Introduction 2. Mode of Polymerisation 2.1 Oligomers, macromers and telechelic macromers 3. Polymer materials: Types and forms 3.1 Thermoplastics and thermosets 3.2 Amorphous and crystalline polymers 3.3 Elastomers (rubbers) and thermoplastic elastomers 3.4 Fibres 3.5 Flat films and sheets 3.6 Surface coatings and paints 3.7 Advanced materials 3.8 High performance polymers 4. Polymer Additives 4.1 Polymer-processing modifiers 4.2 Chemical property modifiers 4.3 Mechanical property modifiers 5. Summary Bibliography

65 66 68 68 68 70 74 77 79 81 84 84 87 88 98 112 117 118

1. INTRODUCTION Polymers play an integral role in modern society. Over 150 million tonnes are made annually. The scale of production varies enormously from a 200,000 tonnes per annum continuous operational plant for commodity polymers to a batch process producing a few kilograms of a specialised polymer (advanced material).

Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00403-0

r 2008 Elsevier B.V. All rights reserved.

65

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J.P. Candlin

Commodity polymers include: low density PE (LDPE) Polyethylene (PE)

linear low density PE (LLDPE) high density PE (HDPE)

Polypropylene (PP) Polystyrene (PS) Poly (vinyl chloride) (PVC)

Although some applications use these commodity polymers as structural components, their principal use is in packaging, e.g., films, bottles and containers. They are each made on a scale of over 10 million tonnes annually. Engineering polymers are often used as a replacement for wood and metals. Examples include polyamides (PA), often called nylons, polyesters (saturated and unsaturated), aromatic polycarbonates (PCs), polyoxymethylenes (POMs), polyacrylates, polyphenylene oxide (PPO), styrene copolymers, e.g., styrene/ acrylonitrile (SAN) and acrylonitrile/butadiene/styrene (ABS). Many of these polymers are produced as copolymers or used as blends and are each manufactured worldwide on the 1 million tonne scale. Advanced materials can be used in extreme conditions, e.g., high temperatures (W2001C), severe chemical environments (e.g., polytetrafluoroethylene (PTFE) with concentrated H2SO4). They are often used as a critical component in a workpiece and are frequently reinforced with glass, carbon or aramid (e.g., Kevlars) fibres. Organic polymers are sometimes referred to as plastics (although, this should be confined to thermoplastic polymers), macromolecules or resins, though the latter is often used to describe raw polymeric material awaiting fabrication. Many polymers are used in various forms that are not associated with normal plastic materials. These include paints and coatings, elastomers (rubbers), adhesives, sealants (caulks), surfactants and also their use in various industrial applications, e.g., ion-exchange resins, membranes.

2. MODE OF POLYMERISATION Polymers are formed via two general mechanisms, namely chain or step polymerisation, originally called addition and condensation, respectively, although some polymerisations can yield polymers by both routes (see Chapter 2). For example, ring opening of cyclic compounds (e.g., cyclic lactides and lactams, cyclic siloxanes) yield polymers either with added catalyst (chain) or by hydrolysis followed by condensation (step). Many polymers are made via vinyl polymerisation, e.g., PE, PP, PVC, poly(methyl methacrylate) (PMMA). It could be argued that the ethylenic double bond is a strained cyclic system. Another aspect is that the two reactants should yield a condensation product with the elimination of a small molecule, e.g., H2O. This is not essential. Thus in

Polymeric Materials: Composition, Uses and Applications

67

the formation of polyurethanes, the key step is the reaction: RNCO þ HOR0 ! RNHCOOR0 The general mechanism for chain polymerisation is (where M = monomer):

M

catalyst

M

M*

activated

rapid

M2*

nM

Mn*

termination rapid M n

whereas, for step polymerisation, the mechanism is: M þ M ! M2 M2 þ M ! M3 M2 þ M2 ! M4 ; etc: In general, Mn þ Mm ! MðnþmÞ The differences between chain growth and step growth polymerisations are shown in Table 1.

Table 1

Chain growth vs. step growth polymerisations

Chain mechanism

Catalyst or initiator required

Step mechanism

Polymerisation can proceed without catalyst Viscosity increases steadily throughout Viscosity increases rapidly at end of reaction polymerisation Monomer concentration decreases Monomer concentration decreases slowly during reaction rapidly before any high polymer formed Intermediates not usually isolatable Oligomers can be isolated at any stage (low concentrations of growing chains) MW independent of time MW increases with time MW generally decreases with MW independent of temperature increasing temperature (because termination reactions are enhanced) Rate of polymerisation is zero initially, Rate of polymerisation is a maximum at rises to a maximum as active centres the start and decreases continuously are formed from the initiator, and as the concentration of the functional then remains constant, before falling groups decreases off when the monomer is consumed Note: MW, molecular weight.

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J.P. Candlin

2.1 Oligomers, macromers and telechelic macromers If the polymerisation is halted deliberately by adding a terminating or chain transfer agent, e.g., a monofunctional agent, or accidentally, e.g., adventitious introduction of poisons (e.g., air, water, solvents), then a polymer with a low molecular weight (MW) may result with a degree of polymerisation (DPn) of perhaps n = 4–20. These materials are called oligomers. With chain polymerisation this is carried out at the start of polymerisation and the chain transfer agent statistically terminates the polymerisation. The MW of the polymer depends on the ratio of chain transfer agent to monomer, for example, the MW of PE and PP prepared by the catalytic polymerisation of ethylene or propylene, respectively, can be controlled by the continuous addition of hydrogen to the feed. With step polymerisation, the progress of polymerisation is measured by viscosity. It can also be estimated from the amount of condensate removed. It can be arranged that these oligomers contain a reactive end group, e.g., hydroxyl, carboxyl, allowing subsequently further polymerisation with a different reactant monomer to take place. These reactive oligomers are called macromers. Finally, some polymerisations can be directed such that the final oligomer or polymer contains two or more reactive end groups capable of extended polymerisation with different monomers. These materials are named telechelic macromers or telechelic polymers.

3. POLYMER MATERIALS: TYPES AND FORMS 3.1 Thermoplastics and thermosets The terms thermoplastic and thermoset refer to the processability of a particular polymer and the properties of the finished article. Thermoplastic polymers are mostly a linear or branched linkage of monomers containing many thousands of repeat units. All the commodity polymers and most of the engineering polymers are thermoplastic. Thermoplastic polymers can be homopolymers or copolymers where two or more different monomers are used. With copolymers, different arrangements of the monomers are possible (see also Chapter 2). Random copolymer Alternating (or regular) copolymer Block copolymer

Graft copolymer

Arbitrary arrangement of monomers in the polymer chain Reciprocal array of repeat units (this occurs when two or more monomers react together to form a complex, which is then polymerised) Contains long sequences of one linkage joined onto another sequence with a different linkage. Di- and tri-blocks are possible Obtained by chemically reacting a second monomer/ polymer chain onto a pre-formed polymer

Polymeric Materials: Composition, Uses and Applications

69

The chemical nature of the repeat units determines the physical and mechanical properties of the polymer. Thermoplastics soften when heated and form a viscous melt; on cooling they solidify and become stiff. This process can be repeated. In the molten condition they can be shaped by injection moulding or extruded into tubes, films or fibres. The viscosity of the molten polymer varies with chemical linkage and MW of the polymer. The higher the MW, the higher the viscosity at a given temperature. As a general rule, the acceptable melt viscosity for extrusion, etc., is 1501C above Tg and 501C above Tm, where Tg and Tm are the glass transition and crystalline melt temperatures, respectively. Inter-chain attraction between the polymer chains determines the DPn necessary to give the polymer the required toughness, strength, etc. For polymers containing heteroatoms, e.g., polyesters, polyamides, DPn of 100–200 is adequate, whereas for polymers with little or no inter-chain attraction, e.g., PE and PP, then DPnW1,000 is recommended. Thermoset polymers (sometimes called network polymers) can be formed from either monomers or low MW macromers that have a functionality of three or more (only one of the reagents requires this), or a pre-formed polymer by extensive crosslinking (also called curing or vulcanisation; this latter term is only applied when sulfur is the vulcanising or crosslinking agent.) The crosslinks involve the formation of chemical bonds — covalent (e.g., carbon–carbon bonds) or ionic bonds. The act of crosslinking can either be an addition reaction (e.g., radical/radical) or a condensation reaction (e.g., alcohol/carboxyl). In the latter, the formation of volatile condensates is often not desirable because they may weaken the structure. Crosslinking reactions involve creating radicals along the polymer chain, which can couple to form a crosslink. A problem is that chain scission may occur. These radicals can be generated from added peroxide or, with more control, by high-energy radiation, e.g., X-rays (synchrotron), electron beams or g-rays (Co-60). For example, crosslinked PE is much tougher, more environmental stress cracking resistant and is often used for wire coating. When cold stretched and then heated it returns to its original shape, hence its use for shrink-wrap films or tubes. Depending on the strength of the crosslink, under most conditions, thermoset polymers do not melt, although with weak crosslinks, e.g., ionic, dipole-dipole, H-bonding, they are capable of being moulded. The normal procedure for the fabrication of thermosets is to add the reagents to a mould and leave to complete polymerisation. An alternative method is to stop the reaction before completion. Then, depending on the extent of polymerisation, the material can be injection or compression moulded, or, if the product at this stage is solid, it can be ground into a powder and compressed (moulding powders). The finished article is then cured by raising the temperature. As the reactants are often liquid, solvents are not used because they may get entrapped within the growing polymer matrix giving a poor surface finish. Conversely, the addition of volatile solvents at this stage is used to generate rigid foams. Polymer linkages that do not release condensates on being formed include polyurethanes (diisocyanate/polyalcohol) and epoxy (ring opening of the epoxy

70

Table 2

J.P. Candlin

Comparison of thermoplastic and thermoset polymers

Thermoplastic

Thermoset

Long-chain molecules, often without branching Soluble in some solvents

Cross-linked 3D structures

Crystalline and/or amorphous Variable MW; determined by solution techniques Can be flexible, soft or brittle Will flow under pressure Can be moulded or fabricated Many highly flammable Sometimes fail catastrophically at high temperatures Can be converted to thermoset by post-treatments

Can be swollen in solvents, but always insoluble Amorphous Very high MW; cannot be determined Rigid, brittle structure Structurally stable Only moulded articles (injection moulding possible with RIM) Many self-extinguishing Have good dimensional stability or fail slowly under load at elevated temperatures Impossible to remove crosslinks

group with polyamines). An advantage of liquid monomers is the ease by which they can be handled. Thus polyurethane articles can be made using reaction injection moulding (RIM). The two reactants are pumped into a mixing chamber then into a mould. Large articles, e.g., car bumpers, garage doors, can be made using this technique. Table 2 contrasts some of the properties of thermoplastic and thermoset polymers.

3.2 Amorphous and crystalline polymers No polymer is 100% crystalline, such as benzoic acid or NaCl, although PTFE can be over 90% crystalline. Conversely, polymers may be 100% amorphous; this occurs when the polymer chains cannot align themselves into a close, organised regular structure. About 50–100 uniform repeat units are necessary for crystallisation to take place. Amorphous regions in the bulk polymer are created when the polymer chain is capable of cis–trans configuration, rotational movement around a single bond or a crankshaft displacement involving several units in the polymer chain. Bulky substituents on the main polymer chain also lead to amorphous regions. Tacticity (see Chapter 2) of the polymer chain (i.e., extent of stereoregularity) also determines the possibility of crystallisation. Stereoregular, isotactic or syndiotactic polymers are often crystalline, whereas the corresponding atactic polymers are amorphous. Thus amorphous atactic PS has a softening temperature of 1001C and atactic PP is a viscous gum at room temperature, whereas syndiotactic PS and isotactic PP have crystalline melting

Polymeric Materials: Composition, Uses and Applications

71

temperatures (Tm) of 2701C and 1601C, respectively. These chain rotations, bulky substituents, etc., require space in which to move. This space is called free volume; it can be estimated by plotting volume (i.e., volume per unit mass) against temperature. Thermoset polymers are not crystalline because the multiple crosslinks do not allow the main chain polymer molecules any movement to form crystals. For all polymers (except those prepared by ‘‘living’’ growth mechanisms, see Chapter 2) because of molecular weight distribution (MWD), amorphous polymers do not have a sharp melting or softening point. Instead they have a broad temperature range of approximately 501C over which, on heating, the polymer changes from a brittle glassy solid to a pliable rubbery material. This change occurs at the glass transition temperature, Tg. The value of Tg depends on the chemical linkage of the polymer chain. Aromatic polymers with stiff, rigid para-linkages have high Tgs, e.g., poly(aryl ether sulfone) (PES) with a Tg of 2251C, whereas aliphatic carbon–carbon linkages, e.g., natural rubber, may have a Tg as low as –731C. In the rubbery, semi-molten state the polymer chains rotate, but on cooling the polymer behaves like a frozen liquid with a completely random structure. The chemical features that prohibit crystallinity are main chain flexibility (e.g., rotation), branching, random copolymers or low inter-polymer chain attraction. Normally, polymers are not miscible with each other and on cooling from the melt will separate into different phases. When miscibility is exhibited, e.g., poly(phenylene oxide) (PPO) and PS, crystallisation does not take place. Some of the properties and differences that amorphous and crystalline polymers exhibit are: (i)

(ii)

(iii)

(iv) (v)

Amorphous copolymers are brittle below Tg; elastomeric above Tg, although amorphous advanced materials with aromatic chains with high Tgs (e.g., PES) are tough at low temperatures. Amorphous polymers display small volume changes (compared with crystalline polymers) on cooling from the polymer melt to a solid, because in the melt the polymer chains are randomly oriented. Thus amorphous and crystalline polymers exhibit about 0.5% and 2.0% shrinkage, respectively. This shrinkage must be allowed for in precision or large articles. It can be compensated for by adding a small amount of foaming agent or filler during fabrication. Films made from amorphous polymers are more permeable to gases than crystalline polymers. More free volume is available for transport of the gases through the film. The amorphous phase is lower in density than the crystalline phase. Amorphous polymers are often transparent. Usually the crystalline phase has a different refractive index than the amorphous phase. This causes scattering and refraction giving the crystalline polymer a milky appearance. Unusually, the refractive index of crystalline isotactic poly(4-methyl pentene-1) is the same as the amorphous phase rendering

72

(vi)

(vii)

J.P. Candlin

the polymer transparent. This makes it particularly suitable for transparent sheets and laboratory ware (replacing glassware). Amorphous polymers will swell or dissolve in solvents. Crystalline polymers are more resistant to solvents; solvation has to overcome the attractive forces that exist within the covalent crystal lattice. If the affinity between the solvent and the polymer chain is low the crystal regions remain intact. Solvents can induce crystallisation. If the solvent is in contact with an amorphous polymer (but potentially crystallisable) diffusion of the solvent into the amorphous regions (plasticisation) lowers the Tg, allowing movement and reorganisation into crystalline lattices; the solvent itself is excluded from the lattice.

Although the chemical structure of the polymer chain may allow crystallisation, this may not be possible for the following reasons: (i)

(ii)

(iii) (iv)

Crystallisation from the polymer melt takes time and may require nucleation. If the cooling is rapid the organisation of the polymer chains into crystals may be too slow, resulting in an amorphous phase. To promote crystallinity the polymer must be re-heated to temperatures between Tg and Tm. This technique is called annealing. Another approach is stretching the polymer to promote crystallisation. This occurs in blow moulding of bottles and the biaxial stretching (drawing) of films. This increases the gas-barrier properties and because the induced crystallites are small (compared to the wavelength of visible light), the polymers are transparent. Amorphous cellulose tri-acetate sheets are used for overhead projector sheets for use in photocopying machines; they do not ‘‘curl up’’ or distort in the heated atmosphere. If poly(ethylene terephthalate) (PET) sheets are used, the biaxial stretching must be equal or it will curl up. Polymeric fibres increase in strength (increased tenacity) on being drawn. This orientation is performed between the Tg and Tm temperatures. (Methods for determining the extent of molecular orientation in polymers are discussed in Chapter 8.) Polymers vary in their rate of crystallisation depending on side chains, etc. Thus with PE crystallisation is almost instantaneous (less than 1 s), whereas nylon 6,6 and PVC (over 1 year to complete crystallisation) are sluggish. PET is slow to crystallise, but poly(butylene terephthalate) (PBT) is more rapid. Thus consideration of final application is critical, such as transparency and dimensional stability. Physical entanglement of the polymer chains restricts the translational movement necessary for alignment and crystallisation. Imperfections in the polymer chain. Insertions for chain polymer growth require ‘‘head-to-tail’’ for the correct stereoregularity (tacticity). A false ‘‘head-to-head’’ inclusion will disrupt the regular pattern. In a similar manner, atactic (non-stereoregular) insertions will produce amorphous polymers.

Polymeric Materials: Composition, Uses and Applications

73

As described above, crystallinity in polymers occurs when the polymer chain is regular and uniform and contains no defects (which can include external degradation, e.g., oxidation), and is critical for fibre applications. This arrangement is aided by inter-chain attraction. If a polymer does crystallise then the role of the amorphous phase becomes less important especially when considering mechanical strength and stiffness and the maximum service temperature. This is because the crystalline regions behave like temperaturesensitive crosslinks. They act like a thermoset when cold, but on heating (above Tm) are mouldable. This arises because emanating from each crystalline region are polymer chains (called tie molecules) that may be incorporated into separate different crystalline regions. The higher the MW of the polymer, the more this occurs and the polymer is much tougher. A significant aspect is the manner in which glass–fibre reinforcement increases the service temperature of semi-crystalline polymers; this is especially important in advanced materials. A value of the maximum service temperature can be obtained from the heat distortion temperature (HDT). This is measured by observing the temperature at which the polymer distorts under controlled stress. Normally with crystalline polymers this is between Tg and Tm of the polymer. With amorphous polymers this is below Tg. This can be seen by plotting modulus vs. temperature. An amorphous polymer has only one thermal transition (Tg), whereas a semi-crystalline polymer has two (Tg and Tm). When reinforced with glass fibres, the HDT of the crystalline polymer is raised to temperatures approaching Tm, whereas with the amorphous polymer the increase in HDT is small and remains below Tg. An illustration is shown in Figure 1 of the increase in HDT at a fixed modulus by the addition of glass fibres to amorphous and semicrystalline polymers. Amorphous

Semi-crystalline neat

glass-filled

glass-filled

modulus

modulus

neat

a fixed modulus

a fixed modulus

HDT neat increase temperature

HDT (glass-filled)

HDT neat

increase

HDT (glass-filled)

temperature

Figure 1 Illustration showing the increase in HDT at a fixed modulus by the addition of glass fibres to amorphous and semi-crystalline polymers.

74

J.P. Candlin

Table 3

Comparison of HDTs for amorphous and semi-crystalline polymers

Amorphous

Semi-crystalline

Heat distortion temperature (1C) Neat

PES

20% glass-fibre reinforced

B215 315 142 250 223 260

203 165 130 100 200 B100

PEEK PC Nylon 6,6 PEI PPS

Notes: PES, poly(aryl ether sulphone); PEEK, poly(aryl ether ether ketone); PC, polycarbonate; PEI, polyetherimide; PPS, poly(phenylene sulphide).

This improvement can be seen from the comparisons in Table 3. Some polymers, especially those with a rod-like, linear aromatic backbone, e.g., X X

X

X

X

X

O where X =

O

,

NH

,

C

O O

or

S

,

O

have a tendency to form crystals even whilst in the molten state or in solution. They are called liquid crystal polymers. They have very high melting points making them difficult to process, although careful introduction of flexible groups (e.g., –CH2–, meta-phenylene) does lower this to some extent. However, in the molten state or in solution with applied shear (e.g., extrusion processes) the polymer chains align together in the direction of flow and the viscosity decreases drastically allowing fabrication. In the solid state they are extremely anisotropic (uni-directional) and when combined with reinforcing fibres, e.g., carbon–carbon fibres, yield some of the highest service temperatures (approaching 4001C) known for polymers. Kevlars (produced from highly oriented poly(paraphenylene terephthalamide) is an example of a liquid crystal polymer.

3.3 Elastomers (rubbers) and thermoplastic elastomers Elastomers are defined as polymers that can be repeatedly stretched to B200% elastic elongation and will return to their original length when released. They can

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be either thermoplastic or thermoset, although with the latter the extent of crosslinking is low, typically 1–5%, i.e., 1–5 crosslinks per 100 backbone chain units. Most metals and ceramics have elastic elongation of less than 2%. Stretching in these materials involves the movement of atoms. In contrast, polymers can be easily elongated because the applied stress promotes linear formation of the polymer backbone. The MW of an elastomer must be high enough to promote chain entanglement thus preventing polymer chains from sliding past each other on applying stress. Because of the linear, organised arrangement of the polymer backbone on stretching, crystallisation may occur. This also helps to increase the strength on stretching (tie molecules). The requirements for an elastomer are: (i) (ii)

(iii) (iv) (v)

High MW to promote chain entanglement. Amorphous, although crystallinity when stretched is often advantageous. This promotes tie molecules and strengthens the elastomer at maximum extensions. The Tm of the crystalline region must be near or below the working temperature such that the crystallites can melt when the stress is removed, e.g., natural rubber, Tg –731C; Tm 251C. Flexible backbone, allowing chain rotation, etc. Low Tg allowing chain movement at ambient temperatures. Thus for room temperature usage this requires a Tg of less than –501C. Low creep value (this is the flow of polymers when stress is applied over long time periods). This is achieved by low level crosslinking (less than 5%).

In some cases the modulus and strength are so low that fillers are often added for stiffness. Carbon black, as a filler, is used extensively in car tyres, and it is thought that the surface bonding with the rubber occurs, thus providing stiffness. Finely divided silica, which has been surface treated with organometallic silicon and titanium compounds, is also used. Covalent crosslinks, once formed, are non-reversible. Once made, they cannot be broken. This limits the processing options to low shear techniques, such as calendaring in which a mangle arrangement with three parallel rollers presses the polymer into sheets, or to adding the crosslinking agent at the last stage. Heat reversible crosslinks, however, allow the elastomer to be treated similarly to a thermoplastic, capable of being extruded or injection moulded at a high temperature whilst behaving like an elastomer at low temperatures. There are various ways of forming covalent crosslinking: (i)

(ii)

Olefinic polymerisation, e.g., ethylene/propylene to which is added a diolefin (diene), where the diene is 1,4-hexadiene or 4-ethylidene norborn-2ene. The resulting polymer is usually called EPDM (ethylene propylene diene monomer). Vulcanisation of unsaturated rubbers, e.g., poly(1,4-butadiene), polyisoprene, random styrene/butadiene rubber (SBR) with sulfur. The sulfur attacks the allylic C–H group to form inter-chain –S–S– linkages.

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(iii)

(iv)

(v)

J.P. Candlin

Peroxide cure of saturated olefinic polymers, e.g., random, non-crystalline ethylene/propylene copolymers (prepared by Ziegler catalysts). The peroxide generates carbon radicals, which couple together forming inter-chain covalent bonds. Dimethyl silicone polymers have no strength. Reaction with peroxide gives random radicals, which link together and stops the silicone chains from sliding past each other on being stretched. Neoprenes is a polymer formed from chloroprene (2-chlorobutadiene). On heating with zinc oxide the neoprene polymer rearranges to give a pendant labile allylic chloride group (–CH = CH–CH2Cl). Further reaction with zinc oxide yields zinc chloride and a stable ether link between the two polymer chains. The copolymer of vinylidene difluoride and per-fluoropropylene (Vitons) on heating releases HF and gives an unsaturated fluoropolymer. Reaction with a diamine introduces crosslinks. This fluoroelastomer has a very high service temperature of over 2001C.

The linkage between two chains can also be ionic. Thus the copolymer between ethylene and methacrylic acid (MA) (up to 15% MA), made by free radical polymerisation, yields a polymer with pendant carboxyl groups. Neutralisation with zinc ions gives a crosslinked, thermo-reversible polymer (Surlyns). The resulting polymer (ionomer) has limited properties, although it is the favoured material for the outer covering of golf balls. Crosslinks prevent the flexible polymer chains from sliding past each other; crystallinity could play a similar role as long as the percentage of crystallinity is small. (Polyethylene has the potential to be an elastomer, but its crystallinity is too high — greater than 60% and therefore behaves like a thermoplastic). A big advantage, however, would be that the elastomer would be thermo-processible. Another approach would be to design a copolymer prepared by block polymerisation, which has one segment that can form crystals. If that is not achievable, one could have an amorphous segment with a high Tg (higher than the service temperature) to form a glassy domain. The other segment would consist of a flexible chain with a low Tg. These segments are often referred to as hard and soft segments, respectively. Following that approach, many thermoplastic elastomers (TPEs) have been synthesised using this principle, e.g., see Table 4. Careful control of the chain length of each block has to be made. An interesting observation arose with the thermoplastic elastomer styrene/ butadiene (S/B) tri-block copolymer (Kratons). These are made by anionic Table 4

Some thermoplastic elastomers

Hard segment

Soft segment

Poly(butylene terephthalate) Aromatic urethane Aromatic polyimides Aromatic polyesters or carbonates

Poly-1,4-butane diol (Hytrels) Poly-1,4-butane diol (spandex) Perfluoropropylene oxide Polydimethylsiloxanes

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polymerisation (living polymerisation). Thus either polystyrene/polybutadiene/ polystyrene (SBS) or polybutadiene/polystyrene/polybutadiene (BSB) tri-blocks can be made. The former has much better elastomeric properties than the latter. This is because the polystyrene end segments have the freedom to move and form a glassy domain (PS Tg, 1001C) together with tie molecules, whereas with polystyrene end-capped with polybutadiene the polystyrene segment is restricted in its movement. The polybutadiene segments have a low Tg of –1001C and therefore will not form a glassy rigid structure at ambient temperatures necessary for added strength on stretching. Polymers with blocks containing different tactcities can be produced, e.g., atactic PP (amorphous)/isotactic PP (semi-crystalline) can be made using metallocene catalysts. They behave in a manner similar to SBS thermoplastic elastomers.

3.4 Fibres Synthetic fibres are thermoplastic materials and are fabricated by either melt processing or from a solution of the polymer in a solvent. Both processes use a spinneret. The main structural requirement is that the polymer must have a linear backbone (with little branching). On drawing or stretching the polymer chains align promoting crystallinity giving the fibre added strength. In principle, there are many polymers suitable for fibres, but for apparel (clothes) and domestic (carpets) use only four types dominate: polyester, polyamide, polyacrylonitrile (often as a copolymer with vinyl chloride) and polypropylene. For melt spinning, it is necessary that the melting temperature of the polymer is not too high as to cause decomposition, and that the melt viscosity is low since it passes through the spinneret holes (diameter approximately 120 mm). Each spinneret plate contains hundreds of these holes. Conversely, the Tg of the fibre must be low enough to permit ironing, but the Tm must be sufficiently high to prevent melting during ironing. For melt fabrication the temperature of the melt is approximately 501C higher than Tm (although with polypropylene this is 1001C higher). Melt spinning is used to make polyester, polyamides (nylon 6 and 6,6) and polyolefin fibres. Wet or solution spinning is used for natural fibres (cellulose derivatives) and some synthetic fibres. This can be achieved by passing a concentrated solution of the dissolved polymer through the spinneret into a coagulating bath, e.g. polyacrylonitrile/dimethyl formamide (DMF) and cellulose/N-methyl morpholine N-oxide (NMMO) (Tencels) into water. With wet spinning, the solvent is evaporated by heat, e.g., aramid/concentrated H2SO4 into water and polyurethane elastomeric fibres/DMF followed by coagulation with water. The main structural/property requirements for fibre formation are: (i)

The polymer chain must be uniform with no defects in chemical composition or stereochemical arrangement. This condition is stricter than for other applications.

78

(ii) (iii) (iv)

(v)

(vi)

J.P. Candlin

Sufficient molecular weight to exhibit chain entanglement, promoting fibre strength during drawing. Linearity of backbone, with little or no branching. The inter-molecular forces between the polymer chains enhance structural cohesion giving the polymer strength during spinning and drawing. This is achieved by incorporating heteroatoms (e.g., N, O) in the polymer backbone thus encouraging H-bonding, dipole–dipole or aromatic– aromatic p-electron attraction. Crystallisation during the drawing process caused by aligning the polymer chains. These small crystallites encompass polymer tie molecules giving the fibre added strength. With amorphous copolymer fibres, e.g., acrylonitrile/vinyl chloride (acrylic fibres), crystallisation does not occur, but the act of drawing optimises the strong dipole–dipole forces and increases the strength of the fibre. Orientation of the crystallites parallel to the fibre axis gives the fibre added strength (tenacity), and because of the rapid rate of drawing, the size of the crystallites is small when compared to the diameter of the fibre.

In principle stretching or drawing of fibres should be undertaken between Tg and Tm, thus minimising brittle fracture. Thus polyester (e.g., PET) and polyacrylonitrile (PAN) fibres are heated during drawing. With wet spinning, the presence of the solvent acts as a plasticising agent and thus decreases Tg, e.g., nylon drawn in an atmosphere of high water humidity. The extent of draw (draw ratio) affects the tenacity of the fibre. Thus for fibres for apparel, i.e., soft, flexible fibres, a low draw is used (100% elongation), whereas for fibres with a high strength, e.g., ropes, tyres, requires a high draw (400%). Originally, this led to irreversibility in finished garment, e.g., kneed stockings. This has been overcome by the steam treatment of the drawn fibre (PET) before weaving. Many other properties have to be considered, especially for apparel fibres, e.g., moisture absorption, ability to dye, drape, texture, weaving characteristics, etc. Many of the properties are influenced by the cross-section profile of the fibre. Thus cotton and some rayons (an artificial synthetic fibre derived from cellulose) are a hollow round fibre; silk has a triangular shape giving it a fine lustre and drape. Using co-extrusion it is possible to make fibres with a nylon 6,6 inner core (Tm 2641C) and a nylon 6 outer shell (Tm 2151C). By applying pressure and heat between these two temperatures to bundles of these two fibres, a non-woven mat can be made. The elastomeric fibre, elastane or spandex (the anagram of ‘‘expands’’) is a hard/soft segmented block copolymer. The soft segment (with a low Tg) can be a polyglycol (e.g., polyethylene glycol or polybutylene glycol) or an aliphatic polyester glycol and has a DPn of approximately 25. This constitutes up to 80% of the polymer weight. The hard segment is a polyurethane or polymer prepared from aromatic di-isocyanates. Strong inter-molecular forces (e.g., H-bonding, crystallinity) and phase separation of the two segments renders the copolymer elastomeric, which allows 600% extensions with full recovery (similar to natural

Polymeric Materials: Composition, Uses and Applications

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rubber, but without the inherent oxidative instability and attack by ozone). The polymer can be processed into fibres by either melt spinning or from solution (using DMF as the solvent). The latter method is used when polyurea is the hard segment, since they decompose on melting. The main application of spandex (e.g., Lycras) is for stretched apparel clothing. It is used to make yarns when combined with other natural and synthetic fibres. Although the main usage of fibres is for apparel, many applications are unique to synthetic fibres. Examples include (i)

(ii)

(iii)

(iv)

High modulus polyethylene fibres are made by dissolving ultra high MW polyethylene (W106) in decalin or paraffin oil (2% solution) at 120–1701C and drawing through a hexane bath. Extended chain polyethylene fibres (e.g., Dyneenas) are used as ballistic-resistant yarns, and have strengths comparable to aramid fibres, but they do not possess high temperature resistance. Melt-spun HDPE (fluff-like, similar to candy floss, made by flash-spinning technology) is loaded onto a moving bed to give a random mat that is consolidated by heat and pressure (Tyveks). These mats allow moisture but not liquid water to pass through. Their main application is in construction, but it also has many other uses, e.g., envelopes, protective clothing. Biodegradable polyester copolymers of lactic/glycolic acids are used as sutures in medical operations. They degrade and dissolve harmlessly in the body. Hollow amorphous aromatic polysulfone fibres, presenting a high surface area, are used as membranes for separating liquids and gases.

3.5 Flat films and sheets Films and sheets are defined as planar flat materials that are self-supporting and flexible. Generally films have a thickness of less than 250 mm, above this thickness they are referred to as sheets. They may consist of one or more layers, usually of different compositions. Films or sheets can be used alone or co-extruded with paper, foil or fabrics. The main application for films is for flexible packaging material, but because of their versatility they can be modified to fulfil many uses, such as electrical insulators, a base for printing and writing, permeable membranes, and many more. Sheet materials tend to be greater than 1 mm thick and are often used as replacements for glass, wood and metal. Examples include window glazing and outdoor signs. Sheets can be transformed into shapes by vacuum moulding (thermoforming).

3.5.1 Manufacturing of films and sheets The techniques following are used for the manufacture of films and sheets: (i)

Mould casting between planar parallel moulds. The polymer or macromer is injected into the mould as a viscous liquid together with a catalyst.

80

(ii)

(iii)

J.P. Candlin

Another approach is the use of RIM using reactant monomers and a catalyst. The viscosity must be low enough to allow for flow of the reactants. This sometimes precludes polymer melts with high viscosity. Solvents are not used because volatilisation may cause bubbles. Continuous casting. In contrast to mould casting, this can use solutions of polymer. The mixture is fed onto a horizontal moving belt and the solvent is removed by evaporation. This technique has the advantages over extrusion process: a. No heat stabiliser is used, thus the sheet has greater clarity without distortion. b. Uniformity of thickness. c. Very wide sheets (over 2 m) can be processed. This is difficult with extruded sheets because of the intricate design of the clothes-hanger die used to prevent warpage caused by polymer chain orientation. Continuous casting however, using molten polymer, has been used providing the viscosity is low enough. Many polymers have been processed by casting, e.g., acrylics, polystyrene, polyamide (nylon 6), phenolics, PVC/plasticiser. Many of these are used in a pre-polymer form, which polymerise on the casting belt, or the polymerisation can be completed later by application of heat. Extrusion processes. Two techniques are used to make very thin films of less than 10 mm thickness. a. Stenter or tenter process. Extruders continuously force the molten polymer through a clothes-hanger die, which is then cooled. The sheet (approximately 500 mm thick) is re-heated (between the Tg and Tm of the polymer) and drawn by pinch or nip rollers, which stretches the sheet in the forward (machine) direction. Simultaneously, clamps (tenterhooks) stretch the sheet sideways. The finished film is then collected on a cooled rotating drum. The resulting film is between 2 and 5 times the original length and width with a corresponding reduction in thickness. This stretching, similar to the drawing of fibres, which promotes orientation and crystallite formation, is called biaxial orientation. It gives the film added strength and gas-barrier properties. In some processes, monoaxial (uniaxial) drawing is employed, e.g., polypropylene, which is then slit into thin strips and fabricated into heavy duty sacks, carpet backing, etc. The stenter process is used to make biaxial oriented poly(vinylidene dichloride) (‘‘cling’’ film), polyester, polyamide and polypropylene films. b. Blown films. The molten polymer is passed through a tubular die, the centre of which contains an air-inlet. Increasing the pressure of the air forces the tube to expand like a bubble, the top of which is clamped together by rotating nip rollers. Thus a continuous thin film, tubular roll is fabricated. The nip rollers are set to stretch the film in the forward direction, whilst the bubble expands the film in the sideways direction. Thus biaxial stretching is achieved. Bi-layers and multilayer films with different polymers are made by having two or

Polymeric Materials: Composition, Uses and Applications

(iv)

81

more concentric dies. This can be used to optimise properties, e.g., one layer has good gas-barrier properties, and the other layer has good tear strength. Biaxial polypropylene (Tm 1651C) is difficult to heat seal (large shrinkage occurs on melting), but co-extrusion with polyethylene (Tm 1151C) allows the bi-layer to be sealed below the melting temperature of polypropylene. Films of polyolefins, polyamides and poly(vinylidene dichloride) are made using this technique. As most of the films are used for flexible packaging, further down-stream surface treatments are usually applied to improve performance. For example, aqueous polymer emulsions, e.g., poly(vinylidene dichloride), or delaminated clay particles improve the barrier properties as will metallising with aluminium vapour. Corona discharge, causing slight surface oxidation, improves printability. Calendering. This method is used to process heat-sensitive polymers, such as plasticised PVC, and also to blend polymer mixtures or add additives. The polymers are fed and heated on hot rolls and squeezed between two or more parallel nip rollers into the form of a thin film or sheet. The process can be easily modified to incorporate backing material, e.g., metal foil, paper and textiles. Only polymers with a high viscosity can be processed by this method.

3.6 Surface coatings and paints Several million tonnes of polymers are incorporated annually into coatings and paints. Coatings are applied for several reasons apart from being aesthetically pleasing, for example: (i) (ii) (iii) (iv)

They form a protective layer, which inhibits corrosion (with metals) and bacterial attack (with wood). They fill and smooth imperfections. They provide a durable decorative and alternative surface finish, e.g., matt or gloss. They are resistant to household cleaning products such as bleach and solvents.

The first paints were based upon linseed oil (obtained from flax). This is an unsaturated long-chain triglyceride, which, with metal activators, crosslinks via radical pathways to form a continuous film on the substrate. Modern paints use synthetic polymers together with either a solvent or suspending medium (e.g., water), which evaporates leaving the deposited film. Exceptions are powder coatings, which require heat for completion. The main requirements for a coating are that it is easy to apply (i.e., low viscosity) and dries to a non-tacky finish within a reasonable time. Originally, this equated to the solution and evaporation of the solvent. However, because of environmental concerns, formulations have tended to shift the concentration of solvents from 80% to less than 20% (known as high solids coatings). Many industrial processes use polymer powders (of approximately 40 mm diameter),

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J.P. Candlin

which are attracted electrostatically to the substrate before being cured by melting or electron beam treatment.

3.6.1 Polymers, resins and binders used in paints These are the most important components of paint. Coatings can be either clear or opaque (containing pigments) and either solvent- or water-based. With solventbased paints, after application, most of the solvent is lost through evaporation. These solvent-based coatings are mostly alkyds (name derived from alkyl/acid) or modified alkyd resins. Normally they contain 30% polymer solids; higher solids content is limited by the increasing viscosity of the system. Alkyds are crosslinked polyesters made from 3- or 4-functional alcohols, e.g., glycerol or pentaerythritol, and a 2-functional carboxylic acid, e.g., phthalic acids and maleic acid. Also added are long-chain unsaturated oils, e.g., vegetable oils. The oligomerised product is dissolved in mineral oil or toluene. On application to a surface, the solvent evaporates and the remaining mixture undergoes catalytic (cobalt naphthenate catalyst) autooxidative crosslinking to form a continuous coating. Modified alkyds include the addition of silicones, phenol-formaldehyde, urethanes, styrene, epoxies and acrylics, which are grafted onto the alkyd backbone, e.g., urethane and epoxy groups are grafted using excess hydroxyl groups in the alkyd formed by reaction with isocyanate and oxirane (epoxy) groups, respectively. Styrene and acrylics modifications are obtained by radical polymerisation and phenol-formaldehyde by reaction of methylol groups with hydroxyl groups. Urethane alkyds are the most important. If the coating is for both outdoor and indoor use then aliphatic di-isocyanates are used. Aromatic di-isocyanates yellow and may crack when used for outside applications. Latex or emulsion polymers are prepared by emulsification of monomers in water by adding a surfactant. A water-soluble initiator is added, e.g., persulfate or hydrogen peroxide (with a metallic ion as catalyst), that polymerises the monomer yielding polymer particles, which have diameters of about 0.1 mm. The higher the concentration of surfactant added, the smaller the polymer particles. In suspension polymerisation, so-called because of the addition of watersoluble suspending agents, e.g., poly(vinyl acetate) (PVA), starch or surfactant, a monomer-soluble catalyst is added (e.g., organic peroxide) resulting in larger porous particles (approximately 500 mm) that readily absorb plasticisers. This is sometimes called bead or pearl polymerisation because of the smooth spherical shape of the polymer particles. Several different monomers may be used together to yield the desired properties. High molecular weight polymers, giving increased polymer toughness, can be prepared without the attendant increase in viscosity or without the necessity for crosslinking. With smaller polymer particle sizes, more pigment may be added to give greater opacity. However, this requires more surfactant resulting in less durability. A high polymer content (W65%) in the emulsion can be obtained. A small amount (o5%) of high boiling solvent is added, e.g., glycols, glycol ethers or alkyl-aromatic compounds depending on the polymer. These solvents plasticise the polymer and promote coalescence of the polymer particles after evaporation of the aqueous phase.

Polymeric Materials: Composition, Uses and Applications

83

The greatest use of latex paints for indoor applications is based upon vinyl acetate, which constitutes 85% of the total polymer usage, the remainder being acrylates (e.g., n-butyl acrylate). For outdoors or bathroom usage, acrylates are the major components. For various applications, e.g., wood paints, styrene copolymerised with acrylates are used. However, yellowing of the styrene units occurs. The mode of polymerisation and crosslinking for coatings is very similar to that of bulk polymers. An important requirement is that premature polymerisation should not take place before application. In the presence of activators, e.g., cobalt naphthenate, many paints on exposure to air polymerise by radical oxidation resulting in crosslinked structures. Stepwise growth polymerisation, e.g., urethanes, is promoted by heat; therefore storage at high temperatures (W501C) should be avoided. A growth area is UV or electron beam curing. This can be via radical polymerisation, e.g., a benzoin derivative, O

OR

C

CHPh

O

OR

C

CHPh

UV Ph

Ph

or cationic polymerisation (with epoxy resins) using aromatic (Ar) onium salts, e.g., sulfonium salts, Ar3S BF4

UV

Ar + Ar2S

BF4 H (from solvent)

Ar2SH BF4

Ar2S + HBF4

The strong acid, HBF4, acts as the catalyst. Cationic polymerisation is used for coatings and printing inks. Several conditions are necessary for satisfactory surface coatings, e.g., nondrip applications. There is a balance between the ease of use and sagging of the paint during and after administration. Thixotropic additives, e.g., organomontmorillonite clays are added. These form 3-dimensional networks, which are easily broken down by shear. Various finishes can be achieved — gloss, satin (or egg-shell) or matt. This is accomplished by the addition of particles of size 1–5 mm of, for example, silica, china clay or the white pigment, TiO2. The degree of mattness depends on various factors, such as particle size, surface treatment of the particles, rate of film formation, and the polymer composition, e.g., urethane/acrylate compared with epoxy/acrylate. The former requires smaller particles; larger particles cannot be used as they create a rough surface.

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One of the largest uses of paints is in the automotive industry and the coatings of metals for decorative and anti-corrosion purposes. This is achieved using electrophoresis. The first pre-treatment provides corrosion resistance by phosphating using a solution of zinc or iron phosphate. Next a water-insoluble polymer is solubilised by converting it into a soluble salt through neutralisation. Thus alkyd resins containing free carboxyl groups (polymer–COOH) are treated with KOH to give the water-soluble salt (polymer–COO~K). In a similar manner, treatment of an epoxy/amino resin with a carboxylic acid, e.g., acetic acid, converts the polymer into a water-soluble quaternary ammonium salt, polymer  NR2 þ CH3 COOH ! polymer  NR2 HY OOCCH3 Electrophoresis of water solutions of these salts and using steel as either the anode or the cathode, respectively, liberates the water-insoluble polymer coating through the reaction: Anode deposition; polymer2COOY K þ

H

ðfrom anodeÞ

! polymer2COOH ðinsolubleÞ

Cathode deposition; polymer2NR2 HY OOCCH3 þ

OHY

ðfrom cathodeÞ

! polymer2NR2 ðinsolubleÞ

For various reasons, cathodic deposition is the most favoured. The main advantages are that complete surface coverage is obtained and also, because the coating-insoluble polymer is an insulator (inhibiting deposition), a uniform coating is achieved.

3.7 Advanced materials These are materials that can be used under extreme conditions such as high temperatures, greater than 2001C, or severe chemical environments or permit a unique application, e.g., highly branched polyethylene oxide does not crystallise; it serves as an electrolyte for lithium ion batteries, with no crystalline regions inhibiting the transport of ions. Many also exhibit properties not normally commonly associated with polymers, e.g., conducting electricity or semiconducting or displaying piezoelectricity. Some can also show (so-called) ‘‘smart’’ behaviour, whereby they can counteract any outside influence or stress.

3.8 High performance polymers These are normally prepared by a step growth mechanism. They can be thermoplastic or thermoset and are often used in composites. Composites are materials that contain two or more phases, one of which acts as a reinforcement

Polymeric Materials: Composition, Uses and Applications

85

for the other, e.g., a binder polymer is combined with fibres made, for example, from glass, carbon, boron or aramid, to generate a tough, stiff, yet mouldable material. Thermosetting polymers are brittle because of the crosslinking that occurs during polymerisation. However, the precursors are liquid and in this state can easily wet and impregnate long fibres masses, mats and cloth. High performance thermoplastic polymers are tough but can deform under pressure and heat. They are often processed via extrusion or injection moulding with short fibres (1–5 mm). Care must be taken to promote random orientation thereby giving isotropic strength (similar to polymer crystallisation of drawn fibres and films). New techniques have been developed, e.g., pultrusion, whereby a continuous web of fibres is passed through a bath of molten polymer, which can be a thermoplastic, e.g., PEEK, or a semi-cured thermoset, e.g., epoxy or unsaturated polyester. The resulting coated fibre is called a prepreg and can be used to wrap around a mould and finally cured at a higher temperature or by radiation. High performance plastics have high temperature stability. They have a very high limiting oxygen index (LOI, sometimes called critical oxygen index (COI)), which is increased when reinforced with glass fibres. Because of the high aromatic content they tend to char on combustion and do not release flammable volatiles. Furthermore, radical decomposition is inhibited by the delocalised aromatic system, which stabilises the propagating radical intermediates. Polymers containing heterocyclic or di-substituted aromatic groups, often called ladder polymers, have outstanding thermal stability (over 5001C for short periods). The ladder structure allows individual bonds to fracture without breaking the chain. They have high strength to weight ratio (comparable with metals), high modulus and are tough and not brittle at ambient temperatures even when they are amorphous. Examples of high temperature polymers are: Poly(ether imides), O

O

C

C

CH3 C

N

N C

C

O

CH3

O

O

n

Ultem® O

O

C

C O

N

N C

C

O

O

n Kapton® Vespel®

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J.P. Candlin

Poly(aryl ether ketones),

O

O

C O

O

C O

n Victrex®

PEK

n

PEEK

Poly(aryl ether sulfones), O O

S n

O PES

O S

CH3 C

O

O

CH3

O n

®

Udel

Aromatic polyamides (aramids),

HN

NH.CO

NH.CO

CO n

HN

CO n

Kevlar®

Nomex®

Aromatic polyesters, O O O

C

C O n

Vectran®

Kevlars has the highest tensile strength and is often used as a reinforcing fibre in composites with, e.g., epoxy, PEEK. The thermotropic liquid crystal polymer Vectrans is made by melt polymerisation of p-acetoxybenzoic acid and 6-acetoxy-2-naphthoic acid, (the corresponding hydroxy acids decompose on melting). Because of its liquid crystal properties the polymer can be spun into fibres from the melt. Kevlars is spun from a solution in concentrated sulfuric acid, and can be melt drawn to give a high modulus (stiff) polymer. Vectrans

Polymeric Materials: Composition, Uses and Applications

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fibres have high tenacities (strength), comparable with Kevlars and has service temperatures up to 3001C. It has many applications, e.g., cut-resistant gloves and clothing, catheters, reinforcement of ropes and yarns. Although Nomexs fibres have tensile strength properties similar to apparel fibres, they also have very high service temperatures (up to 3701C) and high flame resistance. Nomexs is self-extinguishing when removed from a flame because of the formation of char resulting in low smoke generation. It is extensively used in protective clothing and materials, e.g., by fire-fighters, for aircraft fabric, and by racing-car drivers. Nomexs is prepared from the corresponding di-acid chloride/diamine and wet spun from a solution of dimethylacetamide/5% lithium chloride.

4. POLYMER ADDITIVES This is an extremely important area. Commercial polymers are very rarely prepared or used without additives and they often contain a combination of additives. These improve processability of the polymer, its durability, service life under adverse conditions (e.g., temperature, UV light and various chemical environments), strength (e.g., using reinforcing fillers), appearance (colorants), etc. A recent use of additives is to facilitate reprocessing or recycling or, alternatively, to promote decomposition (which is often difficult because the stability is inherent in the polymer’s chemical structure). (The analysis of additives in polymers is the subject of Chapter 14.) Polymer additives may be classified into five groups (although some additives can serve more than one purpose, e.g., plasticisers, carbon black): (i) (ii)

(iii)

(iv)

(v)

Additives that facilitate or control polymer processing, e.g., lubricants, mould-release agents, blowing agents and plasticisers. Chemical property modifiers. These enhance stabilisation against degradation and aging during processing or in use. Degradation usually involves chain cleavage and is usually caused by energy (e.g., shear forces during processing, heat, UV light) or by chemical attack (e.g., oxidation, hydrolysis). Thus many polymers require anti-oxidants, light or heat stabilisers, etc. The promotion of new desirable properties for the polymer such as improved mechanical or electrical properties or dimensional stability. Fillers enhance many of these properties. Aesthetic property enhancers. These additives (e.g., colorants) will improve the polymer’s appearance and make it suitable for various applications. Degradation additives. These additives are usually added for environmental purposes in order to promote the decomposition of polymers after use.

The total world demand for additives is ca. 2 million tonnes per annum (excluding fillers and colorants — with fillers this becomes 20 million tonnes per

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annum). Their concentration can vary from a few ppm to W50% for flame retardants and fillers. The average is ca. 20 wt% of all polymers consumed.

Fillers Plasticisers Reinforcing agents Flame retardants Colorants

Consumption (%) (wt additive/wt polymer) 58 16 (almost solely with PVC) 10 6 5

The additives can be added during the polymerisation (either in the form of a reactive monomer or as an inert material — advantages include better dispersion and increased retention), but they are usually added immediately postpolymerisation of the polymer and extruded with the polymer. Often a concentrated mix with the plastic (master-batch) is prepared by the plastic manufacturer and this can be sold to the fabricators to be added during subsequent processing. When using additives the following precautions should be taken: (i)

(ii)

(iii)

The additives should not exude to the surface of the plastic article (there are some exceptions when surface modifications are required) or lost by volatilisation or decomposition during processing. Defining the end-use of the plastic. Strict controls are enforced when plastics have contact during food preparation or packaging. This is a difficult area because often the plastic manufacturer may not be aware of the final application. The fabricator must therefore ensure that the plastic article containing the additive is in compliance with the regulatory laws of the country where the article is sold. Another difficulty is the toxicity of the additive, e.g., carcinogenic or poisonous (e.g., lead or cadmium pigments) and asbestos fillers. Many additives (especially for plastics with food contact use) require approval from regulatory authorities. This costs money and time and therefore the general pattern is to use proven additives whenever possible. Interaction between the additives. Conversely some additives may serve two purposes (e.g., UV and heat stabilisation; lubricants cannot only aid processing but can also promote mould release).

It is difficult to generalise additives in that they may work with a particular polymer but not with others because of chemical compatibility, processing temperature and conditions.

4.1 Polymer-processing modifiers 4.1.1 Heat stabilisers Some polymers degrade readily when heated to the processing temperature by bond scission. In contrast, if the polymer has a completely aromatic structure (e.g., PES, PEEK) the thermal stability is high (greater than 4001C for short

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periods). Thus, when PVC is heated above 1001C an autocatalytic decomposition occurs and at 1801C it becomes dark brown within a few minutes. Thermal degradation of polymers can occur by three mechanisms (see Chapters 11 and 12): (i)

Decomposition by loss of a side group (probably by a free radical mechanism, possibly activated by radical initiators), CH2

CH

CH

+ HX

CH

X

O where X =

Cl(PVC),

O

C

CH3 (poly(vinyl acetate)).

The Lewis acid, HX, promotes further decomposition eventually giving a conjugated polyene (W6 conjugated bonds are coloured). The mechanism is possibly, H CH2 HC Cl

H C

CH2

CH

CH

CH

Cl

Cl

Cl

(-H and -Cl (=HCl)) H

H

HC

CH

Cl

Cl

C H

H C

HC Cl

CH2

+ MZCl

CH

C

CH

Z

Cl

Cl

stable

-HCl

H C

H C

CH

Cl

H C

H

CH2 C H

allylic Cl (labile)

HC

MZ2

H C

C

CH2 C H

CH Cl

Cl allylic Cl (labile) etc.

Thermal stabilisers for PVC are often heavy metal stearates (lead, barium), tin thiolates (R2Sn(SR2) = MZ2), and work by reacting the allylic

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J.P. Candlin

chloride (which is labile) to form stable compounds. Other stabilisers for PVC are metal salts of maleic acid, which possibly work by a Diels-Alder reaction with the intermediate unsaturated conjugated system. If the PVC is used for food applications (e.g., squash (fruit juice) bottles, chocolate dividers in chocolate boxes) calcium mercaptides may be used. Depolymerisation (un-zipping). The main chain is broken and radicals are formed, which can then undergo intra-molecular rearrangement, e.g., H2 C

H2 C

H2 C

H2 C

H2 C

CH

CH

CH

CH

X

X

X

X

+

CH2

CH

CH

X

X

breakage

H2 C CH

+

X

H2C CH X (monomer)

etc. (leading to depolymerisation)

(iii)

This depolymerisation is inherent in the polymer structure and can be prevented by either making a copolymer (such that when un-zipping reaches the co-monomer moiety it is stopped from going any further (e.g., POM (polyoxymethylene) in which a few percent of ethylene oxide has been incorporated), or by using free radical traps (see anti-oxidants). When depolymerisation occurs, high percentage yields of monomers may be obtained, e.g., POM (100%), PMMA (95%), PS (40%), natural rubber (20%). This information can be utilised in recycling of defect materials by conversion back to the monomer. If the homopolymer decomposes at the fabrication temperature another approach is to make a copolymer that can be melt processed at a lower temperature. For example, polyhydroxybutyrate decomposes at the processing temperature (1901C), whereas the copolymer with valeric acid can be processed at B1601C without decomposition. These aliphatic polyesters are biodegradable and most importantly, the decomposition products are not toxic, hence their use in medical applications (e.g., sutures).

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(iv)

Random chain scission. The initial attack is the same, but an intermolecular reaction occurs. H2 C

H2 C CH X

CH X

formation by bond breakage -see above

+

H2 H2 C C CH H C X

X

H2 C

H2 C CH X

H2 C

H2 C +

CH2 X

C

CH

X

X

+

HC

undamaged polymer chain

H2 C

CH2 C X

X (which can attack undamaged polymer)

When this decomposition occurs the degradation does not give high monomer yields (compared with un-zipping); the products tend to be low MW products. The chain scission and propagation is inhibited by free radical traps (see anti-oxidants). Sometimes heat de-stabilisation is actively sought, e.g., (i)

(ii) (iii)

Mastication. If the MW of the polymer is too high resulting in a high melt viscosity (e.g., natural rubber) or the MWD is too broad giving unstable melt processing conditions (e.g., PP) then mastication using high mechanical shear machinery, e.g., twin-screw extruders, results in a melt processible material. Free radical initiators are sometimes added to accelerate the process. This works by preferentially cleaving the longest chains, thus lowering and narrowing the MWD. Manufacture of carbon fibres, e.g., PAN fibres can be controllably decomposed in an inert atmosphere to give high carbon content fibres. Ablative materials. These polymers decompose to give off volatile materials and a surface char that acts as an insulator (e.g., paints, spacecraft re-entry vehicles). Glass-coated phenolic resins are used in the latter application.

4.1.2 Lubricants These additives reduce the friction between the polymer aggregates or crystallites and also lower the adhesion between the polymer melt and metal surfaces (which occurs in rollers, extruders). This results in: (i)

Lower melt viscosity, thus reducing energy consumption required for processing.

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J.P. Candlin

Improves the dispersion of fillers and pigments. Reduction of wear of metal surfaces, hence improving polymer gloss, smoothness and surface regularity.

Lubricants can be classified as internal or external lubricants. Internal lubricants should be partially miscible with the polymer at processing temperatures (i.e., behave similar to a plasticiser), but phase separate at ordinary temperatures. Whereas plasticisers are completely miscible with the bulk polymer, lubricants have a limited solubility. Examples of internal lubricants are fatty acid derivatives, e.g., stearates (for PVC), waxes and polyethylene oligomers containing polar groups obtained by partial oxidation. Not all polymers require lubricants; LDPE, nylon and PET are self-lubricating. External lubricants have a lower affinity for polymers and exude to the surface (causing blooming) and act by reducing the adhesion between the polymer and the metal surface during fabrication. Excessive lubrication must be avoided because during extrusion some friction between the screw flights and the polymer is necessary for transporting the polymer through the die. Too much lubrication also causes surface haze. Examples of external lubricants are metal soaps, paraffin waxes, silicones and fluoroplastics.

4.1.3 Slip and anti-slip agents Slip and anti-slip agents are added, especially in film production, to either promote or inhibit slip or sliding of film surfaces, respectively. Their function is to control the surface properties such that there is a balance between adhesion or tackiness of film layers and, on the other hand, the slippage of films. Thus slip agents are added during fabrication of plastics that are in contact, for example, with gears and bearings, whereas, anti-slip agents (adhesion promoters), for example, are incorporated to stop the sliding of plastic rolls or stacked bags.

4.1.4 Anti-blocking agents Because of the high quality of surface smoothness of films, wind-up onto rollers causes adjacent film layers to adhere together, either by static electricity or coldflow (creep). This is overcome by adding finely divided fillers (less than 1 mm diameter) of, for example, chalk, silica, crosslinked polyacrylates, which roughen the surface allowing entrapped air to keep the successive layers apart.

4.1.5 Mould-release agents These materials prevent adhesion between chilled rollers in film production or moulds for injection moulding. They behave like external lubricants, and should serve the following requirements: (i) (ii) (iii)

Form a smooth continuous film on the surface. Good chemical resistance and oxidative stability. No detrimental effect on the polymer surface, e.g., blistering, peeling, streaking, discoloration, poor printability, stress cracking.

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93

For injection-moulded articles, although spraying the mould with a release agent is feasible (this is often done for one-off samples) it has many disadvantages, for example, being time consuming or the mould requires cleaning after use to remove residue build-up. For this reason, external lubricants are used. Permanent release metal surfaces can be achieved by treatment with a solution of fluorocarbon oligomers followed by evaporation of the solvent and curing by heat.

4.1.6 Antistatic agents Plastic surfaces can become electrostatically charged through friction, either during processing or post-fabrication handling. This generates several disadvantages: (i)

(ii)

(iii) (iv)

Attraction of dust, which leads to unsightly appearance or malfunction, in applications such as plastic furniture, recording tapes, CDs and DVDs, and packaging. Electrostatic shock from apparel and carpet fibres and plastic floor coverings. This can constitute a fire hazard when handling flammable solvents or fine powders. An uneven feed problem in the hopper (often called bridging) when processing polymer powders. Failure of sensitive electronic equipments, e.g., computers, televisions.

Polymers are inherent insulators and have a high surface and bulk electrical resistance. Reduction of the surface and bulk resistivity is achieved by: (i)

(ii)

(iii)

Surface-active antistatic agents. These are hygroscopic materials and, under humid conditions, form a thin conducting layer of water. They are applied by spraying or dipping and are classified as external antistatic agents. They are not resistant to contact with solvents and can be removed by rubbing. Examples include: cationic (quaternary ammonium, sulfonium or phosphonium salts), anionic (long-chain, sulfonic, phosphonic salts) or non-ionic (ethoxylated fatty acids, sorbitol fatty esters). Internal antistatic agents are added to the bulk polymer before fabrication. They have a low affinity for the parent polymer and migrate to the surface. They offer long-term protection against electrostatic charges. They can be added as a master-batch or concentrate (similar to many additives), which can be diluted as required. Contact food approval has been granted for many of these additives with the exception of some anionic compounds. Conductivity additives (or fillers). These compounds reduce the resistivity of the bulk and the surface of the polymer. Below 10–20% concentration, the resistivity is not affected until a threshold is reached and conduction is observed. Examples include: carbon black, metal powders or fibres (copper, aluminium and silver) and some conducting conjugated polymers. Increasing the concentration of these additives yields conducting polymers that are used for shielding against electromagnetic interference (EMI).

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Conversely, cling film (plasticised PVC/PVDC, (poly(vinyl chloride)/poly (vinylidene chloride), copolymer, which has very high gas-barrier properties) on peeling from a roll generates static electricity thus promoting adhesion to a surface, e.g., ceramics, but not metallic surfaces which conduct the static electricity away.

4.1.7 Plasticisers Additives that soften and make flexible, hard brittle polymers are called plasticisers. They also lower the processing temperature by decreasing the polymer melt viscosity. This allows conversion of polymers, which may decompose at the processing temperature. They achieve this through lowering the Tg by providing internal lubrication between the polymer chains. However, plasticisation does reduce the heat deflection or distortion temperature (HDT) of the polymer thus limiting their usage temperature. Plasticisers are compatible and miscible with their host polymer causing them to swell and allowing them to be used for coating, moulding, spraying (when used as a suspension in a liquid solvent) or calendering, extrusion and injection moulding (when used as a polymer melt). More than 90% of all plasticisers are used with PVC, the remainder being used with PVDC, cellulose diacetate, poly(vinyl acetate) (PVAC), nylons, urethanes and acrylates. There are several theories for the action of plasticisers: (i) (ii)

(iii)

Decreasing inter-polymer chain attraction in the amorphous region of the polymer thus lowering the Tg. Gels are present in polymer melts. These are formed by high molecular weight physical (chain entanglements) or chemical crosslinks. These aggregates are swollen by plasticisers within the gel allowing movement of the polymer chain. Free volume is the internal space in the bulk polymer not occupied by the polymer chain. Thus deformation and flexibility can be visualised as polymer chains hopping from one engaged volume to a free volume. Plasticisers have a large free volume and this permits more migration of the polymer chains.

The most common plasticisers for PVC are phthalate esters prepared from aliphatic C8 alcohols. For high temperature applications higher molecular weight esters are used, e.g., from mellitic acid, which are resistant to volatilisation and are used for PVC interiors in cars (to prevent fogging of windscreens). Aromatic phosphate esters impart flame retardency (although PVC has good flame retardency). When premium-grade PVC products are required, for example, for extraction and migration resistance, high wearability and low temperature flexibility, polymeric esters made from di-functional acids/alcohols are used as plasticisers, for example, adipic acid/propylene glycol, polycaprolactone and ethylene/vinyl acetate/carbon monoxide terpolymers. With suspension polymerised PVC, the polymer particles are 100–500 mm diameter. They are highly porous and the dry powder will absorb large amounts

Polymeric Materials: Composition, Uses and Applications

95

Figure 2 Two methods for applying surface coating of a plastisol onto an uneven surface. Reproduced with permission from D.H. Morton-Jones, Polymer Processing, Chapman & Hall, London, 1989.

of plasticiser thus allowing PVC to be processed by standard techniques, e.g., extrusion. In contrast, with emulsion polymerised PVC the small polymer particles (0.1 mm diameter) are essentially non-porous and when mixed with a plasticiser a mobile mixture called a plastisol (or paint) is produced. On heating to about 1601C, the plasticiser becomes absorbed into the PVC to give a flexible polymer. Plastisols are frequently used for coating materials (e.g., fabric (leather, floor covering), paper (wall-paper), car-body underseal). Two methods of plastisol coating are shown in Figure 2 depending on whether a flat surface (using a knife-on-roller method) or even-thickness coating (reverse roll coating) is required. The use of plasticisers, with other than PVC applications, is extensive. Many polar rubber sealants or caulking materials are plasticised in order to make them more pliable, e.g., polysulfides, polychloroprene (Neoprenes), nitrile rubber. Esters, similar to those employed with PVC, are used to render cellulose diacetate (‘‘Acetate’’) overhead projection sheets more flexible.

4.1.8 Blowing or foaming agents Blowing and foaming agents are solids, liquids or gases (the latter used under pressure) such that when heat and pressure are applied under processing conditions they generate a gas thus producing a foam or cellular plastic. Careful control of process variables (temperature, time and pressure in the moulds) and the nature of the blowing agent is necessary. The amount of blowing agent can vary from less than 0.1 wt% to 5–15 wt%. The former small concentration is added to counteract depressions in thick sections, which occurs in injectionmoulded articles because of the large volume shrinkages of polymers on solidification. The higher concentrations yield lightweight packaging materials, sponge rubber articles, etc. Foamed polymeric materials can have either a closed or open cellular structure. Closed cells tend to be favoured when the pressure is maintained during the expansion. Both types are used for different applications, e.g., closed for thermal and sound insulation, open cell for soaking up liquids by capillary

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J.P. Candlin

action. Weight for weight, foamed plastics are stiffer than non-foamed plastics. Although most foamed plastics are fabricated using injection moulding, expanded polystyrene articles are compression moulded using pre-formed expanded beads. Foams can be rigid, semi-rigid or flexible. This depends on the nature of the final polymer. Thermoset polymers yield rigid foams, whereas elastomers give flexible materials. The size of cells varies from 50 to 100 mm and depends on the polymer and its end use. Cells of uniform size are a necessity. Small, uniform cells are formed by addition of nucleating agents. These are finely divided solids, e.g., silicates, and are particularly useful with physical blowing agents. There are two forms of blowing agents (physical or chemical) and these must satisfy the following requirements: (i) (ii) (iii) (iv) (v) (vi)

Long-term storage stability. Gas release in a controlled temperature, time and pressure range. Low toxicity, odour and colour of both the blowing agent and its decomposition products. Does not affect the stability and processing conditions of the polymer. Produces cells of uniform size. The gas must not diffuse out of the polymer matrix during fabrication too quickly, causing the foam to collapse.

4.1.8.1 Physical blowing agents. These are usually compressed gases (e.g., CO2, N2). These gases, which dissolve in the molten polymer under pressure, are released as bubbles when the pressure is reduced. Nucleating agents are frequently used. Low boiling liquids, e.g., pentane, perform the same function. Originally low temperature boiling chlorofluorocarbons (CFCs), for example CFC 11 and CFC 12, were used for closed cell materials. These have low thermal conductivity when compared with air, CO2 and similar gases, and hence made excellent foamed thermal insulators. CFCs have now been withdrawn because they are responsible for stratospheric ozone depletion. 4.1.8.2 Chemical blowing agents (CBAs). These are solids that decompose to give a gas at the processing temperature. In addition to the demands above, the CBA must possess the following: (i)

(ii) (iii)

The decomposition temperature must be matched with the processing temperature of the polymer (which can be in the range 150–3501C). The decomposition must be rapid (less than one minute) and within a narrow temperature range. The CBA should give a high yield of gas (B200 ml/gm). The blowing agent should have a narrow particle size range (to give cells of uniform size) and be easily dispersed in the polymer.

Very few CBAs have been developed for use with polymers for food contact applications. The most commonly used CBA, which has approval, is powdered wax-coated sodium bicarbonate/citric acid, which decomposes at 160–2101C

Polymeric Materials: Composition, Uses and Applications

97

giving off CO2. The azo compound 1,1-azobisformamide (ABFA), which decomposes giving N2 at B2201C, has also approved food contact use and is employed with PVC plastisol, LDPE, HDPE, PP, EVA and PS. For higher melting polymers, for example, PC, nylon, PET, which require temperatures greater than 3001C for fabrication, blowing agents which decompose at this higher temperature are used, e.g., substituted tetrazoles which give off nitrogen gas. The surface finish of injection-moulded foamed articles are not ideal because of external defects, burst bubbles, etc. This can be avoided by sandwich moulding. This is accomplished by initially injecting a slug of polymer melt into the mould followed immediately by a polymer containing a blowing agent, which chases the initial polymer into all the interstices. Embossed wallpapers (‘‘blown vinyl’’) are made by continuously coating a roll of paper with a liquid PVC plastisol containing a blowing agent. This is then passed through a heating oven causing the plastisol to expand. This is immediately followed by an embossing roller that develops a repeating relief pattern. Cushionflors vinyl floor coverings uses a different technique. This uses the plastisol and a CBA containing a ‘kicker’ or accelerator, e.g., ABFA and ZnO. This mixture decomposes at B1901C compared with B2201C without the kicker. When an ink pattern is printed on the plastisol surface it contains an inhibitor (e.g., fumaric acid and trimellitic anhydride), which complexes the kicker ZnO and prevents it from accelerating the decomposition of the CBA. A final layer of plastisol without the CBA is spread onto the surface, see Figure 3. On heating to B1901C the non-inked areas expand, whereas the inked areas (containing the inhibitor) do not swell. Familiar patterns (tiles, floral) with a relief are produced. A different method of making foams is to generate the blowing agent at the same time as the polymer is being formed. Thus urethane polymers are prepared

cross-section profile

Backing

Coated with plastisol + CBA + kicker (ZnO)

Print; ink, contains inhibitor (fumaric acid)

Coated with transparent wear layer (plastisol without CBA)

Heat to 190°C. Foam produced only in the absence of ink

Figure 3 Cushionflors techniques for obtaining printed/relief PVC plastisol floor covering. Adapted with permission from D.H. Morton-Jones, Polymer Processing, Chapman & Hall, London, 1989.

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J.P. Candlin

by reaction of di-isocyantes and diols in the presence of catalysts (tertiary amines, tin compounds),

OCN

R

NCO + OH

R′

OH

CONH

R

NHCOO

R′

O n

polyurethane

where the hydrocarbon groups, R and Ru, determine the nature of the polymer. If water is present in the diol, or adding water to the low molecular weight prepolymer (which contains isocyanate end groups), reaction with di-isocyanates generates CO2, R

NCO + H2O

RNH2 + CO2

This acts as a blowing agent. If this is the sole source of blowing agent then, again, dependent on the groups R and Ru, flexible foams are generally made by this route. Rigid foams are often made by the addition of a physical blowing agent, e.g., volatile liquids.

4.2 Chemical property modifiers 4.2.1 Anti-oxidants These prevent or retard the autoxidation by atmospheric oxygen of polymers, which often leads to discoloration, embrittlement, cracking, reduction of gloss, and a loss of mechanical properties. They are used in the manufacture of plastics, films, fibres, elastomers, paints, adhesives, etc. The actual mechanism of deterioration varies with the parent polymer, but they all involve radical pathways. The initiation can come from catalyst residues (metallic and nonmetallic), contamination from reactor vessel, UV light or processing equipment or from heat and mechanical processing treatment of the finished polymer. Many of the disintegration pathways involving radicals are common to both autoxidation and decomposition by UV light (see Chapters 11 and 12). The anti-oxidant itself is often consumed in performing its function, although hindered amine light stabilisers (HALS) are self-regenerating. Depending on the polymer, their concentration in the polymer may vary from a few parts per million (e.g., in PE) to several per cent (e.g., in ABS, natural rubber). Because it is impossible to determine all the polymer down-stream end uses, nearly all have food contact approval. To fulfil their role, anti-oxidants must have the following properties: (i) (ii) (iii)

They must be thermally stable and non-volatile at processing temperatures. Be miscible in the polymer. Not leach out of the polymer when in contact with solvents.

Polymeric Materials: Composition, Uses and Applications

(iv) (v)

99

Not corrode the processing equipment with acidic decomposition products. Must be odourless, tasteless and non-coloured (including its degradation products).

Oxidative degradation of polymers is initiated by radicals (Rd) generated in the polymer by heat or mechanical shear during processing or by exposure to UV light. These radicals, in turn, react with O2 to form peroxy and hydroperoxide radicals that promote radical reactions. energy RH

R +H O2 (peroxy radical)

ROO RH

ROOH (hydroperoxide)

ROO + RO + H2O

RO + OH

ROOR where RH = polymer

Thus, if formation of the initial polymer radical (Rd) can be prevented or, if formed, can be rendered harmless, then the stability of the polymer will be enhanced. Polymers that are easily capable of forming radicals are those containing tertiary C–H and allylic C–H groups, e.g., H2 C

H2 C

energy

CH

C CH3

CH3 polypropylene back-bone

H2 C

attack on tertiary group

H C C H

H2 C

H2 C

energy C H2

poly 1,4-butadiene back-bone

H C

H C C H

attack on allylic group

C H2

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J.P. Candlin

Polymers containing no secondary or tertiary C–H or are aromatic (PEEK or Kevlars) or perfluorpolymers (PTFE) are generally resistant to oxidation and require no anti-oxidant additives. However, the high temperature necessary for curing or fabrication of high performance polymers (especially for aerospace applications) can cause oxidation. For this reason, these materials are often prepared and fabricated under a nitrogen atmosphere. Anti-oxidants can be divided into two classes depending on which part of the radical chain they quench. Primary anti-oxidants are radical scavengers and will react with alkyl chain radicals (Rd) or hydroperoxides (ROOH). Secondary antioxidants work in combination with primary anti-oxidants and principally act by converting peroxide radicals (ROOd) into non-radical stable products. Synergism often works when both classes are used together.

4.2.1.1 Primary anti-oxidants. These are sterically hindered phenols and amines (HALS) and aromatic secondary amines. They intercept the radicals as they are formed: O

OH (H3C)3C

(H3C)3C

C(CH3)3

C(CH3)3

R + RH

CH3

CH3 2,6-di-t-butyl-p-cresol (butylated hydroxy toluene, BHT)

The resulting phenoxy radicals are stabilised by: (i) (ii)

Steric hindrance by the bulky t-butyl groups and therefore cannot attack new polymer chains. Resonance to give canonical forms that can dimerise and generate a new anti-oxidant dimer.

(H3C)3C

(H3C)3C

(H3C)3C

C(CH3)3

dimerise O (H3C)3C

CH3

HO (H3C)3C

CH2

HO (H3C)3C

CH2CH2

OH C(CH3)3

Polymeric Materials: Composition, Uses and Applications

(iii)

101

Formation of a quinoid structure.

(H3C)3C

(H3C)3C

O

CH3

O CH3

(H3C)3C

(H3C)3C R

(H3C)3C R O CH3 (H3C)3C

which can react with further radicals. However, quinoid structures do impart a yellow colour to the polymer. A major problem with BHT is that at elevated temperatures volatilisation may occur. Higher molecular weight hindered phenols can be used. Aromatic amine radical scavengers that are derived from 1,4 di-aminobenzene or diphenylamine are also used.

RHN

NHR

R = alkyl group

CH3 Ph

C CH3

CH3 NH

C

Ph

CH3

These act similarly to the phenol anti-oxidants; the N–H group in the amine reacts with the polymer free radical Rd to give a stabilised nitrogen radical and RH. Amine anti-oxidants are more effective than hindered phenols. Thus they are used with unsaturated elastomers and rubbers, which readily form radicals.

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J.P. Candlin

Similar to phenols, they can cause staining and are often used in conjunction with carbon black filled elastomers (e.g., tyres) — although carbon black itself has antioxidant capacity. For non-staining applications, e.g., polypropylene carpets, a sterically hindered amine is used, e.g., H H3C

CH3

N

H3C

CH3

2,2,6,6-tetramethyl piperidene

These compounds also inhibit photo-oxidation and are known as HALS. The mechanism is thought to be (R is the polymer group):

H

R

O

N

OR

N

N

O2

ROO

R = O + ROH

A high level of stabilisation is achieved at low concentrations. This is because of a cyclic process whereby the HALS are regenerated rather than consumed during the stabilisation process. This also promotes long-term protection. To avoid leaching of the anti-oxidant when in contact with oils (vegetable and mineral), petrol and solvents, polar amine compounds are used: O NH

NH

S

CH3

O

Alternatively, an amine monomer that can be incorporated into the polymer chain during polymerisation can be used, e.g., CH3 NH

NH

methacrylamide derivative

CO

C

CH2

Polymeric Materials: Composition, Uses and Applications

103

4.2.1.2 Secondary anti-oxidants. These compounds react with the hydroperoxide and peroxide intermediates. They are usually di-valent sulfur or tri-valent phosphorous compounds:

ROCOCH2CH2 2S

H3C

O

P 3

They function by reducing the intermediates to the corresponding alcohols: R′2S + ROOH

R′2SO + ROH

R′3P + ROOH

R′3PO + ROH

Synergy between primary and secondary anti-oxidants occurs and often a mixture is employed. Also included are metal complexing agents, e.g., EDTA (ethylenediaminetetraacetic acid), citric acid, the purpose of which is to deactivate extraneous metal ions that catalyse polymer oxidation.

4.2.2 Anti-ozonants Although only 10–50 ppb ozone is present in the atmosphere at ground level, higher concentrations occur near photocopying machines; this is sufficient to degrade polymers, especially those with unsaturation in the polymer chain, e.g., elastomers. O

O

O

O

O

O

CH

CH

CH +

CH

O3 CH

CH

polymer chain

ozonide

bond breakage

This can cause surface cracks perpendicular to the direction of stress; stretched elastomers are more susceptible to this cracking. Ozone degradation is a surface phenomenon and hence a physical antiozonant must form a protective barrier. A chemical anti-ozonant can be added during polymer fabrication, but again it must diffuse to the surface. It must also provide a defence over the lifetime of the article. Anti-ozonants can function in different ways: (i)

By diffusing to the surface and forming a physical layer between the elastomer and ozone. Paraffin waxes (CnH2n+2 where n = 20–50) behave in

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(ii)

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this manner — there is no chemical reaction between the wax and ozone. Care must be taken when the article is exposed to solvents (e.g., petrol), which may dissolve the protection. Reaction with ozone directly. This reaction must be more rapid than the reaction of ozone with the polymer. Examples include aromatic amines, e.g., 1,4-diaminobenzene derivatives. Although not illustrated in the reaction scheme above, the down-stream reaction pathways involve radicals. Therefore, anti-oxidants that scavenge these radicals are also added.

4.2.3 Ultra-violet stabilisers UV stabilisers protect polymers by restricting UV penetration to the surface and therefore confine the damage to surface layers. Protection is important because the energy possessed by UV radiation is sufficient to break chemical bonds. The initial breakage can either be by a radical (Norrish type I) or non-radical (Norrish type II) pathway. The effects are similar to degradation of the polymer by oxidation routes; the radical intermediates can be neutralised by anti-oxidants. Many polymers contain chromophores, which may be a result of their chemical structure or generated during their preparation or fabrication, arising from monomer, solvent, trace metal and catalyst residues. These chromophores will absorb UV light and be excited to a high-energy state. Examples include olefinic, aromatic and ketonic groups. This energy can be lost by radiation, e.g., fluorescence or phosphorescence, or heat or energy transfer to neighbouring chromophores. If none of these pathways are available, photodegradation takes place with bond cleavage and the possible formation of radicals. These radicals react with oxygen to form perxoy radicals and hydroperoxy compounds. Photoexcitation can also act like a sensitiser and convert relatively non-reactive ground-state triplet oxygen into highly reactive singlet oxygen, which again will promote autoxidation of the polymer. Polymers containing keto groups are particularly susceptible to photodecomposition (indeed they are often added to stable polymers to make them photo-degradable). Norrish type I (radical): O CH2

CH2

C CH2

O

UV CH2

CH2

C

CH2

+ CH2

radical decomposition

CH2 + C O

CH2

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Norrish type II (non-radical): O CH2

C

O

H

UV

CH2

CH

H2C

CH2

non-radical decomposition

H +

C CH2

HC

H2C

O CH2

H

C C H2 O

CH2

C CH3

Several techniques can be used to stop UV degradation: (i) (ii) (iii)

Screens or coatings. These block out UV radiation, e.g., pigments (TiO2), carbon black. Radical scavengers, which intercept the generated radical pathways — similar to anti-oxidants. Often HALS are used. Energy quenchers. These absorb energy from the photo-excited state of reactive singlet oxygen and dissipate it as heat. They are often metal chelates and their action is:

UV chromophore

excited chromophore

triplet O2 quencher

singlet O2 (reactive)

quencher chromophore + excited quencher

quencher + heat

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Examples of energy quenchers are:

octyl

O S

S NH2R

Ni

M

C

RN2

S O

octyl

2

where M = Ni or Co

(iv)

These compounds are multifunctional additives. They can act as heat stabilisers, radical traps, decompose hydroperoxides, UV absorbers, etc. UV absorbers. This is the largest class of UV stabilisers. They work on the same principle as sun-screen lotions; they contain chromophores that can absorb light in the 280–400 nm region and release the excess energy as heat and not high-energy radiation. They must be stable under processing conditions and should not react with the polymer nor decompose with UV radiation.

Because it is the UV-B radiation (280–320 nm) that causes the degradation, the absorption spectra of the UV-absorber must coincide with these wavelengths. UV-A (320–400 nm) does not cause damage (it is not energetic enough) and UV-C (wavelength less than 280 nm) does not reach the troposphere (it is filtered out by ozone in the stratosphere). The problem is to find an additive that absorbs UV-B but does not have an absorption ‘‘tail’’ in the UV-A and visible wavelengths, and therefore would have a yellow appearance. Many UV absorbers are based upon either 2-hydroxybenzophenone or 2hydroxytriazole derivatives, (the corresponding 3-hydroxy-compounds are not effective). These work via the following mechanisms: H

H O

O

O UV

C

energy absorption

O

C

release of energy (as heat) H

O

UV energy absorption

N

H N

N N

O

N heat release

N

To increase the longevity, UV absorbers with reactive groups which can be incorporated into the polymer chain or high molecular weight substituents are

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used. Because many of the decomposition pathways involve radicals, a combination of anti-oxidants and UV stabilisers are often employed.

4.2.4 Flame retardants Many polymers are inherently flammable. Furthermore, they often melt, volatilise and emit flammable and toxic vapours. Legislation now dictates the many polymers used in construction, fibres, furniture, advertising signs in shopping malls, must possess combustion resistance. The combustion cycle may be represented as shown in Figure 4. The initial step is the thermal degradation of the polymer giving rise to volatile products. At this stage there is probably no involvement of oxygen. These volatile products, e.g., monomers by depolymerisation, react with oxygen to give heat and flames, which does not involve radicals. Heat liberated by the flames causes further degradation of the polymer, which, together with the initial source of ignition, promotes further combustion, etc. Interference with any of these steps will stop or delay total combustion. These include: (i) (ii) (iii) (iv)

Use thermally stable polymers. Promote char formation, (many of the advanced materials have high char yields). Use radical scavengers. Use endothermic reactions to counterbalance exothermic combustion.

Many of these approaches have been employed to contribute to fire or flame retardency: (i)

Use polymers with naturally low flammability. The threshold of polymers can be qualitatively estimated by determining the LOI of the polymer. This gaseous products

flame gas phase oxygen

volatile products

heat

heat from ignition source

thermal degradation

solid polymer char residue

phase boundary

heat

thermal oxidation

Figure 4 Combustion pathways illustrating the burning of polymers.

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uses polymer samples of a standard size, and is measured by recording the volume percentage of O2 in an O2/N2 mixture that will sustain flaming combustion for 3 min after the source of the ignition has been removed. Some examples of LOI are: Polymer

LOI

Polyoxymethylene Polyethylene and polypropylene Poly(methyl methacrylate) Polystyrene Cellulose Poly(ethylene terephthalate) Nylon 6 and nylon 6,6 Polycarbonate Poly(phenylene oxide) Aramid (Kevlars) PES and PEEK PVC (unplasticised) PVDC (unplasticised) Carbon (char) PTFE

15.3 17.3–17.6 17.5 18 20 22 23–26 29 31 31 35–37 45 60 65 90

(ii)

↑ flammable ------- air -----------↓ non-flammable

Adding flame retardant additives. These reduce the efficiency of combustion by: a. Cooling of the polymer’s pyrolysis zone, e.g., aluminium trihydrate, Al2O3.3H2O (used in B50% of applications). Above 2501C, water of hydration evolves endothermically thereby lowering the temperature of the flame and diluting flammable gaseous pyrolysis products. Additionally, the residual Al2O3 provides a thermal barrier by coating the polymer surface. Al2O3 also suppresses smoke generation. b. Reducing radical pathways. The most important propagating combustion reactions are: Hd þ O2 ! HOd þ Od

ðexothermicÞ

Od þ H2 ! HOd þ Hd ðexothermicÞ Organo halogen compounds (RX, where X = Cl, Br) on heating generate HX by reaction with the polymer (poly–H): RX Ð Rd þ Xd poly  H þ Xd Ð polyd þ HX H2 þ Xd Ð Hd þ HX which react with the free radical propagating intermediates to give less reactive species: Hd þ HX Ð H2 þ Xd HOd þ HX Ð H2 O þ Xd

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Either high melting point compounds (often aromatic bromine compounds) or halogen-containing monomers that have been incorporated into the polymer (e.g., p-bromostyrene in PS) can be used. If antimony compounds (e.g., Sb2O3) are also included, a synergistic interaction occurs forming SbX3, which is a very efficient radical trap: Sb2 O3 þ 6HX Ð 2SbX3 þ 3H2 O

(iii)

(iv)

Furthermore volatile SbX3 decomposes in the heat of the flame to generate fine particles of Sb2O3, which form sites for radical recombination. A problem with these gas-phase radical quenching agents is that the volatiles emitted are acidic and corrosive. Promoting char formation by adding phosphorus compounds (e.g., red phosphorous or ammonium polyphosphate, (NH4PO3)n). These additives cause the polymer to swell (intumescence) and form a carbonaceous char on the polymer surface that thus insulates the bulk of the polymer (ammonium polyphosphate is particularly useful for cellulose textile fibres (e.g., cotton)). Melamine and melamine salts (e.g., borates, phosphates) act in a similar manner promoting char formation and intumescence. Thermosets or highly crosslinked polymers give high char yields. Similarly, many high performance polymers, e.g., PEEK, PES, polyetherimide (PEI), not only have high LOI values but also tend to decompose to a char. Surface oxygen barrier formation by using boron compounds (e.g., H3BO3, borax (Na2B4O7)). They prevent combustion by forming a glass-like coating. They are not very efficient, but they are not expensive.

Allied to flammability is smoke density suppression especially in confined spaces, e.g., airliners, houses, warehouses. Many aromatic compounds burn with a smoky flame (e.g., styrene), whereas corresponding aliphatic compounds tend to burn with a clean ‘‘transparent’’ flame. This is because air-borne poly-aromatic vapours decompose to give volatile carbon (smoke) in low oxygen environments. Finely divided magnesium or aluminium hydroxides (or a 3:1 combination) are currently the best smoke suppressants. They also neutralise the acidic vapours produced from halogen-containing flame inhibiters. The more finely divide they are the more efficient they become. Unfortunately, most fatalities in fires occur by inhalation of toxic vapours. These can be carbon monoxide (which arises from incomplete combustion), cyanides (from nitrogen-containing polymers) and chlorides (from chloropolymers). These are the adverse consequences of flammable polymer combustion. They can be overcome by using breathing apparatus, face masks, etc.

4.2.5 Biocides (also called fungicides, bactericides, slimicides, anti-microbials, etc.) Most polymers of high molecular weight in their pure state are resistant to attack by microorganisms, for example, although commercial polyethylene is resistant,

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oligomers of less than 600 MW are eventually consumed. Bacterial attack on the polymer can lead to discoloration, mildew, odours, embrittlement and eventually structural degradation and product failure. Ironically, an active field of research is to promote bacterial degradation in landfill sites. Most trading polymers contain a variety of additives, e.g., plasticisers, lubricants, stabilisers, etc., and it is these additives that promote bacterial attack on the polymer. At the same time, degradation by other routes provides pathways for bacterial attack by creating hydrophilic surfaces. Because many industrial and domestic services are supplied by underground plastic pipes and cables, care must be taken when choosing additives to make sure that the polymer is not vulnerable to attack. There are two considerations to be applied when using biocides: (i)

(ii)

Reduce the amount of biocide. This is particularly true for plasticised PVC. Alternatively choose plasticisers that are less liable to attack. Thus aliphatic plasticiser esters are very prone, whereas phthalates, polymeric esters and chlorinated hydrocarbons are fairly resistant. To be effective the biocide should migrate to the surface of the polymer in sufficient concentration to perform its function. This migration should not occur too quickly (bacterial attack is a slow process, sometimes taking years to begin) or it will be leached away.

Not all additives increase biological attack. Heat stabilisers for PVC fabrication, e.g., tin and lead organometallic compounds, promote fungal resistance. Biocides are naturally toxic to lower organisms and therefore must be handled with care. Strict government rules control the sale and use of biocides, especially those used in food contact applications. They are added at the fabrication stage. The morphology of the polymer article is important, e.g., high surface area articles, such as foams, biodegrade more rapidly. The use of biocides is spread across the whole polymer range, e.g., paints, ropes, textiles, fibres, etc. Many are copper, silver or arsenic compounds and also various heterocyclic compounds, e.g., isothiazolines (which have some structural resemblance to penicillin).

4.2.6 Anti-fogging agents Fogging of plastic films used for packaging or agriculture, spectacle lenses, crash helmets, etc., is caused by water droplets. This decreases the transparency and is aesthetically not desirable. Surface-active agents may be added during the processing of films (internal addition) or by surface treatment of the film (external addition). These tend to reduce the surface energy of the film/water droplet interface promoting a continuous film of water thus enhancing transparency. Examples include hydrophilic surfactants, such as sorbitol or glycerol fatty acid mono- or di-esters. If the packaging is in contact with food it must have the necessary approval.

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4.2.7 Degradation additives This is a relatively recent area of research and development. It has come about because of various reasons: unsightly plastic articles, over-flowing landfill sites, enhancing humus in soils thus avoiding combustion methods that may generate toxic vapours, etc. These additives promote disintegration of polymers into non-toxic low molecular weight fragments through various routes. This is achieved by thermal, photo-oxidation, hydrolytic, chemical, mechanical or biological pathways. Many degradation avenues are available: random chain scission, side group elimination and un-zipping of the polymer chain. Three main routes have been followed: (i)

(ii)

(iii)

Photodegradation. This involves initiation by sunlight or UV radiation. The intermediate radicals eventually lead, via hydroperoxides and peroxides, to organic carbonyl compounds. These, in turn, are oxidised to carboxylic acid derivatives, which are biodegradable. The blending of polymeric organic carbonyl compounds, e.g., ethylene/carbon monoxide copolymer, with the parent polymer, e.g., polyethylene, gives a plastic film material that degrades within 3 months. Although dithiocarbamates of nickel(II) and cobalt(II) are multifunctional for the prevention of heat and UV degradation, the iron(III) analogue behaves differently. Initially, when added to the polymer it acts normally, but after an induction period (1–2 weeks) it functions like a photo-degradent. Furthermore, the time for the polymer film to degrade to flakes can be controlled by the amount of iron(III) dithiocarbamate added. For instance, when used in agriculture the complete breakdown of the film can be timed to coincide with the harvesting season. The degradation period can be controlled from weeks to 1–2 years. Biodegradation. This principle is to blend a completely biodegradable polymer with an inert polymer matrix. Many naturally occurring polymers are biodegradable, e.g., the polysaccharides, pullulan and chitin, in addition to synthetic polymers, e.g., polycaprolactone, polyethylene succinate and poly(vinyl alcohol). The most important additive is starch. This can be blended with polyethylene using water or glycerol as a plasticiser — up to nearly 50% starch, although normally 6–15% is used. Synthetic polymers. A different approach is to use a synthetic polymer that is biodegradable (after initial hydrolysis) and can be processed using standard methods. These include copolymers from hydroxybutyrate/ hydroxyvalerate (made from bacteria), polylactic acid and polyglycollic acid (made from the corresponding cyclic anhydrides). These are too expensive to compete with starch/PE but are used for added-value products, e.g., sutures.

Perhaps the greatest benefit of plastic degradation is in the use of plastic films (e.g., PE, PP) in agriculture, especially as mulching films. This involves the covering of growing plants with film. Gains include: less water required for irrigation, increased temperatures (killing dangerous microorganisms), avoiding

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rain run-off of fertiliser. The greatest advantage is the ease of disposal; after use, the degraded polymer flakes are just ploughed into the soil.

4.3 Mechanical property modifiers 4.3.1 Fillers and coupling agents Fillers were initially introduced to reduce costs; they have significantly lower cost than low cost commodity polymers. However, fillers are now added to polymers to enhance performance in many applications. Many of these benefits have emerged because of the greater adhesion between the polymer-filler interface. This arises from the use of coupling agents, which provide a bond, both physical and chemical, between the filler and the polymer matrix. The size and shape of the filler plays an important role. Generally, the smaller the size the greater the property improvement. Size distribution is also paramount. Packing of the filler within a polymer matrix is improved when a combination of large and small particles is used (the smaller particles occupying interstices left by the larger particles). Higher concentrations (or loadings) of the filler are possible and improved properties result. The shape also affects the properties of the filled polymer. Thus, using fibres brings about reinforcement of the polymer. The properties that can be affected arising from fillers include: (i) (ii) (iii)

(iv) (v) (vi) (vii)

Improved stiffness or rigidity (modulus). Improved protection from heat distortion. Reduced coefficient of thermal expansion. This reduces the shrinkage that occurs in the conversion melt to solid during processing. Also, compatibility between polymer/metal adjoining closures over the range –201C to 401C. Plastics expand and contract several times that of metals. Alteration of density of the polymer to a either higher or lower value by using solid or hollow fillers, respectively. Reduced creep (long-term stress). Improved abrasion resistance. Increased surface hardness.

Many other specific properties have been noted, e.g., decreased flammability and anti-blocking. Fillers can be grouped into various categories depending on shape. Spherical fillers include calcium carbonate (size B1 mm diameter and quantitatively the most important filler). This can be ground mechanically to a fine powder or, for smaller particles, by precipitation from solutions or slaked lime using carbon dioxide. Dolomite (calcium/magnesium carbonate) and barium sulfate are prepared and applied similarly. Silica can be either pulverised from quartz or flame hydrolysed from silicon tetrachloride to give ultra-fine, sub-micron diameter powder. These fillers increase the density of the base polymer. Decreasing the density can be achieved using hollow glass microspheres, flyash (from coal-burning power stations) or volcanic ash.

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Other spherical fillers include carbon black. This has several roles particularly in combination with elastomers, e.g., black pigment, anti-oxidant and UV stabiliser, reinforcing filler, and an electrical conductor when used at 60% concentration. Wood flour is particularly effective in phenol/formaldehyde and melamine or urea/formaldehyde thermoset resins because the phenolic lignin component in the wood reacts with the methylol groups (–CH2OH) in the growing polymer. An important feature of fillers is their aspect ratio (length versus diameter or thickness). When this is large, as occurs in fibres (glass, polymeric and carbon), whiskers, plate-like natural minerals (e.g., micas, talc, kaolin), graphite, etc., many properties are improved, especially tensile strength, rigidity, etc. However, none of these improvements are possible unless the interfacial force between the filler and the bulk polymer is strong enough. Since many of these fillers are inorganic with surface hydroxyl groups a bond between the polymer and filler is likely to be weak. It would also be prone to hydrolytic cleavage. Thus a coupling agent is necessary to bridge the different materials together, and enable transfer of any external stress from the polymer to the reinforcing filler. Coupling agents are chemicals with a dual function. They react with the surface groups (usually hydroxyls) on the filler and contain chemical groups compatible with the polymer matrix, either by physical (e.g., entanglement) or chemical means (e.g., hydrogen bonding, dipole/dipole interaction) (Figure 5). For silica fillers, hydrolytic stability is best when M = Si; for other fillers, e.g., calcium carbonate then titanate- or zirconate-coupling agents are preferred. In some examples it is not necessary to prepare the organometallic-coupling agent R2MX2 beforehand. Thus coating glass fibres with a heptane or alcohol solution of titanium alkoxide promotes adhesion between the fibre and polymer, e.g., acrylic, polyolefins, polyester, polyamide and other thermoplastic resins. Glass fibres dominate this field either as long continuous fibres (several centimetres long), which are hand-laid with the thermoset precursors, e.g., phenolics, epoxy, polyester, styrenics, and finally cured (often called fibre glass reinforcement plastic or polymer (FRP)). With thermoplastic polymers, e.g., PP, short fibres (less than 1 mm) are used. During processing with an extruder, these short fibres orient in the extrusion/draw direction giving anisotropic behaviour (properties perpendicular to the fibre direction are weaker). Glass fibres are fragile and break easily because of surface defects. This is overcome by treating virgin fibres with water-soluble sizing agents. These protect

+ OH

R

X M X

R

-2HX

R

O filler

filler

OH

M O

R

Figure 5 Schematic of the attachment of coupling agent to a filler particle. X = Cl, OCH3, carboxyl; M = Si, Ti, Zr; R = long-chain alkyls or oligomers that contain grafted polar groups, e.g., amides and carboxyl.

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the glass fibres before usage and can be easily washed off. Sometimes the sizing agents can act as coupling agents.

4.3.2 Impact modifiers This is a growth area — how to improve the properties, particularly impact properties of the base polymer. Many plastics can be either tough or ductile with a high impact strength and can withstand a rapid force without fracturing, or they can be brittle and shatter easily, especially at low temperatures. To overcome this, polymers are blended with a more flexible polymer, which dissipates the energy of impact through facile polymer chain movement. This implies that the impact modifiers must have a low glass transition temperature. Furthermore, they must not be miscible with the parent polymer, in contrast with plasticisers, which must have compatibility with the polymer. They must retain or increase the heat distortion temperature, not lower it as occurs when plasticisers are used. Impact modifiers are added at the blending stage and should be welldispersed discrete particles of diameter B1 mm. They must have good adhesion at the modifier/polymer interface in order to transfer the energy efficiently. Loadings of 5–15% of modifier are usually required to be effective. Transparency is often required. This is achieved by arranging that the particle size of the modifier to be below that of the wavelength of visible light (0.4–0.8 mm). This can normally be achieved by emulsion polymerisation, e.g., polybutadiene, polystyrene. Adhesion and surface compatibility between the polymer and modifier can be achieved by surface grafting of polar groups, e.g., acrylonitrile, various acrylates, onto the impact modifier surface before blending. Crystalline polymers, e.g., nylon, poly(butylene terphthalate), are not easily impact-modified. The crystalline domains can act as crack initiation sites. Amorphous polymers with high Tgs are more amenable to modification, e.g., PS, PVC, PC, although PC is tough because of H-bonding that occurs between the polymer chains. The largest use of modifiers are with PS and PVC. High-impact PS (HIPS) was made originally by mechanically blending polybutadiene (PB) and PS. The current method is to dissolve PB in styrene monomer and initiate emulsion polymerisation. This results in a grafted copolymer with PB acting as the core and PS as the surface graft. This forms a single-phase transparent alloy with PS; the homopolymers PS and PB are non-miscible and will not form a clear blend. There are various requirements for impact-modified PVC. The most demanding is for outdoor sidings and window frames, where lifetimes of 20 years are expected. Because butadiene polymers or copolymers (e.g., acrylonitrile/butadiene/styrene (ABS), methyl methacrylate/butadiene/styrene (MBS)) are susceptible to UV degradation these polymers are usually not employed; instead acrylate polymers are used for these applications. Although the main use of impact modifiers is with thermoplastics, thermosets also benefit. The agent is added at the monomer stage. Thus epoxy polymers can be made less brittle by the addition of rubbers. Care has to be taken that the high temperature properties of the thermoset are not compromised.

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4.3.3 Nucleating agents Many of the properties of a polymer depend upon the presence or absence of crystallites. The factors that determine whether crystallinity occurs are known (see Chapter 2) and depend on the chemical structure of the polymer chain, e.g., chain mobility, tacticity, regularity and side-chain volume. Although polymers may satisfy the above requirements, other factors determine the morphology and size of crystallites. These include the rate of cooling from the melt to solid, stress and orientation applied during processing, impurities (catalyst and solvent residues), latent crystallites which have not melted (this is called self-nucleation). All of these parameters are not under control. To deliver a more uniform distribution of crystallites, specific nucleating agents are added whilst processing. It has also been shown that many of the desirable properties are the result of small regular spherulites (or nascent crystals). Furthermore, other advantages of controlled nucleation include: (i) (ii) (iii)

Increase of the crystallisation rate. Increase of the temperature at which crystallisation commences on cooling from the melt, thereby reducing injection moulding time. Small crystallite size, less than 0.5 mm, reduces light scattering, thereby making the polymer transparent.

Nucleating agents should possess the following requirements: (i) (ii) (iii) (iv) (v) (vi)

Small particle size (preferably less than 0.5 mm diameter). High melting point. Insolubility in the polymer melt. Surface compatibility with the polymer allowing good dispersibility. Adequate thermal stability with no odour or staining during processing. Have food contact approval.

There appears to be no physical (e.g., crystal habit or morphology) or chemical (e.g., surface groups) correlation to identify which nucleating agent works best with which polymer matrix. However, it is known that dibenzylidene sorbitol works best with PP (it is sometimes called a clarifier because it enhances transparency), and inorganic benzoate salts are successful with PET.

4.3.4 Aesthetic property modifiers These enhance the appearance of the polymer, but play no role in the chemical, physical or mechanical properties of the base polymer. The main difficulty is that if the finished assembled article is made from different grades of the same polymer or from different polymers, then, particularly with different polymers, the combination must be uniform. For example, bathroom suites are often made from different materials, e.g., ceramics, baths (polyacrylates), trimmings (PVC, PP). The colorants therefore have to undergo different processing conditions and it is essential that in the final products the colour is the same.

4.3.4.1 Colorants. This is often the determining feature of a plastic article. Two types of colorants are used: pigments and dyes. Pigments are mostly inorganic

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and insoluble in the polymer matrix. They should be dispersed uniformly throughout the polymer. Dyes are organic based and tend to be soluble in the polymer. Dyes are liable to be more brilliant and vivid and more transparent than pigments, which are duller and opaque. This is because the colour with pigments is by reflection only, rather than the removal of the complementary colours by dyes. Both pigments and dyes must fulfil the following requirements: (i) (ii) (iii) (iv)

Must be thermally stable under process conditions. Have chemical compatibility with either the base polymer or accompanying additives. Have a reasonable lifetime without fading, colour change, bleeding, etc. Be non-toxic or have food contact approval. Also, on disposal (combustion or landfill) must not generate harmful materials.

Pigments can be either inorganic or organic. White pigments are the most widely used (they are often added with other colorants to give the finished article increased brightness). Titanium dioxide is by far the most important white pigment, since it imparts a high degree of reflectance and whiteness because of its high opacity (maximum light scattering with minimum light absorption). Two crystalline forms exist, rutile and anatase. Rutile (0.25 mm diameter) has the higher refractive index and is capable of greater reflectance in the visible spectrum. Anatase (0.18 mm diameter), on the contrary, scatters and therefore reflects more into the UV part of the spectrum. This confers a bluish tinge, which compensates the yellowness of some polymers. TiO2 actually promotes photoand oxidative degradation of the polymer and at the surface erodes a white powdery deposit of TiO2 results (chalking). This is prevented by initially coating the TiO2 particles with silica and alumina. Other pigments include zinc sulfide (white), iron oxides (brown), chromium oxides (green) and carbon (black). Good dispersibility is essential. To aid this the surface of the pigment is often coated with hydrophobic groups (similar to fillers). Because of toxic considerations, both lead chromate (yellow) and cadmium sulfide (red) are being phased out of usage. Synthetic ultramarines (made by fusing kaolin, sodium carbonate and sulfur) can be manufactured to give blue, pink and violet shades. Organic pigments include azo condensation products and metal phthalocyanins. These tend to agglomerate during compounding giving a spotted appearance. Dyes are miscible with the polymer and hence do not have dispersion problems. They include many of the dyes that have been developed for dying fibres, e.g., azo and anthroquinone derivatives. They are particularly useful for transparent articles, e.g., automotive taillights, decorative film. They can be added either as a dry powder or as a colour concentrate (requiring 10-fold dilution). Colorants have been developed for special effects. Pearlescent or iridescent give an attractive appearance. They are often used for coating paper (e.g., cosmetic packaging). The pigment consists of thin platelets, less than 1 mm thickness, which have a high refractive index, e.g., mica coated with TiO2.

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Interference patterns with the reflective and refractive light occurs that varies with the viewing angle. Thin metallic flakes of, for example, aluminium, copper, bronze, coated with a dye are used extensively in automobile wheel hub-caps, and ‘‘metallised’’ car-body paint finishes. Optical brighteners, optical bleachers or fluorescent pigments absorb UV light (B350 nm) and instantly emits it in the blue/violet region (B425 nm) of the spectrum. This has the effect of counterbalancing the yellow tinge of many plastics. However, they tend to perform a similar function as UV stabilisers. If they are both present, more brightener has to be added. Typical concentrations are 10–500 ppm and they are often based on stilbene structures. Their main application is in toys, packaging and road/safety signs. Phosphorescent pigments work by absorbing UV-visible light and slowly emitting it at longer wavelength light as an after-glow. Di-valent cation substitution of zinc sulfide is often the most popular choice.

5. SUMMARY The use of plastics in society is increasing at the rate of 5–10% per annum. The main application is in packaging and all the major commodity polymers are involved. Although excess packaging has been blamed for saturating landfill sites, it must be remembered that packaging does reduce the loss of goods which occurs through breakage and especially food spoilage. In the developed world, packaging results in less than 2% food wastage (an improvement from 15% which occurred before World War II) compared with 30–50%, which currently occurs in the under-developed world. Packaging also allows easy handling of goods. Improved tear strength (LLDPE compared with LDPE) has permitted a halving of the amount of polymer used in disposable shopping bags. Over the past 20 years no new commodity polymer has been developed. This is because of the advances in fabrication, blends (both miscible and nonmiscible), fibre reinforcement, etc. Thus films with up to 11 different polymer layers have been developed. High performance polymers are being used to make articles that are normally manufactured from metals. This is because of a higher strength-to-weight ratio. Modern passenger aircraft are now made with an ever-increasing usage of composites (e.g., epoxy/carbon fibres). Military aircraft development has led the way in this area. In the future, plastics and polymers will be important in developing ‘‘smart’’ materials. These are materials that can counteract any external force by reinforcing itself. An example is the repair of cracks in airplane fuselage and wings. Incorporated in the composites are hollow cenospheres containing separately the components for making a thermoset polymer, e.g., epoxy oligomer and catalyst (e.g., amine). As the crack progresses, the cenospheres are broken and the ingredients mix to form a polymer and heal the fracture.

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BIBLIOGRAPHY There are many reference sources that expand the knowledge of polymer composition, uses and applications. These include scientific encyclopaedias (often arranged in an alphabetic manner), together with speciality books — especially on how additives improve and extend the uses of polymers. In multi-volume references and other specialist books listed below, the ISBN(13) has been given. The original sources can be traced through Internet sites (e.g., GOOGLEs) using, for example, where appropriate, the ISBN number or by searching the title given in italics. 1 2 3 4 5 6 7 8 9 10 11 12

Kirk-Othmer Encyclopedia of Chemical Technology, 5th ed., Wiley, Chichester, 2007. Ullmann’s Encyclopedia of Industrial Chemistry, 7th ed., Wiley-VCH, Weinheim, 2007. Encyclopedia of Polymer Science and Technology, H.F. Mark (Ed.), 3rd ed., Wiley, New York, 2004. Encyclopedia of Polymer Science and Technology, Concise, H.F. Mark (Ed.), 3rd ed., Wiley, New York, 2007. ISBN-13: 978-0470046104. M.P. Stevens, Polymer Chemistry: An Introduction, 3rd ed., Oxford University Press, Oxford, 1999, ISBN-13: 978-0195124446. Polymer Handbook, J. Bandrup, E.H. Immurgut and E.A. Grulke (Eds.), 4th ed., Wiley, Chichester, 2003. ISBN-13: 978-0471479369. A.B. Strong, Plastics: Materials and Processing, 3rd ed., Prentice Hall, New Jersey, 2006, ISBN-13: 0131145580. C.A. Harper, Handbook of Plastics, Elastomers and Composites, 4th ed., McGraw-Hill Professional, New York, 2002, ISBN-13: 978-0071384766. F. Rodriguez, C. Cohen, C.K. Ober and L. Archer, Principles of Polymer Systems, 5th ed., Taylor & Francis, London, 2003, ISBN-13: 978-1560329398. J.C. Salamone, Concise Polymeric Materials Encyclopedia, CRC Press, Boca Raton, 1998, ISBN-13: 978-0849322266. Concise Encyclopedia of Polymer Processing and Applications, P.J. Corish (Ed.), Pergamon Press, New York, 1991. ISBN-13: 978-0080370640. N.P. Cheremisinoff, Concise Encyclopedia of Polymeric Engineering Terms, Butterworth-Heinemann, Oxford, 2001, ISBN-13: 978-0750672108.

Polymer additives: 13 J. Murphy, Additives for Plastics Handbook, 2nd ed., Elsevier B.V., Amsterdam, 2001, ISBN-13: 978-1856173704. 14 Plastics Additives Handbook, H. Zweifel (Ed.), 5th ed., Hanser-Gardner, Cincinnati, 2001. ISBN-13: 978-1569902950. 15 Polymer Modifiers and Additives (Plastics Engineering), J.T. Lutz and R.F. Grossman (Eds.), Marcel Dekker, New York, 2001. ISBN-13: 978-0824799496. 16 Chemistry and Technology of Polymer Additives, S. Al-Malaika, A. Golovoy and C.A. Wilkie (Eds.), Blackwell Science Inc., Malden, 1999. ISBN-13: 978-0632053384. 17 Speciality Polymer Additives: Principles and Applications, A. Al-Malaika, A. Golovoy and C.A. Wilkie (Eds.), Blackwell Science, Oxford, 2001. ISBN-13: 978-0632058976. 18 Plastics Additives: An A-Z reference, G. Pritchard (Ed.), Kluwer Academic Publishers, Dordrecht, 1998. ISBN-13: 978-0412727207. 19 Plastics Additives Handbook, R. Gachter and H. Mu¨ller (Eds.), 4th ed., Hanser-Gardner Publications, Inc., Cincinnati, 1993. ISBN-13: 978-3446175716. 20 Plastics Additives: An Industry Guide, E.W. Flick (Ed.), Vol. 1, 3rd ed., Plastic Design Library/William Andrew Publishing, New York, 2001. ISBN-13: 978-0815514640.

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21 B. Wendel, Plastic Additives: Guide and Reference, CRC Press, Boca Raton, 2002, ISBN-13: 9781587160752.

The section on polymer additives has been modelled on three articles in the Journal of Chemical Education by M.P. Stevens; these are: J. Chem. Ed., 70(6) 444; 70(7) 535; 70(9) 713; (1993).

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SECTION II: Polymer Chain Analysis

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CHAPT ER

4 Chain Structure Characterization Gregory Beaucage and Amit S. Kulkarni

Contents

1. Introduction to Structure in Synthetic Macromolecules 1.1 Dimensionality and statistical descriptions 1.2 Chain persistence and the Kuhn unit 1.3 Coil structure and chain scaling transitions 1.4 Measures of coil size Rg and Rh 2. Local Structure and Its Ramifications 2.1 Tacticity 2.2 Branching 2.3 Crystallization 2.4 Hyperbranched polymers 3. Summary References

123 123 125 127 132 134 134 139 153 163 165 166

1. INTRODUCTION TO STRUCTURE IN SYNTHETIC MACROMOLECULES 1.1 Dimensionality and statistical descriptions Synthetic polymers display some physical characteristics that we can identify as native to this class of materials, particularly shear thinning rheology, rubber elasticity, and chain folded crystals. These properties are inherent to long-chain linear and weakly branched molecules and are not drastically different across a wide range of chemical make-ups. We can consider these features to define synthetic macromolecules as a distinct category of materials (see also Chapter 2). The realization of this special category of materials necessitated the definition of a structural model broad enough to encompass polyethylene to nylon yet specific enough that detailed analytically available features could be used to define the major properties of interest, especially those native to this class of materials. This structural model for polymer chains is based on the random walk statistics Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00404-2

r 2008 Elsevier B.V. All rights reserved.

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Figure 1 Two examples of random walks: 10,000 steps on a cubic lattice.

observed by Robert Brown in studies of pollen grains and explained by Einstein in 1905. It is a trivial exercise to construct a random walk on a cubic lattice using a PC (personal computer), see examples in Figure 1. From such a walk we can observe certain features of the general model for a polymer chain. The chain structure differs from conventional structures in that it does not display an obvious surface and incorporates a significant fraction of solvent within the structure. We can notice: (i) (ii) (iii)

the two walks appear different despite using exactly the same algorithm, bunching of steps makes walks seem non-random, in fact bunching is a signature of a random process, and one simulation is of no use in describing the general features of the structure, we must consider a time average or an average over different structures in space.

A classical description of such a structure is of no real use. That is, if we attempt to describe the structure using the same tools we would use to describe a box or a sphere we miss the nature of this object. Since the structure is composed of a series of random steps we expect the features of the structure to be described by statistics and to follow random statistics. For example, the distribution of the endto-end distance, R, follows a Gaussian distribution function if counted over a number of time intervals or over a number of different structures in space,     3 3=2 3ðRÞ2 Pð R Þ ¼ exp  (1) 2ps2 2ðsÞ2 This function is symmetric about 0, the starting point as indicated by the symmetric term R2. Since the distribution is symmetric, the mean value /RS ¼ 0 and we must consider the second moment as a measure for the size of the structure, /R2S. For a series of n steps of length lK, where lK is the Kuhn step

Chain Structure Characterization

length, we can consider two contributions to /R2S, n X n  n X n  n  2 X  X  X hri  ri i ¼ nl2K R ¼ ri  rj ¼ ri  rj þ j¼1 i¼1

j¼1 iaj

125

(2)

i

where the first term for i6¼j is 0 since there is no correlation in direction between steps i and j and the second term yields the result nl2K since there are n steps where i ¼ j; ri is the position vector of the ith segment. By considering that, Z  2 R ¼ R2 PðRÞdR ¼ s2 (3) we find that the variance, s2 (square of the standard deviation), for the random walk is given by (2), nl2K. Polymer chains in dilute and semi-dilute solutions display a statistical structural hierarchy that differs in essence from the explicit structural hierarchy displayed, for example, by proteins in the native state. In proteins the primary residue sequence gives rise to secondary helical coil and beta sheet structures. These secondary structures compose a complex tertiary structure and higher order associations of protein chains. For synthetic polymers the hierarchy begins with the persistence unit that builds upon short-range interactions in a statistical sense at low chain index difference. Chain persistence can be measured using viscometry, dynamic light scattering or static scattering measurements. Dynamic measurements yield directly the Kuhn length that has been shown to be equivalent to twice the statically measured persistence length. The Kuhn length, lK, is the physical step length for a synthetic polymer chain.

1.2 Chain persistence and the Kuhn unit The persistence length, lP, was introduced by Kratky and Porod [1–3] as a direct measure of the average local conformation for a linear polymer chain. The persistence length reflects the sum of the average projections of all chain segments on a direction described by a given segment. Kratky described the features of the persistence length in a static small-angle scattering pattern; in particular, a regime of dimension 1 in the small-angle scattering pattern corresponds to Kratky and Porod’s definition of the persistence unit [4–6]. The mass-fractal dimension of an object can be directly determined in a scattering pattern through the application of a mass-fractal power-law [7]. Using these laws, an object of mass-fractal dimension df displays a power-law described by, IðqÞ ¼ Bqdf , for 1pdfo3. (B, a constant, is the power-law prefactor, which depends on the system; for example, for Gaussian conditions B is given as, B ¼ 2G=R2g where G is the Guinier prefactor, and Rg is the radius of gyration.) A power-law of 2 is expected for the Gaussian regime, since nBR2, and a power-law of 1 for the persistence regime, where the chain appears to be statistically composed of rods. To resolve the persistence length, lP, a log–log plot of I(q) versus q can be made and the two power-law regimes matched with lines of slopes 2 and 1, Figure 2 [3]. The intersection of these two lines in q

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Gregory Beaucage and Amit S. Kulkarni

100 8 6

q*Kratky/Parod

4

-2

2

Intensity (cm)-1

10

8 6 4 2

-1 1

8 6 4 2

0.1 0.001

2

3

4 5 67

2

3

4 5 67

0.01

2

0.1

3

4 5 67

1

q (Å)-1

Figure 2 Kratky/Porod graphical analysis in a log–log plot of corrected small-angle neutron scattering (SANS) data from a 5% by volume deuterated-PHB sample in hydrogeneous-PHB (polyhydroxybutyrate). The lower power 2 line is the best visual estimate; the upper line is shifted to match a global unified fit. Key: left, q corresponds to best visual estimate; right, plot to match global unified fit. The statistical error in the data is shown. Reprinted with permission from Beaucage et al. [3]. Copyright 1997, American Chemical Society.

is related to the persistence length through 6/(pqintersection) ¼ lP (see Ref. [4], p. 363). q is the absolute value of the momentum transfer vector, q ¼ 4(p/l) sin(y/2), l is the wavelength of the scattered radiation and y is the scattering angle. (Equivalently, a ‘‘Kratky plot’’ of Iq2 vs. q can be made to account for Gaussian scaling, and the deviation from a horizontal line can then be used to estimate lP. This approach has been summarized in several reviews (see Ref. [4] and Appendix G, p. 401 of [8]). The statistical segment length, lssl, is a related parameter defined as the scaling factor between the chain’s radius of gyration, Rg, and the square root of the number of chemical mer units in the chain, nchem, where Rg ¼ 2lssl(nchem/6)1/2. For a freely jointed, Gaussian chain, where the Kuhn unit is a chemical mer unit, 2lssl ¼ lK ¼ 2lP and nK ¼ nchem. The specific definitions of these terms becomes important for chains with bond restrictions where nK6¼nchem and 2lssl6¼lK, that is, the Kuhn segment and the persistence length are both independently measurable physical parameters while, in most cases, the statistical segment length is an arbitrary parameter which depends on the chemical definition of a chain unit. In general, lK ¼ 2lP as noted above [9–11]. When the global chain scaling deviates from Gaussian, such as in good and poor solvents, the statistical segment length refers to an equivalent-Gaussian chain, which does not physically exist. Even under

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127

these deviatory scaling conditions, there remains a scaling relationship between lssl and lK [12], and the persistence length and Kuhn step length retain their physical definitions. Although the definition of the persistence length by Kratky and Porod [1,2] appears to be somewhat vague in terms of real space, it is the only physical parameter that can be independently determined that directly reflects local chain conformation at thermodynamic equilibrium. Because of this, the persistence length is a focus of calculations of chain conformation using chemical bond lengths and angles [4,8,13]. In the more complicated chemical structures, seen in biology for instance, such calculations become tedious and are subject to some degree of uncertainty due to the dominance of secondary chain architecture. In fact there has been little experimental verification of ab initio calculations of the persistence length for polymers more complicated than mono-substituted vinyl polymers. The issue becomes complicated when chain secondary structures such as tacticity and helical coiling become important to chain conformation [14–19]. A direct measure of the persistence length using small-angle scattering remains the most robust approach to describing local chain conformations. A combination of the Kratky–Porod approach with modern scattering functions and an understanding of fractal scaling laws offer hope in describing both chain conformation as well as the statistical thermodynamics of these complicated systems [12]. For a detailed description of the use of small-angle scattering to quantify the persistence length the interested reader is referred to Ref. [3].

1.3 Coil structure and chain scaling transitions As mentioned above, for sizes on the order of the persistence unit the coil size follows the scaling law, l K  n1 c

(4)

where c is the bond length and n is the number of bonds in a persistence unit. This indicates that the Kuhn unit [20] is on average a linear structure as can be verified with scattering measurements where the scattered intensity scales as I(q) Bq1 at high q. At larger sizes and smaller scattering vector q a different, steeper scaling behavior is observed for synthetic polymers. This regime reflects the distribution of Kuhn units in space along a curved path that follows either a self-avoiding or a random walk. For a self-avoiding walk (SAW) the coil end-to-end distance, R, scales with, RSAW  n3=5 lK

(5)

where n is the number of Kuhn units of length lK. If self-avoidance is removed by screening of excluded volume the coil can take a Gaussian configuration where the coil size scales with: RGaussian  n1=2 lK

(6)

Equation (6) is the result of a calculation of the root mean square (RMS) endto-end distance from the summation of Equation (2). Equation (5) cannot be

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Gregory Beaucage and Amit S. Kulkarni

obtained by such a direct calculation since it involves non-random chain scaling due to long-range interactions. Equation (5) is obtained by considering a comparison between Equation (1) and the Boltzman distribution function for a system at thermal equilibrium,   EðRÞ PB ðRÞ ¼ exp  (7) kT which yields a function for the free energy of the Gaussian chain, E ¼ kT

3R2 2nl2K

(8)

For a chain with excluded volume the probability of the chain avoiding one segment of volume Vc is PEx(R) ¼ 1Vc/R3. The total number of combinations of two chain units is n(n1)/2!Bn2/2 so the total probability of exclusion is,  1 0 Vc  n2 =2   2 n ln 1  3 Vc n2 Vc R @ A  exp  PEx ðRÞ ¼ 1  3 ¼ exp (9) 2 R 2R3 Through multiplication of this probability with the Gaussian function Equation (1), and by comparison with Equation (7), ! 3R2 n2 V c þ E ¼ kT (10) 2R3 2nl2K Equation (10) yields decidedly non-Gaussian behavior and the chain end-to-end distance probability function using Equation (10) in (7) cannot be analytically integrated for moments such as the RMS end-to-end distance. For this reason a different approach is used to define a preferred chain size for the SAW using a derivative rather than an integral. A probability function proportional to the probability of a chain starting at radius of 0 having an end in a spherical shell of a radius R from the center is given by, ! 3R2 n2 V c 2  WðRÞdR ¼ kR exp  dR (11) 2R3 2nl2K This function displays a maximum at the preferred chain end-to-end distance R that can be found by setting the first derivative to 0, pffiffiffi  n 5  n 3 R R 9 6 V c pffiffiffi  ¼ n (12) 16 l3K Rn0 Rn0 where Rn0 is the maximum probability for the Gaussian function, !1=2 2nl2K n (13) R0 ¼ 3 Equation (12) can be simplified by considering large ðRn =Rn0 Þ so that ðRn =Rn0 Þ5 ðRn =Rn0 Þ3 to yield the scaling relationship, Rn  lK n3=5 which is the expression for a SAW.

(14)

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129

In Equation (10), Vc represents a hard-core repulsion that is entropic in nature since it is linearly dependent on temperature in the expression for energy. Repulsion is generally associated with enthalpic interactions and we can consider the effect of an enthalpic interaction. Since Vc is associated with a single Kuhn unit we consider the average enthalpy of interaction per pair-wise interaction and the number of pair-wise interactions per Kuhn unit, ðPP þ SS Þ  PS (15) 2 where ePP is the average polymer–polymer (PP) pair-wise interaction energy, eSS is the average solvent–solvent (SS) pair-wise interaction energy, and ePS is the average pair-wise interaction energy for polymer–solvent (PS). Each Kuhn unit has z pair-wise interactions, where z is the coordination number (on a cubic lattice for instance). To remove the kT dependence introduced by Equation (10) we write, D ¼



zD kT

(16)

and V c;enthalpic ¼ V c ð1  2wÞ

(17)

where the factor 2 is included since there is no redundancy in interactions in Equations (15) and (16) when used in Equation (10). The free energy for an isolated chain with enthalpic interactions can be written, ! 3R2 n2 V c ð1  2wÞ þ E ¼ kT (18) 2R3 2nl2K Equations (18) and (16) define a temperature where Gaussian behavior is observed (the phase separation temperature) where w ¼ 1/2 and thermal energy is just sufficient to break apart PP and SS interactions to form PS interactions. Equation (12) using (17) for Vc is called the Flory–Krigbaum equation. This expression indicates that only three states are possible for a polymer coil at thermal equilibrium: (i) (ii) (iii)

the normal condition in solution reflected by a SAW, a unique condition seen exactly at the phase separation temperature reflected by Gaussian scaling, and the collapsed state at temperatures below the phase separation temperature for an upper critical solution temperature (UCST) system.

For a chain at equilibrium no other states are possible! The SAW, Equations (14) and (18), is the normal condition for a polymer chain in solution and this can be easily verified by observation of the fractal scaling regime in neutron scattering measurements. Polymers generally have limited solubility and it is often possible to bring a polymer solution to the phase separation point thermally, either by cooling (e.g., polystyrene in cyclohexane, Figure 3 and Section 1.4) or by heating (e.g., poly(vinyl methyl ether) in water).

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3000

Rg 2500

Radius (Å)

2000 Rh 1500

1000

500

0 20

30

40

50

60

Temperature (°C)

Figure 3 Radius of gyration, Rg, and hydrodynamic radius, Rh, versus temperature for polystyrene in cyclohexane. Vertical line indicates the phase separation temperature. Reprinted with permission from Sun et al. [21]. Copyright 1980, American Institute of Physics.

It has been found experimentally that chain scaling just at the phase separation temperature follows the Gaussian prediction of Equation (2). However, it is known that the overall coil size varies with temperature, which indicates that the three-state model is incomplete. It is possible to resolve the apparent discrepancy between an expanding coil size and fixed chain scaling by considering a size-dependent thermodynamics within the coil. This is possible for high polymers because the energy expression in Equation (18) depends on coil size through n. For example, the energy of a chain calculated using Equation (18) is different for a chain of 500 Kuhn units compared to a chain of 1,000 Kuhn units. However, a chain of 1,000 Kuhn units is composed of 2 chains of 500 units and many chains of smaller sizes. Smaller chains have less entropy from Equation (18) and would be expected to thermally phase separate first. For example, as temperature is dropped towards the phase separation temperature in a UCST system we observe that the coil decreases in size. The coil at the small sizes reaches a point of phase separation at a higher temperature than the coil at large sizes. Locally we observe three regimes of scaling: (i) linear persistence at smallest sizes, (ii) Gaussian at intermediate sizes, where there is insufficient entropy for miscibility, and (iii) expanded coil SAW at large sizes, where there is sufficient entropy for miscibility. The size scale for transition between the latter

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131

two sizes is termed the thermal (or thermic) blob. Coils can show a gradual change in size with cooling due to changes in this thermal blob size. The chain also follows only the three possible states (Gaussian, SAW, or collapsed). Once the entire coil has reached the miscibility limit the chain finally phase separates just after displaying true Gaussian scaling on cooling for a UCST system. The thermal blob has been verified using small-angle neutron scattering (SANS) [22]. The understanding that polymers display an ability to accommodate thermal changes through scaling transitions was a major development in theoretical physics with ramifications to other chain and network structures such as proteins, DNA, and elastomers. Similar scaling transitions on external perturbation are known for stress, tensile blob, and concentration, concentration blob, as well as other possible chain perturbations. Concentration is of particular importance since it allows an understanding of the progression from a good solvent to the melt with increasing concentration. This progression is also of a gradual type despite the required three discrete state prediction and we explore the possibility of a scaling transition within the coil to explain this behavior. In progressing from a dilute solution to a concentrated solution and to the melt state we expect miscibility to decrease and the coil to contract. For a coil in dilute solution the coil displays two sizes, the overall coil size or end-to-end distance and the Kuhn length. As concentration increases a point is reached where the concentration within a coil, n/R3, is matched by the solution, cn ¼ k n=R3 ¼ k n4=5

(19)

where the latter expression relied on Equation (14); c is known as the overlap concentration. At this point coil overlap occurs and we do not expect thermodynamic parameters to depend on the overall coil size but on a new size introduced due to the increasing concentration. We can consider a scaling transition to occur at a size scale x associated with the overall coil size R and the reduced concentration,  c P x  R n  nð3þ4PÞ=5 (20) c The last equality is obtained by considering Equation (19). Since we know that the scaling transition size is not dependent on n above c, then P ¼ 3/4 and,  c 3=4 xR n (21) c This concentration-dependent scaling, transition is known as the concentration blob. At large size scales the coil displays Gaussian scaling, while at small size scales the coil displays SAW scaling since the coil at sizes larger than the scaling transition exists in a melt-like state where interactions are screened. At the transition size SAW scaling is obeyed x ¼ lK nx3/5, so with Equation (21), nx is equal to (c/c)5/4, and with Gaussian scaling at large size scales,  c 3=4  c 5=8  c 1=8 1=2 R ¼ x nx ¼ RF0 n ¼ R (22) F0 c cn cn RF0 is the Flory radius describing the coil size at concentrations below c.

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Equation (22) has been confirmed by a variety of techniques including neutron scattering, dynamic light scattering, and osmotic pressured measurements [23]. As concentration increases the concentration blob decreases in size until the Kuhn length is reached and the coil displays concentrated or melt Gaussian structure. The coil accommodates concentrations between the overlap and concentrated through adjustment of the concentration blob size. A similar scaling transition has been proposed to account for the response of an isolated coil to tensile stress [24,25]. If a force is applied to a Gaussian coil Equation (8) can be used to calculate the response of the coil since at thermal equilibrium the applied force FBdE/dR so, F¼

dE 3kT ¼ R dR nl2K

(23)

which defines the spring constant for an isolated coil. For weak perturbations the end-to-end distance R is close to n1/2lK so FB3kT/Rt, where Rt is the tensile blob size. This can be rearranged to express a size dependent on the applied force F, 3kT (24) F Rt decreases in size for larger applied forces. Equation (24) describes a size scale governed by a balance between the thermal energy of the coil and the applied force. For sizes larger than this scaling transition the coil presents no resistance to the applied force and we expect a linear structure with RBnt Rt. For sizes smaller than this scaling transition we expect to observe the native scaling of the chain either Gaussian or SAW scaling. A similar behavior can be observed when straightening a kinked string, that is large scales straighten out earlier with increasing applied force compared to smaller features. For the tensile blob, thermal blob, and concentration blob we find that the coil accommodates external stress (thermal, concentration, or force) through a scaling transition that leads to two regimes of chain scaling. This directly impacts the free energy of the chain, the mechanical response, and the coil size. Rt ¼

1.4 Measures of coil size Rg and Rh Models of the polymer coil are based on the end-to-end distance, which is generally not directly available as a quantitative feature. Coils in dilute solution can be characterized in terms of the radius of gyration, Rg, which is a statistical measure of the distribution of mass about the center of gravity or in terms of the hydrodynamic radius, Rh, that is usually determined through the use of Stokes law and a measurement of a drag coefficient or friction factor, fdrag, for the coil, Fdrag ¼ f drag ucoil

and

f drag ¼ 6pRh Z0

(25)

where ucoil is the velocity of the coil, Z0 the viscosity of the pure solvent, and Fdrag the force associated with drag of a moving coil in a solvent. Under the

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133

assumption that the coil is non-draining (Kirkwood Reisman theory), Rh reflects the radius of a sphere enclosing the coil. There is no clear means to verify the non-draining assumption and generally Rh should be considered a value that scales with the end-to-end distance. The radius of gyration, however, has an analytic relationship to the coil end-to-end distance. R2g is expressed as, n 1X R2g ¼ ðri  RG Þ2 (26) n i¼1 where RG is the center of mass, RG ¼

n 1X ri n j¼1

(27)

Combining Equations (26) and (27) yields, R2g ¼

n X n  n X n n X n  X  2 1 X 1 X i  j l2 ¼ 1 ri  rj ¼ i  j l2K K 2 2 2 2n i¼1 j¼1 2n i¼1 j¼1 n i¼j j¼1

l2K ½z þ 2ðz  1Þ þ 3ðz  2Þ . . . ðz  1Þ2 þ z ð28Þ n2 where z ¼ n1. The last series can be obtained by constructing an n n matrix of i versus j with values of |ij| and recognizing that the matrix is symmetric about i ¼ j. The bracketed expression in Equation (28) can be rewritten, ¼

z  X p¼1

z z X X  zðz þ 1Þðz þ 2Þ n3 ffi z þ 1  p p ¼ ð z þ 1Þ p p2 ¼ 6 6 p¼1 p¼1

(29)

using N P

up ¼

u¼1

N pþ1 N p pnp1 þ þ pþ1 2 12

for po3

(30)

Using Equation (29) in (28), R2g ¼

 2 R nl2K ¼ 6 6

(31)

Equation (31) applies to monodisperse systems. For polydisperse systems R2g reflects a high-order moment of the distribution, the ratio of the 8th to the 6th moment of the distribution in mean size. For this reason Rg will correlate with the largest sizes of a distribution. There are several advantages to Rg as a measure of size over the end-to-end distance. For branched, star and ring structures the end-to-end distance has no clear meaning while Rg retains its meaning. Further, Rg is directly measured in static scattering measurements so it maintains a direct link to experiment.

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2. LOCAL STRUCTURE AND ITS RAMIFICATIONS 2.1 Tacticity Local chain structure is governed by chemical make-up, configuration, and conformation. Polymer chain conformation refers to the different orientations of the repeat units brought about by bond rotations. Configuration, however, cannot be changed by simple bond rotations, and refers to how the units add into the polymer sequentially during polymerization. An example of different polymer chain configurations is that brought about by head-to-head addition of repeat units as opposed to head-to-tail addition. In the case of vinyl polymers (–CHX–CH2–) the substituted carbon is usually designated as the head, and the unsubstituted methylene unit is designated as the tail. Tacticity in polymers (see also Section 3.4.2, Chapter 2): Polymers formed from substituted monomers, like vinyl polymers, display tacticity which has bearing on the final polymer properties like degree of crystallinity, crystalline phase structure, and melting temperatures as well as glass transition temperature for di-substituted vinyl polymers. Tacticity or handedness describes the stereochemical arrangement of a chain unit relative to other chain units. The smallest unit of tacticity is a diad composed of two mer units. The linkage point between two mer units along a single-bond carbon backbone chain can be made in two distinguishable ways as shown in Figure 4. In Figure 4(a), the position of the substituent R group can be either in the top or bottom location — two enantiomers. While the groups can rotate about the C–C bond this will not reverse the stereochemical arrangement as can be seen in Figure 4(b) in the Newman projection. This can more clearly be seen if one considers a walk along the polymer chain from the left P, over the C–C bond and then to the right P. On this walk the substituent group will either be to the right or to the left regardless of rotation of the C–C bond. In this case distinguishing the chiral state of the mer depends on the walker’s observation since the walker can H (R) H (R)

H P

P

P P

H (a)

R (H)

R (H )

H (b)

Figure 4 Sketch of two possible stereochemical arrangements for a chiral monomer. P represents the polymer chain, R represents a vinyl substitutent on a carbon, H represents hydrogen. (a) Linear sketch showing one conformation and two configurations (bracketed and unbracketed). The apex of bonds is a tetrahedrally bonded carbon atom (solid and dashed circles). (b) Newman projection of the same monomer showing the free rotation about the C–C bond.

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135

distinguish between right and left. In the absence of the walker the two states are not distinguishable. This is because handedness is only defined relative to the handedness of an observer. Free of an embedded observer a molecule can inherently define handedness by two neighboring chiral centers. For two chiral centers along a polymer chain a diad can identify two states, similar enantiomers or a meso diad (m) and dissimilar enantiomers or a racemic diad (r). In a meso diad a walker along the chain would find substituent groups both on the right side, for example, in the walk described above. There are two possible arrangements of meso diads (left–left or right–right) and two possible arrangements of racemic diads (right–left or left–right) so that an unbiased stereochemical arrangement would contain 50% meso diads. This could be one description of an atactic or non-tactic polymer. However, few properties of polymers are associated with diad tacticity since most properties are associated with longer groupings of mer units. For example, the stereochemistry of diads has little direct effect on the ability of long sequences of a chain to form a helix and to crystallize. Finally, there is no quantitative analytic technique to directly measure diad tacticity in polymers. The smallest unit that can be observed, by nuclear magnetic resonance (NMR), for instance, requires groupings of three mer units. This is because NMR relies on splitting of resonances associated with the distinguishing of different neighboring chiral groups. For a given mer unit two neighboring mer units can be equally observed leading to a group of 3 mer units. This triad can have one of three arrangements, mm (isotactic), rr (syndiotactic), or mr/rm (heterotactic). Since there are twice as many possible arrangements of heterotactic, a random mixture of triads would result in 25% isotactic, 25% syndiotactic, and 50% heterotactic triads. This could be an alternative definition of an atactic polymer. It should be noted that a polymer defined as atactic by diads could be 100% heterotactic or could have many other stereochemical arrangements of triads. Then there is a limited connection between tacticities as measured at different orders in going from lower to higher order (diads to triads). We can use statistics to predict the most likely triad arrangement associated with a given diad distribution. Higher-order tacticities are associated with only one lower-order distribution. Generally, we are interested in the highest possible order of tacticity since this governs the properties of a macromolecule. Highorder stereochemical arrangements do not have names associated with their states since a plethora of arrangements are possible. Generally, we speak of odd orders, 3 (triad), 5 (pentad), 7 (heptad), etc., due to the nature of the NMR measurement mentioned above.

2.1.1 Determination of tacticity (stereoregularity) The tacticity or distribution of asymmetric units in a polymer chain can be directly determined using NMR spectroscopy and infrared (IR) spectroscopy and has been studied for a variety of polymers. Figure 5(a) and 5(b) show the proton NMR spectra [26,27] and IR spectra [28,29], respectively, for the two stereoisomers of poly(methyl methacrylate) (PMMA), syndiotactic and isotactic PMMA. These two structures in a polymer like PMMA give rise to different signatures in both the techniques. In the case of the NMR spectra [26,27], the

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(a)

(b)

r

6.40 τ

(a)

8.14

10.00

8.78 8.95 9.09

% ABSORBANCE

160

80 SYNDIOTACTIC PPMA

ISOTACTIC PMMA

0 3100 2800 1800 1650 1525 (b)

700 WAVENUMBERS cm-1

Figure 5 (a) Proton NMR spectra for syndiotactic (upper) and isotactic (lower) poly(methyl methacrylate). Reproduced from Sperling [27]. Copyright 2006, John Wiley & Sons, Inc. (b) IR spectra for syndiotactic and isotactic poly(methyl methacrylate). Reprinted with permission from O’Reilly and Mosher [28]. Copyright 1981, American Chemical Society.

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137

occurrence of a peak at 8.78 ppm chemical shift (tetramethylsilane peak at 10.00 ppm) as seen in the lower spectrum of Figure 5(a) corresponds to the meso placement of the alpha methyl units and hence represents an isotactic PMMA spectrum. The upper spectrum in Figure 5(a) with a peak at chemical shift of 9.09 ppm corresponds to the racemic placement of the alpha methyl units and hence a syndiotactic PMMA spectrum. The sensitivity of the chemical shift of the alpha methyl protons is accepted to be a fundamental feature reflecting the stereochemical configuration of PMMA. These specific shifts arise from triad sequences in PMMA. Higher-order sequences can be detected in different polymers by going to higher magnetic fields. From the IR spectra shown in Figure 5(b) [28,29], peak assignments can be made for the two configurational isomers of PMMA and are given in Table 1. Some basic aspects of the selection rules for IR spectroscopy and Raman scattering for the detection and characterization of stereoregularity for such polymers are given in Ref. [30]. Similar studies have been conducted on poly(vinyl chloride) (PVC) to assign different IR signatures obtained from different stereo-configurational isomers. The sensitivity of the nC–Cl bond on the stereochemical environment has been utilized using IR spectroscopy. The characteristic vibrations of the nC–Cl bonds are inherently tied in to the configuration as well as the conformation of the

Table 1 [28]

IR peak assignments (cm1) for isotactic and syndiotactic poly(methyl methacrylate)

Isotactic

Syndiotactic

Peak assignment

1,465 1,190 996 950 759

1,450 1,190 998 967 749

d(CH2), da(CH3-O) Skeletal gr(CH3-O) gr(a-CH3) g(CH3) and skeletal

d and g, deformation modes; da , antisymmetric; gr rocking.

Table 2 IR peak assignments for poly(vinyl chloride) based on polymer conformation and configuration [31] Peak (cm1)

Conformational assignment

Configuration

602 619 639 651 676 697

TTTT long sequences TTT short sequences TTTT long sequences TTTG syndiotactic TGuGu syndiotactic TGTG isotactic

Syndiotactic Syndiotactic Syndiotactic Syndiotactic Syndiotactic Isotactic

T, trans; G, gauche (Gu represents a gauche configuration where the rotation about the bond is in the opposite direction to G).

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polymer. The effects of configuration and conformation on the IR peak assignments for PVC are given in Table 2 [29,31]. The commercialization of polypropylene (PP) had been revitalized with the advent of metallocene and vanadium-based catalyst systems, which result in highly stereoregular isotactic and syndiotactic PP, respectively [32]. The advent of these catalyst systems has enabled the synthesis of these PP isomers with enhanced physical properties [33] and applications [34]. Recently Rojo et al. [32] have devised a rheology-based technique to differentiate between stereoisomers of PP. The procedure involves plotting the loss tangent (d) as a function of the complex modulus G as shown in Figure 6 [32]. Differentiating between syndiotactic and isotactic PPs is based on the higher values of Newtonian viscosities, terminal relaxation times, and activation energies for flow for syndiotactic PP samples [32]. Positive identification and differentiation of isomers is possible by plots like the one shown in Figure 6, i.e., plots of loss tangent values versus complex modulus [32]. A consequence of tacticity/stereoregularity is the production of regular helical coiling of the polymer chain. Helical coiling is a secondary structure for synthetic polymers associated with the primary structure of the tactic sequence. Using IR spectroscopy, it has been possible to assign some unique bands to

90

80

70

δ (˚)

60

50 sPP 1 sPP 2 sPP 3 Met-iPP 1 Met-iPP 2 Maxwell model for Met-iPP 1 Maxwell model for sPP 1

40

30

20 100

101

102

103

104

105

106

G* (Pa)

Figure 6 Loss tangent (d) plotted as a function of complex modulus G for a series of syndiotactic and isotactic polypropylene. Reproduced with permission from Rojo et al. [32]. Copyright Wiley-VCH Verlag GmbH & Co. KgaA. iPP, isotactic PP; sPP, syndiotactic PP; Met-iPP, metallocene-catalyzed PP (see Ref. [32] for full details).

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139

tacticity in polymers with helical chain structure. These bands are classified as the helix bands and regularity bands [30]. The helix band not only depends on the nature of tacticity, but on the sequence length of the stereo-configuration. Thus additional microstructural information can be obtained from such IR studies. The values of such absorption bands for some common polymers like PP and polystyrene can be readily found in texts on this subject [30].

2.2 Branching The presence of branches along the main chain of a polymer molecule significantly alters the static and dynamic properties of the polymer [35]. The presence of structural branching is not limited to commercial polymeric materials like polyolefins, but plays an important role in altering the properties of a broad spectrum of materials, which can be classified as nano-particulate ceramic aggregates, polymeric networks and gels. Branch content and nature has a strong influence over structure–property relationships of these materials. For example, the presence of branch content dictates the crystallization behavior [35] of commercial polyolefins and copolymers, the mechanical properties of crosslinked macromolecules, and the nature and extent of reinforcement obtained from aggregated inorganic materials like silica and titania [36–41] when dispersed in an organic polymeric matrix. The need of quantifying branch content in such materials is of vital significance not only to predict the structure–property relationships dictating characteristic material performance in end-applications, but also to gain a better understanding of the underlying thermodynamic and kinetic processes [42–52] governing the synthesis of these materials. Estimating branch content through the development of novel analytical approaches has been a quest for materials scientists for well over five decades. One of the very first approaches to estimate branch content in polymers was using size exclusion chromatography (SEC) (vide infra). The solution properties of a branched polymer molecule differ vastly from that of its linear analogue. The vital difference between a branched and a linear polymer molecule is in the size that they exhibit in solution. SEC essentially fractionates a polydisperse polymer sample into monodisperse fractions based on their molecular size in solution. Hence estimating branch content for polydisperse polymers from SEC is based on this disparity of molecular sizes of branched and linear polymer molecules. NMR spectroscopy has been a very effective tool to estimate branch content in polymers on a quantitative basis. It has the added advantage of being able to discern the branch lengths up to a certain degree. 13C-NMR spectroscopy has been mostly used to carry out such an analysis and depends on the calculations of the chemical shifts arising due to the presence of structural branching. Favorable rheological properties are an essential requirement for the commercialization of polyolefins like polyethylene. The ease of processability of the polymer melt, obtained through modifications in the microstructural features, is as important as the end use mechanical properties of these polymers. Presence of long-chain as well as short-chain branching, LCB and SCB, respectively, more or less dictates the rheological behavior of most commercial

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polyolefins. Inherently, various studies have been conducted over the years linking the melt behavior to the underlying polymer chain microstructure. As already stated, apart from the importance of estimating branch content for determining structure–property relationships, the quest to ascertain the branch content information also has some motivation for enhancing our understanding of some fundamental phenomenon, e.g., phase separation [42–51] between polyolefin blends of high-density polyethylene (HDPE) and linear low-density polyethylenes (LLDPEs) has been reported in literature, where the amount of branches in the linear low-density material govern the occurrence of micro-phase separation. Similarly, even crosslinked materials like poly(dimethylsiloxane) (PDMS) [52] exhibit phase separation driven by a disparity in the topological features of the two phases. The presence of short-chain branching and its estimation has been fundamental to discerning the crystallization kinetics and mechanisms in commercial polyolefins like ethylene-alkene copolymers.

2.2.1 Types of branching in polymers The nature and amount of branch content in macromolecular systems is diverse and plays a fundamental role in their characteristic behavior [53–57] (see also Chapter 2). Apart from molecular weight and molecular weight distributions (MWDs), the nature of branching leading to different topological features can be considered as one the most fundamental features dictating the properties of macromolecules. The classification of many systems is based on the nature of their topological features. Branching in commercial polyolefins is classified as long- or short-chain branching. The presence of either long- or short-chain branching has a unique effect on the properties of these polymers. Long-chainbranched polymers are usually classified to be described as randomly branched polymers. Short-chain branching in polymers leads to structures usually defined as ladder-architecture. Graft-copolymers, where short branches of one polymer are present on the backbone of a second polymer are a special case of ladder polymers. Multi-arm star polymers have also been extensively studied for their unique properties. Dendrimers and hyperbranched polymers (HBPs) represent another class of highly branched polymers. HBPs are similar in structure to dendrimers, but lack a central core from which growth occurs through hierarchical levels as in dendrimers, and are usually synthesized in a one step process. The schematic representation of these various branched architectures is shown in Figure 7. The crystallization kinetics of commercial polyolefins is to a large extent determined by the chain microstructure [58–60]. The kinetics and the regime [60] of the crystallization process determine not only the crystalline content, but also the structure of the interfaces of the polymer crystals (see also Chapter 7). This has a direct bearing on the mechanical properties like the modulus, toughness, and other end use properties of the polymer in fabricated items such as impact resistance and tear resistance. Such structure–property relationships are particularly important for polymers with high commercial importance in terms of the shear tonnage of polymer produced globally, like polyethylene and polyethylene-based copolymers. It is seen that in the case of LLDPE, which is

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141

Figure 7 Schematic representation of different types of branched structures as discussed in the text.

essentially a copolymer of ethylene and 1-alkenes like hexene and octene, giving rise to butyl and hexyl branches, respectively, on a polyethylene backbone, apart from the amount of 1-alkene comonomer, branch content, and small-chain branch length, the primary modulator controlling the crystallization behavior is the sequence length distribution arising from these short-chain branches [58,59,61]. Hence, characterizing the sequence length distribution using spectroscopic techniques is as important as quantifying the short-chain branch content. HBPs [62–64] represent a special class of polymers with a unique set of properties. The development of synthesis chemistries of these materials has been fueled by the numerous potential applications such materials are expected to have. Characterization of the chain structure of such topologically unique materials is critical to understanding and predicting their properties.

2.2.2 Size exclusion chromatography SEC (also known as gel permeation chromatography (GPC)) is routinely used to characterize the MWD in a polydisperse polymer sample (see also Chapter 6). Fractions with different molecular weights are separated by passing a solution of the polymer through a series of columns on the basis of their hydrodynamic volume [65–68], which is the product of the intrinsic viscosity (limiting viscosity, [Z]) and the viscosity average molecular weight M v . The universal calibration curve, obtained from standard polymer samples of known MWD is used to compare with the elution profile for the given polymer sample. Most modern SEC setups are equipped with a triple detection system. They consist of an inline viscometer detector (VD), a refractive index detector (RID), and a light scattering detector (LS). The VD can be used to continuously monitor the intrinsic viscosity [66,67] of the eluting fractions, with the concentration of the given fractions being ascertained by using the RID.

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Figure 8 Difference in the size of a branched polymer molecule (b) compared to its linear analogue (a) of the same molecular weight in solution.

Though SEC is used to characterize the MWD in a polymer sample, it separates a polydisperse polymer sample on the basis of the hydrodynamic size of different fractions and not their molecular weights [66,67]. Hence a branched polymer molecule and a linear polymer molecule of equal size cannot be differentiated by a SEC technique, since both of these would elute out at the same time. For a branched polymer molecule and its linear analogue (having the same molecular weight as the branched molecule) the radius of gyration of the linear polymer will be greater [66] than that of the branched molecule, as can be seen in the schematic shown in Figure 8. In their seminal work in 1949, Zimm and Stockmayer [69] defined the ratio of the mean square radii of gyration of a branched and a linear polymer of equal molecular weight as the parameter g and is related to the parameter gu, which is the ratio of the intrinsic viscosities of a branched and a linear polymer [65–69]. D E R2g where g ¼ D Eb ; R2g

g0 ¼ ge and g0 ¼

(32)

½Zb ½Zl

l

where e is a scaling constant, hR2g i the mean square radius of gyration, [Z] the intrinsic viscosity, and the subscripts b and l refer to the branched and linear polymer, respectively. The intrinsic viscosity and molecular weight measured in a SEC experiment correspond to the actual branched molecule being run through the column. The Mark–Houwink equation can be used to calculate the intrinsic viscosity of the linear analogue with the same molecular weight as the branched polymer being run through the SEC and is given by, ½Zl ¼ KMa

(33)

where K and a are constants for a given polymer–solvent pair. This analytical procedure results in the estimation of the parameter g. The Zimm–Stockmayer relationship (Equation (34) [69]) is used to estimate the branch content. The Zimm–Stockmayer relationship is specific to the nature of the branch content. It requires a prior knowledge of the functionality of the branch point in the main chain, as well as the dispersion in the branch lengths (whether the branch lengths are monodisperse or random) [66–68]. For polydisperse branch lengths

Chain Structure Characterization

with tri-functional branch points, g is given as [66–69], ( )   6 1 ð2 þ nw Þ1=2 ð2 þ nw Þ1=2 þ ðnw Þ1=2 ln 1 g3 w ¼ nw 2 ðnw Þ1=2 ð2 þ nw Þ1=2  ðnw Þ1=2

143

(34)

where the subscripts 3 and w indicate tri-functional branch points with polydisperse branch lengths and nw is the weight average number of branches per molecule. The parameter nw then needs to be converted to express branch content in conventional terms of number of branches per 1,000 backbone carbon atoms, and is given as [67] (for polyethylene), LCB nw ¼ ð14; 000Þ 1; 000C M

(35)

where M is the molecular weight, and 14,000 corresponds to the molecular weight of 1,000 repeat units of a –(CH2)– molecule. In spite of the analytical nature of SEC to estimate branch content in polymers, it represents a relative/secondary technique to those based on indirect calculations of iterative solutions of Equations (32) and (34) [68]. There is a disparity in the experimental conditions and the theoretical assumptions involved in estimating branch content. SEC experiments are carried out in good solvents (good solvent scaling for the polymer molecules) whereas the Zimm– Stockmeyer relationships were derived for theta solution conditions (e ¼ 1/2), which imply a Gaussian scaling. The effect of these assumptions on different branched polymer systems cannot be estimated. The sensitivity of the detectors used in a SEC experiment dictate the accuracy of the obtained results (Figure 9). Molecular weight sensitive detectors like VD and LS show poor response in the low-molecular weight tail of the chromatogram, whereas concentration sensitive detectors like differential refractive index detectors (DRI) have a poor response in the high-molecular weight slice of the raw data [70]. Multi-detector configurations (triple detector) seem to have overcome some of these difficulties; though it has led to an increased complexity in the experimental procedures. The disparity in the intrinsic viscosity of a branched polymer compared to a linear analogue is used to estimate branch content by using SEC. The presence of short-chain branching does not significantly alter the intrinsic viscosity of a polymer molecule. The reduction in [Z] due to short-chain branching is estimated to be only 0.01 times [62] that due to long-chain branches. Hence the sensitivity of SEC to estimate short-chain branching is limited, and only high levels of long-chain branching can be estimated effectively, where comparative data is lacking as discussed below in the section concerning NMR spectroscopy.

2.2.3 Nuclear magnetic resonance spectroscopy NMR spectroscopy can be utilized to obtain branch content information for commercial polymers in a direct quantitative manner. Polyethylene and PVC are the two commercial polymers that have been studied extensively for branch content determination by this technique [71–75]. Obtaining branch content information from such polymers has been dealt with, by using high-resolution

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Figure 9 SEC: Response versus retention volume for (a) RID, (b) VD, and (c) LS detector for the same sample. Reproduced from Beer et al. [70]. Copyright 1999 John Wiley & Sons, Inc. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.

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145

13

C-NMR spectroscopy. This technique involves assignment of the specific shifts in the resonance peaks arising due to a branch point in a carbon backbone chain. Conventionally, these resonance shifts have been calculated for up to five carbon atoms from the branch point [76]. Such an analysis results in the direct estimation of the branching density in a polymer sample like polyethylene. In the case of PVC, the approach is not as simple as for the case of polyethylene, with complications arising due to the stereochemical isomerization in structure due to the presence of the chlorine side groups along the main chain [70]. This necessitates the removal of the chlorine atoms via a reductive de-chlorination process using either lithium aluminum hydride [77] or tri-butyl tin hydride [78]. Once the de-chlorination step is complete, the branch content in PVC can be obtained similar to polyethylene using high-resolution 13C-NMR spectroscopy. The technique of obtaining the shifts in the NMR resonance peaks due to branch points was developed by Grant and Paul [79], also, for example, described in Refs. [29,80], and shall be briefly discussed below.

Grant and Paul Chemical Shifts. The technique of obtaining branch content information from NMR for polymers utilizes an empirical relationship given by Grant and Paul [29,79,80]. The Grant and Paul empirical relationship [29,79,80] can be used to calculate the values of the chemical shifts for carbon atoms in the vicinity of a branch point in a hydrocarbon polymer. The empirical relationship was obtained from NMR studies on alkanes. The chemical shift of any carbon atom in a 13CNMR can be decomposed as a sum of contributions from its nearest five neighboring carbon atoms. The value of the chemical shift for any carbon atom C, is given as, Chemical Shift ¼ 2ða þ b þ g þ d þ Þ þ C (36) where a, b, g, d, and e are called Grant and Paul parameters, and C is a constant, the values are outlined in Table 3 [29,80]. This empirical relationship cannot be used without accounting for some correction terms, which take into account the molecular geometry of the bonded neighbors. This is especially essential when calculating the chemical shift of a branch point carbon atom. These correction terms were given by Grant and Paul to be as follows [29,80]. In Table 4, 31, 21, and 11 represent tertiary, secondary, and primary carbon atom, respectively (Figure 10), and 31(21) represents correction for a tertiary carbon bonded to a secondary, as in a methine group to a methylene. In a study conducted Table 3

Grant and Paul parameters obtained from alkanes [80]

Grant and Paul parameters

Shift (ppm)

a b g d e C

8.61 9.78 2.88 0.37 0.06 1.87

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Gregory Beaucage and Amit S. Kulkarni

Table 4

Correction values for branched polymers [80] Shift (ppm)

31(21) 21(31) 11(31)

2.65 2.45 1.40

Figure 10 Schematic representation of tertiary (31), secondary (21), and primary (11) C atoms.

by Randall [81], the temperature dependence of these correction terms was evaluated. This resulted in slight modifications of the values of the corrections terms. The temperature dependence of these correction parameters were determined by 13C-NMR on highly branched hydrogenated polybutadiene [81]. Using this technique, high-resolution NMR can be utilized not only to obtain branch content information in terms of the branching density in the polymer molecule, but also to estimate the length of the branches. Herein lies a limitation of using NMR to estimate branch content information. The Grant and Paul empirical relationship results in the estimation of specific peak shifts for a branch point carbon atom with different branch lengths provided the branches are smaller than six carbon atoms long, beyond which the branch would be assigned as a long-chain branch by NMR. In a polymer like polyethylene, a branch just about greater than six carbon atoms, does not constitute a long-chain branch, when it’s manifestation on the rheological properties are concerned. It is more apt to define a branch as being a long-chain branch, depending on the number of entanglement units present. Recent studies by Liu et al. [82] have expanded the scope of using NMR to detect branch lengths up to 10 carbon atoms. Liu et al. [82] were able to assign chemical shits values to carbon atoms in a branch longer than six carbons by using ultra-high frequency 13C-NMR (188.6 MHz). NMR remains a very useful technique to estimate branch content in hydrocarbon polymers and constitutes a direct quantitative approach. However, using NMR in quantifying branch content has a drawback in that the results for the branch content obtained will always overestimate long-chain branching, i.e., branches longer than about six carbons. Hence, the sensitivity of NMR to determine branch content is limited to high levels of short-chain branching. But

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147

NMR is an effective tool for the determination of total number of branch sites, nbr, in a polymer chain.

2.2.4 Rheology The rheological behavior of polymer melts is a critical aspect determining the processing parameters of most melt-processed polymers like polyolefins. The presence of structural long-chain branching profoundly alters the behavior of polymer melts, even at extremely low levels. While NMR remains an effective means of quantitatively estimating the number of branch sites in a polymer molecule, its utility in characterizing the feature important to rheological behavior, the volumetric contribution of long-chain branching, is limited. The volumetric contribution of long-chain branches to a polymer molecule can be expressed as [83], zp jbr ¼ (37) z where p is the occupied volume or the mass of a minimum (conducting) path across the polymer (the main chain backbone) and z is the occupied volume or mass of the entire branched structure. Since this feature is critical to rheology of polymers, and its manifestations apparent at even very low levels of long-chain branching, it is natural that numerous studies have been reported in the literature that use rheology to quantify long-chain branching. The presence of long-chain branching has a profound effect on the rheological properties of commercial polymers [84–90], especially the new generation of metallocene catalyzed polyethylenes [91–98]. As was discussed in the previous section on NMR, the definition of what constitutes a long-chain branch is more apt, if it is based on the presence of number of units of entanglements that the branch length represents. Studies have shown that long-chain branches of the order of 2–3 times [53–57] the entanglement molecular weight, Me, strongly affect rheological behavior. It is generally accepted that it is the linear viscoelastic properties of branched polymers as opposed to the non-linear viscoelastic properties that can provide optimum quantification of LCB [84,99], since the disparity in the non-linear viscoelastic properties could be assigned to both, branching as well as the higher molecular weight fractions in a generally polydisperse commercial polymer, and can be equally due to high-molecular weight fractions or branching [84,99]. Covering the enormous volume of the number of rheological approaches to quantify long-chain branching reported in the literature is beyond the scope of this chapter, and hence, only a few key studies shall be discussed in this section. Lai et al. [100] proposed the use of the Dow Rheology Index (DRI) as an indicator for comparing branching level in industrial polymers. For a linear polymer molecule, like unbranched polyethylene, the viscosity of the polymer as a function of the applied shear rate is given by the Cross equation [84,100],  Z 0  n Z g ¼ (38) 1 þ lg

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Gregory Beaucage and Amit S. Kulkarni



where Z0 is the zero shear rate viscosity, g the shear rate, and l the characteristic time given as 3.65 105 l ¼ Z0. The DRI given by Lai et al. [100] is expressed as,  

3:65 105 l=Z0  1 (39) DRI 10 In the absence of long-chain branching, the DRI is expected to be zero and would have positive values for polymers with long-chain branching. It should be noted that the application of the DRI is limited to polymers with a narrow MWD, Mw/Mno2, since it cannot delineate the differences arising from polydispersity and long-chain branching. Shroff and Mavridis [85] proposed the long-chain branching index (LCBI). Though the DRI proposed by Lai et al. [100] estimated differences in branch content between different polymer samples, its restricted applicability to narrow dispersion polymers was a serious limitation. The LCBI [85] was developed to overcome this shortcoming of the DRI. LCBI essentially derives from the theory of branched polymer molecules as given by Zimm and Stockmayer [69]. The primary assumption involved in the approach taken by Shroff and Mavridis [85,101] is that, at very low levels of long-chain branching, the polymer molecules can be considered to be essentially linear. Hence for such a polymer, the Zimm–Stockmayer parameter g [69], is equal to 1. For the calculation of the LCBI, one needs to experimentally measure the zero shear rate viscosity of the polymer sample. The presence of long-chain branches enhances the zero shear rate viscosity [85], and the LCBI is essentially a measure of the amplification in the zero shear rate viscosity due to long branches. The LCBI is given as, ! 1=a Z0 3 1=a3 LCBI ¼ 1 (40) k3 ½Z where Z0 is the zero shear viscosity and [Z] is the intrinsic viscosity and the constants k3 and a3 are obtained by fitting an equation of the type [85], Z0 ¼ k3 ½ZaL3

(41)

where [Z]L is the intrinsic viscosity of a linear polymer. The first term on the right-hand side of Equation (40) is the viscosity enhancement factor due to long-chain branches. LCBI is zero for a linear polymer, and would have positive values in the presence of long-chain branching [85]. Some attempts have been made to correlate rheological behavior with NMR data. One such technique is based on the work of Wood-Adams and Dealy [102], who proposed obtaining the MWD from complex viscosity data, and called it viscosity MWD. In this technique, the weight fraction as a function of reduced molecular weight m (m ¼ M/Mw) is plotted against m to get the MWD. Their observation that long-chain branching caused departures in the viscosity MWD as compared to MWD obtained from GPC measurements [84], led to the development of a technique to estimate branch content with quantitative analysis based on NMR studies. They proposed a routine for quantifying the branch

149

Chain Structure Characterization

content based on this observation, using a factor called the peak ratio, which is the ratio between the m value of the peaks in the distributions obtained by the two techniques, given as [84], peak ratio ¼

GPC MWD peak viscosity MWD peak

(42)

Figure 11 shows such a deviation in the peaks of the MWD obtained from the two techniques [84]. The LCB content for the polyethylene sample shown in Figure 11 was estimated to be 0.8/104 C by NMR. Wood-Adams and Dealy [84] obtained a correlation between the shift values, and the branch content from NMR measurements, given as, LCB ¼ 0; for PRo1 104 C LCB ¼ 1:125 logðPRÞ; for PR 1 ð43Þ 104 C where PR is the peak ratio, defined in Equation (42). As can be seen, most rheological techniques involve estimating the branch content by developing semi-empirical relationships that correlate the presence of long-chain branched structure to the derived rheological properties of such structures. Determination of branch content using dynamic rheology has its share of experimental drawbacks. The frequency limitations of most dynamic rheometers, means that dynamic measurements cannot be carried out in the frequency range of interest. This means that data must be extrapolated by means of viscosity models or using the time–temperature superposition. Simple viscosity models cannot appreciate the rheological complexities of a long-chain branched structure. Secondly, long-chain branching is a thermorheologically complex 1.2 1

w(log m)

0.8 0.6 0.4 0.2 0 0.001

0.01

1

0.1

10

100

m

Figure 11 Molecular weight distribution obtained from viscosity (o) and GPC (solid curve) measurements from the studies of Wood-Adams and Dealy [84]. Reprinted with permission from Wood-Adams and Dealy [84]. Copyright 2000, American Chemical Society.

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structure [103,104] meaning that the simple time–temperature superposition principle used often to extrapolate rheological data need not be valid.

2.2.5 Small-angle scattering In a new analytical approach developed by Beaucage [83] and Kulkarni and Beaucage [105], branch content information and some fundamental parameters associated with the topology of a branched system can be estimated from smallangle scattering (X-ray or neutron) data. This technique can be applied to scattering data from long-chain-branched polymers, under some assumptions, since this analytical approach was primarily developed for non-thermodynamically stabilized structures like nano-particulate aggregates. Small-angle scattering from an aggregated system can be described in terms of local scattering laws like the Guinier’s law [83,105–107]: ! q2 R2g IðqÞ ¼ G exp (44) 3 where I(q) is the scattered intensity, q ¼ 4psin(y/2)/l, y the scattering angle and l the wavelength of radiation, and R2g the coil or aggregate radius of gyration and G is defined as N p n2p where Np is the number of polymer coils in given volume and np is a contrast factor equal to the electron density difference between the polymer coil and the solvent for X-ray scattering; and the power law [83,105–107] IðqÞ ¼ Bf qdf

(45)

where Bf is the power-law prefactor, taking account of local features like size and surface/mass scaling. Since these local laws are limited to describing features smaller than the overall aggregate size, they cannot independently describe overall structural features like branching and topology [83]. Thus, small-angle scattering would prove to be ineffective to estimate the branching characteristics of a polymer or an aggregated nano-particulate material. Beaucage [83] showed that on combination of the information obtained from different local laws, a different picture emerges. The basis of the analytical approach proposed by Beaucage [83] is the assumption of any branched systems to be composed of monodisperse primary particles aggregating to form the overall branched structure. Such a description can be considered to be applicable to branched polymers as well as nano-particulate ceramic aggregates, e.g., by considering the primary particles to be the Kuhn step in polymers, or the smallest individual particle in a ceramic aggregate. Further, such a structure could be considered to be linear or branched, as shown in Figure 12 [83]. The number of primary particles in the backbone chain, p, shown in Figure 12b represents the minimum path through the aggregate. A scaling relationship between the degree of aggregation z, the minimum path p, and the overall structural size R2 and size of the primary particle R1 can be given as [83,108–110],  df R2 (46) pc ¼ z ¼ R1

Chain Structure Characterization

p

151

dmin

R2

R1

a)

b)

Figure 12 (a) Branched chain aggregate, (b) Branched chain aggregate; decomposed into the minimum path, p, and the branches [83]. Reprinted with permission from Beaucage [83]. Copyright 2004, American Physical Society. (See Color Plate Section at the end of this book.)

where c is known as the connectivity dimension, which is equal to 1 for a linear chain and df for regular objects (rod, disk, or sphere). A second scaling relationship between the above terms could be expressed in terms of the minimum dimension dmin [108,109] as,  dmin R2 p¼ R1 df c¼ ð47Þ dmin where dmin represents the mass-fractal dimension of the minimum path (Figure 12b). These parameters, which describe the topology of a branched structure are determined from a static scattering experiment, and the branch content can be calculated in terms of fraction of material occupied in the branches and is given as [83],  dmin df zp R2 1 ¼ 1  zc1 ¼ 1  jbr ¼ (48) z R1 which can be readily obtained from Equations (46) and (47). The parameter dmin could be calculated from the modified power-law prefactor equation to account for branched structures and expressing it as [83],   G2 dmin df G Bf ¼ (49) df 2 Rg2 where G2 is the Guinier prefactor for the aggregate, Rg2 the aggregate radius of gyration, df the mass-fractal dimension and dmin is defined in Equation (47). Since all parameters in Equation (48), except dmin, are determined using Equations (44) and (45), Equation (49) can yield dmin, c (Equation (47)), and jbr (since z ¼ G2/G1

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Figure 13 Branch fraction as a function of z and c [83]. The figure shows an estimate of the optimum range of branch content determination. Reprinted with permission from Beaucage [83]. Copyright 2004, American Physical Society.

where the subscripts 1 and 2 refer to the primary and aggregate structures fit with Equation (44)). Figure 13 [83] shows the sensitivity of the branch content calculated from such a measurement. This estimation should be good in the range of interest for most commercial long-chain-branched polymers (low c, high z) as well as ceramic aggregates. Beaucage [83] showed that it could be possible to get branching information for polymers using this approach. In Figure 14, where neutron scattering data for branched polystyrene is fit to the unified equation [83,107,110–112], it was shown that it is possible to calculate the parameters dmin and c, from such a fit [83]. These model branched polystyrene samples were synthesized by using divinyl benzene (10%) as a comonomer, to obtain controlled levels of branching but where the placement is random. Though such an approach would give an estimate of the branch fraction jbr, in terms of the volume fraction occupied by branches, it lacks information about the number of branch sites in the polymer. Thus, it would be necessary to use such a technique as a complementary approach with other techniques, like NMR, to get a complete picture of branch content. Development of mathematical analysis of scattering data to estimate size distributions in the structure can provide additional information about the

Chain Structure Characterization

153

Figure 14 Neutron scattering data from branched polystyrene fit to the unified equation [83]. Reprinted with permission from Beaucage [83]. Copyright 2004, American Physical Society. (Both the branched PS fractions were synthesized using divinyl benzene as a comonomer. Fraction F2 has a weight average molar mass of 18 108 g/mol and fraction F5 has a weight average molar mass of 2.0 108 g/mol, see Ref. 147.)

overall structure of the polydisperse branched species. Thus, scattering also offers the potential to describe the distribution in branch lengths through recent application of techniques such as the maximum entropy method [110,113–120].

2.3 Crystallization The presence of short-chain branching obtained by incorporating a-olefins like 1-hexene and 1-octene as co-monomers during polymerization of ethylene have a huge impact on its crystallization behavior [58,59,61]. These ethylene-a-olefin copolymers comprise what are known as LLDPEs. The development of the linear low-density class of polyethylenes has been critical in enhancing the processing characteristics of this polymer. LLDPEs have been synthesized by both, homogeneous metallocene catalysts as well as the heterogeneous Ziegler-Natta

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type of catalysts [61]. This section deals with the effects of short-chain branching in such systems on the crystallization behavior of such polymers. (Characterization of the crystalline phase is considered by Alamo in Chapter 7 of this book.) The effect of short-chain branching, the placement of short-chain branching in terms of both, inter and intra-chain heterogeneity and the molecular weight of these polymers dictate the crystallization behavior, and hence play a vital role in the processing as well as the end use properties that can be obtained from such copolymers. The determination of sequence length distribution, which happens to be a ‘‘grey area’’ in this field, also shall be briefly discussed in terms of its importance and a new analytical technique published in a recent paper that makes an attempt to obtain the sequence length distribution quantitatively.

2.3.1 Effect of molecular structure on crystallization The presence of short-chain branches on the backbone of a flexible polymer like polyethylene has a complex effect on the crystallization process. This is in some part due to a general lack of understanding of how branched moieties affect the crystallization process [58]. It is widely believed that short-chain branches act as defects along the polymer chain and are excluded from the crystals, especially in the secondary nucleation step [58,59]. The process of secondary nucleation occurs by placing one stem of the polymer chain on the face of a crystal, which then facilitates the growth through spreading which would be energetically more feasible than the secondary nucleation step. The schematic shown in Figure 15 depicts this process, with i being the rate of secondary nucleation and g is the rate of surface spreading. The values of these two parameters decide the regime in which the crystallization process is occurring [58–61]. Before discussing the effect of short-chain branching on the kinetics of crystallization process, it is necessary to revisit the theory of secondary nucleation and the concept of regimes as given by Lauritzen and Hoffmann

b L

σe

g a

i σ

Figure 15 Schematic representing the secondary nucleation process and growth at the crystal face by spreading. The rates of these two processes are i and g, respectively. (See Color Plate Section at the end of this book.)

Chain Structure Characterization

155

[60]. Secondary nucleation is essentially a crystal growth process. Secondary nucleation occurs by the deposition of a stem of the polymer molecule on a preexisting crystal-face as shown in Figure 15. The overall rate of this process is given by the following expression [58],     Kg Un G ¼ G0 exp  exp (50) RðT  T 1 Þ fTDT where, the first exponential contains terms related to diffusion and transport, and [58] Kg ¼

nbsse T 0m kDH f

(51)

In Ref. [58] these terms are defined as: G is the linear growth rate, U the activation energy for transport of the segments to the crystallization site, R the gas constant, T the crystallization temperature, and TN the temperature at which all motions associated with viscous flow cease, defined as Tg 201C. DT is the undercooling, T0m 2T. Kg is defined as Kg ¼ nbaae T 0m =DH 0f k where n is 4 for regimes I and III and 2 for regime II (see below). f is a correction factor used to compensate for changes in Dh0f with temperature at high undercoolings, defined as f ¼ 2T=ðT þ T 0m Þ. See Ref. [58] for full details and explanation. Table 5 given below has the important characteristics of the three regimes associated with this process. In regime I, the rate of deposition of the secondary nucleus is much lower than that of spreading, in regime II these two processes have equivalent rates, and in regime III growth occurs through deposition of multiple nuclei, without any significant contribution from the spreading process [121,122]. The presence of short-chain branches has a complex effect of crystallization, primarily due to the inherent heterogeneity in structure of individual polymer molecules that exhibit considerable levels of short-chain branches. It is known that in the LLDPEs, which are synthesized using the conventional heterogeneous Ziegler-Natta catalyst systems, the distribution of the short-chain branching is not uniform across different molecular weight chains [58,59,61]. The short-chain branches are believed to be preferentially located on the shorter chains as opposed to the longer, higher molecular weight chains [58,59,61]. This essentially means that a LLDPE sample consists of linear high-molecular weight chains and highly branched short chains. To separate the effect of molecular weight and branching on the crystallization process, Lambert and Phillips [58] conducted isothermal crystallization studies on a series of ‘‘cross-fractionated’’ [58] LLDPE samples. These samples gave them the ability to look at the effects of these two Table 5

n

Relationship between rate parameters i and g in the three regimes, and the value of n Regime I

Regime II

Regime III

i{g 4

iBg

iWg

2

4

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Gregory Beaucage and Amit S. Kulkarni

structural parameters of molecular weight and branching separately. Since the low-molecular weight fractions would have a higher degree of branching, these samples could be analyzed for the effects of branch content on the kinetics of the crystallization process. It would make sense to first discuss what variations in the crystallization process could be expected due to the presence of branches, before presenting the results from the work of Lambert and Phillips [58]. Branch points are considered as defects along the main chain, and hence have to be excluded from the secondary nucleation step. This would inherently lead to a decrease in the rate of secondary nucleation, i. This is in accord with the theory given by Andrews et al. [123] which put forth the idea that presence of defects on the main chain caused an ‘‘inverse logarithmic’’ [58,123] decrease in the growth rate. The process of spreading, though energetically favored as compared to the secondary nucleation step, occurs through the diffusion of the polymer chain onto the surface created by the secondary nucleus deposition. This is essentially a kinetically controlled process, and reptation [59,124] is believed to be a primary mechanism in this transport process. It is well known that the presence of branching affects the reptation process, since the presence of a branch point means that reptation can occur only if it is accompanied by the retraction of the branch [124]. Figure 16 shows the tube model for reptation and how the presence of branches is expected to significantly alter the relaxation times for the polymer molecule. Since branching would be expected to affect both the rate of secondary nucleation and spreading, the presence of branches would also determine the regime in which the crystallization process occurs. Figure 17 from the work of Lambert and Phillips [58] shows the effect of branching in low-molecular weight fractions of LLDPE on the linear growth rates of the secondary nucleation process. Sample H-1 is the linear control sample and the degree of branching increased in the following order for the other samples S-7WS-1WS-4 [58,59]. These samples contained hexyl branches at between 4 and 22 branches/1,000 C (octene was used as the comonomer). As can be seen in the plot the transition between Regime I and Regime II occurs at lower temperatures with increased branching. The transition temperature shifts from 125.31C for the linear sample (H-1) to 123.11C for sample S-7 [58]. From the calculations for the rate parameters i and g, it was seen that the rate of both the secondary nucleation and spreading

Figure 16 Tube model for reptation of a branched polymer molecule from the work of Blackwell et al. [124]. Reproduced with permission from Blackwell et al. [124]. Copyright 2000, The Society of Rheology, Inc.

Chain Structure Characterization

logG + U* 12.3R(T-T_)

1.5

157

H-1 S-4 S-1 S-7

Tb = 123.6C

Tb = 123.3C 0.5

Tb = 123.1C -0.5

Tb = 124.1C

-1.5

-2.5 10.0

14.0

18.0 1/TΔT f

22.0

(x105)

Figure 17 Effect of branching on the secondary nucleation and linear growth rates from the work of Lambert and Phillips [58]. The effect of branching on the Regime I–II transition can also be seen. Reprinted with permission from Lambert and Phillips [58]. Copyright 1994, American Chemical Society.

decreased with increased branching. The interesting result though was the different extents to which branching affected these parameters. The decrease in the rate of secondary nucleation was more pronounced than the decrease in the rate of spreading. This could explain the decrease in the transition temperatures between Regime I and II. Since the rate of secondary nucleation was seen to be affected more than the rate of spreading, it was obvious that this would lead to an extension in the temperature window over which the Regime I was exhibited. In subsequent calculations, Lambert and Phillips [58] also showed that the value of free energy of folds, se, decreased with increased branching, which pointed to a greater occurrence of non-adjacent re-entry process. The greater reduction in the secondary nucleation rate compared to the spreading rate pointed in the direction of total rejection of branched moieties from the secondary nucleation process [58]. The cross-fractionated samples used here allowed for isolating the effects of short-chain branching and molecular weight on the crystallization process. In a companion paper, Lambert and Phillips [59] looked at the combined effect of branch content and molecular weight. The samples used in this work included high-molecular weight fractions with branching. The results from the lower molecular weight branched samples [59] (called as intermediate molecular

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Gregory Beaucage and Amit S. Kulkarni

weight samples) were similar to the results from their previous paper [58], i.e., they saw a reduction in the crystallization rates, and a reduction in the transition temperature between Regime I and II. The results on the linear growth studies from the work of Lambert and Phillips [59] are shown in Figure 18a. Sample S-5, which was a branched sample with about 6 branches/1,000 C, had the highest molecular weight in this series with a weight average molecular weight of around 89,000 [59]. This sample did not display Regime I behavior. The entire data set obtained for this sample was ascribed to the Regime II of crystallization. This could be due to a direct result of its molecular weight, which is high enough so as to suppress Regime I. Reptation would be slower at higher molecular weights, and this would lower the rate of spreading, g, and the occurrence of entanglements could enhance the secondary nucleation step, thus increasing the value of i. The results seen for sample S-5 were corroborated from the results for the higher molecular weight fractions in which Regime I crystallization was totally absent (Figure 18b). Most of these high-molecular weight samples exhibited Regime II and III. As in the low-molecular weight samples, these samples also showed a branch content dependency on the transition temperature between Regimes II and III (it was between Regime I and II in case of the low-molecular weight samples). Additionally, as could be seen in the case of sample S-6, Regime II is absent due to its very high molecular weight (174,000 Mw). The complex effects of branching and molecular weight on the kinetics and nature of the crystallization process are depicted in Table 6. The main conclusions from this work are that the presence of branching usually suppresses the transition temperature between regimes, essentially suppressing the higher-order

1

b

F - 3 (0) S - 5 (6.67) S - 8 (13.64) S - 2 (16.28) E - 65 (32)

0

LOG 1/t1/2 + U* /2.3R (Tc-T∞)

LOG 1/t1/2 + U* /2.3R (Tc-T∞)

a

-1

-2

-3

-4

1 NBSI 484 (0) S - 6 (2.86) S - 3 (5.46) S - 9 (11.05)

0

-1

-2

-3

-4 4

7

10

13

16

1/TΔTf (x10)

19

22

7

9

11

13

15

17

1/TΔTf (x10)

Figure 18 Effect of branching on the secondary nucleation and linear growth rates from the work of Lambert and Phillips [59]. (a) Low molecular weight samples. Sample S-5 exhibits only Regime II behavior as explained in the text. (b) High molecular weight samples. Reprinted with permission from Lambert and Phillips [59]. Copyright 1996, Elsevier.

Chain Structure Characterization

159

Table 6 Schematic representation of the effects of branching and molecular weight on the crystallization kinetics and the appearance of the Regimes in crystallization

Regime I

Regime II

Regime III

Linear Low Mol Wt Low Mol Wt Branched High Mol Wt High Mol Wt Branched

crystallization regime, whereas higher molecular weights usually suppress the lower-order regime due to a reduction in the rate of spreading due to kinetic effects of molecular weight on a diffusive process like reptation. The LLDPEs used in the work of Lambert and Phillips [58,59] were obtained from heterogeneous Ziegler-Natta catalysts. It was known that the distribution of short-chain branches in polymers obtained from such a catalyst is not uniform. To study the effect of the sequence length distribution, which essentially is determined by how the branches are distributed, Kim and Phillips [125] compared the isothermal crystallization behavior of LLDPEs obtained from both Ziegler-Natta as well as metallocene catalyst systems. The ethylene-octene copolymers obtained from the homogeneous metallocene system showed a linear decrease in the peak melting temperatures as a function of branch content (Figure 19a) [125]. This linear dependency was not seen in the case of the heterogeneous catalyst system (Figure 19b) [125]. In fact, the depression in the peak melting temperatures in the Ziegler-Natta catalysts was not as pronounced as in the case of the metallocene polyethylenes. This important result showed that though the presence of branches had an impact on the crystallization behavior of these polymers, the primary modulator was the distribution of these branches or the sequence length [125]. Thus heterogeneity in the polymer chain microstructure was the deciding factor in the crystallization behavior of these materials. The conclusion that metallocene catalysts give rise to more uniform copolymers with little inter-chain heterogeneity or intra-chain heterogeneity as compared to Ziegler-Natta catalysts has been contended in the literature [126]. Mirabella and Crist [126] performed calorimetric studies on a series of ethyleneoctene/hexene copolymers obtained from both Ziegler-Natta and metallocene catalysts. The peak melting temperatures for some of these samples are shown in Figure 20 as a function of the comonomer content. They observed a linear dependency in the reduction of the peak melting point with increasing branch content in both the cases. They concluded that the assumption that Ziegler-Natta catalyst systems give rise to compositionally heterogeneous copolymers is

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Gregory Beaucage and Amit S. Kulkarni

a

b 130.0

HLDE MLPE

130.0

L4-0

115.0 H7-O

115.0

Tm(°C)

100.0

L10-O L13-O

H17-O H16-O

100.0

L30-B L40-P L18-O L24-O

Tm(°C)

H10-O

85.0

70.0

85.0

70.0 Low Mw

55.0

55.0

L93-P

High Mw Medium Mw

L39-O

40.0 0.000

0.025

0.050

0.075

40.0 0.00

0.100

0.01

0.02

0.04

PB

SCB/1000C

Figure 19 (a) Peak melting temperature as a function of the branch content in ethyleneoctene copolymers (labelled –O, and symbol K; B (symbol, &) and –P (symbol, W) are for ethylene-butene and ethylene-propylene copolymers, respectively) and obtained from homogeneous metallocene catalysts show a linear profile. (b) Ziegler-Natta ethylene-octene copolymers do not show a linear relationship between peak melting point and branch content [125]. Reproduced from Kim and Phillips [125]. Reprinted with permission of John Wiley & Sons, Inc.

140

140 130

ZN fractions Metallocene fractions Metallocene whole

110 100

ZN fractions Metallocene fractions

130

Tm(°C)

Tm(°C)

120

120

90

110

80

100

70 60 0.00

0.02

0.04

0.06 0.08 XH

0.10

0.12

0.14

90 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

XO

Figure 20 Linear dependence of peak melting temperature with branch content in terms of comonomer (left: hexene; right: octene) content from the work of Mirabella and Crist [126]. Reproduced from Mirabella and Crist [126]. Copyright 2004, John Wiley & Sons, Inc. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.

incorrect [126]. The reason for the disparity in this behavior observed in their study compared with the work of Kim and Phillips [125] could be because of the molecular characteristics of the samples used. The high-molecular weight copolymers used by Kim and Phillips [125] had a maximum branch content of about 16 branches/1,000 C, whereas copolymers with comparable molecular weight in the work of Mirabella and Crist [126] had branch content as high as

Chain Structure Characterization

161

84 branches/1,000 C as estimated from NMR spectroscopy. The disparity in the work of Mirabella and Crist [126] could be because of this large difference in the branch content of their samples.

2.3.2 Metallocene and Ziegler-Natta catalyst systems In light of the literature reports that indicate an overbearing significance of the catalyst systems used on the occurrence of inter- and intra-chain heterogeneity in ethylene-a-olefins copolymers, this section shall briefly review the structure of Ziegler-Natta and metallocene catalysts. The Ziegler-Natta catalysts most used currently are titanium tetrachloride supported on magnesium chloride with triethylaluminium used as a co-catalyst [127]. This is essentially a heterogeneous system with the monomers being polymerized, and represents sites with differing catalytic activity and hence close control of the macromolecular architecture is not possible [128]. However, metallocene catalysts represent a sandwiched system with only a single active site, and are homogeneous since they can be dissolved in hydrocarbons [128]. The activity of metallocene catalysts received a huge boost by the synthesis of a co-catalyst methylaluminoxane [129]. These systems can have an activity of about 10,000 times [128] that of Ziegler-Natta polymerizations and are needed at extremely low loadings. Figure 21 shows the structure of methylaluminoxane and some frequently used metallocene catalysts. These are some key advantages that the metallocene catalysts have over conventional Ziegler-Natta catalysts and hence it is highly probable that interand intra-chain heterogeneity expected in ethylene-a-olefins copolymers can be controlled through the use of the metallocene system.

2.3.3 Sequence length distributions The previous sections in this chapter have tried to stress upon the significance of distribution of sequence lengths in polyethylene-based copolymers. The sequence length of interest in a system of ethylene-octene copolymers would be the number of methylene units before a hexyl branch point. As was discussed, this parameter has a greater impact on the crystallization behavior of these polymers than any other structural feature like branch content, or the comonomer fraction. The importance of sequence length distributions is not just limited to crystallization behavior, but also determines the conformational,

Figure 21 Structure of methylaluminoxane (extreme left), and some metallocene catalyst systems. Reproduced from Kaminsky [128], with permission of The Royal Society of Chemistry.

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Gregory Beaucage and Amit S. Kulkarni

morphological, rheological, and mixing properties of the copolymer. Though techniques like 13C-NMR spectroscopy can determine the sequences, this technique is usually limited, in that it cannot positively differentiate sequences longer than six carbon atoms long. In some very recent work by Karssenberg et al. [130], attempts have been made to improve the analytical ability of a technique like NMR spectroscopy to effectively predict the distribution of sequence lengths in polyethylene-alkene copolymers. They analyzed the entire 13C-NMR spectrum for homogeneous ethylene-propene copolymers. They used quantitative methods based on Markov statistics to obtain sequence length distributions as shown in Figure 22 [130]. The 0.3

(a)

Normalized ethylene sequence length distribution Normalized ethylene sequence mass distribution

nE (S) WE (S)

0.25 0.2 0.15 0.1 0.05 0 0

20

10

30

Sequence length (s) 0.9

(b)

Normalized ethylene sequence length distribution Normalized ethylene sequence mass distribution

0.8

nP (S) WP (S)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

1

2

3

4

5

6

Sequence length (s)

Figure 22 Sequence length distributions for ethylene-propene copolymers (Karssenberg et al. [130]). Top: normalized ethylene sequence length distribution; bottom: normalized propylene sequence length distribution. Reproduced from Karssenberg et al. [130]. Copyright 2006, John Wiley & Sons, Inc. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.

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163

accuracy of such a technique will have to be established by carrying out similar analysis on copolymers obtained from Ziegler-Natta catalysts, and could serve as direct proof of the blocky-nature of branch distribution in such systems.

2.4 Hyperbranched polymers Synthesis and characterization of HBPs have become topics of great interest in the past 15 years and HBPs are characterized by a randomly branched structure as opposed to the controlled molecular topology of dendrimers [131]. Various synthesis routes exist and have been developed recently, though the very first synthesis was carried out from condensation of ABx type of monomers with xX2 [132,133]. Other synthesis routes include the original single monomer synthesis using ABx (xX2) monomers, via self-condensation [134], self-condensing vinyl polymerization [135], ring opening polymerization [136], and proton transfer polymerization [137]. A generic route to the synthesis and structure of a HBP is shown in Figure 23. In addition, double monomer synthesis routes have been developed where the reaction of A2 and Bx (x W 2) monomers, yields structures that can be described as HBPs [138]. Interest in the field of HBPs has seen a phenomenal increase in recent years, in part due to the exciting possibilities offered by these topologically unique materials. The molecular architecture of HBPs has lead to numerous potential applications of these materials like special classes of optical [139], magnetic [140], and conductive [141] materials. HBPs have also found applications in nano-composite films [142], as biomaterials [143] and molecular encapsulates [144]. One of the main reasons for the unique properties of HBPs is the molecular geometry of these disordered structures, in addition to their degree of branching, molecular weight, and polydispersity. The random branched structure of HBPs potentially yields a number of structural isomers, which has a bearing on the final properties of these materials. Like dendrimers, HBPs generally exhibit greater solubility compared to linear polymers. The glass transition temperatures of HBPs can also be very sensitive to the various numbers of structural isomers that could be present for any given chemistry. Conventionally, degree of branching (Db) has been used as a tool to quantitatively describe the architecture of HBPs. Different groups or units in a HBP can be classified as being linear (L), branched (B), or terminal (T) as shown

Figure 23 General structure of a hyperbranched polymer synthesized by the polymerization of AB2 monomer.

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Gregory Beaucage and Amit S. Kulkarni

in Figure 24. The degree of branching, Db, according to this classification of individual units is expressed as the ratio [22,145–146], Db ¼

BþT BþTþL

(52)

of the sum of branched and terminal units to the total number of units in the HBP. 13 C-NMR can be used to give a quantitative estimate of such branch contents for HBPs. The different chemical environments of the terminal, branched, and linear units can be resolved in the NMR spectra of some of the polymers with this architecture. Such specific assignments in a NMR spectrum are based on the line widths of the resonance peaks, which in turn are inversely proportional to the mobility of those species [145,146]. The mobility of the units would be expected to increase and have the following trend, TWLWB. Hence from such a measurement, quantitative estimates of Db to characterize the architecture of such polymers can be established.

a) B

B

AB

terminal (t)

B

BA

AB

branched (b)

linear (l)

b) Branched Linear

Branched

Linear

O O

Terminal

O

O OCH3

O

OCH3

OCH3

Terminal

O

O O

O

OCH3

O

O

O

O

O

O

O

OCH3

O

O OCH3

OCH3

Figure 24 (a) Classification of different units in a hyperbranched polymer, branched, linear, and terminal [145]. Reproduced from Feast et al. [145] with permission from The Royal Society of Chemistry. (b) branched, linear, and terminal units in hyperbranched poly(dimethyl 5-(4-hydroxy butoxy) isophthalate) [146]. Reproduced from De Luca and Richards [146]. Copyright 2003, John Wiley & Sons, Inc. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.

Chain Structure Characterization

165

3 1

119.9

119.8

2

119.7

119.6

119.5

119.4

Figure 25 13C-NMR spectrum for poly(dimethyl 5-(4-hydroxy butoxy) isophthalate) [146]. Reproduced from De Luca and Richards [146]. Copyright 2003, John Wiley & Sons, Inc. Reprinted with permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.

A 13C-NMR spectrum for poly(dimethyl 5-(4-hydroxy butoxy) isophthalate) [146] is shown in Figure 25. The terminal units with the highest mobility (peak 1) is to the left of the spectrum, whereas the least mobile branched units (peak 2) are at the right, whereas the linear units with intermediate mobility (peak 3) are seen as the central peak.

3. SUMMARY Polymer chain structure is characterized by a hierarchical model based on statistical scaling transitions in a polymer coil at thermal equilibrium. On the smallest scale short-range enthalpic interactions dominate and the chain displays local persistence associated with the Kuhn length. At larger sizes the structure depends on a balance between thermal energy, chain entropy, and long-range interaction enthalpy. The large-scale structure is based on the Brownian model with perturbations associated with concentration, temperature, externally applied force and structural topology related to chain branching. These factors can lead to changes in the chain scaling. A linear coil displays four possible largescale states, extended chain in response to an external field, SAW, Gaussian, and collapsed states. The coil can respond to perturbations through the formation of a size of scaling transition, which is called a blob. Depending on the perturbation the nature of the scaling transition varies. These include concentration blob, thermal blob, and tensile blob. Other scaling transitions are likely to exist in response to structural perturbations. The effects of tacticity and short-chain branching on persistence were discussed as well as the control of crystalline

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morphology. Methods to quantify long-chain branching and the consequences on the coil model were also presented. Finally a brief discussion of HBPs was given. Effective deduction of polymer chain structure can be obtained using a variety of analytic and empirical pathways. The multitude of variables associated with fundamental features associated with a polymer chain, e.g., architecture (linear, branched, cyclic, etc.), crystallization (crystalline morphology), chemistry (block, alternating, or random copolymers), conformation and configuration can be effectively characterized with an equally diverse set of characterization tools. From very basic information regarding the hydrodynamic features of the polymer chain/coil as deduced by viscometry, to complex information regarding the tacticity and branching from techniques based on NMR spectroscopy, chain structure characterization often is the crux of obtaining structure–property relationships. Light scattering is often used to obtain information regarding the molar mass of the polymer sample, and is often used in conjunction with other detector systems in GPC. Techniques based on IR spectroscopy are critical in the chemical characterization of the basic building blocks of a polymeric system, the functional group analysis. Critical information regarding the structure of an individual polymer chain has also been effectively characterized with the advent of neutron scattering techniques. Through the application of specific techniques, it is possible to extract information critical for addressing specific problems, ranging from material selection to failure analysis, and is an integral part of developing any effective structure–property relationship road map.

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CHAPT ER

5 Chain End Characterisation Anthony T. Jackson and Duncan F. Robertson

Contents

1. Introduction 2. End Groups in Free Radical Polymers 3. End Groups in Condensation Polymers 4. End Groups in Polymers from Ionic Polymerisation 5. Closing Remarks Acknowledgements References

171 175 182 194 201 201 201

1. INTRODUCTION The characterisation of end group functionalisation from synthetic polymers is important for a number of reasons, and is described in this chapter with particular reference to industrial polymeric systems. End group functionality can be important to the application for the polymeric system, e.g., the end groups are very important in prepolymers for polyurethanes, so that efficient formation of soft blocks and hard blocks, plus cross-linking, can occur. Knowledge of the end groups of a polymer often gives evidence for the polymerisation methodology employed to make the material. Information on the initiators and end-cappers, plus chain transfer agents can be obtained. An example reaction scheme for polymerisation of a free radical polymer system is shown below in Figure 1. The resulting end group fragments in the polymer, therefore, indicate which initiators, chain transfer agents and terminating agents were used (or if no specific terminating agents or chain transfer agents have been employed, such as when disproportionation occurs). The end group functionality of condensation polymers is typically defined by the monomers employed to make these materials. An example is shown below for a common polyamide polymer, namely nylon (see Figure 2). These polymers

Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00405-4

r 2008 Elsevier B.V. All rights reserved.

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Initiation I R• + M

→ →

2R• RM•

Propagation RM• + M RMn• + M

→ →

RM2• RMn+1•

Chain Transfer RMn+1• + AH A• + M AMn• + M

→ → →

RMn+1H + A• AM• AMn+1•

→ →

RMx My R (RMx-H) + (RMy+H)

Termination RMx•+ RMy• RMx•+ RMy•

Combination Disproportionation

Figure 1 Reaction scheme for the free-radical polymerisation (I is the initiator, R the fragment of initiator, M the monomer and AH the chain transfer agent).

O

O

n HOC(CH2)x COH + n +1 H2N(CH2)y NH2

−n +1 H2O

O

O

H2N(CH2)y NH[C(CH2)x CNH(CH2)y NH]nH Nylon

Figure 2 Reaction scheme for the formation of Nylon.

are typically made by reacting a di-amine with a di-acid, such that amine end groups are produced. It is also possible that material with acid end groups is present and possibly cyclic oligomer. The other common type of synthetic polymer made by condensation polymerisation is the polyester, typically manufactured by the reaction of a di-ol with a di-acid. Many ionic polymerisation routes (both cationic and anionic) are also used to make industrial polymers. The end group functionality typically depends on the initiator used to make the polymer. Several modern analytical instruments are powerful tools for the characterisation of end groups. Molecular spectroscopic techniques are commonly employed for this purpose. Nuclear magnetic resonance (NMR) spectroscopy, Fourier transform infrared (FTIR) spectroscopy and mass spectrometry (MS), often in combination, can be used to elucidate the end group structures for many polymer systems; more traditional chemical methods, such as titration, are still in wide use, but employed more for specific applications, for example, determining acid end group levels. Nowadays, NMR spectroscopy is usually the first technique employed, providing the polymer system is soluble in organic solvents, as quantification of the levels of

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end groups can often be obtained directly. Calibrations are required for quantification of end groups by means of FTIR spectroscopy. The data obtained from mass spectrometric techniques is most commonly used to obtain qualitative information on end group structure. The sensitivity of many mass spectrometric techniques allows structural information on minor end groups to be obtained, often not available from NMR and FTIR spectroscopy data. The most commonly used NMR spectroscopy techniques are 1H and 13C NMR. The inherent lower sensitivity of 13C NMR, due to the low natural abundance of the 13C isotope, can reduce its applicability for characterisation of polymers of high molecular weight. Characterisation of a lower molecular weight fraction of the polymer, which can often be produced by chromatographic (e.g., using gel-permeation chromatography, GPC) fractionation or solvent extraction, often enhances the end group information that can be obtained. One of the main advantages of FTIR spectroscopy over NMR techniques is that the former does not require the polymer system to be soluble. Data can often be directly obtained from solid polymer, and while not an absolute technique, FTIR spectroscopy can be effective in comparing end group levels in differing molecular weight (MW) samples of the same polymer, sometimes through application of absorption subtraction between their mid-infrared spectra. FTIR microscopes also allow data to be obtained from much more localised regions than available with NMR investigations. This can be useful, for example, in highlighting the cause of a processing-difference-induced defect as a consequence of an end group (MW) difference, such as was the case for a gel-like defect observed in a polysulfone (PES), and characterised as arising from polymer with a lower concentration of aryl–Cl end groups, see Figure 3 [1]. Even though the amount of sample is often not a problem for polymer characterisation, contamination analysis often requires that analysis be performed on a smaller amount of material than that can be analysed by means of NMR spectroscopy. MS-based techniques can also be employed on relatively small amounts of sample, but typically require the polymer to be soluble in organic solvents. Matrix-assisted laser desorption/ ionisation-time of flight (MALDI-TOF) is the most commonly employed mass spectrometric technique, as the simplest data are obtained for end group analysis. Electrospray ionisation-mass spectrometry (ESI-MS) is occasionally preferred for end groups that do not remain intact in the MALDI-TOF technique, as the former is a ‘softer’ methodology. The ESI-MS data obtained from synthetic polymers can often, however, be quite complex due to the nature of the ionisation mechanism. Tandem mass spectrometry (MS/MS) techniques can be employed to obtain additional end group information. The MS/MS method involves selection of individual oligomers prior to fragmentation. The fragments obtained often contain additional information about end group structure to that generated by either MALDI-TOF MS or ESI-MS. The combination of a number of these techniques often provides complementary information on end group structure and hence the mechanism of polymerisation. The synergy between MALDI-TOF MS and NMR spectroscopy is particularly powerful, with MS/MS providing additional information where necessary. MALDI-TOF MS provides information on individual oligomers,

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2.2

Absorbance

1.7

1.2

0.7

0.2 850

800

750 700 Wavenumber / cm-1

650

600

Figure 3 FTIR microscopy absorbance spectra (100 mm aperture) recorded from a microtomed section through a defect area of a PES film. The upper spectrum is characteristic of the base film; the lower spectrum is representative of the defect area. The difference in relative intensity of the band at 760 cm1 can be clearly seen; this band is attributable to the aryl–Cl end group. The consequence of this difference was the aryl–Cl end group deficient material processed differently giving rise to a gel-like feature in the polymer film. Reproduced with permission from Chalmers and Everall [1]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA.

whereas NMR spectroscopy data are an average from the whole sample. The data from the former technique can, therefore, be employed to generate information from samples containing varying end group structures. One of the main advantages of MS/MS is that it can be employed to generate information on individual end group structures, whereas MALDI-TOF MS only provides information on the combined mass of both the initiating and terminating functionalisation. Specific examples of how these three techniques may be combined together to generate a full picture of end group functionality in a polymer system are provided below. Three particular examples are described in detail in order to emphasise the methodology; these are the characterisation of end groups from acrylic polymers, from polyesters such as poly(ethylene terephthalate) (PET), and polymers from ionic routes that is highlighted by polyethers. Extraction of low molecular weight fractions from higher molecular weight materials may be required in order to generate structural information, due to the low levels of end groups present. This is particularly important for MALDI-TOF MS and 13C NMR spectroscopic characterisation of end group structure. And while the various NMR and MS methodologies offer good synergies in characterising end groups from many polymer systems, these techniques typically require that the polymeric system is soluble in an organic solvent.

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2. END GROUPS IN FREE RADICAL POLYMERS This section focuses on describing on how end group structures can be determined from one particular polymer that was generated by free radical polymerisation (see Figure 1), namely poly(methyl methacrylate) (PMMA, 1). CH3 R′

CH2C

n

R′′

O C OCH3 1

The methodology employed, however, is applicable to many other free radical polymers generated from vinyl monomers (such as, e.g., polystyrene). It should be noted that this methodology is also equally applicable to many polymers generated by condensation and ionic polymerisation routes. PMMA is an industrially produced polymer that has many applications including for kitchen fittings (such as work surfaces) and bathroom furniture (e.g., acrylic baths, sinks and showers), signage, lighting and (more recently) television screens [2]. The major benefits of this polymer are its water-clear colour and stability to ageing, even under severe conditions. Traditional routes of manufacture are by radical polymerisation in which an initiator (possibly peroxide or azo-based) is employed with termination by disproportionation (resulting in a mixture of saturated and unsaturated chain ends). Additional use of a chain transfer agent (e.g., a thiol) can change the majority of both the initiating and terminating chain ends and aid control of the molecular weight distribution [2]. This polymerisation route is described by Figure 1 (vide supra). The combination of NMR- and MS-based techniques is a powerful methodology for generating information on these end group structures. Industrial PMMAbased polymers are often of relatively high average molecular weight, but the high polydispersity of these materials means that a lower molecular weight fraction can often be obtained and characterised by these techniques. A number of controlled living radical polymerisation techniques have been explored over the last decade or so [3], with some commercial polymers resulting from this research. These living radical polymerisation routes include nitroxidemediated polymerisation (NMP) [4], atom-transfer radical polymerisation (ATRP) [5,6] and reversible addition-fragmentation chain transfer (RAFT) [7] polymerisation. These polymerisation routes offer possibilities in controlled architecture of polymers and copolymers that are not typically available from regular free radical polymerisation. These three living radical polymerisation routes result in polymers with different end group structures. Spectroscopic techniques are typically key in understanding the end group structures of these polymers [8,9]. As an example, a description of how these analytical techniques may be employed to characterise the end group structures of PMMA polymers generated by ATRP is described below. The mechanism of ATRP may be described by the scheme shown below (Figure 4). This results in polymer with either bromide- or chloride-terminating

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groups, as this functionality is part of the initiator used for the polymerisation and is key to the radical shuttling mechanism that is proposed for ATRP (where X is Br or Cl in Figure 4). The other fragment of the initiator (Ru in Figure 4) should form the initiating (a) end group of the polymer chain from this mechanism. A combination of NMR spectroscopy, MS and FTIR spectroscopy has been employed to verify that the end group structures proposed from this mechanism are correct and, in addition, generate information on any other end group structures resulting from side reactions during polymerisation [10,11]. An ATRP polymer of methyl methacrylate (MMA), made with ethyl-2bromoisobutyrate as the initiator such that 2 may describe the expected structure, was initially characterised by means of 1H and 13C NMR spectroscopy [11]. The resulting 13C NMR spectrum is displayed below in Figure 5 (the region of the spectrum, where the carbonyl resonances occur, between approximately 171–179 ppm is shown in an expansion), with the proposed assignments annotated along with the corresponding letters on the anticipated dominant structure (i.e., 2, shown in an expanded 13C letter labelled form below the spectrum). Several key resonances in the 13C NMR spectrum are consistent with those expected for the proposed end group structures. Peaks a (from non-equivalent methyl carbons at 29 and 22 ppm), b (a quaternary carbon at 41 ppm), c (methylene from the ethyl ester at 60 ppm) and d (methyl group from the ethyl ester at 13 ppm) provide evidence for the presence of the ethyl-iso-butyrate group at the initiating (a) end of the polymer, along with some resonances from the first MMA unit attached to this moiety. Data indicating that the terminating (o) bromide end group is present are provided by peaks from the terminal MMA unit, labelled m (terminal MMA methyl group at 25 ppm), n (terminal MMA quaternary carbon adjacent to bromide group at 58 ppm) and o (carbonyl of terminal methyl ester group from MMA at 172 ppm). The proposed structure accounts for all of the major peaks in the spectrum, indicating the proposed structure (2) dominates for this polymer. Estimations of the average molecular weight of the polymer can be calculated from a comparison of integration values for selected peaks from the backbone with those from the end groups [11]. CH3

CH3

CH3

H3CC

CH2C

O C

O C

H3CH2CO

n

Br

CH3 H3C

CH2C CH2C

O C

O C

n-2

2

CH2

OCH3 O

H3CH2CO

OCH3

CH3 C COCH3 C O O

H3CC

3

CH3

CH3

CH2

CH3

CH3

H3CC

CH2C CH2C

H3CC

CH2C H

O C

O C

O C

O C

n-1

H3CH2CO

O C

OCH3 OCH3 4

n

H3CH2CO

OCH3 5

177

Chain End Characterisation

CH3 MTn

R′X

R′

CH2C

R′

n MMA

MTn

n-1

O C MTn+1X

CH3

C H2C X O C

OCH3 OCH3 Dormant CH3

CH3 R′

CH2C O C

n+1

MT

X

Etc.

CH2C

n-1

O C

OCH3 OCH3 Active

Figure 4 Reaction scheme for ATRP of PMMA (RuX is the initiator, X the Br or Cl and MT the catalyst).

h j

i

g/k

f

h

j

c

f

d

o 178 b

177

176

175

174

173

172 ppm

e a

l

m n

60

55

50

45

40

35

30

25

20

15

ppm

a m f f CH3 CH3 CH3 CH3 l n b g j k H3CC CH2C CH2C CH2CBr a e n-2 o h h h O C O C O C O C d i i i H3CCH2O OCH3 OCH 3 OCH3 c

Figure 5 13C NMR spectrum from PMMA generated by ATRP with ethyl-2-bromoisobutyrate as initiator (see text for details).

178

Anthony T. Jackson and Duncan F. Robertson

MALDI-TOF mass spectrometry was employed to generate confirmatory evidence of the end group structures from the same PMMA polymer [10]. An expansion of the resulting MALDI-TOF mass spectrum is shown in Figure 6. This partial spectrum effectively covers the range of one repeat unit of the polymer (between mass-to-charge ratio (m/z) 1860–1960), which is approximately 100 Da. Interestingly, the dominant series of peaks in this spectrum, emphasised by the expansion, do not have mass-to-charge ratios consistent with the expected structure. Lithium bromide was added as the cationisation agent in the experiment, so peaks from lithiated molecule ions (i.e. [2+Li]+) were expected to be observed in the MALDI-TOF mass spectrum. This component was expected to have a monoisotopic peak at m/z 1901.9 (C91H147O36BrLi for the lithiated 17-mer of structure 2) and a low intensity peak is indeed noted in the spectrum (labelled 2 in Figure 6). Furthermore, the isotope pattern is similar to that expected for a component containing a bromide group (with equivalent amounts of 79Br and 81Br). Previous work [11] indicated that this major component was fragmenting in the ion source of the MALDI-TOF mass spectrometer, leading to the formation of oligomer with a lactone end group

3 Theoretical Isotope Distribution 3

100

% 5

3* 4 2 1900

0 1860

1870

1880

1910

m/z

1890

1920

1900

1910 m/z

1920

1930

1940

1950

1960

Figure 6 Partial MALDI-TOF mass spectrum from PMMA generated by ATRP with ethyl-2bromoisobutyrate as initiator (inset shows theoretical isotope distribution for lithiated 18-mer of structure 3). (Peak labelled 3 arises from post-source decay of 3 [10].)

Chain End Characterisation

179

(structure 3), via loss of methyl bromide from 2. The peak from this lactoneended oligomer, labelled 3 in Figure 6, clearly does not contain any bromine atoms (from the isotope pattern). This demonstrates an important feature of MALDI-TOF MS that with high enough resolution to generate isotope patterns (i.e., using the reflectron mode of operation), such that information on the presence (or not) of elements (e.g., Br and Cl) can be established, distinctive isotope distributions can be obtained. This can provide confirmatory evidence for the presence of some end group structures. A comparison between the theoretical isotope pattern of C95H152O38Li, for the lithiated 18-mer of 3 (see inset in Figure 6), with that experimentally obtained indicates that they are very similar. Furthermore, the experimentally observed monoisotopic peak at m/z 1907.9 is very similar to that expected (m/z 1908.0) for this oligomer. Heating of this polymer [10] generated material that was proposed, from the MALDI-TOF MS and NMR data, to contain little or none of the original bromide terminating end group, with the lactone end group dominating (i.e., oligomer with structure 3). This indicates that this lactone end group is formed by loss of methyl bromide during heating, as well as in the MALDI-TOF MS process (from the original polymer) [10]. A characteristic band from the carbonyl group in the 5-membered lactone ring [12] is clearly discerned in the FTIR spectrum obtained from this heated polymer at approximately 1780 cm1 [10], with low levels of this functionality also probably present in the original polymer (see Figure 7). This demonstrates how FTIR can be employed to provide confirmatory evidence for the presence of selected end group structures in polymers. Evidence for a competing disproportionation mechanism (see Figure 1) for the termination of chain ends is provided by the combined presence of the peaks from 4 and 5 in the MALDI-TOF mass spectrum of this PMMA polymer (see Figure 6) [10]. Confirmation of the presence of the unsaturated and saturated chain ends, arising from disproportionation, was obtained by means of 1H and 13 C NMR spectroscopy, respectively [11]. Another PMMA polymer, generated by ATRP with p-toluene sulphonyl (tosyl) chloride as the initiator, such that structure 6 was the expected dominant end group structure, was also analysed by means of NMR spectroscopy and MALDI-TOF MS. Both 1H and 13C NMR spectroscopy provided data that indicated that the expected tosyl group and chloride functionality were the dominating functionalities at the initiating (a) and terminating (o) chain ends, respectively. The MALDI-TOF MS data from this polymer indicated that 6 was indeed the major component. The partial MALDI-TOF MS spectrum (from m/z 1475–1575), which approximately covers one repeat unit of the polymer, is displayed in Figure 8. Lithium bromide was again used as cationisation agent, so the presence of the major component was expected to be confirmed by observing a monoisotopic peak from the 13-mer at m/z 1497.7 (C72H111SO28ClLi, see theoretical isotope pattern for 13-mer in inset of Figure 8). The dominant peak in the expansion of the experimental spectrum is indeed seen at this mass-to-charge ratio (m/z 1497.7). In addition, close similarities are detected between the

180

Anthony T. Jackson and Duncan F. Robertson

Absorbance

PMMA A-30 mins at 150°C

PMMA A PMMA B

1800

1750

1700

1650

Wavenumber (cm-1)

Figure 7 FTIR spectra from PMMA (two batches, labelled PMMA A and PMMA B) generated by ATRP with ethyl-2-bromoisobutyrate as initiator, before and after heating (only PMMA A was heated) to 1501C for 30 min.

theoretical and experimental isotope distributions from these peaks, indicating that the chlorine functionality is present in this polymer. O H3C

CH3

S

CH2C Cl

O

O C

H3C

n

CH3 H3C

S

CH2C CH2C

O

O C

n-2

CH3 C COCH3 C O O CH2

OCH3 O

OCH3 6

7

O H3C

O

CH2

CH3

S

CH2C

O

O C

CH2C

n-1

O C

OCH3 8

O H3C

OCH3

CH3

S

CH2C H

O

O C

n

OCH3 9

The fragmentation in the MALDI-TOF MS experiment noted from the brominated polymer is less prevalent in this chlorinated material, but evidence for the lactone-ended oligomer (7) is still noted (see Figure 8). Evidence for the competing disproportionation mechanism is again provided by the presence of peaks proposed to be from unsaturated (8) and saturated (9) end-functionalised oligomer [10]. The data indicate that this disproportionation reaction is a minor termination pathway, as low intensity peaks are noted for 8 and 9 (as for 4 & 5 from the brominated analogue).

Chain End Characterisation

181

6 Theoretical Isotope Distribution

6

100

7*

7 %

89 1490

1500

m/z

1510

0 1480

1490

1500

1510

1520

1530

1540

1550

1560

1570

m/z

Figure 8 Partial MALDI-TOF spectrum from PMMA generated by ATRP with p-toluene sulfonyl chloride as initiator (inset shows theoretical isotope distribution for lithiated 13-mer of 6). (Peak labelled 7 arises from post-source decay of 7 [10].)

Additional evidence for the structures of end groups from many free radical polymers, including styrenes [13–15] and methacrylates [15–18], can be obtained by MS/MS. This technique was employed to generate end group information from the chlorinated PMMA sample. Selection of an individual oligomer enables data to be obtained on one end group functionality. In this case, a lithiated oligomer (11-mer at m/z 1297.6) from the major component in the sample (i.e., 6) was selected for characterisation by MS/MS and the resulting spectrum is displayed in Figure 9 [10]. Previous data from methacrylates demonstrated that two major series of fragment ion peaks were observed in the MS/MS spectra, at low mass-to-charge ratios, that could be employed to generate information about the end group structures [17,18]. Two series of peaks, labelled A and B in Figure 9, indicate that the proposed end group structures for the chlorinated oligomer are as expected, i.e., tosyl and chloride groups as the initiating (a) and terminating (o) end groups, respectively. Peaks at m/z 128 and 228 (see fragmentation scheme in Figure 9) from the A series indicate that the chloride end group functionality is present in this oligomer. The other series (B), with peaks at m/z 262 and 362, is indicative of the presence of the tosyl group as

182

Anthony T. Jackson and Duncan F. Robertson

Relative Intensity (%)

100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

[M + Na – CH3Cl]+ B Series (+Li+) 262 362

G S O

CH2

C CH2

O C

C C H2

O C

OCH3

G

H3C

H3C

H3C

O H3C

A Series (+Li+) 228 128

C CH2

O C

OCH3

7

CH3

CH3

C CH2

C Cl

O C

OCH3

O C

OCH3

OCH3

A B

A

O

CH3 S CH2 C Cl

B Li

H3C

O

O C

11

+

OCH3

100

200

300

400

500

600

700 m/z

800

900

1000 1100 1200

Figure 9 MS/MS spectrum from lithiated 11-mer of PMMA generated by ATRP with p-toluene sulfonyl chloride as initiator (i.e., 6). Proposed fragmentation scheme is shown for assignment of peaks from the A and B series, indicating how end group information may be gleaned.

the initiating functionality. The peaks from each series are separated by a massto-charge ratio (m/z) equivalent to the mass of the repeat unit of the polymer (i.e., 100 Da). The residual mass, after subtracting the mass of a number of (whole or partial) repeat units and the mass of the cation from the mass-to-charge ratio of the fragment ions, is the mass of the end group [17,18]. Peaks labelled G are from internal cleavages and do not aid identification of end group structure. The above data demonstrate how a combination of analytical techniques can be employed to generate end group information from polymers generated by a free radical polymerisation mechanism. In the example described, the use of ESI-MS might have provided more information on the presence of bromide end groups [19,20], as these polymers do not fragment when this technique is used. MS is a particularly powerful complementary technique for characterising the end groups of free radical polymers, as end group composition can be hidden by more intense backbone resonances and hence is not always clearly observed in NMR data.

3. END GROUPS IN CONDENSATION POLYMERS Another important area of polymer chemistry for which end group analysis is often sought is in the polyester industry. This section will attempt to describe

Chain End Characterisation

183

methods that have been used to determine end group concentrations in polyesters, using PET as the main focus, given it is the best known of the aromatic polyesters. Many valid methodologies will be described, or referenced, before concentrating on the particular methodologies used more recently in our own laboratories. Over the past 25 years or so, synthetic polymeric materials have played a significant role in enhancing the ability to package materials (especially foodstuffs) in a safe and convenient manner that is appreciated by both the retailer and the consumer. PET polymers have played a major role in this area, with significant developments in high barrier containers for carbonated soft drinks, high-strength films, excellent gas barrier packaging for sensitive foodstuffs and materials of high clarity. Other significant factors that have played a part in this growth are the portability, lightweight nature and recyclability of PET. It is also a strong, tough, flexible thermoplastic that readily crystallises and can be oriented into highly ordered structures. PET is a polycondensation polymer based on the reaction of terephthalic acid (TA) and mono-ethylene glycol (MEG) or alternatively with di-methyl terephthalate (DMT) plus MEG (Figure 10). For preparing PET polymer for applications such as carbonated soft drinks bottles, the PET polymerisation is a two stage process involving the formation of a base polymer first at approximately 2901C and then a solid-state polymerisation (SSP) stage from which preforms are made. End group determination is of great importance in the characterisation of PET, as end group concentration is an important consideration for making a successful resin choice that will satisfy specific customer needs. Carboxyl and hydroxyl are typically the two major end groups in PET. Establishing an understanding and control of the end group balance is important in controlling both the manufacturing process, especially the SSP reaction, and also the downstream processing. Indeed, the high lateral spatial resolution available with FTIR microscopy was used to highlight differences between hydroxyl and carboxyl end group concentrations between the edges and centres of sections microtomed from a series of PET granules taken from various stages within a solid-phase polymerisation cycle. In the reported study, significant concentration differences were observed for the two positions following the SSP step [1,21]. The carboxyl end is known to catalyse both the polymerisation and hydrolysis reactions. The level of each is process dependant, with the ester interchange process tending to give the lowest carboxyl level in the final product. Some of the possible end groups in PET, along with their mechanisms of formation, are shown below in Figure 11. The carboxyl end can also thermally degrade to form vinyl end groups [22–24], which occur along with the formation of acetaldehyde (Figure 11). This is a side reaction that needs to be avoided, as acetaldehyde can taint mineral water and carbonated soft drinks if present at high levels (W20 ppm) in the bottle polymer. Hence lower temperatures (around 1601C) are used in the SSP phase to minimise the formation of acetaldehyde. Several techniques for determination of end group structure in polyesters have been described in the literature [25–31]. Many analytical procedures have

184

O n H3COC

O COH + n +1 HOCH2CH2OH

O COCH3 + n +1 HOCH2CH2OH

O

- n+1 H2O

O

HOCH2CH2O(C

- n+1 CH3OH

COCH2CH2O)nH

O HOCH2CH2O(C

O COCH2CH2O)nH

Figure 10 Reaction schemes for formation of PET from terephthalic acid and ethylene glycol (top) and di-methyl terephthalate and ethylene glycol (bottom).

Anthony T. Jackson and Duncan F. Robertson

O n HOC

Chain End Characterisation

185

been used, in particular, for the calculation of carboxyl end group concentration. These include acidimetric titration, potentiometric titration and radiochemical determination. Chemical treatment is part of the initial procedure in all of these cases, which in itself gives an advantage to the spectroscopic techniques where no pre-treatment is necessary. The procedure proposed by Campanelli and co-workers [32], for example, was based on potentiometric titrations using ethanolic potassium hydroxide, with the hydrolysed sample dissolved in one of two solvent systems dependent on the extent of hydrolysis. A mixture of di-methylphenol and chloroform, suitable for solubilising the polymers as well as high molecular weight oligomers, was used for calculation of carboxyl group concentrations up to about 1.5 meq carboxyl groups per gram of sample. Di-methylsulfoxide was used as solvent for polymers with higher carboxyl group concentration and for dissolution of TA monomer. Ward and Patterson [33–35] introduced the use of infrared spectroscopy for end group determination in the late 1950s. This technique was based on measurement of absorption bands that characterise the considered end groups, on the assumption that the carboxyl and hydroxyl units were the only end groups in PET. Comparison of the spectrum before and after deuteration of the sample enabled confirmation of the assignments and calculation of Beer–Lambert absorption coefficients for those end groups. FTIR spectra, showing the region of interest (4000–1800 cm1) for the measurement of end groups in PET, are shown below (Figure 12). These are FTIR transmission spectra of PET, prepared as an amorphous pressed film from the melt (approximately 0.1 mm thick), before and after drying the PET film under vacuum. The absorption band due to hydroxyl end groups is clearly evident at approximately 3,542 cm1; the broad absorption due to carboxyl end groups has a band maximum approximately 3,256 cm1 but is overlapped by other PET absorption bands. The end group concentrations can be calculated from their FTIR absorption spectrum using the Beer–Lambert Law. The original calibration of the IR absorption versus end groups was based on measurement of the deuterium content of the water obtained from combustion of deuterated PET polymer assuming that only carboxyl and hydroxyl end groups were present. Later calibrations were based on measurements of standards generated from model compounds [36]. In the original work of Ward and Patterson a comparison (absorbance subtraction) was made between the IR spectra recorded from protonated and deuterated spectra of amorphous PET film samples; this aided establishing the peak position maximum positions of the –OH and –COOH bands and defining background absorption levels for their concentration determinations; the –OD and –COOD band maximum occur at 2,604 cm1 and 2,458 cm1, respectively [37]. A simple conversion for PET gives (in the case of acid ends): ½COOH ¼ Corr:AbsCOOH 104 =plCOOH where [COOH] is the concentration of carboxylate groups in g equiv./106 g polymer, p the sample density in g cm3, l the film thickness in cm, Corr.AbsCOOH

186

O

O

O

COCH2CH2OC

O

C-

-C

COCH2CH2OH

-C

O

O

-C

O

O

-C

O -C

O -C

Figure 11

O

COCH CH2

+

O

-C

+

HOCH2CH2OH

-C

+

HOCH2CH2OH

-C

O

O

O COCH2CH2OH

O

COCH2CH2OH

-C

COCH2CH2OH

O

O

O

O

COCH CH2

+

O

O

COH

+

O

O

-C

COH

H3CCH

O

COCH2CH2OC

O

O COCH2CH2OCH2CH2OH + H2O

O COH

+

Reaction schemes for formation of PET oligomers with different end group structures.

O

C- + H3CCH

HOCH2CH2OCH2CH2OH

Anthony T. Jackson and Duncan F. Robertson

O -C

Chain End Characterisation

Absorbance

-OH end group ~3542 cm-1

-COOH end group ~3256 cm-1

187

PET containing absorbed water

Absorbed water

Vacuum dried PET

4000

3500

3000 Wavenumber /cm-1

2500

2000

Figure 12 Expansion (4000–1800 cm1) of absorbance FTIR spectra recorded from a PET film, before and after drying.

the absorbance of carboxyl ends corrected for background absorbance of PET with no COOH end groups and eCOOH the band aborptivity. FTIR spectroscopy has been found to be a reliable technique for end group determination in PET and shows good agreement with results from titration and 1 H NMR measurements. The absorbance bands from carboxyl and hydroxyl end groups have been shown to interfere to some extent. A simultaneous curve fitting procedure has been developed, in recent years, to separate the two peaks, in order to give more representative values for the respective end group measurements [38]. (The IR method of Ward and Patterson [34,35] has been adapted for determining the end group concentrations in poly(butylene terephthalate) [39] and poly(ethylene naphthalene-2,6-dicarboxylate [40].) Early work on polyester end group analysis by NMR spectroscopy was carried out by Page and Bresler [41]. They used the labile protons in the hydroxyl groups of both the carboxylate and hydroxyl end groups. As these labile protons are by nature broad resonances in the proton NMR spectrum other methodologies have been developed over the years to better measure these end groups. The advantage of using NMR for these measurements is that NMR is an inherently quantitative technique, in that line intensity, or the area under each signal, in the spectrum is proportional to the number of hydrogen (or other observed nucleus) atoms in that group. Measurement of the peak area is carried out by integration. NMR-based techniques also offer the advantages of relatively small sample requirement and the measurements being quick and reliable. One of the issues in using solution state NMR for PET analysis is that, due to the high crystallinity content of the polymer, it is fairly difficult to dissolve. Harsh

188

Anthony T. Jackson and Duncan F. Robertson

solvents are required; some examples of which are 3-chlorophenol, 1,1,1,3,3,3hexaflouro-2-propanol (HFIP) and trichloroacetic acid or trifluoroacetic acid. We prefer to use 1,1,2,2-tetrachloroethane-d2 (TCE) in our laboratory. Experiments need to be performed at elevated temperatures (100–1201C) to keep the sample in solution (in TCE). The spectra displayed below show how this solvent can be used to obtain appropriate NMR resonances from PET that can be used to detect and quantify the end groups of the polyester. Figure 13 shows a full 1H NMR spectrum of PET, in TCE solvent, acquired at 1001C. Resonances a and b are from the terephthalate and ethylene glycol derived protons, respectively. Resonances c and d arise from the protons in diethylene glycol (DEG), which is formed as a side reaction in the PET polymerisation process. An expansion of the ethylene glycol-based region of the spectrum is shown in Figure 14. Proton NMR techniques have been described for characterising end groups [42–44], the methodology below being that which is used in our laboratory. Resonances e and f in Figure 14 arise from the hydroxyl end group in PET. Integration of resonance f versus resonance b (or the resonance from the

O

a

a

-(C a

a

O

O b b COCH2CH2O)x - (C

a

a

O

c d d c COCH2CH2OCH2CH2O)y-

a

a

a

b

c

d

9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Chemical Shift (ppm)

Figure 13

1

H NMR spectrum of PET in TCE solvent.

0

189

Chain End Characterisation

b O -C

O

e f COCH2CH2OH

c d

e f

5.0

4.9

4.8

4.7

4.6

4.5

4.4

4.3 4.2 4.1 4.0 Chemical Shift (ppm)

3.9

3.8

3.7

3.6

3.5

Figure 14 Expansion (3.50–5.02 ppm) of ethylene glycol region of 1H NMR spectrum of PET.

terephthalate moiety) gives a direct measure of the number of hydroxyl end groups present relative to the number of polymer repeat units. The number of these end groups per 100 polymer repeat units can be calculated, for example, if the integral of resonance b is set to 400 and the integral of resonance f is divided by 2 (because it is a resonance from –CH2OH). Figure 15 shows this same expanded region when di-methyl terephthalate is used as the monomer. The only difference is the sharp single peak labelled g, which arises from residual methyl ester end groups. This resonance sits on top of the triplet arising from the –CH2OH (f) end (at 400 MHz) and, therefore, deconvolution software is used to measure these residual methyl ester ends. Acquiring data at room temperature is probably most important for the carboxylate end measurement, as any polymer degradation at elevated temperature could form additional acid end groups. As an example of NMR methodology that is not carried out in TCE, consider the following for the measurement of carboxylate ends in polyesters. The sample is dissolved in a mixture of HFIP and trichloromethane and spectra are acquired at room temperature (see, e.g., Figure 16). Dissolution in HFIP causes the carboxylate end groups to become functionalised and form an aromatic secondary carbon ester [45,46] as shown in Figure 17. A mediated reaction is required to enable a rapid esterification of the acid end groups at room temperature, hence avoiding generation of additional acid end

190

Anthony T. Jackson and Duncan F. Robertson

b

c

e

d O -C

O

g COCH3

f

5.1

5.0

4.9

4.8

4.7

4.6 4.5 4.4 4.3 4.2 Chemical Shift (ppm)

4.1

4.0

g

3.9

3.8

3.7

3.6

Figure 15 Expansion (3.60–5.20 ppm) of ethylene glycol region of the 1H NMR spectrum of PET, when di-methyl terephthalate has been used as the monomer.

groups. Resonances at 6.3 and 6.7 ppm in the 1H NMR spectrum (Figure 16) can hence be ignored in end group calculations, as these occur due the mediators added and the resultant side reactions. Resonance h (6.0 ppm) occurs from the hexafluoro ester (from the derivatised acid end group of the PET) and this can be quantified against the polymer chain (resonance a) in a similar way to that described previously. Fluorine (19F) NMR can also be used for this end group measurement [47], as the reaction involves formation of a fluoro ester. The formation of vinyl end groups has been mentioned previously as an undesirable side reaction in the PET polymerisation process. It is important to be able to measure these end groups, as acetaldehyde is evolved during formation of this moiety, which can cause taint in carbonated soft drink applications. Figure 18 shows a spectrum obtained in TCE at 1001C, showing a resonance from the vinyl end group that can be quantified relative to the polymer backbone. This resonance is usually very low in intensity and difficult to measure accurately. One way of enhancing this resonance is to set the decoupler in the 1 H NMR experiment to be on top of the other half of the vinyl end resonance. This has the effect of collapsing the multiplicity of the resonance shown (i in Figure 18) and hence increasing the intensity above the noise in the spectrum. We then find it preferable, in our laboratory, to use a peak height measurement

191

Chain End Characterisation

a

O

O

h COCH(CF3)2

-C

h

8.5

8.0

7.5

7.0

6.5

6.0

Chemical Shift (ppm)

Figure 16 Expansion (5.80–8.65 ppm) of 1H NMR spectrum of PET, showing acid end groups.

O -C

O COH

O + HOCH(CF3)2

-C

O COCH(CF3)2 + H2O

Figure 17 Reaction scheme for conversion of acid ends to esters by addition of 1,1,1,3,3,3hexaflouro-2-propanol (HFIP).

method rather than integration (as the integration is very difficult to carry out accurately, due to the vast differences in the intensities of the two resonances that are being compared). Although this methodology may not be very accurate in absolute terms, it is repeatable and, in an industrial laboratory, a method that is able to measure and compare these end group levels in some way is essential. There are many other methodologies that can be used to measure end groups of polyesters by NMR. The examples above represent methods that we are using in our own work. Another powerful analytical technique for measurement of end groups in polymers is MALDI-TOF MS. The advantage of this technique is that information on individual oligomers can be obtained. Detection of higher molecular weight cyclic oligomers (i.e., those with no end groups) is also possible [48], unlike by means of NMR spectroscopy and FTIR spectroscopy. Direct quantification of end group levels, from the MALDI-TOF MS data, is difficult due to the likely

192

Anthony T. Jackson and Duncan F. Robertson

b

O

d

c

O

i COCH CH2

-C

e

f

i

5.2

Figure 18

1

5.1

5.0

4.9

4.8

4.7 4.6 4.5 4.4 4.3 Chemical Shift (ppm)

4.2

4.1

4.0

3.9

3.8

3.7

H NMR spectrum of PET showing a vinyl end group resonance.

ionisation efficiency differences for oligomers with hydroxyl and carboxylate ends. Relative levels of end groups (and cyclic oligomer) in multiple samples can be visualised from the data. The presence of hydroxyl and carboxyl end groups can be discerned from the data, with differentiation between oligomers containing zero, one and two acid end groups. One issue with end group interpretation is the isobaric nature of oligomer containing two hydroxyl ends with that containing one acid end and one hydroxyl end group with one diethylene glycol (DEG) unit in-chain. The presence or lack of carboxylate salt ends, however, (derived from the cation used in the MALDI-TOF MS experiment, as shown below) can be employed to differentiate between these two species. So, for example, if a lithium salt is used as the cationisation agent, the following reaction occurs (to partially convert some of the acid ends to carboxylate salt): CO2 H þ Liþ ! CO2 Li þ Hþ An example (partial) spectrum, indicating how end group information can be gleaned by MALDI-TOF MS, is shown in Figure 19. Peaks are annotated with numbers corresponding to those for the proposed structures of the oligomers present in this low molecular weight sample of PET. Cyclic oligomers (structures 10–12), including those containing DEG units (11 with one unit of DEG and 12 with two units). Linear oligomers (structures 13–17) are also clearly present in the sample, including hydroxyl functionalised material (13–15) and lower levels with acid end groups (16–17). Linear oligomer containing DEG units can clearly be

193

Chain End Characterisation

100 10 10

13

11 16

%

14

17′′

16′

17 15

12 950

0 500

750

1000

1250

1500

1750

1000

2000 m/z

1050 m/z

2250

1100

2500

2750

1150

3000

3250

Figure 19 MALDI-TOF mass spectrum from low molecular weight PET sample. Inset shows expansion of MALDI-TOF spectrum from m/z 950–1170, with peaks annotated with numbers corresponding to proposed assignments (see text for assignments).

discerned (e.g., 14 which is hydroxyl ended oligomer with one DEG unit). Confirmation of the presence of acid functionalised material from conversion of these end groups to carboxylate salt in the MALDI experiment (as described above) is possible from peaks annotated as 16u and 17uu in Figure 19. Conversion of the one acid end group in oligomer 16 to carboxylate salt gives rise to peak 16u. In addition, 17uu is derived from conversion of the two acid end groups in 17 to lithium carboxylate. TE

TE

n

10

HOE

TE

n

n

TEE

11

H

HOE TE

13

n

TE

n

H

16

n

TEE

2

12

TEE H

HOE

1

14

HO

T =

TE

1

TE

n

TEE H

15

HO

TE

n

TH

17

O

O

C

CO

E =

CH2CH2O

2

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Anthony T. Jackson and Duncan F. Robertson

4. END GROUPS IN POLYMERS FROM IONIC POLYMERISATION There are a number of commercially important synthetic polymers produced by cationic [49,50] or anionic polymerisation [51,52] routes. An example is shown in Figure 20 for poly(propylene glycol) (PPG), which is a polymer commonly used as the soft segment in polyurethane polymers. PPG is produced by the anionic ring-opening polymerisation of propylene oxide [53], as described by the reaction scheme shown in Figure 20, with an alcohol (ROH) as initiator and a base such as potassium hydroxide (therefore M is typically K) as catalyst. Alcohols such as water (R is –H) or di-propylene glycol (R is –OCH(CH3)CH2OCH2CH(CH3)OH) can be used as initiators, in order to produce di-hydroxyl end-capped PPG (structure 18). Chain transfer can result in formation of impurities in the desired end group functionality, as shown in Figure 20 for formation of allyl-initiated PPG (structure 19). This impurity is typically more prevalent in PPG polymers of higher average molecular weight. It results from ring opening of propylene oxide to form a derivative of allyl alcohol (H2CQCHCH2OM+) that reacts with further units of propylene oxide to form oligomers. Isomerisation of allyl end groups can result in the formation of isopropenyl end functionality, as described in Figure 20. HO CH2CHO H

H2C

n

CHCH2O CH2CHO H n

CH3

CH3

18

19

Initiation RO-M+ + P



ROP-M+

Propagation ROP-M+ + Pn



ROPnP-M+

Termination ROPnP-M+ + ROH



ROPn+1H + RO-M+

Chain Transfer P + RO-M+ H2C=CHCH2O-M+ + P H2C=CHCH2OP-M+ + Pn

→ →

Isomerisation H2C=CHCH2OM+ H3CCH=CHO-M+ + P H3CCH=CHOP-M+ + Pn

→ →





H2C=CHCH2O-M+ + ROH H2C=CHCH2OP-M+ H2C=CHCH2OPnP-M+

Allyl

H3CCH=CHOM+ H3CCH=CHOP-M+ H3CCH=CHOPnP-M+

Isopropenyl

Figure 20 Reaction scheme for the anionic polymerisation of propylene oxide to form PPG (R is the part of alcohol initiator, M the metal from the catalyst and P the propylene oxide).

195

Chain End Characterisation

Di-hydroxyl end-capped PPG (18) is an intermediate in the formation of a common polyurethane prepolymer (20). End group functionality of this intermediate is important, as this hydroxyl functionality is modified to form the prepolymer. Any different end group structures could lead to the presence of prepolymer that will not form polyurethane of the desired structure. The desired reaction of the intermediate (18) to form the prepolymer (20) is described in Figure 21. Reaction of one unit of the intermediate (18) and two units of methylene diphenyl 4,4u-diisocyanate (MDI) results in the formation (nominally) of the prepolymer (20). O O C N

CH2

O

NHCO CH2CHO CNH

CH2

n

N C O

CH3

20 O H2C

CHCH2O CH2CHO CNH

CH2

n

N C O

CH3

21

O

O

OCNPhCH2Ph [NHCO(CH2CHO)nCONHPhCH2Ph]x NCO CH3 22

A combination of NMR spectroscopy and MALDI-TOF MS is commonly employed in our laboratory for the characterisation of PPG polymers. Analysis of di-hydroxyl end-capped PPG (18) is initially described. The 1H NMR spectrum [54] can be used to confirm the backbone structure of the polymer, as can be seen in Figure 22 (a and b are from the backbone of the polymer, with c from the methyl side chains). Peaks of low intensity, downfield of those from the backbone of the polymer, in the 1H NMR spectrum may be used to identify and quantify the allyl functionality in the polymer [55]. These resonances (d, e and f) are

HO CH2CHO H n

+

2O

C N

CH2

N C O

CH3 PPG

MDI

O

O O C N

CH2

NHCO CH2CHO CNH n

CH2

N C

CH3 Prepolymer

Figure 21 Reaction scheme for the reaction of PPG with MDI to form a polyurethane prepolymer.

O

196

Anthony T. Jackson and Duncan F. Robertson

d e f H2C CHCH2O CH2CHO d

e

n

f

c

CH3

6.0 5.9 5.8 5.7 5.6 5.5 5.4 5.3 5.2 5.1 5.0 4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4.0 Chemical Shift (ppm)

a&b

a b CH2CHO

n

CH3 c

6.5

6.0

5.5

5.0

4.5

4.0 3.5 3.0 2.5 Chemical Shift (ppm)

2.0

1.5

1.0

0.5

Figure 22 1H NMR spectrum from di-hydroxyl end-capped PPG. Inset shows expansion of spectrum indicating assignments for allyl end groups of polymer.

annotated in the expansion of the 1H NMR spectrum shown in Figure 22, along with a structure indicating the protons giving rise to these peaks. End group isomerisation of allyl end groups to isopropenyl ended species (i.e., as shown in Figure 20) can be followed, in solution, using 1H NMR, as is shown in Figure 23 [56]. Gradual conversion of polymer containing allyl ends (Figure 23(a), 0 h) to all isopropenyl ends (Figure 23(c), 594 h) can be visualised by resonances from the unsaturated portions of the end group functionalities. A spectrum taken at an intermediate time (Figure 23(b), 89 h) shows a mixture of both allyl and isopropenyl functionality is present. Proposed assignments of the resonances from these two end group functionalities are shown in Figure 23(a) (allyl) and Figure 23(c) (isopropenyl). The presence of hydroxyl end groups in PPG can be assigned from 13C NMR data (Figure 24), with resonances (g) observed between 65–68 ppm in the spectrum shown in Figure 24. There are two different resonances here (g) due tacticity effects in the polymer (meso/racemic (m/r) isomerisation of the terminal dyad). Estimations of the amount of these ends in the polymer, along with the average molecular weight of the PPG, can be made from the 13C NMR data. Confirmation of the presence of allyl and hydroxyl functionality in PPG polymers can be gleaned from MALDI-TOF MS data. An example spectrum for a sample of PPG 2000 is shown in Figure 25. These data can be used to generate information about both the end groups and the average molecular weight [57].

Chain End Characterisation

197

Figure 23 Monitoring of isomerisation of allyl end groups of PPG to isopropenyl functionality over time by means of 1H NMR spectroscopy: (a) 0 h, (b) 89 h and (c) 594 h. Reproduced from Ref. [56] with permission of John Wiley & Sons, Inc.

The major distribution, centred at approximately 2000 Da as expected, can be assigned as from di-hydroxyl end-capped oligomers of PPG (18). Addition of lithium salts in the MALDI sample preparation procedure leads to the generation of [18 + Li]+ ions as the major species. A series of low-intensity peaks below

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Anthony T. Jackson and Duncan F. Robertson

g CH2CHO CH2CHOH n CH3 CH3

g

78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 Chemical Shift (ppm)

80

75

70

65

60

55 50 45 40 Chemical Shift (ppm)

35

30

25

20

15

Figure 24 13C NMR spectrum from di-hydroxyl end-capped PPG. Inset shows expansion of spectrum indicating assignments for hydroxyl end groups of polymer.

18

100

%

19

0 1000

1500

2000

2500 m/z

3000

3500

Figure 25 MALDI-TOF mass spectrum from di-hydroxyl end-capped PPG, indicating the presence of hydroxyl and allyl end-capped oligomers (see text for description of peak annotation).

199

Chain End Characterisation

O

h CH2

CH2CHO CNH n CH3

N C O

h

3.95

7.5

7.0

6.5

6.0

3.90 3.85 Chemical Shift (ppm)

5.5

5.0 4.5 4.0 3.5 Chemical Shift (ppm)

3.0

2.5

2.0

1.5

1.0

Figure 26 1H NMR spectrum from MDI/PPG polyurethane prepolymer. Inset shows expansion of spectrum indicating assignment for functionalised end groups of polymer.

approximately m/z 1,600 arise from the presence of oligomers containing an allyl group and a hydroxyl functionality (19). The presence of these latter oligomers at lower average molecular weights is expected from knowledge of the chemistry, but MS is the only way of demonstrating this. It is not possible, however, to easily distinguish allyl and isopropenyl functionality using MS, due to the isobaric (and isomeric) nature of the two species. However, NMR easily distinguishes these two moieties, as described above. NMR spectra (1H in Figure 26 and 13C in Figure 27) from polyurethane prepolymer, formed by the reaction described in Figure 21, indicate that the desired product has been made [58]. Singlets (h at 3.87 ppm in the 1H spectrum, Figure 26, and i at 40.7 ppm in the 13C spectrum, Figure 27) in the spectra indicate that the hydroxyl functionality has been modified by MDI units to form the desired product with isocyanate end groups. Residual levels of hydroxyl end groups can be detected from 13C NMR data, to give an indication of the degree of functionalisation. Allyl end groups should not be modified in the end-capping reaction and hence can still be detected in the 1H NMR spectrum. Furthermore, it is also possible to detect other functionalities from these data. Confirmation of the modification of the hydroxyl end groups from the PPG can be accomplished by analysis using MALDI-TOF MS [59]. An example MALDI-TOF mass spectrum of a prepolymer based on PPG 2000 is shown in Figure 28. End group and average molecular weight data can be gleaned from the spectrum. The dominant distribution of peaks centred at approximately m/z 2,500

200

Anthony T. Jackson and Duncan F. Robertson

O

i CH2

CH2CHO CNH n CH3

N C O

i

41.0

40.5 Chemical Shift (ppm)

152 144 136 128 120 112 104 96 88 80 72 64 Chemical Shift (ppm)

56

48

40

32

24

16

8

Figure 27 13C NMR spectrum from MDI/PPG polyurethane prepolymer. Inset shows expansion of spectrum indicating assignment for functionalised end groups of polymer. 20

100

% 21 22 x =2 22 x =3

22 x =4

0 1000

2000

3000

4000

5000 6000 m/z

7000

8000

9000

Figure 28 MALDI-TOF mass spectrum from MDI/PPG polyurethane prepolymer. Peaks from functionalised oligomers are annotated with numbers corresponding to those described in the text.

Chain End Characterisation

201

indicates that the desired product (20) has been formed. Chain-extended oligomer (22) can be detected, which contains MDI units with both isocyanate groups reacted with hydroxyls to form urethane bonds. Reaction of oligomers from the PPG 2000 that contained allyl functionality with MDI leads to the formation of 21. The presence of these species is confirmed by the series of peaks (annotated as 21 in Figure 28) seen below m/z 1,500. The presence of other, minor, end group functionalities can also be detected by MALDI-TOF MS. The combination of NMR and MALDI-TOF MS data again gives both complementary and confirmatory evidence for the presence of differing end group functionalities in these polymers. The synergy of these two techniques is very important for the analysis of end groups in alkoxylates. Characterisation using only one of these two techniques can lead to either wrong assignments or certain end group functionalities not being detected. Isomeric content, for example, can be missed by only employing MALDI-TOF MS.

5. CLOSING REMARKS Although this chapter has focused essentially on three examples that highlight the synergy between NMR spectroscopy and MS for characterising end groups, and the complementary role of FTIR spectroscopy to some solid-state characterisations, particularly from a viewpoint of product research and development, we are aware that there are other studies and methods used for characterising and quantifying end group levels in organic polymers. For instance, near-infrared (NIR) spectroscopy, while not used as a tool to characterise polymer end group functionality, has been used for both product composition quality assurance and process control for end group concentrations. Other examples of applications of mid-infrared to end group measurements may be found in two recent publications [60,61].

ACKNOWLEDGEMENTS Dr Neil Everall, Ian Priestnall and Malcolm Beckett (all Intertek MSG, Wilton, Redcar, UK) are thanked for useful discussions and help with preparation of the manuscript. The authors would like to thank AkzoNobel (ATJ) and Intertek MSG (DFR) for permission to publish the work.

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CHAPT ER

6 Determination of Molecular Weights and Their Distributions Simone Wiegand and Werner Ko¨hler

Contents

1. Introduction 2. Distribution Functions and Averages 3. Methods Based on Colligative Properties 3.1 Membrane osmometry 3.2 Vapour pressure osmometry 4. Viscometry 5. Scattering Techniques 5.1 Static light scattering 5.2 Dynamic light scattering 5.3 Other scattering methods 6. Liquid Chromatography 6.1 Size-exclusion chromatography 6.2 Field-flow fractionation 7. Analytical Ultracentrifuge 8. Other Methods 8.1 Mass spectrometry 8.2 Nuclear magnetic resonance 8.3 Infrared spectroscopy 8.4 Electrophoresis 9. Practical Examples 9.1 Characterization of rigid-rod polymers 9.2 Scaling laws 10. Conclusion Acknowledgements References

205 208 212 213 215 218 220 220 225 228 228 228 232 235 237 237 239 240 240 241 241 243 247 248 248

1. INTRODUCTION In contrast to biological macromolecules such as proteins, synthetic polymers are, in general, polydisperse. Their molar masses, which show a broad distribution of Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00406-6

r 2008 Elsevier B.V. All rights reserved.

205

206

Simone Wiegand and Werner Ko¨hler

varying width depending on the mode of synthesis, around some average value, directly influence both microscopic parameters, such as molecular diffusion coefficients, and macroscopic material properties, like melt viscosity or brittleness. As a consequence, precise knowledge of the molar mass distribution or, at least, of certain molar mass averages, is of fundamental importance both for basic research on polymeric materials and for their commercial application. Since serious work in polymer science and technology without knowledge of the molar mass appears impossible, its measurement has always been a prime task in polymer analysis and the starting property for any subsequent research. Strictly speaking, the terms molar mass and molecular weight refer to different quantities. Molar mass is the mass of one mole of polymer molecules and measured in g/mol, whereas molecular weight is dimensionless and refers to the weight (mass) of a single polymer molecule measured as multiples of the atomic mass unit u. The numerical values of both quantities are identical. Usually, no such strict distinction is made in the literature, and also in this contribution both terms will be used as synonyms for the strict term molar mass. Experimental methods for determining molar masses, such as viscometry [1,2], have been employed since the early days of polymer science, and the development of new and more powerful techniques and instrumentation, like mass spectrometry or multidimensional chromatography, still continues today. Owing to the diverse nature of polymers, there is no single method available that can provide the complete molar mass distribution function for all macromolecules and cover the entire molar mass range from oligomers to high polymers. In production control a single measurement of, e.g., the intrinsic viscosity, may suffice, but in advanced polymer research only the combined results from a number of different techniques will provide sufficient information in all but the most trivial cases. One can differentiate between absolute methods and those that need a proper calibration. For instance, fractionating techniques like the widely used size exclusion chromatography allow the determination of the molar mass distribution function only under certain assumptions and with proper calibration. Other experimental methods provide a model-free access to specific averages of molecular properties, such as the weight average molar mass or the z-average mean square radius of gyration obtained from static light scattering or the number average molar mass from membrane osmometry. For a correct interpretation of experimental data a precise knowledge of the respective statistical weights and averages is of utmost importance and the relevant definitions will be presented in the first section. In the subsequent sections follows a discussion of different experimental methods and their strengths and limitations. Practical examples taken from the literature are presented for every major experimental method discussed. If available, references to recent review articles or textbooks will be given. As a guide for the reader, Table 1 lists some features of the experimental techniques discussed in this chapter. For each method it is specified whether it allows the determination of an average molar mass and also of the distribution. Estimates of the molar mass range, typical sample amounts and the operating

Table 1 Experimental methods to obtain molecular weight distributions and averages for polymers. For each method it is indicated whether absolute values (a) are obtained or whether a calibration or knowledge of a scaling law (c) are required. The sample amounts listed in the table are typical numbers, which might vary depending on the sample properties and the equipment available. The operating expense covers roughly the cost of equipment and personnel, time for measurement and interpretation. Average

Distribution

M range (g/mol)

Amount/mg

Operating expense

Colligative methods Membrane osmometry Vapour pressure osmometry

Mn (a) Mn (a, c)

– –

104oMo106 Mo5 104

200 200

Low Low

Mw (a) hMn i1=n (c) z

– (c)

MW104 MW5 102

300a 50a

Moderate to high Moderate to high

Liquid chromatography Size exclusion chromatography Field-flow fractionation

Mn, Mw, Mz (c) Mn, Mw, Mz (c)

(c) (c)

Mo107 MW103

10 10

Moderate Moderate

Analytical ultracentrifuge Sedimentation velocity Sedimentation equilibrium

Mn, Mw, Mz (a) Mw, Mz (a)

(a) –

MW103 MW103

100 100

High High

Mass spectrometry MALDI-TOF-MSb Viscometry

Mn, Mw, Mz (a)

(a)c

Mo106

10

High

Ubbelohde viscometer

MZ (c)



MW102

150

Low

End group analysis Nuclear magnetic resonance Infrared spectroscopy (IR)

Mn (a) Mn (a)

(a) (a)

Mo3 104 Mo104

10 10

High Moderate

Scattering techniques Static light scattering Dynamic light scattering

Depends on molar mass. Matrix-assisted laser desorption ionisation time of flight mass spectrometry. Only narrow distributions.

b c

207

a

Determination of Molecular Weights and Their Distributions

Method

208

Simone Wiegand and Werner Ko¨hler

expense are also listed. These numbers are only rough estimates and certainly depend on specific properties of the polymer like solubility or refractive index and optical absorption, which are directly related to the detection sensitivity. The focus of this chapter is on the characterization of synthetic polymers. We will discuss methods based on colligative properties, which depend on the number of molecules present and yield number average molecular weight, such as vapour and membrane osmometry, viscosity and scattering methods. In the liquid chromatographic section, we will only discuss conventional size exclusion chromatography. Then we will discuss the basic principles and recent developments of the ultracentrifugation methods. In the last section we will briefly discuss some spectroscopic methods, which are often combined with liquid chromatography methods to obtain more detailed chemical information for different fractions. Electrophoresis, which is of high importance in biochemistry, will only be discussed briefly. The few results for synthetic polyelectrolytes are summarized in some review articles [3–5]. The interested reader can find a recent book in the same series [6] that summarizes the most recent developments and techniques in this field.

2. DISTRIBUTION FUNCTIONS AND AVERAGES Some fundamental definitions and properties of distribution functions are summarized briefly in this section. The most important statistical weights, averages, and moments frequently encountered in polymer analysis are introduced [7]. Most quantities defined here will feature later again in the discussion of the individual analytical techniques. Basic definitions: Let X be some property of a polymer chain such as the degree of polymerization, molar mass, radius of gyration, or comonomer content of a copolymer, etc. In general, the polymer is heterogeneous with respect to X, which can assume discrete values Xi. We now define for molecules with X ¼ Xi . ni Mi mi ¼ niM Pi/NL xi ¼ ni = Pi ni P wi ¼ mi = i mi ¼ ni Mi = i ni Mi

Number Molar mass Total mass Relative frequency (mole fraction) Mass fraction (weight fraction)

NL is Avogadro’s number.

In many experiments average values of the property X are determined that depend on the statistical weights gi imposed by the respective experimental technique: P gi X i hXig ¼ iP (1) gi i

Determination of Molecular Weights and Their Distributions

More generally, the qth moment of X is P q gi X i  q i X g¼ P ¼ mðgÞ q ðXÞ gi

209

(2)

i

ðgÞ

The average is identical to the first moment, hXig ¼ m1 ðXÞ, and the variance is 0P 12 gi X2i gi X i   B i C i ¼ X2 g  hXi2g ¼ P @ P A gi gi P

s2g;X

i

(3)

i

Examples: Examples of important averages frequently encountered in macromolecular science are the number (Mn), weight (Mw), z- (Mz), and viscosity average (MZ) molar masses P ni Mi i (4) M n h M in ¼ P ni P P w i Mi ni M2i i i Mw hMiw ¼ P ¼P (5) wi n i Mi i

P i

M z h M iz ¼ P i

ni M3i ni M2i

0P

MZ hMa i1=a w

11=a wi Mai B C ¼ @ iP A wi

(6)

(7)

i

a is the exponent from the Mark–Houwink–Sakurada equation for the intrinsic viscosity ½Z ¼ KMa, the weight average of which is P wi ½Zi   i ½Z w ¼ P (8) wi i

and is obtained from viscometry measurements. Mn can be determined from colligative properties such as osmotic pressure, freezing point depression, or boiling point elevation (Section 3). Static light scattering gives Mw together with the z-averaged mean square radius of gyration P ni M2i R2g;i D E i (9) R2g ¼ P z ni M2i i

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Simone Wiegand and Werner Ko¨hler

Dynamic light scattering (DLS), however, allows for the measurement of the z-average of the inverse hydrodynamic radius [8] P ni M2i R1 h;i  1  i (10) Rh z ¼ P 2 ni Mi i

Frequently it is of advantage to express various averages in terms of moments, m, for example P ni M1i hM1 in mðnÞ ðMÞ i h M in ¼ P ¼ ¼ 1ðnÞ (11) 0 0 n i Mi hM in m0 ðMÞ i

P i

h M iw ¼ P

ni M2i

i

hMiz ¼ P i

ni M3i ni M2i

(12)

ðnÞ hM3 in m3 ðMÞ mðwÞ m1ðzÞ ðMÞ 2 ðMÞ ¼ ¼ ¼ hM2 in mðnÞ m0ðzÞ ðMÞ mðwÞ 1 ðMÞ 2 ðMÞ

(13)

ni Mi

i

P

ðnÞ hM2 in m2 ðMÞ mðwÞ ðMÞ ¼ ¼ 1ðwÞ hM1 in mðnÞ m0 ðMÞ 1 ðMÞ

¼

¼

The polydispersity s2 hMiw hM2 in ¼ ¼ n;M2 þ 1 2 hMin hMin hMin

(14)

serves as a crude measure for the width of the molar mass distribution. Continuous distribution functions: Some experiments, such as liquid chromatography or mass spectrometry, allow for the determination of continuous or quasicontinuous distribution functions, which are readily obtained by a transition from the discrete property variable Xi to the continuous variable X and the replacement of the discrete statistical weights gi by the continuousR probability density g(X). 1 For simplicity, we assume g(X) as being normalized: 1 gðXÞdX ¼ 1. Averages and moments of a quantity YðXÞ are defined by analogy to the discrete case as Z 1 hYig ¼ YðXÞgðXÞdX (15) 1 q mðgÞ q ¼ hY ig ¼

Z

1

½YðXÞq gðXÞdX

(16)

1

Finally, the cumulative distribution function GðXÞ is defined as the integral function of the differential distribution function gðXÞ: Z X GðXÞ ¼ gðX0 ÞdX0 ð17Þ 1

gðXÞ ¼

d GðXÞ dX

(18)

Determination of Molecular Weights and Their Distributions

211

GðX0 Þ is the fraction of polymers with property value X less than or equal to X0. Since gðXÞ is normalized, limX!1 GðXÞ ¼ 1. Reaction mechanisms and molar mass distributions: The molar mass distribution of a synthetic polymer strongly depends on the polymerization mechanism, and sole knowledge of some average molar mass may be of little help if the distribution function, or at least its second moment, is not known. To illustrate this, we will discuss two prominent distribution functions, as examples: the Poisson distribution and the Schulz–Flory distribution, and refer the reader to the literature [7] for a more detailed discussion. The statistical growth of a constant number of chains in a living polymerization leads to the narrow Poisson distribution of the mole fraction as a function of the degree of polymerization N: xðNÞ ¼

nN1 en GðNÞ

(19)

n ¼ hN in  1 and G(N) is the gamma function. The corresponding distribution in terms of mass fractions is wðNÞ ¼

NnN1 en GðNÞðn þ 1Þ

(20)

The polydispersity decreases with increasing degree of polymerization and depends only on hN in : hN iw 2 1 ¼ 1 þ hN i1 n  hN in  1 þ hN i n hN i n

(21)

The much broader Schulz–Flory distribution 1 N1 wðNÞ ¼ hN i2 n Nð1  hN in Þ

(22)

with a constant polydispersity of hN iw =hN in ¼ 2 is known from radical polymerization [9]. Figure 1 shows both a Poisson and a Schulz–Flory distribution with the same number average degree of polymerization hN in ¼ 50. The respective weight averages hN iw differ almost by a factor of two and are marked by arrows. Despite their vastly different shapes, both distribution functions would yield identical molar masses hMin in experiments based on colligative properties, such as membrane osmometry. Note that the x-axis in Figure 1 is logN, despite the labeling as N, as is common practice in plots with logarithmic axes. As a consequence, wðlogNÞ ¼ wðNÞj

dlogN 1 j ¼ wðNÞN dN

has to be plotted on the y-axis as the correct distribution function.

(23)

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Simone Wiegand and Werner Ko¨hler

1.5 w

Poisson

w(log N)

1

0.5 w

Schulz-Flory

0

10

100

1000

N

Figure 1 Poisson and Schulz-Flory distribution with identical hNin ¼ 50. The arrows indicate hNiw ¼ 51 (Poisson) and hNiw ¼ 100 (Schulz–Flory).

3. METHODS BASED ON COLLIGATIVE PROPERTIES Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as m M ¼ NL (24) n In the case of a polydisperse polymer it is still the total number n of solute molecules that is measured and the total mass m of solute molecules that is known from sample preparation, resulting in the number average molar mass M n ¼ h M in : P P P mi ni Mi =N L ni Mi m i i i P ¼ P ¼ hMin (25) NL ¼ NL P ¼ NL n ni ni ni i

1

i

Derived from the Latin word colligere ¼ to collect, assemble.

i

Determination of Molecular Weights and Their Distributions

213

Table 2 Approximate change of colligative properties for solutions of polymers with M ¼ 20 kg/mol at 1 wt% concentration according to Ref. [10] Colligative property

Change

Boiling point elevation Freezing point depression Vapour pressure lowering Osmotic pressure

DT ¼ 0.0013 K DT ¼ 0.0025 K Dp ¼ 0.4 Pa p ¼ 1500 Pa

Since the signal is proportional to the number of solute molecules, the sensitivity of colligative methods generally decreases at a rate inversely proportional to M. In Table 2 the signal strengths of various colligative methods are compared for a polymer solution (M ¼ 20 kg/mol) at a concentration of 1 wt% [10]. Boiling point elevation and freezing point depression are of very low sensitivity, and for practical purposes membrane and vapour pressure osmometry are employed almost exclusively.

3.1 Membrane osmometry Osmosis is the passage of a pure solvent into a solution separated from it by a semipermeable membrane, which is permeable to the solvent but not to the polymeric solute. The osmotic pressure p is the pressure that must be applied to the solution in order to stop the flow. Equilibrium is reached when the chemical potential of the solvent is identical on either side of the membrane. The principle of a membrane osmometer is sketched in Figure 2. The osmotic pressure is given by   m 1 @DGm p ¼ ðV s Þ (26) @n~ s p;T;n~ p ~ s and n~ p the molar concentrations of the Vm s is the molar volume of the solvent, n solvent and the polymer, respectively, and DGm the Gibbs free energy of mixing. Equation (26) reduces in the limit of infinite dilution to the well-known Van’t Hoff equation p RT ¼ (27) c h M in hMin is the number average molar mass of the solute (polymer), R ¼ 8.315 J/K mol the gas constant, and c the polymer concentration in polymer mass per volume solution. Finite concentrations are treated in terms of a virial expansion   p 1 ¼ RT þ A2 c þ A3 c2 þ    (28) h Mi n c which, in case of dilute solutions, usually can be terminated after the second virial coefficient A2. A2 accounts for both excluded volume effects and repulsive

214

Simone Wiegand and Werner Ko¨hler

π = ρgh

solvent

solution

Figure 2 Principle of membrane osmometry. r is the solvent density, g the acceleration of gravity, and h the difference between the fluid levels in both chambers.

or attractive forces between the solute molecules. Within the framework of the Flory–Huggins lattice model with interaction parameter w it takes the form [11]  h i1 1 2  w Vm A2 ¼ (29) s rp 2 Vm s is the molar volume of the solvent and rp the density of the polymer. For polydisperse polymers A2 is a more complex average, which shall not be discussed here in detail [7]. For good solvents and high concentrations, the influence of the 3rd virial coefficient A3 cannot be ignored, and p=c versus c sometimes does not lead to a linear plot. In these cases, a linearization can frequently be obtained with the approximation A3 ¼ A22 hMin =4 by plotting [12,13]  p 1=2  RT 1=2  1 ¼ 1 þ A2 hMin c (30) h M in c 2 Experimental considerations: Today, solid-state pressure transducers with a high mechanical stiffness are employed to ensure a reasonable response time. Membrane materials are cellulose, cellulose acetate, porous glass, or Teflons. The choice of the optimum membrane strongly depends on the system under investigation and is a major experimental problem in membrane osmometry [14]. The membrane must be inert and compatible with the solvent. The low molecular weight cut-off should be as low as possible. To avoid long equilibration times due to ballooning, the membrane material should have a high solvent permeability and sufficient mechanical stiffness and tensile strength. Osmometers with automatic pressure compensation and flow cells [15–17] have been developed for rapid measurements.

Determination of Molecular Weights and Their Distributions

215

Practically, polymers with molar masses between 2 104 and 2 106 g=mol can be characterized by membrane osmometry, but measurements of Mn o104 g=mol have also been reported with fast instruments and suitable membranes [16]. The lower limit is set by insufficient retention of short polymer chains. Above M  2 106 g=mol, the osmotic pressure, which is proportional to M1 , is too low for a reasonable signal-to-noise ratio. An advantage of the low molar mass cut-off is that impurities with a very low molar mass can permeate through the membrane and, hence, do not contribute to the measured osmotic pressure. Their equilibration time may, however, be different from that of the solute, leading to complex time-dependent signals. For a typical experiment, a series of solutions with concentrations between 1 and 10 g/L is prepared. Solutions and pure solvent, which defines the baseline, are injected alternately into the solution chamber of the osmometer and enough time is given for the pressure to equilibrate. Equilibrium is reached after seconds to days, depending on the instrument, the membrane, and the sample. p=c is plotted as a function of c according to Equation (28). The value extrapolated back to c ¼ 0 gives hMin , and A2 is obtained from the slope. Figure 3 shows measurements with an osmometer with a very short equilibration time of only a few seconds. The instrument contains a flow cell based on a poly(acrylonitrile) membrane [17]. The small pore size together with the rapid response results in a very low effective cut-off around 5 kg/mol [16]. Note, however, that even an infinitely fast osmometer is not able to yield the correct molar mass of permeating solutes due to the Staverman effect [18], which accounts for the reduced osmotic pressure due to solute molecules that are able to permeate through the membrane, even though they have not yet done so.

3.2 Vapour pressure osmometry Vapour pressure osmometry is the second experimental technique based on colligative properties with importance for molar mass determination. The vapour pressure of the solvent above a (polymer) solution is determined by the requirement that the chemical potential of the solvent in the vapour and in the liquid phase must be identical. For ideal solutions the change of the vapour pressure p of the solvent due to the presence of the solute with molar volume Vm s is given by p0  p c ¼ Vm (31) s h M in p0 p0 is the vapour pressure of the pure solvent. Practically, the small change in vapour pressure is difficult to measure, and the Clausius–Clapeyron equation is employed to translate the vapour pressure difference at constant temperature to a temperature difference at constant vapour pressure [19]: dp DH vap p ¼ dT RT 2

(32)

216

Simone Wiegand and Werner Ko¨hler

(a) 480

500

460

(π/c) / (J/kg)

440

Δp / Pa

400

300

420

60 40 20

0

1

2

200

3 c / (g/L)

4

5

6

100

0

0

5

10 t / m in

15

20

(b) flush

pressure transducer

flush

out

in

holder gasket membrane

solvent solution

seal glass tube

Figure 3 Membrane osmometry. Top: concentration series with multiple injection of polystyrene (PS, 5,250 g/mol) in toluene. Concentrations: 1.07, 1.91, 2.94, 4.11, and 5.03 g/L. Multiple solvent injections establish the baseline (subtracted). Inset: data evaluation for concentration series of PS (5,250 g/mol) and PS (47,400 g/mol) in toluene. Bottom: design of osmometer equipped with flow cell. Reproduced with permission from Lehmann et al. [16]. Copyright 1996 American Chemical Society.

Determination of Molecular Weights and Their Distributions

217

DH vap is the molar heat of vaporization. Hence, Dp DT DH vap p c ¼ xp ¼ V m ¼ s p T RT hMin

(33)

In principle, DHvap can be obtained from other sources and hMin can be calculated from Equation (33) without any a priori assumptions. In reality there are always thermal leaks and the instruments are calibrated with a known standard. If DV / DT is the measured voltage difference and K the instrument calibration constant, hMin is obtained as [20]  1 DV hMin ¼ K lim (34) c!0 c As for the case of membrane osmometry, non-ideality is accounted for by a virial expansion (Equation (28)). Experimental considerations: Sample preparation and data evaluation are similar to membrane osmometry. Since there is no lower cut-off as in membrane osmometry, the method is very sensitive to low molar mass impurities like residual solvent and monomers. As a consequence, the method is more suitable for oligomers and short polymers with molar masses up to hMin  50 kg=mol. Today, vapour pressure osmometry faces strong competition from mass spectrometry techniques such as matrix-assisted laser desorption ionisation mass spectrometry (MALDI-MS) [20,21]. Nevertheless, vapour pressure osmometry still has advantages in cases where fragmentation issues or molar massdependent desorption and ionization probabilities come into play. Technically, two matched thermistors are placed within a thermally insulated compartment with a saturated solvent atmosphere. A droplet of solvent is placed onto one, a droplet of solute onto the other thermistor (Figure 4). Solvent will condense into the solution droplet and raise its temperature until the solution has the same vapour pressure as the solvent. At this point, the temperature difference between the two droplets is read. Solvents with sufficient vapour pressure, such as toluene, tetrahydrofuran, or chloroform, are best suited for strong signals, but water has also been used successfully. ΔT thermistors

solution

solvent

solvent vapor

Figure 4 Principle of operation of a vapour pressure osmometer.

218

Simone Wiegand and Werner Ko¨hler

4. VISCOMETRY The most obvious characteristic of a solution of a high polymer is that its viscosity is considerably higher than that of the pure solvent, even when the concentration of polymer is quite small [22]. The suggestion was first made by Staudinger in 1930 [1,2] that the relative magnitude of this increase in viscosity could be quantitatively correlated with the molecular weight of the polymeric solute. In a polymer solution the specific viscosity is defined as Zsp ¼ ðZ  Z0 Þ=Z0 with the solution and solvent viscosity Z and Z0 , respectively. The intrinsic viscosity (Staudinger index) of a polymer is defined as Zsp 5 Vh ½Z ¼ lim ¼ NL (35) c!0 c 2 M The specific viscosity Zsp of a dilute solution of spheres is directly related to their hydrodynamic volume V h . N L denotes Avogadro’s number. Typically the intrinsic viscosity ½Z follows a scaling law, the so-called Mark–Houwink– Sakurada equation: ½Z ¼ KMa

(36)

The scaling exponent a can be related to the particle shape. One finds a ¼ 2, 0, 0.5, and 0.8 for a thin rod, solid sphere, ideal chain, and swollen chain, respectively. For most polymers K and a have been tabulated [23]. For a monodisperse sample Equation (36) can be used for a crude determination of the molar mass:  1=a ½ Z M¼ (37) K   For polydisperse samples, the weight average intrinsic viscosity ½Z w is measured (Equation (8)) and the so-called viscosity averaged molar mass is obtained:   !1=a   ½Z w hKMa iw 1=a MZ ¼ ¼ ¼ hMa i1=a (38) w K K MZ is usually between Mn and Mw and closer to Mw (compare with Section 2). Figure 5 shows three different types of capillary viscometers often used for viscosity measurements of polymer solutions. The disadvantage of the Oswald viscometer is that the viscometer has to be charged with the solution to a precise level and fine adjustments need to be made at the temperature of measurement. The Ubbelohde viscometer, also frequently referred to as the suspended level viscometer, is particularly useful when a series of different polymer concentrations is to be measured. The filling volume needs not to be adjusted precisely. The largest dilution ratio obtainable is limited only by the ratio of the volume of bulb B to that of the volume between the bottom of bulb B and the top of bulb C. For the compact version (Figure 5(c)) smaller sample volume is needed. There are also capillary viscometers available that can be coupled with liquid

Determination of Molecular Weights and Their Distributions

(a)

(b)

219

(c)

D C

A B

Ostwald

Ubbelohde dilution (normal)

Ubbelohde dilution (compact)

Figure 5 Sketch of the (a) Oswald viscometer, (b) Ubbelohde dilution viscometer in the normal form, and (c) compact form.

chromatography for on-line viscosity measurements. These instruments derive the viscosity from the pressure drop across a thin capillary through which a constant solvent flow is sustained. For all capillary instruments the time t needed for a certain volume V of the solution to flow through a thin capillary of length l and radius R is measured. Assuming a laminar flow, the Hagen–Poisseuille equation can be applied, leading to V pDp 4 ¼ R (39) t 8Zl If the density does not change significantly with concentration, the specific viscosity Zsp ¼ t=t0  1 can be approximated from the times measured for the solution (t) and solvent (t0). The dimension of the bore diameter of the capillary needs to be chosen carefully to minimize kinetic corrections. A detailed discussion of correction effects and other pitfalls can be found in the book by Van Wazer et al. [24]. Experimental considerations: For the measurement typically several concentrations are prepared and the specific viscosity Zsp or reduced viscosity Zred ¼ Z=Z0 are extrapolated to zero concentration. In the literature three different approaches are used to obtain the intrinsic viscosity and, with known ½Z–M relation, the molar mass. Schulz–Blaschke [25] Huggins [26] Kraemer [27]

Zred ¼ [Z]+[Z]KSB Zsp Zred ¼ [Z]+[Z]2KHc (ln Zred)/c ¼ [Z]+[Z]2KKc

(40)

The coefficients depend on the interactions between the solute molecule and the solvent. For good solvents typical values are KSB  0:3 and

220

Simone Wiegand and Werner Ko¨hler

KH  0:3; . . . ; 0:4. Furthermore the difference KH –KK is approximately equal to 0:5 [7]. A viscosity online detector in a size exclusion chromatography (SEC) instrument allows for a universal calibration for polymers with known K- and a-values. For polymers that are only soluble at high temperature, e.g., polyolefines, high-temperature detectors are available, which can be operated up to 2001C. In addition to molar mass measurements, viscosity detectors have also been employed successfully to obtain structural information of branched polymers [28]. The molar mass dependence of the intrinsic viscosity of rigid chain polymers cannot be described by a simple scaling relation in the form of Equation (36) with molar mass independent of K and a over a broad molar mass range. Starting from the worm-like chain model, Bohdanecky´ proposed [29] the linearizing equation  2 1=3 M ¼ AZ þ BZ M1=2 (41) ½Z where AZ and BZ are related to the persistence length and the hydrodynamic diameter of the polymer chain. Equation (41) has been employed to determine a persistence length (see Chapter 4) of 13 nm for polydisperse poly(p-phenylenes) with sulfonate ester- and dodecyl side groups [30] (Section 9.1).

5. SCATTERING TECHNIQUES Light scattering is a quite powerful tool that provides information not only about the molecular weight but also the radius of gyration and the second virial coefficient. It is not a suitable method for very low molecular weights below Mo104 g=mol, because of the low scattering strength. It is an absolute method and is, in general, also suitable for polyelectrolytes if long-ranged electrostatic interactions are sufficiently screened. Complications occur in the case of mixed solvents and copolymers. For polydisperse samples light scattering yields mass weighted molecular weights hMiw . This has to be taken into account, if one compares the results with other methods such as SEC.

5.1 Static light scattering In a static light scattering experiment the mass average molecular weight Mw of a dissolved polymer can be determined [31–33]. The components of a light scattering set-up are illustrated in Figure 6. In the elastic light scattering experiment the incident light with the vacuum wavelength l induces oscillating dipoles, which radiate a scattered wave of the same wavelength as the incident light. The unpolarized or vertically polarized scattered light is typically detected by a photomultiplier or an avalanche diode detector. The observed scattering intensity depends on the polymer concentration, the size and mass of the polymer, interactions and the optical contrast of the polymer in the solvent. The latter is

Determination of Molecular Weights and Their Distributions

221

Figure 6 Sketch of a typical light scattering set-up. Typically in the static light scattering experiment the incident beam is polarized vertically (v), while the scattered light is detected unpolarized (vv and vh). ~ ki and ~ ks are the wave vectors of the incident and scattered light, respectively.

reflected in the refractive index increment ð@[email protected]Þp;T , which describes the change of the refractive index increment n with increasing polymer concentration c at constant temperature T and pressure p. In static light scattering experiments the time-averaged scattering intensity Is is recorded at different scattering angles y, which is the angle between the direction of the incident and the scattered light. Often the scattering vector q ¼ ð4pn=lÞsinðy=2Þ is used instead of the scattering angle, which makes it directly possible to compare results obtained for different wavelengths. In general the scattering intensity IðqÞ / PðqÞSðqÞ is proportional to the product of the form factor PðqÞ and the structure factor SðqÞ. The form factor PðqÞ accounts for the single particle properties, such as size and molar mass, while the structure factor SðqÞ accounts for interactions between the solute particles. Using the theoretical considerations of Debye and Rayleigh for coherent scattering of light, Zimm [34] derived the fundamental equation for static light scattering ! q2 R2g Kc 1 ¼ 1þ (42) þ 2A2 c Rðq; cÞ M 3 with the optical constant K ¼ ð@[email protected]Þ2p;T 4pn2solvent =ðN L l40 Þ, the molar mass M, the radius of gyration Rg and the second virial coefficient A2. For polydisperse polymers the weight average molar mass hMiw and the z-average mean square radius of gyration hR2g i are measured. The refractive index increment ð@[email protected]Þp;T z

has to be looked up in reference tables or needs to be determined independently. Very accurate values can be obtained with an interferometer [35]. Practically the reduced scattering intensity Rðq; cÞ is determined as the difference between the scattering intensity of the solution RðsolutionÞ and the solvent RðsolventÞ according to Rðq; cÞ ¼ RðsolutionÞ  RðsolventÞ ¼ RðstandardÞ

rðsolutionÞ  rðsolventÞ n2solvent rðstandardÞ n2standard

ð43Þ

222

Simone Wiegand and Werner Ko¨hler

where rðsolutionÞ, rðsolventÞ, rðstandardÞ, nsolvent , and nstandard are the volume corrected scattering intensities and refractive indices for the solution, solvent, and standard, respectively. The measured scattering intensities are related to the scattering intensity of a known standard, for which the absolute Rayleigh ratio RðstandardÞ is that of the standard solvent. The absolute Rayleigh ratio RðstandardÞ has been measured for various solvents and wavelengths [36,37]. The knowledge of this absolute scattering ratio makes static light scattering an absolute, calibration-free method. It should be pointed out, that the absolute molecular weight can only be as precise as the determined Rayleigh ratio for the standard solvent at a certain wavelength. Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ð@[email protected]Þm  ð@[email protected]ÞA;0 . ð@[email protected]Þm is the increment determined in the mixed solvents in osmotic equilibrium, while ð@[email protected]ÞA;0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!       Mapp @n @n @n  ¼ 1 (44) @c m @c A;0 @c A;0 Mw The true second virial coefficient can be calculated via A2 ¼ A2;app ðMapp =Mw Þ. In the case of copolymers the heterogeneity parameters need to be considered in the analysis. If we assume an AB-copolymer the heterogeneity parameters are given by X  P¼ xA;i  x¯ A Mi wi (45) i

and Q¼

X i

2 xA;i  x¯ A Mi wi

(46)

  The deviations in composition xA;i  x¯ A are weighted by the z-statistical weights wi Mi . The apparent molecular weight Mapp is given by n  n 2 nA  nB A B Mapp ¼ Mw þ 2P þQ (47) n n nA @[email protected] and nB @[email protected] are with respect to the components A and B and n the overall refractive index increment of the heterogeneous copolymer [32].

Determination of Molecular Weights and Their Distributions

223

Experimental considerations: Static light scattering allows the simultaneous determination of the molar mass, the radius of gyration, and the second virial coefficient, which are important parameters in the characterization of polymer solutions. This holds also for the less common X-ray and neutron scattering experiments (cf. Section 5.3). A graphical analysis of the scattering intensities according to Equation (42) is called a Zimm-plot. Typically, one prepares a dilution series of at least four concentrations and determines the scattering intensities for all concentrations, the solvent and the standard in the entire available scattering angle range, typically from 201 to 1601. Using Equation (43) and the optical constant leads to a Kc=R-values for each concentration and scattering vector q. According to Equation (42) the Kc=R-values for a fixed concentration are extrapolated to q ¼ 0. The slope of the extrapolated values (open squares in Figure 7) is equal to 2A2 kc, with k an arbitrary chosen constant to shift the data for clarity. Additionally the Kc=R-values are extrapolated at fixed scattering vector to infinite dilution (open circles in Figure 7). The slope gives R2g =ð3MÞ and the intersect of both extrapolated lines is inverse to the molecular weight M. Unfortunately, the extrapolations to obtain the molecular weight, the radius of gyration and the second virial coefficient are not always as simple as suggested by Equation (42). Figure 8 shows a Zimm plot for xanthan in 10 mM sodium chloride (NaCl) solution [38]. The plot clearly shows deviations from the linear behavior in dependence on q indicating that the linear approximations (q2 R2g =3  1) are no longer valid. The deviations from the linear behavior reflect the form factor dependence. Non-linearities in the concentration dependence may indicate higher order virial coefficients become important. Although not so

Figure 7 Schematic Zimm plot: The determined Kc=R values (), the extrapolated values for fixed concentrations to q ¼ 0 (&), and the extrapolated values for fixed scattering vector to infinite dilution (3) c ¼ 0.

224

Simone Wiegand and Werner Ko¨hler

Figure 8 Zimm plot for xanthan in an aqueous solution of 10 mM NaCl. Reproduced with permission from Berth et al. [38]. Copyright 1996 American Chemical Society.

often displayed in the literature these sort of deviations from the linear behaviour are very often observed. And not always is the origin of the curvature clear [39]. In order to describe the data a quadratic extrapolation needs to be used. The inverse of the intercept leads to a molecular weight of Mw ¼ 3:12 106 g=mol and the limit of the two slopes with y ! 0 and c ! 0 lead to a radius of gyration with Rg ¼ 264 nm and a second virial coefficient of A2 ¼ 5:5 104 mol mL=g. If the curves are moderately bent often a Berry plot [40] instead of a Zimm plot is used. Berry proposed plotting the square root of c=R against c and sin2 ðy=2Þ, because these plots show less curvature. As a reason for this it was presumed that the contribution of the third virial coefficient A3 becomes significant, and that A3 / A22 . This procedure is similar to the one described for membrane osmometry (Equation (30)). For very high molecular weights, the ordinate intercept is close to zero, and the values obtained for Mw and Rg become very uncertain. In this case often the Guinier method [41] is used plotting lnðR=KcÞ as a function of sin2 ðy=2Þ for each concentration and then plotting the slopes and intercepts at y ¼ 0 against concentration. A careful characterization of copolymers is quite time consuming and a combination of methods as discussed in Section 6.1 might be considered. In practice the situation is often complicated by an amphiphilic character of the copolymers, which leads additionally to micelle formation.

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5.2 Dynamic light scattering In static light scattering only the time average of the scattered intensity is recorded, while DLS measures the scattered intensity with a time resolution of milliseconds or even tenths of nanoseconds. These fluctuations in the scattered intensity can be related to dynamical processes within the sample. As long as the solution is highly diluted and the solute particles move independently, the particles follow Brownian dynamics. This implies that the probability Pðr; tj0; 0Þ to find a particle at time t at the position r, which was originally located at t ¼ 0 at r ¼ 0, is given by [42]   Pðr; tj0; 0Þ ¼ ð4pDtÞ3=2 exp r2 =4Dt (48) The temporal evolution of Pðr; tj0; 0Þ is determined by the diffusion coefficient D. Owing to the movement of the particles the phase of the scattered light shifts and this leads to intensity fluctuations by interference of the scattered light on the detector, as illustrated in Figure 9. Depending on the size of the polymers and the viscosity of the solvent the polymer molecules diffuse more or less rapidly. From the intensity fluctuations the intensity autocorrelation function   gð2Þ ðtÞ ¼ IðtÞIðt þ tÞ (49) is calculated. t is any arbitrary delay time. The intensity autocorrelation function g2 ðtÞ decays for ergodic systems from the mean square intensity limt!0 gð2Þ ðtÞ ¼ IðtÞ2 to the asymptotic square of the mean intensity 2 limt!1 g ð2Þ ðtÞ ¼ IðtÞ . This is a consequence of the so-called Siegert relation, which relates the time autocorrelation function of the scattered field to that of the scattered intensity. For a detailed discussion of this point see Refs. [42,43]. After normalization to the asymptotic baseline, g2 ðtÞ decays from two to unity if measured with a perfect instrument. A real instrument always suffers from some loss of coherence, and for a monodisperse solution of ideal, non-interacting solute molecules the intensity autocorrelation function g2 ðtÞ takes the form gð2Þ ðtÞ ¼ A þ Bjgð1Þ ðtÞj2

Figure 9 (A) Intensity fluctuations caused by random particle motion. (B) Intensity autocorrelation function versus time.

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A and B are instrumental factors and gð1Þ ðtÞ the electric field correlation function which is related to the translational diffusion coefficient D by gð1Þ ðtÞ ¼ expðGtÞ ¼ expðq2 DtÞ

(51)

with G as decay rate. For infinite dilution (neglecting interactions) the diffusion constant can be related to the hydrodynamic radius Rh of the polymer by the Stokes–Einstein equation D ¼ kB T=6pZRh , with the dynamic viscosity Z, temperature T, and the Boltzmann constant kB. In a more realistic case of a polydisperse solution, gð1Þ ðtÞ will be a sum of exponentials (one for every molecular weight species present) and Equation (51) becomes Z 1 ð1 Þ g ðtÞ ¼ GðGÞ expðGtÞdG (52) 0

Here GðGÞ is the distribution function of decay rates G. In order to approximate G(G) the lower moments can be determined [45,46] according to         ln gð1Þ ðtÞ ¼ Gt þ 1 m2 Gt 2  1 m3 Gt 3 þ    (53) 2 3 2! G 3! G P with m2 and m3 being the second and third moments mi ¼ i ðG  GÞi . For unimodal distributions of slightly polydisperse polymers in solution, the following relation has been derived [46] m2  ðMz =Mw  1Þ=4 (54) 2 G which is valid in the approximation Mz =Mw  1:25. The average G is given as a zaverage of the decay rates P ni M2 Gi G ¼ P i 2 ¼ hG iz (55) n i Mi and consequently the hydrodynamic radius is an inverse z-average (cf. Section 2, Equation (10)). Recently, Frisken [47] derived a different expression for gð2Þ by expanding the correlation function in terms of the moments about the mean:   m m 2 gð2Þ ¼ B þ bexp 2Gt 1 þ 2 t2  3 t3 (56) 2! 2! Frisken was able to show that this function is more robust to poor guesses and leads to consistent results compared to Equation (53) when different numbers of points are fitted. Experimental considerations: Frequently a numerical inverse Laplace transformation according to a regularization algorithm (CONTIN) suggested by Provencher [48,49] is employed to obtain GðGÞ. In practice the determination of the distribution function GðGÞ is non-trivial, especially in the case of bimodal and n-modal distributions, and needs careful consideration [50]. Figure 10 shows an autocorrelation function for an aqueous polyelectrolyte solution of a low concentration (c ¼ 0.005 g/L) at a scattering vector of q ¼ 8:31 106 m1 [44].

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Figure 10 Polarized field autocorrelation function g(1) for poly(p-phenylene) Mw ¼ 2.1 106 g/mol) in water, which is denoted CVV ðtÞ in the original work [44]. The subscript indicates that both the incoming beam and the scattered light are vertically polarized. The correlation function was recorded for a solution with a concentration of c ¼ 0.005 g/L at a scattering vector of q ¼ 8.31 106m1. The inset shows the distribution function of the relaxation times determined by an inverse Laplace transformation.

The inset shows a unimodal distribution of relaxation times t ¼ G1 obtained by a CONTIN analysis. Besides CONTIN there is a number of alternative techniques [51] for the determination of the distribution from the correlation function. Detailed discussions of this topic have been given by Stock and Ray [52] and by Sˇteˇpa´nek [50]. A way to increase the precision of the value Mw =Mn extracted from DLS is to consider several correlation functions and to look for a single answer. Sˇteˇpa´nek [50] developed a method to determine the polydispersity of polymer samples with narrow distribution by measuring several correlation functions with different sample times on a linear correlator. With this procedure polydispersities in the range Mw =Mn ¼ 1:05  2 can be determined. DLS is a rapid method, typically measurements can be made within a few minutes, and only small quantities of sample ( 50 mg) are needed. The polymers might be suspended in any clear liquid. The samples need to be prepared carefully. Dust needs to be avoided by filtering the samples. Also air bubbles will falsify the results. In the case of more complex systems, such as micellar solutions or copolymer solutions, charged impurities with long range interactions need to be avoided, because they might influence the phase behavior of the systems. The main disadvantage of the method is, that in DLS it is not the molar mass distribution that is obtained, but the intensity-weighted composite of the decay rates Gi of all species present in the solution. In order to obtain for instance the distribution of weight fraction cðMÞ of the polymer as a function of molar mass as obtained by SEC the following scaling law G ¼ aMb and the weighting factor GðGÞ / cðMÞM needs to be used (Section 9.2).

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5.3 Other scattering methods In principle it is also possible to perform a static scattering experiment using other radiation sources such as neutrons or X-ray radiation. In a typical polymer analysis those sources are often not readily available, therefore we only briefly discuss these possibilities. For instance Kirste et al. [53] determined the molecular weight of various poly(methyl methacrylates) in the molecular range between 6,000 and 106 g/mol by neutron scattering. A big advantage of neutron scattering compared to light scattering is the possibility to characterize very low molecular weight polymers (Mw ¼ 1; 000 g=mol). This can be achieved by contrast variation [54]. For polydisperse samples the disadvantage of the low sensitivity of DLS for low molecular weights can be overcome by a more sophisticated technique the so-called Thermal Diffusion Forced Rayleigh Scattering (TDFRS) method, availability of which is currently limited to a few scientific laboratories. For instance it has been shown that the molecular weight distribution of a mixture of two narrow polystyrenes (Mw /Mn I1.03) with molar masses of Mw;1 ¼ 48 kg=mol and Mw;2 ¼ 556 kg=mol at equal concentrations (c1 ¼ c2 ¼ 0.0029), dissolved in ethyl acetate leads to a distribution function which is in good agreement with the SEC results, while the DLS data are dominated by the high molecular weight polymer [55]. Again it needs to be pointed out, that all methods have their weaknesses and it is certainly not justified to regard the SEC distribution as the true molar mass distribution, as it may suffer from calibration problems, solute–column interactions, peak broadening, and a molar mass dependence of the contrast factor @[email protected], and hence the detector sensitivity.

6. LIQUID CHROMATOGRAPHY 6.1 Size-exclusion chromatography SEC or gel permeation chromatography (GPC) is one of the widely used chromatographic techniques [56,57]. In contrast to the already discussed colligative and scattering methods it is not an absolute method and requires proper calibration with some known polymer standards. One obtains not only the average molar masses (Mn , Mw , Mz ) but the complete molar mass distributions. Figure 11(A) shows a principle sketch of a SEC set-up. The eluent (solvent) is pumped at a constant flow rate through the system. A small amount of polymer solution (typically 200 mL) is injected manually or with an autosampler. The main part comprises a set of columns (typically 3–4 columns+pre-column) typically packed with microporous styrene-divinylbenzene, porous glass, or silica. In the routine analytical laboratory it is especially useful to have a pre-column in order to collect impurities that might be present in the samples. If many different samples are to be analyzed, it is necessary to check the reliability of the columns frequently to avoid artefacts due to residues from previous samples still held on the column. In order to avoid problems, samples should be purified before they

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229

high mass low mass injection separation eluted eluted

injection loop

columns detector unit

pump waste detector

eluent

(A)

chromatogram injection

(B)

time

Figure 11 (A) Sketch of the basic components in a typical SEC set-up. (B) Principle of separation by SEC.

are injected onto the column. The pre-column should be replaced frequently to protect the column set. The separation process, illustrated in Figure 11(B), is based on the molecular hydrodynamic volume of the polymer species. Higher molar mass species that are too large to penetrate into the pores of the stationary phase elute first; smaller ones that can diffuse into the pores appear at later times corresponding to higher elution volumes. The total volume V t occupied by the eluent within the column is the sum of the interstitial or void volume V 0 , which is equal to the volume of the mobile phase, and the volume V p within the pores. Different molecular weight fractions elute at a certain retention time corresponding to retention volume V R : V R ¼ V0 þ kV p

(58)

The coefficient k is a measure of how much time a polymer with a certain chromatographic radius Rc spends within the pores of radius rp . The factor k can vary between 0 (V R ¼ V 0 ; molecules are too large to penetrate the pores; exclusion limit) and 1 (V R ¼ V 0 þ V p ¼ V t ; all pores are accessible to the solute; separation threshold). For some polymers, like polystyrene or poly(methyl methacrylate), narrow standards of known molar mass and small polydispersity are commercially available, which can be used for calibration. Unfortunately, such standards are not available for all polymers and then the obtained true molar masses of a specific polymer might differ by a factor of two from the value obtained by calibration with, e.g., polystyrene [30] (see Section 9.1). This problem can be resolved by the so-called universal calibration, which is based on the finding that the retention volume of a polymer is a single-valued function of the hydrodynamic volume of the polymer, irrespective of its chemical nature and

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structure. The hydrodynamic volume Vh of a polymer is proportional to the product of intrinsic viscosity and molar mass Vh ¼

2 4 ½ZM pR3c 5N L 3

(59)

which we set equal to its chromatographic volume. If two polymers have the same retention volume or retention time, the product ½Z1 M1 ¼ ½Z2 M2 is constant. Using the Mark–Houwink–Sakurada relation ½Z ¼ KMa [7] one finds   K1 1þa1 1=ð1þa2 Þ M2 ¼ M K2 1

(60)

For many polymers K and a values can be found in the Polymer Handbook [23]. In a recent study by Vanhee et al. [30] the universal calibration has been applied using the polystyrene (PS) calibration curve to characterize rigid rod poly(p-phenylenes) (PPP). It turned out that due to its larger persistence length, PPP with a certain mass requires a much larger volume than PS for the same molecular weight. Ron et al. employed universal calibration for the characterization of erodible copolymers [58]. Experimental considerations: Detectors used to monitor concentration changes in the column effluent can be classified into three categories according to their sensitivity to different statistical weights. In the first case the signal is proportional to the mass fraction or concentration (differential refractometer, UV spectrometer). The second group contains detectors that are sensitive to cM (light scattering) and in the third group the signal is proportional to c=M (vapour pressure osmometry). Often it is useful to use several online detectors or combine the SEC instrument with other methods. For instance the combination of a light scattering detector or a flow-membrane osmometer with a concentration detector allows an absolute calibration of the elugram. This is particularly useful for novel polymers in research and development, where a universal calibration is not possible, because the K and a values are unknown. In the case of heterogeneous polymers the experimental methods need to be refined. In order to analyze those polymers it is necessary to determine a set of functions f i ðMÞ, which describe the distribution for each kind of heterogeneity i. This could be the mass distributions of the blocks in a diblock copolymer. The standard SEC methods fail here and one needs to refine the method, e.g., by performing liquid chromatography at the critical point of adsorption [59] or combine SEC with methods, which are, for instance, sensitive to the chemical structure, e.g., high-pressure liquid chromatography (HPLC), infrared (IR), or nuclear magnetic resonance spectroscopy (NMR) [57]. Most widely used is the two-dimensional combination of SEC and HPLC for copolymer characterization. The typical HPLC instrument is very similar to an SEC apparatus. While the ideal SEC separation is exclusively determined by entropy changes, in HPLC or adsorption chromatography it is assumed that no

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entropic effects take place and the distribution is exclusively determined by enthalpic effects. This means that large molecules, which interact more strongly with the column, elute after the small molecules. The mobile phase needs to dissolve the sample, but it should also minimise interactions between solute and the stationary phase and it needs to be compatible with a specific detector. Under certain circumstances it might also be required to run a solvent gradient, where the miscibility of the components is a necessary condition. Figure 12 shows a schematic representation of 2D chromatography set-up combining SEC and HPLC. The main part is an eight-port injection valve with two storage loops. In the first step loop 1 is loaded by HPLC and in the mean time loop 2 is analyzed by SEC. In the next step the loops are exchanged. Typically the HPLC separation requires more time due to lower flow rates, therefore it is advantageous first to load one loop by HPLC and later to analyze the fraction by SEC. In the case of copolymers it is also necessary first to separate the polymers according to their chemical composition, such as blocklength ratio, before analyzing the molecular weight distribution. An important feature for such an automated set-up is the proper coordination of the flow rates of both systems. Furthermore one needs to pay attention to the fact, that a further dilution of the sample takes place when a fraction is injected into the SEC system. Therefore, detectors with a high sensitivity are required. A combination of infrared spectroscopy with size exclusion chromatography has a wide application range in the characterization of copolymers, adhesives, impurity profiling in polymers and branching in polyolefines [60–65]. Commonly, the solvent used as a mobile phase absorbs strongly in the

Figure 12 Schematic representation of 2D chromatography using an eight-port injection valve and two storage loops. (A) In the first position of the valve the storage loop 1 is loaded with the HPLC eluent, while the content of the storage loop 2 is analyzed by SEC. (B) In the second valve position storage loop 2 is loaded with HPLC eluent and the content of loop 1 is analyzed according the molecular size of the solute.

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infrared (IR), so that practical use of an IR cell is only possible for some solvents. There are commercial interfaces available, which remove the solvent either by a pneumatic nozzle or in an ultrasonic/vaccuum nebulizer. The non-volatile substrates will for instance then be deposited on a slowly rotating germanium disk, which is then automatically or manually transfered to a Fourier transform infrared (FT-IR) spectrometer. The pneumatic nozzle typically works for solvents with a boiling point around 1001C. For less volatile solvents the required temperatures at the nozzle become high and the allowed flow rates are very low, so that the ultrasonic/vaccuum nebulizer is more suitable. Special care has also to be taken to use volatile buffers instead of salts if needed in aqueous SEC. If further structural information is required, it is possible to use the deposited material in other instruments such as an NMR or mass spectrometer. NMR and IR are powerful spectroscopic techniques, which provide additional information about the compositional details of a sample. However, they are often unable to differentiate between a polymer blend A þ B and a copolymer consisting of A and B. For such complex polymer compositions a combination of liquid chromatography and spectroscopic methods is helpful. In his recent review Pasch [57] discusses a couple of examples. In conclusion one can say that SEC is a very powerful method for polymer characterization, especially in combination with other composition sensitive or absolute calibration methods. A big advantage is also that the sample amount is fairly small, typically 10 mg. For more complex polymers, such as polyelectrolytes, enthalpic effects often become dominant and also for rather high molecular weight polymers chromatographic methods such as field-flow fraction (FFF) techniques might be more suitable. For fast routine measurements linear columns are often used.

6.2 Field-flow fractionation FFF is a family of flexible elution techniques capable of simultaneous separation and measurement. The FFF mechanism combines elements of chromatography and field-driven techniques such as electrophoresis and ultracentrifugation. Different properties of the polymers or colloidal particles can be determined depending on the applied field. The fundamental principle of FFF is illustrated in Figure 13(A). The separation of the sample takes place inside a narrow ribbonlike channel. This channel is composed of a thin piece of sheet material (usually 70–300 mm thick Mylars or polyimide) in which a channel is cut. This is then usually clamped between two walls of highly polished plane parallel surfaces through which a force can be applied. Figure 13(B) illustrates the separation process. Component Y forms a distribution closest to the accumulation wall and is entrained in the lowest laminar flow band. It is gradually separated from component X moving in a faster band of the flow profile. How close the solute particles are to the accumulation wall is determined by the interplay between the applied field and homogeneity-restoring back diffusion. The retention time tr is

233

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Field Outlet

Inlet

Field

Spacer

Channel

(A)

Flow vector

Y

X

w

(B)

Figure 13 (A) Sketch of the basic components in most FFF channels. (B) Distribution of two arbitrary components and the unequal flow displacement velocities for the two species.

given approximately by jFjw tr (61) ¼ t0 6kB T t0 is the void time (the emergence time of a non-retained tracer), w the channel thickness and jFj the strength of the applied field. A separation of two components is only possible when the force increment between the two species is large enough. If an electrical field is applied (electric FFF) particle charge or mobility can be determined. If a centrifuge is used (sedimentation FFF), the effective mass of the solute particles can be determined. A thermal gradient (thermal FFF) correlates with thermal diffusion parameters. A cross-flow of carrier liquid (flow FFF) leads to a particle size determination. Practically, thermal FFF (th-FFF) and flow-FFF (fl-FFF) are of most relevance for the determination of molecular weights and molecular weight distributions. To our best knowledge the sedimentation-FFF has been only used for separation of colloidal particles in the sub mm and micrometer range. A recent review article by Co¨lfen and Antonietti discusses the characterization of polymers and colloids by FFF techniques in great detail including pitfalls and practical examples [66]. Experimental considerations: Th-FFF is driven by a temperature gradient. The channel is usually composed of two metallic blocks (with high heat conductivity, preferably copper) with highly polished even surfaces between which a spacer ( 100 mm) is clamped. The typical dimensions of the metal block are 40–60 cm length, 3–6 cm width, and a thickness of 2–3 cm. The temperature gradient is applied perpendicular to the solvent flow. Usually the upper plate is heated to avoid convection. Often rather high temperature gradients, exceeding 10,000 K/cm are applied, corresponding to temperature differences between the hot and the cold wall of up to 100 K. The thermal diffusion drives the solute particles either more towards the cold or to the warm side with a molecular weight or particle-size dependent penetration length of the concentration distribution into the parabolic channel flow profile, which then leads to a separation of the different molecular

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weight species. In the literature one often finds the statement that the movement of the macromolecules in a temperature gradient is always in the direction from hot to cold [66–68], but this is not always the case [69,70]. In a fl-FFF the bottom wall of the channel consists of an ultrafiltration membrane on top of a porous frit material through which a fraction of the carrier flow exits. This creates a secondary cross flow perpendicular to the primary longitudinal channel flow. The crossflow drives any sample molecule or particle down to the membrane surface. This crossflow-induced drift will be counteracted by Brownian motion so that an exponential concentration distribution layer is established. The thickness of this layer therefore depends on the magnitude of the diffusion coefficients. A slowly diffusing component (high molecular weight) will accumulate relatively closer to the membrane surface than a more rapidly diffusing species because the slow diffusion is less effective in counteracting the crossflow-induced drift. The high molecular weight species therefore travel with lower speed through the channel, resulting in an elution order where components arrange themselves according to decreasing diffusion coefficients, i.e., increasing hydrodynamic size. This retention order is characteristic for sample materials in the submicron size range. A different retention order occurs in fl-/hyperlayer FFF when the particle size exceeds about 1 mm [71]. Often the flFFF technique is a good alternative characterization method for water-soluble polymers [66]. Th-FFF is especially suitable for synthetic polymers in organic solvents in the molecular weight range between M ¼ 104  107 g=mol using temperature differences DT  10  100 K. The list of polymers that have been successfully characterized is as long as for other methods. References to the original works can be found in the recent review by Co¨lfen and Antonietti [66]. From the th-FFF retention data it is possible to obtain a molar mass distribution after a suitable calibration for the determination of the Mark– Houwink–Sakurada constants (straight-line plot of logðD=DT Þ versus log M [72]). The thermal diffusion coefficient DT describes the mass diffusions induced by a temperature gradient [73]. Another possibility is to couple an absolute molar mass detector like a light scattering detector or a suitable detector combination, such as an on-line viscometer coupled with a refractive index detector. This possibility does not require prior knowledge of DT . If copolymer samples are investigated in th-FFF coupled with a viscometer, both the average molecular weight and the average composition are accessible [74]. Th-FFF is also a good technique if polydispersities of very narrow samples from anionic polymerization need to be determined. This was demonstrated for polystyrene from band-broadening data in th-FFF with a higher accuracy than the results obtained by SEC on the same samples [75]. While polymers in the range M ¼ 104  107 g=mol are well resolved by th-FFF, polymers of lower molecular weight (B103 g/mol) need an inconveniently high DT (B150 K) for retention, and problems of boiling solvent, etc. arise. However, successful separations of polystyrene down to 600 g/mol have been described using very high temperature gradients in a pressurized th-FFF channel [76].

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FFF and SEC chromatography are largely complementary in application. SEC works best with low molecular weight materials, FFF with high. Both techniques can be combined with different detectors such as multi-angle light scattering, refractive index detection, etc. A major advantage is that for the th-FFF experiment no filtration is required, which always bears the risk of sample loss. For both techniques artefacts due to overloading and sample specific effects like charge interactions as in the case of polyelectrolytes can modify the retention behaviour. Although FFF has essentially a one-phase nature and no stationary phase is present, sample-wall interactions can modify the elution time of the solute. To check for artefacts it is often necessary to run several experiments with the same sample under varying conditions. Nevertheless the FFF family is certainly a flexible analytical technique with a wide molecular weight range from 1,000 up to 1018 g/mol.

7. ANALYTICAL ULTRACENTRIFUGE Though not very widely used today, analytical ultracentrifugation is one of the most fundamental and versatile techniques in polymer analysis [77,78]. Similar to colligative methods and light scattering it rests on a well-established thermodynamic theory without having to resort to questionable a priori assumptions. Furthermore, there are no complicating interactions between the sample and a membrane or a chromatographic column. Under the influence of a gravitational (centrifugal) field, a solute particle of mass m ¼ M=N L immersed in a solvent of density r at a distance r from the rotor axis experiences three forces. Within the frame of reference of the rotor, spinning with angular velocity o, these are the centrifugal force Fc , the buoyant force Fb , and the frictional force Ff : Fc ¼ mo2 r ¼ NML o2 r

(62)

Fb ¼ m0 o2 r ¼  NML v¯ ro2 r

(63)

Ff ¼ fu

(64)

N L is Avogadro’s number, f the particle friction coefficient, u the velocity and v¯ the partial specific volume of the solute [79,80]. Inertial forces are negligible and the balancing of the above forces yields the sedimentation coefficient s¼

u Mð1  v¯ rÞ ¼ o2 r NLf

(65)

In the limit of infinite dilution the friction coefficient can be related to the single particle translational diffusion coefficient D¼

kT f

(66)

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and the Svedberg equation for the molar mass is obtained: s RT (67) D 1  v¯ r Finite concentrations are accounted for by a virial expansion of both D and s1 [12], M¼

leading to

D ¼ D0 ð1 þ kD c þ   Þ

(68)

s1 ¼ s1 0 ð1 þ ks c þ   Þ

(69)

  D 1 uc ð1  v¯ rÞ ¼ RT þ 2A2 c þ    s M

(70)

with the second virial coefficient Auc 2 ¼ ðkD þ ks Þ=ð2MÞ. Eventually, sedimentation leads to the build-up of a concentration gradient which gives rise to a diffusion current jD ¼ Drc. In the stationary state jD js ¼ cu ¼ co2 rs, resulting in

(71)

exactly balances the sedimentation current



RT 1 dlnc ð1  v¯ rÞo2 r dr

(72)

for a dilute solution of a monodisperse polymer. In case of polydisperse solute Equation (72) takes the form dc ð1  v¯ rÞo2 r X ¼ ci Mi dr RT i

(73)

It is rather straightforward to show that proper integration over the cell from the meniscus (rm ) to the bottom (rb ) yields the weight and z-average molar masses Mw and Mz [12]:  1 Z rb rcðrÞdr (74) Mw ¼ ½RTðcðrb Þ  cðrm ÞÞ ð1  r¯vÞo2 rm

    

1 dc dc 1 1 Mz ¼ RT rb  rm ð1  r¯vÞo2 ðcðrb Þ  cðrm ÞÞ dr b dr m

(75)

All quantities on the right-hand side are experimentally accessible. Experimental considerations: In a modern analytical ultracentrifuge the rotor is equipped with multiple sample cells of 100 mL volume or less and rotates at up to 6 104 revolutions/min, resulting in strong gravitational fields as high as 2:5 105 g. By selection of a proper angular velocity of the rotor, a very broad molar mass range from oligomers (103 g/mol) to high polymers (107 g/mol) can be analyzed. The radial concentration profile is analyzed by detection systems that are synchronized to the revolving rotor. Contrast is generated either by optical absorption of the polymer in the visible or near UV or by a concentration dependent refractive index. Formerly, refractive index changes were detected by

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means of Schlieren optics, but today these have been replaced by Rayleigh interferometers [81]. In addition to these traditional detection methods, also fluorescence [82,83] and turbidity [84] detection systems have been developed. A comprehensive treatment of modern ultracentrifugation equipment and applications can be found in the recent book of Ma¨chtle and Bo¨rger [78]. The two main experimental techniques for molar mass determination are the sedimentation velocity run at high rotor speeds and the sedimentation equilibrium run at moderate rotor speeds. In a sedimentation velocity run, s is determined from the sedimentation of the solute in an initially homogeneous solution, which shows up as a sharp boundary moving with the sedimentation velocity u towards the bottom of the cell. D is either obtained from, e.g., DLS experiments, from the diffusive spreading of the sedimentation boundary, or from model calculations or empirical relations between D and M. The partial specific volume v¯ is either measured or calculated. Knowing s, D, and v¯ , the molar mass M is obtained from Equation (67) or from a concentration series according to Equation (70). From a sedimentation velocity experiment the molar mass distribution function (mass fractions) can be determined [12,85,86]. Figure 14 shows the result of a sedimentation velocity experiment on a sample with a very broad particle size distribution, consisting of ten discrete polystyrene dispersions with particle diameters ranging from 67 to 1,220 nm [84]. The smeared-out steps correspond to the transit of the sedimentation front of the respective species through the slit of the detection system. In a sedimentation equilibrium run, the stationary radial concentration profile, which is established after a few hours for a 1-mm column, is analyzed according to Equation (72) or, in case of polydisperse samples, Equations (74) or (75). Contrary to the sedimentation velocity experiment, the diffusion coefficient D is not required. Chemically heterogeneous polymers can be analyzed in a density gradient experiment, where a high-density salt such as CsCl is added. Under the influence of the strong gravitational field the mixed solvent develops a density gradient. The different sample constituents accumulate at the respective positions where their density is matched by the one of the solvent, leading to a characteristic banding of the solution [81]. In addition to the determination of molar mass distributions and various molar mass averages there are many experiments, requiring sometimes sophisticated data evaluation, that can be carried out with an analytical ultracentrifuge. Examples are the analysis of association, the analysis of heterogeneity, the observation of chemical reactions, and protein characterization, to mention only a few. A detailed discussion is beyond the scope of this article, but there is excellent literature available [77–79,81,87–89]

8. OTHER METHODS 8.1 Mass spectrometry In principle, MALDI-TOF (MALDI-Time Of Flight) analysis allows for the determination of the complete polymer mass distributions and, from that, the calculation of various molecular weight averages like Mn and Mw and the

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Figure 14 Particle size distribution of a ten-component mixture of narrow polystyrene dispersions. Left: intensity measured as function of t with a turbidity detector. Right: integral and differential particle size distribution. Reproduced from Ma¨chtle [84] by permission of The Royal Society of Chemistry.

polydispersity D ¼ Mw =Mn. In the case of extremely low polydispersities, the molecular weight distributions can often be measured more exactly than with conventional methods. However, for polydisperse samples the error increases with increasing width of the polymer distribution. Pasch [90] demonstrated that the differences in the determined polydispersities between SEC and MALDITOF are in the range between 2.1% and 11.8% for samples with very low polydispersities between D ¼ 1:04  1:06. These differences increase to 10.6–20.5% and 48–73% when the polydispersities increase to a range of D ¼ 1:08  1:10 and D ¼ 1:4  3, respectively. Molecular weights for very high

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239

molecular weight polymers around 106 can only be determined in case of extremely narrow standards [91] or monodisperse biopolymers [92]. In a standard MALDI-TOF setup polymers with a low polydispersity (D  1:05) and a molecular weight around 15,000 can easily be measured. The problems for the determination of broad distributions functions arise mainly from fragmentation, multiple ionization, and molar mass dependent ionization and desorption probabilities. The strength of mass spectrometry is the chemical characterization of the samples as, for instance, the end group analysis in the case of oligomers or low molecular weight polymers (see Chapter 5). In principle an oligomeric resolution can be obtained. From the absolute mass of each signal of the distribution, the mass of the end groups can be determined using the mass of the repeat unit and the mass of cation used for ionization. This is a fast way to verify expected end groups after a polymerization or functionalization. Therefore, MALDI-TOF mass spectrometry has gained popularity in end group analysis over the traditional methods such as NMR, IR, UV, elemental analysis, or titration techniques. It needs to be pointed out, that the investigation of some technically important polymers like polyolefines has not been very successful so far. Owing to their inert nature they are difficult to dissolve and also difficult to ionize. Typically one needs for the ionization process some heterogeneities or double bonds in the polymer. For some insoluble substances a solvent-free sample preparation method has been developed that allows a characterization by MALDI-TOF mass spectrometry [93]. For polydisperse samples a combination of SEC and mass spectrometry is ideal. In practice three different approaches have been realized: on-line systems, ‘‘on-line’’ set-up via interface and off-line systems. In principle the mass spectrometer can be used as an on-line detector. The problem is, that MALDITOF is based on the pulsed desorption of molecules from a solid surface in the gas phase and, therefore, it is a priori not compatible with liquid chromatography. For practical purposes it turns out that the method is limited to fairly low molecular weights (Mo2000 g/mol) because polymers with higher masses break down into fragments during the ionization process [94–96]. This problem can be overcome by the use of such automated interfaces as the LC interface or PROBOT interfaces [90]. Using the off-line method the sample is pre-fractionated by SEC and then the resulting narrow fractions are analyzed by MALDI-TOF. A combination of SEC and mass spectrometry has frequently been used and many examples are discussed in the excellent book by Pasch and Schrepp on MALDITOF mass spectrometry of synthetic polymers [90]. In this book the interested reader finds also many technical details on matrix/solvent combinations, which have been successfully used for various polymers.

8.2 Nuclear magnetic resonance NMR allows the determination of molecular weight by near end [97] or end groups [98]. The method is limited to rather low molecular weights below 3 104 g/mol, because for higher molecular weight the number of end groups eventually

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diminish to the point where a quantitative determination becomes impractical. On the basis of the intensities of the peaks characteristic for the end group or near end groups the number of end groups can be determined. If the polymer is completely linear, quantitative determination of all end groups provides a direct measure of the number of molecules present and hence of the number average molecular weight Mn . In very few cases solid-state NMR has been used to determine molecular weights for polyethylene [99]. In general solid-state NMR is not so suitable due to the long relaxation times of the end groups, which lead to long measurement times. The strength of NMR is in chemical structure characterization and also the possibility to determine the chain branching, tacticity or to obtain further details of the microstructure.

8.3 Infrared spectroscopy With infrared spectroscopy the molecular composition of polymers is determined by analyzing the characteristic vibrations of functional groups. IR spectroscopy is one of the traditional end group characterization techniques and allows, as with NMR spectroscopy, the determination of number averaged molecular weight Mn for low molecular weight polymers. But its strength is the possibility to analyze the microstructure of polymers and their relationship with macroscopic properties. Often the concentration signal in the SEC separation process is detected by an IR detector. Technically important is the characterization of polyolefines, here the detector is connected to a high-temperature SEC. IR spectroscopy is seldomly used for pure molecular weight determination.

8.4 Electrophoresis Capillary electrophoresis has been very successfully applied for separation of proteins and carbohydrates, and in DNA sequencing. So far very little work has been reported on the separation of synthetic or industrial polyelectrolytes. It has been demonstrated that capillary electrophoresis is a useful technique to separate synthetic anionic and cationic polymers, such as polystyrenesulfonic acid or polyvinylypyridinium hydrochloride in the molecular weight range between 1.5 and 1,500 kg/mol [100–103]. In the case of neutral water-soluble synthetic polymers such as polyethylene glycols most of the separations reported in the literature are limited to the oligomeric range (up to molar masses around 10 kg/mol). For all macromolecules the electrophoretic migration needs to be modified by exclusion or sieving, because for large molecules the electrophoretic mobility becomes independent of the size. Owing to the wide variety of shapes, architectures, sizes, and chemical properties, the capillary electrophoresis often has to be uniquely tailored for the polymer [5], which requires a lot of time and experience. Recent reviews [3–5] give an overview on the progress of the separation of synthetic macromolecules by capillary electrophoresis in the recent years. Technical details and pitfalls in the everyday analytical practice are discussed in the book by Engelhardt [104].

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Capillary electrophoresis has also been combined with other analytical methods like mass spectrometry, NMR, Raman, and infrared spectroscopy in order to combine the separation speed, high resolving power and minimum sample consumption of capillary electrophoresis with the selectivity and structural information provided by the other techniques [6].

9. PRACTICAL EXAMPLES 9.1 Characterization of rigid-rod polymers Typically, characterization of a new polymer cannot be accomplished by a single measurement with one particular apparatus. Especially for polymers where no standards with narrow molar mass distributions exist, in most cases a combination of different experimental techniques is necessary for a satisfactory characterization. For such materials, very often additional information besides the pure molar mass distribution, e.g., the persistence length, is required. In the following we will discuss the characterization work for a rigid-rod poly (p-phenylene) (Figure 15), which had been synthesized with nine different degrees of polymerization (fractions), named P1–P9 [30]. Owing to the very low conformational entropy of stiff polymers, sulfonate ester and dodecyl side chains had to be added for sufficient solubility. These rigid-rod polymers served as precursors for highly charged polyelectrolytes, which can undergo self-assembly into micellar super-molecular aggregates [44,105,106]. Since there were neither narrow calibration standards available nor Mark– Houwink–coefficients known, a simple chromatographic measurement of the molar mass distribution with concentration detection was not feasible. In a first step, static light scattering and membrane osmometry were employed to obtain model-free values for Mw and Mn . Zimm plots similar to the one in Figure 8 were constructed for the evaluation of the light scattering data according to Equation (42), which additionally yields the radius of gyration hRg iz and the second virial coefficient A2 (Table 3). Membrane osmometry measurements were carried out with the capillary osmometer shown in Figure 3. Owing to the short equilibration time of the instrument and the low cut-off molar mass of the membrane, solute permeation through the membrane, which would show up as a drift of the baseline, did not cause problems even for the lowest molar mass fraction. Mn was obtained from

CH3

SO2 R

t−Bu R= n

C12 H 15

Figure 15

SO2 R

t−Bu

Poly(p-phenylene) with side-groups for improved solubility [30].

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1=2

Table 3 Light scattering (Mw , hR2g i ), membrane osmometry (Mn), and viscosity ([Z]) data for the nine poly(p-phenylene) fractions P1–P9 Fraction

P1 P2 P3 P4 P5 P6 P7 P8 P9

Mn

[Z]

(kg/mol)

hR2g i1=2 (nm)

(kg/mol)

(mL/g)

189 157 113 101 90 64 40 38 27

45.6 40.2 29.7 33.0 29.4 19.4 15.7 – –

99 76 54 48 36 39 22 23 16.5

331 275 180 176 127 125 67 78 45

Mw

the concentration dependence of the osmotic pressure for every fraction according to Equation (28). With the aim to establish an ½Z–M relation (Equation (36)) for universal calibration and for the determination of the persistence length, intrinsic viscosities were measured with an Ubbelohde capillary viscometer. The respective data are also included in Table 3. Strictly speaking, monodisperse samples would be required for the determination of the Mark–Houwink coefficients. Since, however, the polydispersities of the nine individual fractions are only moderate (Mw =Mn  2) and since both Mw and ½Z are measured as weight averages with the same statistical weights, the error introduced by the incorrect treatment of the polydispersity could be neglected. Scaling laws like Equation (36) for semiflexible rigid-rod polymers with persistence length lp can only be expected in the rigid-rod limit for short chains with lm  l  lp , l being the contour length and lm being the length of a monomer unit, and in the flexible coil limit for long chains with l lp . For intermediate chain lengths Equation (41) gives a more adequate description of a semiflexible polymer. In Ref. [30] it has been shown that, for the limited molar mass range of the samples investigated, both equations can equally well be used for universal calibration of the SEC. The apparent scaling factor a  0:96 is expected to be molar mass dependent and will eventually approach 0.5–0.8 in the high polymer limit. Figure 16 shows the molar mass distributions of polymer P3 after universal calibration based on Equations (36) and (41), which are almost indistinguishable. The polystyrene calibration yields significantly too high molar masses, since it strongly overestimates the flexibility of the polymer chain. In Ref. [30] the consistency of the approach is demonstrated by recalculating the respective molar mass averages Mw and Mn of the nine polymer fractions from the SEC elugrams after universal calibration, which agree very well with the

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243

wi / g

1.0

0.5

0.0

3

4

5

6

log (Mi / g mol-1) Figure 16 SEC molar mass distribution of poly(p-phenylene) P3 in THF after universal calibration based on Equations (31) (dashed) and (36) (dotted) and with polystyrene calibration (solid line).

absolute values measured by light scattering and membrane osmometry. In particular the Mn values, which had not been used for establishing the universal calibration, show a remarkable agreement. From the two parameters AZ and BZ in Equation (41) a persistence length of lp ¼ 13 nm could be derived.

9.2 Scaling laws Many polymer properties can be expressed as power laws of the molar mass. Some examples for such scaling laws that have already been discussed are the scaling law of the diffusion coefficient (Equation (57)) and the Mark–Houwink– Sakurada equation for the intrinsic viscosity (Equation (36)). Under certain circumstances scaling laws can be employed advantageously for the determination of molar mass distributions, as shown by the following two examples.

9.2.1 Dynamic light scattering In Ref. [107] it has been demonstrated how, based on the scaling law for the diffusion coefficient, molar mass distributions can be calculated from time correlation functions obtained from scattering experiments. DLS is a versatile experimental technique, which is readily available in many laboratories. As discussed in Section 5.2, the field autocorrelation function gð1Þ ðtÞ

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(Equation (51)) contains all information about the distribution function GðGÞ of the decay rates G ¼ Dq2 (Equation (52)). GðGÞ is obtained from an inverse Laplace transform of Equation (51). The computation of GðGÞ is a rather difficult task and a short discussion has been given in Section 5.2. In order to calculate the molar mass distribution, the scaling law (Equation (52)) G ¼ aMb needs to be known. Since the intensity of the light scattered by all molecules of molar mass M and concentration c(M) is proportional to the z-statistical weight c(M)M, the molar mass distribution in concentration units is obtained as [107] cðMÞ / GðGðMÞÞMa j

dGðMÞ j / GðGðMÞÞM1ba dM

(76)

with a ¼ 1 in case of DLS. In Ref. [107] the procedure above has been employed for the measurement of the molar mass distribution of a broad molecular weight polystyrene, obtained by radical polymerization with ethylacetate as solvent. The scaling parameters for this polystyrene in this marginal solvent have been determined to be a  2:8 104 cm2 =s and b  0:52 [107]. The upper curve in Figure 17 shows the resulting molar mass distribution in comparison with the one obtained by SEC. The weak signal contributions from the short polymer chains and problems associated with the inverse Laplace transform usually lead to significant deviations of the thus determined molar mass distribution. Some of these problems, but not all, can be avoided by utilizing the transient holographic grating technique of TDFRS, where a more even signal contribution from the different molar masses can be achieved. Depending on the way the experiment is performed, the parameter a in Equation (76) is either a ¼ 0 for short exposure times (tp ¼ 0:05 s in Figure 17) or a ¼ b for long exposure times (tp ¼ 2 s in Figure 17). The molar mass distributions are reasonable approximations of the one obtained by the fractionating technique, however they exhibit an erroneous bimodal structure, which results from problems with the Laplace inversion by means of the CONTIN method [48,49]. Table 4 summarizes the various molar mass averages obtained by the different dynamic scattering techniques and by the fractionating SEC method. There is a good agreement between all methods for Mw, whereas Mn is obviously overestimated by DLS and by the long exposure TDFRS. The large differences for Mz are difficult to interpret, since SEC with a concentration detector may also not have sufficient sensitivity in the high-M tail of the distribution.

9.2.2 Analytical ultracentrifuge A nice example for the utilization of scaling laws in sedimentation velocity runs with the analytical ultracentrifuge has been published by Ma¨chtle and Bo¨rger [78]. For the polyelectrolyte sodium polystyrene sulfonate (NaPSS) in 0.5 molar NaCl solution they found a scaling law for the sedimentation coefficient at

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245

3

PCS

c(M)

2

τp=2s

1

τp=0.05s

0

103

104

105

106

107

M / g mol-1

Figure 17 Molar mass distributions of polystyrene in ethyl acetate obtained by dynamic light scattering (photon correlation spectroscopy, PCS) and TDFRS with short and long exposure time tp . The dashed curves represent the distribution as determined by SEC. Reproduced with permission from Rossmanith and Ko¨hler [107]. Copyright 1996 American Chemical Society.

Table 4 Molar mass averages (in kg/mol) calculated from the molar mass distributions obtained by SEC, short and long exposure TDFRS, and DLS

Mn Mw Mz

SEC

TDFRS (0.05 s)

TDFRS (2 s)

57 285 640

58 237 434

107 275 509

DLS

121 262 1,229

Source: From [107].

infinite dilution: s0 ¼ KMa ¼ 0:024½SM0:46

(77)

[S] denotes the Svedberg unit (1013 s). Once such a scaling law is available, it can be used in conjunction with a rapid measurement of the sedimentation coefficient

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in the dilute limit, from which M is immediately obtained from the inversion of Equation (77): M ¼ ðs0 =KÞ1=a . The more time-consuming task is the establishment of the scaling law, which requires a series of polymer samples of narrow molar mass distribution and known molar mass. Their sedimentation coefficients have to be measured as a function of concentration and extrapolated back to c ¼ 0 in order to obtain s0 ðMÞ (Figure 18). The same authors then discuss the determination of the entire molar mass distribution from sedimentation velocity runs via scaling laws for the polymer polystyrene in cyclohexane, where the scaling law is also known [78]: s0 ¼ 0:01343½SM0:50

(78)

The procedure first requires the determination of apparent integral sedimentation distribution functions at different scanning times from the time-dependent concentration profiles. These are then corrected for diffusion and finite concentration effects by extrapolating to infinite scanning time and zero concentration to obtain the integral sedimentation distribution GðsÞ and its derivative, the differential sedimentation distribution gðsÞ. Since a concentration sensitive detector has been employed, the molar mass distribution in terms of weight fractions, wðMÞ, is finally calculated utilizing the scaling relation Equation (78): ds (79) wðMÞ ¼ gðsÞ dM

Figure 18 Scaling law of sedimentation coefficient s0 for NaPSS. Measurements of s at finite concentrations (left) and plot of s0(M) (right). Reproduced with permission from Ma¨chtle and Bo¨rger [78].

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Mathematically, this procedure is very similar to the one discussed above for the DLS case.

10. CONCLUSION With this chapter we have tried to provide an overview of experimental techniques for determining molecular weight averages and molecular weight distributions. All methods discussed here have their specific advantages and weaknesses and differ very much in their complexity. The choice of the ‘best’ method strongly depends on polymer properties, the information needed for a particular purpose, and on the available resources. Yet another aspect in the analytical characterization of polymers may be speed. Under certain circumstances some methods are superior compared to others. Vapour pressure osmometry, for instance, works well for low molecular weight, while FFF techniques and light scattering work better for high molecular weight polymers. SEC can be used over a very broad molecular weight range, but calibration and solute interaction with the column material may be a problem. Typically, the operating expense for the characterization grows with the complexity (heterogeneity) of the polymer. For a crude estimation, one might differentiate between four different classes of polymers: 1. 2. 3. 4.

simple homopolymers where monodisperse standards are available homopolymers where no monodisperse standards are available water soluble polymers and polyelectrolytes copolymers (random, diblock, triblock)

Simple homopolymers, where monodisperse standards and suitable solvents are available, are easily characterized by SEC. Homopolymers for which no monodisperse standards are available additionally require some more elaborate detection system for transformation of the retention time into molecular weight. This can be done by, e.g., universal calibration. Alternatively, an absolute molar mass detector, like an on-line light scattering detector or mass spectrometer, can be used. If only average values are of interest, non-fractionating absolute techniques like light scattering and osmometry may be adequate. Ultracentrifugation can provide both a number of different averages and the distribution function, but it is expensive and its availability is limited to a small number of laboratories. In production control it might be sufficient to know the relative mass compared to previous batches. In those cases a chromatographic technique without absolute calibration, or even viscosity measurements, may be sufficient. Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,

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but in the case of highly polar water-soluble polymers enthalpic interactions with the column frequently become important. Often the fl-FFF technique is a good alternative characterization method for water-soluble polymers. Nevertheless, also in this case it is necessary to check whether polymer–polymer or polymer– wall interactions lead to artefacts. Additionally, one needs to select the carrier fluid carefully. Most challenging is the characterization of complex polymers, which are heterogeneous in more than one distributed property, as for instance copolymers. For such complex polymers one cannot follow a simple recipe, but rather one needs to resort to a polymer-specific measurement scheme. Often complex polymers require a combination of different analytical techniques. One approach can be to separate the compounds according to their chemical composition and in the second step to determine the molecular weight distribution or vice versa. Here the two- or multidimensional chromatographic techniques are extremely useful. Some of the detectors, for example, a light scattering detector or a membrane osmometer, can be built in as on-line detectors, but many of these combinations are not commercially available and, thus, mainly limited to larger research laboratories. Other detectors, like a mass spectrometer, may require a special interface or off-line sample collection. We hope that this chapter on the molecular weight determination of synthetic polymers has illustrated that in the case of a complex polymer it is preferable to use several experimental methods for the molecular weight determination to obtain a full picture. Owing to the different sensitivity of the various methods some are blind for low molar masses while others are blind at low concentrations. As exemplified, often scaling laws can be utilized to compare results of different methods and different sensitivities.

ACKNOWLEDGEMENTS We are grateful for fruitful discussions with Dieter Lilge, Katja Klimke, Wolfgang Radke, Hans Joachim Ra¨der, and Manfred Wilhelm. We thank Malte Kleemeier and Adam Patkowski for carefully reading the manuscript and their constructive criticism.

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SECTION III: Polymer Morphology and Structure

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CHAPT ER

7 Phase Structure and Morphology Rufina G. Alamo

Contents

1. Phase Structure and Morphology 1.1 Phase structure 1.2 Characterization of the liquid-like phase 1.3 Characterization of the interphase 2. Supermolecular Morphology 2.1 Lamellar thickness 3. Concluding Remarks Acknowledgements References

255 257 267 271 274 284 286 287 287

1. PHASE STRUCTURE AND MORPHOLOGY The properties of semi-crystalline polymers are very dependent on the chain microstructure and the crystalline morphology adopted upon crystallization or on processing. The well-known fact that crystallinity controls the properties of these materials raised interest in investigating the details of the liquid–solid transformation, and the degree and type of chain organization, from early stages and in parallel with the development of polymer science. In this chapter we will describe in some detail the fundamental elements of the semi-crystalline structure, the large-scale macromolecular organization and most customary methods of characterization of crystalline and non-crystalline regions. For polymer molecules to adopt long-range three-dimensional order, they must have both a high degree of chemical regularity and a high degree of relative motion in the melt.1 A major difference between the crystalline state developed by long-chain molecules and that of small organic molecules, metals or ceramics is inherent to the covalent connectivity between repeating units in a polymer molecule. While individual atomic or low molecular weight species 1

Some polymers with a high degree of chemical regularity and high glass transition temperatures degrade before crystallization. For example, PES [poly(aryl ether sulfone)] is chemically regular but essentially amorphous.

Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00407-8

r 2008 Elsevier B.V. All rights reserved.

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occupy equivalent points in each unit cell, in long-chain polymers the covalent connectivity of repeating units sets a unique correspondence to perpetuate crystallographic symmetry. The continuity of long-chain molecules impacts in a very unique way the structure and morphology that evolves from the initial complex melt. The pioneering works of Storks [1] and Keller [2] established that lamellar crystallites are the fundamental three-dimensional entities that develop upon crystallization of chain molecules from solution or from the melt. The widespread observation of lamellar crystallites, with the chain axis preferentially oriented normal to the basal plane with thicknesses much lower than the contour length of the molecule, represented a major advance in the understanding of the morphological features of crystalline polymers [3–7]. The molecules fold back and forth and, except for the very low molecular weight polymers, may traverse a crystallite many times and connect two or more lamellae. This molecular connectivity is a unique feature of polymer crystallization. It defines the amorphous interlamellar or liquid-like region as well as the interfacial region in which the order of the chains emanating from the crystalline phase is dissipated [8]. The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb’s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. The crystalline state of polymers can be described by a set of hierarchical structures. At the most fundamental level there is the unit cell or primary crystallographic repeated unit. Increasing complexity and, at a larger-scale level, the polymeric lamellae integrate the long-chain connectivity between crystalline and non-crystalline regions. It is in the crystalline regions where the repeated symmetry of continuous crystallographic units is found. The next level of organization corresponds to lamellar aggregates or supermolecular structures. At this level spherical aggregates (spherulites) of different degrees of order are most often found [9–12]. The crystalline lamellae are an important feature of the semicrystalline structure. A schematic representation of the lamellae for a meltcrystallized system is given in Figure 1. The figure displays the coexistence of the three major phases, crystalline, liquid-like and interfacial. Most macroscopic properties are a direct function of the relative content of these phases. Diverse viewpoints about the character of these phases and conformational details of chain units connecting crystallites have evolved historically and can be found in a series of reviews [13–33]. Interest in understanding the details of the crystalline structure arises from the fact that crystallinity controls the properties of semi-crystalline polymeric materials. The characterization of each of the phases of the structure has long

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Crystalline Interfacial Amorphous

Figure 1 Semi-crystalline lamellae. Crystalline, interfacial and liquid-like (amorphous) regions are indicated.

been of scientific and technological research interest and many techniques and different analyses have been used and improved in the last three decades to define and quantify these phases.

1.1 Phase structure 1.1.1 Characterization of the crystalline phase Related to the ordered crystalline region of primary interest is the fractional content of material that is truly crystalline. Standard measurements of the crystallinity level include wide-angle X-ray scattering (WAXS) [34], density measurements [35], differential scanning calorimetry (DSC) [36,37] and Raman, infrared (IR) and nuclear magnetic resonance (NMR) spectroscopies [38–40]. Depending on the technique used, the measurement involves determination of a volume- or mass-based fraction of crystalline material. The early information obtained from most of these techniques was analyzed following a structural model for semi-crystalline polymer consisting of two phases, crystalline and liquid-like [41]. Recognizing the need for a phase of intermediate order, the determination of the degree of crystallinity was revisited to include a more complex three-phase system [42].

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1.1.2 X-ray diffraction The use of wide-angle X-ray diffraction (WAXD) to obtain the degree of crystallinity involves the analysis of a discrete set of crystalline reflections (Bragg spacings) that are superposed upon a broad amorphous halo. The crystallinity (Xx-ray) is obtained directly from the diffractogram after subtraction of the amorphous halo. There are two general methods for this subtraction. If the completely non-crystalline material is available, a diffractogram pattern is obtained in the same angular range. In this diffractogram the ‘‘halo’’ is properly scaled and subtracted from the diffractogram of the semi-crystalline polymer. One example of this procedure is shown in Figure 2 for isotactic poly(propylene), iPP [43]. Here, hydrogenated poly (2-methyl-1,3-pentadiene) was used as a model atactic poly(propylene) since it is completely amorphous at room temperature. Once this subtraction is accomplished the mass-based degree of crystallinity is calculated as: Ic Xx-ray ¼ (1) I c þ KI a

Figure 2 X-ray diffractograms recorded at room temperature. (a) Metallocene-synthesized isotactic poly(propylene), mmmm ¼ 0.996 crystallized at 1451C. (b) Atactic poly(propylene). Reproduced with permission from Ref. [43]. Copyright John Wiley & Sons, Inc., 1999.

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Ic is the sum of the area of all crystalline reflections corrected for Lorentz, polarization and thermal effects, and Ia the area of the amorphous halo. K is a proportionality constant to account for the relative scattering efficiencies of the amorphous and crystalline material. For many systems K is usually close to 1 [44–50]. The actual corrections to each of the observed crystalline reflections are complex and the factors involved depend on the diffractographic plane. Detailed analyses for iPP were carried out by Natta [51] and Mo and Zhang [52] who obtained K values of 2.03 and 1.25, respectively. In a slightly different approach Weidinger and Hermans [53] studied diffractograms of iPPs with different but unknown, crystallinity levels. After subtraction of the halo, the Ic vs. Ia plot displayed a linear regression that yielded limiting values at Ia ¼ 0 (100% crystalline, I oc ) and Ic ¼ 0 (100% amorphous, I oa ). With those limiting values, the level of crystallinity follows directly from I c ¼ Xx-ray I oc I a ¼ ð1  Xx-ray ÞI oa

ð2Þ

These methods, and the most simple one with K ¼ 1, were comparatively analyzed in a series of iPPs with crystallinity levels ranging from B0.50 to B0.80. The results are shown in Table 1. For this system, the corrections proposed by Natta and the most simple subtraction method (K ¼ 1) gave similar results. The values obtained by the Hermans–Weidinger method are only slightly lower; however, the method developed by Mo and Zhang yield consistently higher values. From this comparison, it appears that the most used simple method with K ¼ 1 gives reasonable crystallinity values. When the diffractogram of the pure amorphous polymer is not available at room temperature, the shape of the halo can be deduced either by peak fitting or estimating the halo pattern from the corresponding shape of the molten material. The uncertainties associated with these methodologies arise from the need to give a Table 1 Comparison of degree of crystallinity for metallocene isotactic poly(propylenes) from wide-angle X-ray scattering analyzed by different methods Mwa

Crystallization mode

Xx-ray (1)

Xx-ray (2)

Xx-ray (3)

Xx-ray (4)

102,500 182,000 200,500 327,000 403,500 439,000 349,500 346,500 335,500

Tc ¼ 1551C (7 days) Tc ¼ 1551C (7 days) Tc ¼ 1551C (7 days) Tc ¼ 1551C (7 days) Tc ¼ 1551C (7 days) Tc ¼ 1551C (7 days) Quenched to 01C Quenched to 01C Quenched to 01C

0.74 0.71 0.74 0.69 0.74 0.73 0.62 0.57 0.54

0.82 0.80 0.82 0.78 0.82 0.81 0.73 0.68 0.65

0.72 0.68 0.72 0.68 0.72 0.68 0.58 0.53 0.48

0.77 0.74 0.78 0.74 0.77 0.74 0.64 0.59 0.54

Notes: (1), Method of Natta et al. [51]; (2), method of Mo and Zhang [52]; (3), method of Hermans and Weidinger [53] and (4), from Isasi et al. [43]. a iPP, Mw/Mn ¼ 2.270.2

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Intensity

(110)

(200)

10

15

20

25

30



Figure 3 Non-linear least-squares curve fitting of the orthorhombic WAXS profile of an ethylene 1-decene random copolymer with 2.7 mol% branches. The two crystalline reflections and the amorphous halo are shown.

functionality (Gaussian, Lorentzian, Voigt or mixtures) to each of the crystalline and non-crystalline peaks. Curve-fitting procedures are based on minimization of the difference between experimental and calculated spectra using a non-linear leastsquares method [54]. Figure 3 is an example of the fitting procedure to two crystalline reflections and the amorphous halo for a random ethylene/a-olefin copolymer. A relative crystallinity or ‘‘crystallinity index’’ has been used as an approximate method [55,56]. The simplest procedure involves determination of the intensity at a single scattering angle (2y), in reference to the value for the amorphous halo at the same angular reflection. This method, for example, was useful to follow the variation of crystallinity of an iPP during isothermal melting [57]. The need to construct a more or less arbitrary baseline in the methods described above is a potential source of error in the determination of crystallinity by X-ray [58]. This error is minimized in a treatment by Ruland that analyzes data in a wide range of scattering angles and accounts for the natural diffuse scattering of crystalline polymers [59,60]. Theoretically, this is the most accurate method because the integration expands over a very wide angular range. Modifications and further improvements [61,62] to the original laborious method permit a similar accuracy from experimental data collected in a narrower angular range.

1.1.3 Density Volume and mass-based expressions for the degree of crystallinity are easily derived from the experimentally measured density (r) of a semi-crystalline polymer. The method is based on an ideal crystalline and liquid-like two-phase model and assumes additivity of the volume corresponding to each phase

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(Vc, crystalline; Va, amorphous). The densities of the pure crystalline (rc) and pure amorphous (ra) polymer must be known at the temperature and pressure used to measure r. The value of rc can be obtained from the unit cell dimensions when the crystal structure is known. The value of ra can be obtained directly for polymers that can be quenched without crystallization, poly(ethylene terephthalate) is one example. However, for most semi-crystalline polymers the value of ra is extrapolated from the variation of the specific volume of the melt with temperature [16,63]. From the mass balance, rV ¼ rcVc + raVa, and volume additivity, Va ¼ VVc, the volume and mass fraction crystallinities are written, respectively.   r  ra rc r  ra and XrðmÞ ¼ XrðvÞ ¼ (3) rc  ra r rc  ra The experimental determination of density can be carried out by picnometry, density gradient column or by dilatometry.

1.1.4 Thermal analysis The enthalpic change from the solid to the liquid-like phase of a semi-crystalline polymer can be obtained from DSC [16]. The mass-based degree of crystallinity (XDSC) is calculated as the ratio of the heat of fusion of the sample (DH) and the value per mole of purely crystalline polymer (DHc). XDSC ¼

DH DH c

(4)

This is a relatively fast and popular method that requires only a few milligrams of sample. DH is obtained from a measurement of the area under the melting peak obtained at a constant heating rate, in reference to the heat flow value of a standard. Although Equation (4) is conceptually correct, the application to experimental data should be undertaken cautiously, especially when an arbitrary baseline is drawn to extract the area under the DSC melting peak. The problems and inaccuracy of the calculated crystallinities associated with arbitrary baselines have been pointed out by Gray [36] and more recently by Mathot et al. [37,64–67]. The most accurate value requires one to obtain experimentally the variation of the heat capacity during melting (Cp(T)) [37]. However, heat flow (dq) values can yield accurate crystallinities if the primary heat flow data are devoid of instrumental curvature. In addition, the temperature dependence of the heat of fusion of the pure crystalline phase (DHc) and pure amorphous phase (DHa) are required. For many polymers these data can be found via their heat capacity functions (ATHAS data bank [68]). The melt is then linearly extrapolated and its temperature dependence identified with that of DHa. The general expression of the variation of Cp with temperature is    dXDSC ðTÞ Cp ðTÞ ¼ XDSC ðTÞCp;c ðTÞ þ ð1  XDSC ÞCp;a ðTÞ  ðDH a ðTÞ  DH c ðTÞÞ dT (5)

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In this expression the major contribution to

melting is the excess heat capacity term, ðDH a ðTÞ  DH c ðTÞÞ dXDSC ðTÞ=dT . For sharp melting, DHðTÞ ¼ ðDH a ðTÞ  DH c ðTÞÞ is often a very small contribution, and dXDSC/dT corresponds to deviations from the linear regions of the thermogram prior and after the transition. Given that most polymers melt at temperatures well below the equilibrium value, the temperature dependence of DHc must be taken into account. These corrections could make an important contribution to the value of the crystallinity, especially for polymers with low degrees of crystallinity that melt at temperatures much lower than the equilibrium melting. In one example, the crystallinities of polyethylenes and random ethylene 1-octene copolymers calculated by the Cp measurement method were 15–50% larger than the values obtained by the standard determination of peak area [69]. Moreover, in a study with iPPs negligible differences were found for crystallinities calculated by the two DSC methods when the temperature correction of DHc is applied [70]. For these poly(propylenes) the experimental melting had relatively flat baselines. Thus, the common area determination and application of Equation (2) from flat DCS melting baselines is a good approximation for determination of crystallinity, provided the temperature correction to DHc is applied. The approximation to the temperature dependence of the heat of fusion is given by the factor: f ¼ 2T=ðT þ T m Þ, which is applicable for some polymers [71]. In this expression T is the observed melting temperature and Tm the equilibrium value defined as the melting temperature of an infinitely thick crystal. It has also been inferred that differences found between crystallinities measured by density and those from heat of fusion by DSC area determination, as given for polyethylenes in the example of Figure 4 [72], may be related to baseline uncertainties, or not accounting for the temperature correction of DHc. Given that similar differences in crystallinity from density and heat of fusion were reported for isotactic poly(propylene) [43] and poly(aryl ether ether ketone ketone), PEEKK [73], other features of phase structure that deviate from the twophase model may be involved in the crystallinity discrepancy.

1.1.5 Raman and infrared spectroscopy Both vibrational spectroscopies are valuable tools in the characterization of crystalline polymers. The degree of crystallinity is calculated from the ratio of isolated vibrational modes, specific to the crystalline regions, and a mode whose intensity is not influenced by degree of crystallinity and serves as internal standard. A significant number of studies have used both types of spectroscopy for quantitative crystallinity determination in the polyethylenes [38,74–82] and other semi-crystalline polymers such as poly(ethylene terephthalate) [83–85], isotactic poly(propylene) [86,87], poly(aryl ether ether ketone) [88], poly(tetrafluoroethylene) [89,90] and bisphenol A polycarbonate [91]. In Raman spectroscopy, for example, there are three spectral regions that give structural information about the crystalline state of the polyethylenes. The internal modes, which give quantitative information with respect to the elements of phase structures, are in the region of approximately 900–1,500 cm–1 [38,74,75]. The longitudinal acoustic mode (LAM), which gives the ordered sequence length distribution, lies in the range of about 5–50 cm–1 [92–99]. The disordered LAM

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0.6 0.5

XDSC

0.4 0.3 0.2 0.1 0 0

0.1

0.2

0.3

0.4

0.5

0.6



Figure 4 Plot of degree of crystallinity (XDSC) from DSC against crystallinity (Xr) determined by density measurements. (D), hydrogenated polybutadienes; (’), ethylene 1-butene copolymers; (&), ethylene 1-octene copolymers. Reprinted with permission from Ref. [72]. Copyright 1984 American Chemical Society.

(DLAM) is in the region of 200 cm–1 and gives a measure of the long-range conformational disorder [100–103]. Analysis of the Raman internal modes to yield quantitative data of the phase structure of the polyethylenes was originated by Strobl and Hagedorn [38]. They used the intensity of the CH2 bending band at 1,416 cm–1 as characteristic of the pure orthorhombic crystalline region, as this is the component of this vibration that is split by the orthorhombic crystal field. The total integrated intensity of the twisting region, 1,250–1,350 cm–1 (IT), is independent of the degree of crystallinity, thus, serves as an integral intensity standard. For a completely crystalline specimen, the ratio of intensities, I1,416/IT ¼ 0.46. Accordingly, the mass-based degree of crystallinity (ac) is calculated as: I 1;416 ac ¼ (6) 0:46 I T The content of liquid-like region (aa) is obtained by deconvoluting the intensity in the twisting region into a narrow band centered at 1,295 cm–1 and a melt-like broader component centered at 1,303 cm–1. Thus, I 1;303 aa ¼ (7) IT In addition, the amorphous (liquid-like) content can be determined from the skeletal stretching region by the relation aa ¼

I 1;080 0:79 I T

(8)

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Intensity

The factor 0.79 was found using the spectrum of the molten polymer. Further work on different types of polyethylenes found 0.43 for the factor in Equation (6), and complex band profiles in the 1,080 cm–1 region of the melt structure [104]. For a large amount of experimental data, ac+aa 6¼ 1; the difference has been attributed to the region with intermediate order, the interphase (ab) [38,72,74,75,77–80,105]. The Raman spectrum over this region of an ethylene-lhexene copolymer given in Figure 5 illustrates the deconvolution by curve fitting of regions of interest to extract quantitative data of phase structure. The agreement between the degree of crystallinity obtained by Raman and the value from heat of fusion for a large number of polyethylenes covering a wide range of crystallinities is excellent for crystallinities WB60% as shown in Figure 6. The data for lower crystallinities correspond to branched polyethylenes and ethylene copolymers for which ac is 5–10% lower than XDSC. Corrections for the temperature dependence of DHc, not done in the x-axis of this figure, will increase XDSC and make the difference slightly larger. The difference is attributed to the broad melting range of the structurally irregular chains and the need to start the DSC run at sub-ambient temperature to maximize the linearity of the baseline. Hence, XDSC includes the contribution of a small amount of crystallinity that has already disappeared at room temperature. Because ac is measured at ambient temperature, this contribution is absent in the determination of ac. Conversely, very good agreement was found between the crystallinities measured by Raman (ac+ab) and those obtained from density [106]. IR spectra can also be very useful in determining the degree of crystallinity when pure crystalline and pure liquid-like absorptions can be identified. The method follows the Lambert–Beer law that correlates the absorbance of ordered

1000

1100

1200

1300

1400

1500

1600

Wavenumber (Δυ) cm-1

Figure 5 Raman spectra of orthorhombic ethylene 1-hexene copolymer with band fitting. The crystalline band at 1,416 cm1, and amorphous bands at 1,303 cm1 and 1,080 cm1 are used to compute the crystallinity content: ac ¼ 0.52, and the amorphous content: aa ¼ 0.42. (See Color Plate Section at the end of this book.)

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Figure 6 Plot of the degree of crystallinity from Raman (ac) against crystallinity from heat of fusion (XDSC) for linear and branched (————) polyethylenes and for ethylene copolymers. Reproduced from Polymer Journal with permission from Ref. [106]. Copyright 1985, The Society Polymer Science, Japan.

entities (A) with the extinction coefficient Kc of these regions, the density r and thickness (d) of the specimen. A ¼ Kc Xir r d

(9)

This technique has been successfully applied to linear polyethylene (PE). For example, in this polymer of the three rocking mode bands in the 725 cm–1 region, two sharp bands near 730 and 722 cm–1 are associated with the crystalline fraction, and a third broad component, overlapping the 722 cm–1 band, represents the amorphous component [107–110]. The broad liquid-like band was identified in the spectra of molten linear PE and n-alkanes in which the 730/722 cm1 doublet is replaced by a broad band centered near 723 cm1 [107]. From the overlapping spectral region, crystalline and amorphous bands are deconvoluted by standard curve-fitting methods. A second useful region for crystallinity determination of PE is the methylene scissoring modes in the 1,420–1,475 cm1 region. Again, two of these bands 1,473 cm1 and 1,463 cm1 appear from the splitting of this mode by the crystal field; they are thus crystalline bands, the third at 1,487 cm1 is broader and is associated with the amorphous regions [107]. The ratio of the crystalline band at 1,894 cm1 to the internal standard 1,303 cm1, corrected by their corresponding extinction coefficients, has also been used for crystallinity measurement. Using IR methods the degree of crystallinity of polyethylene was identical to the calculated by density [110], and the same as that

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from heat of fusion [107] and from WAXS [111], indicating a good correspondence between the three methods. In addition to quantitative crystallinity data, IR and Raman have been proven valuable tools to extract information on chain conformation in the three major phases [112–114], local order in amorphous polymers [115,116] high throughput characterization [117] and structural and polymorphic changes on heating and cooling semi-crystalline polymers [118–120].

1.1.6 NMR spectroscopy Both 1H and 13C solid-state nuclear magnetic (NMR) spectroscopy have been used to determine the degree of crystallinity in polyethylenes [121–129]. Fully relaxed 13C NMR spectra, obtained under high-power dipolar-dicoupling and magic angle spinning, display distinct resonances for the disordered amorphous carbons (B31 ppm) and those associated with the ordered orthorhombic crystalline regions (32.8 ppm) [124]. The intensity of each region is obtained by peak deconvolution. The example of Figure 7 gives evidence for good agreement between crystallinities obtained from 13C NMR and WAXS-determined crystallinities in the same polyethylenes [129]. In recent work spin diffusion [130], as well as a sequence that combines a spin diffusion filter prior to cross-polarization, were applied to quantify the phase content of polyethylenes and styrene-isoprene block copolymers [131]. Further detailed NMR studies of the relaxation properties of the crystalline regions have identified a heterogeneous behavior with respect to motions in the megahertz frequency range, those responsible for the spin-lattice relaxation [126]. The T1C relaxation of the crystalline phase obtained via inversion recovery with cross-polarization cannot be fitted to a single exponential function. It requires two or three components that are associated with regions of different structural order [132]. Two orthorhombic 100

XNMR

90 80 70 60 50 50

60

70

80

90

100

Xx-ray

Figure 7 Plot of the degree of crystallinity (XNMR) by obtained by 13C NMR against crystallinity (XX-ray) obtained by wide angle X-ray diffraction for an unfractionated linear polyethylene sample crystallized in different conditions (data from Ref. [129]).

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crystalline components with distinctly different dynamics were detected in a series of different types of polyethylenes using different solid-state NMR pulse sequences [133]. NMR cannot distinguish whether the more mobile region is localized close to the boundary with the liquid-like region or randomly dispersed within the more rigid all-trans component. Nonetheless, the former could be taken as the more plausible scenario because the presence of a diffuse region where the order is dissipated is expected in the semi-crystalline structure [126,128].

1.2 Characterization of the liquid-like phase While characterization of the type of crystallographic symmetry in the crystalline regions is straightforward from the WAXD patterns of oriented specimens, the characterization of the configurational properties of the polymer chains connecting crystallites in the interlamellar region has been elusive. Predictions of the state of order and topological details have been based on comparative studies with the molten system [134–138] or by theoretical simulations [139–143]. Concerning linear polyethylene, inelastic neutron scattering (INS) gave evidence by direct experimentation that the molecular conformation of the chains in the interlamellar regions of solid samples had the same random coil dimensions as those in the melt [144]. The experiments confirmed the prevailing view that, upon solidification of flexible chains, the random conformation was preserved in the amorphous (liquid-like) region. Hence, once accounts are made for the interfacial region where the chain-order emerging from the crystal is dissipated, the dimensions of the chain in the remainder interlamellar region have the characteristics of random coil in the melt. Spectroscopic methods have been most useful to infer properties of the liquidlike region. For example, the DLAM of the Raman spectra of polyethylenes gives information about the degree of conformational disorder of polyethylenes [102,103]. The frequency of the DLAM band depends on the ratio of the number of trans to gauche bonds and the chain length. For the linear chains this band in solid samples had the same similarities as for the pure melt. Examples are illustrated in Figure 8. The spectra shown are for a high molecular weight linear polyethylene with a room temperature crystallinity level of 0.42. The corresponding spectrum of the melt of the same polymer is shown in Figure 8(d); it is characterized by a broad band at B200 cm1. This band is also present in the room temperature spectrum of the solid sample, Figure 8(a). As the temperature is initially increased, the intensity of this band increases slightly while the frequency remains constant. In the molten state, 1471C, the DLAM becomes more intense but the frequency is unchanged. This result indicates that the amorphous region of the bulk crystallized linear chain has the same random conformation as that of the molten sample, in analogy to the neutron scattering results. The DLAM frequency of random copolymers of ethylene behaves in a different manner [103]. For these copolymers ethyl and longer branches are excluded from the crystal region. The branches accumulate in the interlamellar

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Figure 8 Plot of low frequency Raman spectra of a high molecular weight linear polyethylene that was initially quenched at 701C as a function of temperature. Spectra obtained at (a) room temperature, (b) 571C, (c) 871C and (d) 1471C. Reprinted with permission from Ref. [102]. Copyright 1986 American Chemical Society.

region increasing the number of gauche bands in this region [72,80]. This effect translates into an increase of the Raman DLAM band with increasing branching content, and parallels the measured and calculated decrease of the characteristic ratio of model copolymers with increasing branching content [145,146]. Changes by the accumulation of branches in the interlamellar region were also followed by analysis of the angular position of the amorphous halo (2yhalo) [54]. For the same crystallographic phase, the peak of the halo correlates with short-range

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Decene(q)

20

2 Theta (Halo)

Linear PE Decene(an)

19.8

19.6

19.4

19.2 0

5

10

15

20

Comonomer Content (Mol%)

Figure 9 Room temperature variation of peak 2yhalo for ethylene 1-decene copolymers quenched (q) and annealed at room temperature (an). The value for the linear polymer is also given.

intermolecular van der Waals interactions and with the characteristics of the radial coil. As shown in Figure 9 for a series of quenched, and annealed ethylene l-decene copolymers, the 2yhalo decreases linearly with increasing comonomer reflecting the increase of the average backbone carbon–carbon intermolecular distance in the amorphous region. Bulkier branches expand the coil further; as a consequence, the 2yhalo is shifted to lower values [54]. The conformational properties of the liquid-like and glassy states of polyethylene terephthalate (PET) have been amply studied by vibrational spectroscopy [147,148], and solid-state NMR [149]. The issue of concern is the degree of trans/gauche isomerization that the chain undergoes from the equilibrium population in the liquid-like state to either (i) the semi-crystalline state or (ii) the glassy state. It has been found that while the crystalline regions adopt the all-trans conformations, the preferentially gauche, unperturbed random conformational statistics and chain dimensions of the melt are preserved in amorphous and glassy PET, in agreement with Flory’s predictions [149]. In more recent studies, attempts have been made to extract the structure of the amorphous regions using position annihilation lifetime spectroscopy (PALS). The temporal changes of positrons trapped in a material due to interactions with host electron are followed in this spectroscopy [150,151]. Positrons annihilate either as free positrons or from a bound state with a host electron, termed positronium (Ps), an analogue of the hydrogen atom [152]. The Ps can exist either in a singlet spin (parapositronium, pPs) or a triplet spin (orthopositronium, oPs) state. While self-annihilation of pPs is a fast allowed process, annihilation of oPs proceeds via reaction with an electron of the host, such that the value of the lifetime (t3) and the intensity (I3) of oPs are sensitive to the state of order, and free volume of the polymeric matrix where oPs annihilates. Changes in free volume in the interlamellar region of semi-crystalline polymers are resolved by this technique.

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The PALS technique has been used to determine the contents of amorphous and interfacial regions of linear polyethylenes with different crystallinities [153,154] and of ethylene- and propylene-based random copolymers [155–159]. The results for a series of ethylene l-octene random copolymers with increasing mol% comonomer are given in Figure 10 [158]. Here the content of crystals was obtained from WAXS. In the calculation the authors assumed that all noncrystalline regions of linear polyethylene were in a rigid amorphous state, while those of the copolymers were a mixture of mobile and rigid amorphous. For the ethylene 1-octene copolymers studied, the interfacial regions calculated from PALS are significantly larger than the values obtained from the Raman internal modes analysis [72,74]. The use of 13C NMR is another effective probe with which to investigate the non-crystalline region of semi-crystalline polymers. Solid-state 13C NMR spectra display resonances that can be assigned to carbons in the crystalline and noncrystalline environments, thus confirming the coexistence of both regions [124,125,160]. The 13C NMR spin-lattice relaxation times (T1c) of the two regions usually differ by over two orders of magnitude [161,162]. Thus, by adopting appropriate pulsing programs, it is possible to separate the amount of carbons associated to each relaxation. In particular, it is possible in favorable situations to compare T1c of the non-crystalline region of semi-crystalline polymers with that of the pure melt. In one example, the T1cs of the non-crystalline methyl, methine and methylene carbons of iPP, 70% crystalline, were compared at room temperature with those of model atactic poly(propylene), hydrogenated poly(2-methyl-1,3pentadiene) [163]. It was found that, within the experimental error, the T1c values of each of the carbons were the same in both polymers. The conclusion can then be reached that the fast segmental motion, at or near the Larmor frequency of

Figure 10 Degree of crystallinity from WAXS, interfacial content from PALS and amorphous content from PALS for an ethylene 1-octene copolymers as a function of increasing 1-octene. Reproduced with permission from Ref. [158]. Copyright 2002 Elsevier Ltd.

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5–500 MHz, which determine the T1cs, are the same for the non-crystalline region of isotactic poly(propylene) and for atactic poly(propylene). This in turn indicates that the disordered chain structure is the same for the two cases. A similar comparison can be made with cis-poly(isoprene), natural rubber, by taking advantage of the fact that the polymer is very slow to crystallize [164]. Consequently, the comparison can be made between the supercooled, noncrystalline polymers at 01C and the semi-crystalline polymer (31% crystalline) at the same temperature. The T1c values for each of the five carbons involved were again found to be the same for the completely disordered polymer and the semicrystalline one, so that a similar conclusion can be made with regard to their chain structure. An analogous comparison cannot be made with linear polyethylene since this polymer crystallizes very rapidly. However, by varying the molecular weight and crystallization temperature, a crystallinity range from 0.57 to 0.90 can be obtained at room temperature [165]. The T1 values for such samples are essentially constant with deviations being only about 75% from the average value. The effective correlation time was calculated to be the same as that of the interior chain carbons of pure molten n-alkanes. Thus, the fast internal segmental motions, which determine T1, are the same in the non-crystalline regions of linear polyethylene and the melts of the low molecular weight n-alkanes. Moreover, the major differences in morphological forms that can be developed influence this type of motion [165,166]. For both linear and branched polyethylene T1c is a continuous, monotonic increasing function over a temperature range that encompasses both the crystalline and completely molten polymers. Poly(ethylene oxide) and poly(trimethylene oxide) behave in a very similar manner [166]. The aforementioned results for several different polymers clearly demonstrate that the rapid segmental motions as reflected in the T1 measurements are the same for the non-crystallization region and the completely molten polymer.

1.3 Characterization of the interphase The interfacial zone is by definition the region between the crystallite basal surface and the beginning of isotropy. Due to the conformationally diffuse nature of this region, quantitative contents of the interphase are most often determined by indirect measures. For example, they have been computed as a balance from one of the sum of the fractional contents of pure crystalline and amorphous regions. The analysis of the internal modes region of the Raman spectrum of polyethylene, as detailed in the previous section of this chapter, was used to quantify the content of the interphase region (ab). A factor analysis of the Raman spectra of a set of linear polyethylenes identified the existence of a third component in addition to the pure crystalline and pure amorphous components [78]. The characteristics of the Raman spectrum of the interphase were very similar to that of the crystalline spectrum indicating that the interphase retains a significant degree of order. Using the Raman method, the content of interphase in linear polyethylenes was found to increase with molecular weight [74–76,78]. For molecular weights below

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B20,000 g/mol, ab is only about 5% and increases to 15–20% for the higher molecular weights. Unfractionated ultra high molecular weight reactor powders display even higher contents of interphase [77]. The increase of interphase with comonomer content in random ethylene copolymers [72,79,80,167] is correlated with the accumulation of topographical defects, entanglements, structural irregularities and comonomer preferentially at the interphase. Analogous to the factor analysis results in linear polyethylene, a structural study of bisphenol A polycarbonate by Raman spectroscopy, WAXS and DSC concluded that the interfacial region was partially ordered [91]. Heat capacity measurements at the glass transition temperature, Tg, are based on the same differential concept. The weight fraction of amorphous phase is calculated as the ratio of changes of heat capacity of the semi-crystalline sample DCp(s) over the change in heat capacity of the melt (DCp(m)) at the glass transition. For a two-phase system, the degree of crystallinity is given as: Xcp ¼ 1 

DCpðsÞ DCpðmÞ

(10)

However, it has been found for many systems that Xcp þ DCpðsÞ =DCpðmÞ a1, and the semi-crystalline structure is better described by a three-phase model. The region of intermediate order was initially defined as an inter-crystalline phase [168,169]. Further, detailed studies identified the portion of non-crystalline polymer that does not contribute to the heat capacity at Tg as the ‘‘rigid amorphous phase’’ [170]. This portion is structurally assigned to the region between crystalline and amorphous phase, or to the interphase [171–174]. The determination of the rigid amorphous fraction requires a precise knowledge of Tg and of the degree of crystallinity at Tg preferably by a method other than the thermodynamic one. In spite of the long empirical extrapolation of DCp from the melt to Tg, the contents of interfacial region obtained by this method are similar to values obtained by vibrational spectroscopies [175]. A combination of DSC, NMR, WAXD and small-angle X-ray scattering (SAXS) analysis of the phase structure of aliphatic poly(amides) concluded that about 20% of the mass was in a rigid amorphous conformation inside the crystals [176]. Dielectric relaxation [171,177–180] and solid-state NMR spectroscopy [121–123,181–185] have been used extensively to isolate and quantify the structural region of intermediate order. In NMR spectroscopy, resonance spectra are interpreted as pertaining to nuclei in three different conformational environments. The most extensive work has been carried out analyzing proton broad-line and 13C DD-MAS (dipolar decoupling magic angle spinning) NMR spectra of polyethylenes. 1H spectra were deconvoluted into a broad (immobile) component characteristic of the crystalline regions, a narrow component associated with short-range motions (mobile) in the liquid-like regions, and an intermediate component corresponding to the interfacial region of intermediate mobility [121–123,181–185]. A detailed analysis by spin diffusion concluded that the interfacial region of linear polyethylenes is more dense than the amorphous ˚ thickness [183]. In a study of linear polyethylenes, as the and averages B50 A molecular weight increased from 13,000 g/mol to 3,400,000 g/mol the content of

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interface calculated from deconvolution of the broad-line 1H NMR spectra, increased from 6% to B18%. Concomitantly, the crystalline content decreases from 94% to 64% and the amorphous content increases from 0.2% to B19% as molecular weight increases [123]. The changes reflect the increase of entanglements per chain as molecular weight increases. Similarly, 1H spin-lattice relaxation processes are described in terms of three components with different T1 values [186]. High-power dipolar decoupled 13C NMR spectra under magic angle spinning have also been analyzed in reference to three-phase systems. The DD-MAS 13C NMR spectrum of linear polyethylene displays two distinct resonances associated with carbons in crystalline (32.8 ppm) and non-crystalline (31 ppm) environments [124]. The spin–spin relaxations (T2c) of the carbons in the noncrystalline regions display two components. One with T2c ¼ 2.4 ms is associated with highly mobile carbons of the liquid-like region. The second component with T2c ¼ 44 ms can be assigned to carbons with more restricted motion in the interface. On this basis, the 13C NMR spectrum was resolved into three components using pure Lorentzian-shaped peaks. The content of each component is obtained from peak fitting of the experimental spectra using non-linear regression. Interfacial contents obtained in different polymers using this method are listed in Table 2 [187–192]. Clearly, the interface is a significant component (15–30%) of the phase structure of the polymers listed. In a comparative study of the crystallinity of isomeric aliphatic polyamides by NMR, DSC and X-ray, the NMR-based crystallinity was obtained by a two component fit of the proton broad-line spectra and their associated mobilities by T1r determination. Compared to the crystallinity estimates from DSC and WAXS, the content of rigid material obtained from NMR is significantly higher, but comparable to the crystallinity determined by SAXS. The difference with the DSC value was associated with a fraction of intermediate order within the crystalline phase [193]. Deuterium and 31P NMR spectra of poly(butylene terephthalate) and poly(bis (phenoxy) phosphazene) have also been analyzed on the basis of three conformational environments [194,195]. Significant interfacial contents of up to 25% were extracted from this analysis. In a more qualitative manner, an Table 2

Interfacial content determined by DD MAS 13C NMR

Polymer

Linear polyethylene M ¼ 2.5 105 (fraction) M ¼ 3.0 106 (unfractionated) M ¼ 4.0 104 (unfractionated) M ¼ 1.85 105 (unfractionated) Isotactic-poly(propylene) Poly(e-caprolactone) Poly(tetramethylene oxide)

ab

0.16 0.18 0.16 0.20 0.30 0.30 0.22

Reference

[125] [125] [127] [290] [190] [291] [192]

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interphase was included in addition to crystalline and amorphous regions to describe the semi-crystalline structure of a large variety of polymers. Among them are analysis of NMR spectra and those associated with chain dynamics of poly(vinyl alcohol) [196], syndiotactic poly(propylene) [197], poly(ethylene naphthalene-2,6-dicarboxylate) [198], poly(aryl ether, ether ketone) [199] and poly(ethylene terephthalate) [200].

2. SUPERMOLECULAR MORPHOLOGY Although spherulites are the most common form of supermolecular structures that are observed in crystalline polymers, they are not the only morphological type of lamellar aggregates [201]. A common progression of the development of spherulites starts from an initial small bundle of lamellae that grows longitudinally and spreads and branches off transversally like a sheaf. Radial growth continues until impingement between neighboring spherulites, thereby ending as a polyhedral ‘‘grain-type’’ structure such as the examples given in Figure 11 for isotactic poly(propylene) and linear poly(ethylene). Spherulites are birefringent, hence, when viewed with polarized light in an optical microscope, black extinction regions give rise to the appearance of a Maltese cross with arms parallel and perpendicular to the direction of the retardation path. Thin-section transmission electron microscopy (TEM) has been the usual, preferred technique to characterize lamellar morphology. Contrast between amorphous and crystalline regions is obtained by acid etching or staining. The details of etching with chlorosulfonic or permanganic acid have been described in different works [202,203]. Staining with RuO4 has been described as well [204]. The acid or staining medium penetrates and accumulates preferentially in the amorphous region. Optical and electron transmission microscopy give a two dimensional view of the supermolecular morphology and lamellar structure. In contrast, scanning election microscopy (SEM) gives a three-dimensional view

Figure 11 Left: Spherulites of a Ziegler–Natta isotactic poly(propylene) with Mw ¼ 271,500 g/mol and mmmm ¼ 0.95, isothermally crystallized at 1481C. Right: Banded spherulites of a linear polyethylene with Mw ¼ 53,600 g/mol slowly cooled from the melt.

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of the specimen surface. At high magnifications SEM can supply details of the lamellar structure [205]. Recent developments have allowed atomic force microscopic (AFM) studies to follow the course of spherulite development and the internal lamellar structures as the spherulite evolves [206–209]. The major steps in spherulite formation were followed by AFM for poly(bisphenol) A octane ether [210,211] and more recently, as seen in the example of Figure 12 for a propylene l-hexene copolymer [212] with B20 mol% comonomer. Accommodation of significant content of l-hexene in the lattice allows formation and propagation of sheaf-like lamellar structure in this copolymer. The onset of sheave formation is clearly discerned in the micrographs of Figure 12 after crystallization for B10 h. Branching and development of the sheave are shown at later times. The direct observation of sheave and spherulitic formation by AFM supports the major features that have been deduced from transmission electron and optical microscopy. The fibrous internal spherulite structure could be directly observed by AFM. Polymer spherulites may display extinction patterns more complex than the Maltese cross [213]. A pattern also commonly observed is concentric rings that have regular periodicity, as illustrated in the example of Figure 11 for ring spherulites of polyethylene [214]. Alternating dark and white bands result from a periodic change of orientation of the birefringent entities along the spherulite radius. Electron microscopic studies of replica of fracture surfaces of meltcrystallized polyethylene, containing spherulites with periodic extinction rings, show thin lamellae that change their orientation periodically along the radius of the spherulite. The period is identical with that of the extinction rings observed under the polarizing microscope [215]. Both molecular weight and crystallization temperature can alter the resulting supermolecular patterns. The influence of crystallization temperature has been studied for fractions of poly(ethylene adipate) [216], poly(trimethylene terephthalate) [217], polyethylene oxide [218], poly 1,3-dioxolane [219] and linear polyethylene fractions [220] among others. In some systems the morphological change correlated with a change of growth regime [216,219–221]. The patterns observed as a function of crystallization temperature for poly(ethylene adipate) are shown in Figure 13. Typically, axialites form at high crystallization temperature (Figure 13(A)), banded spherulites are found as the crystallization temperature is lowered. At relatively low crystallization temperatures the spherulites are no longer banded, though a well-defined Maltese cross remains. Studies of the effect of molecular weight on spherulite formation in linear polyethylene fractions indicate that structures with a high order of spherical symmetry develop only in a range of chain lengths [222,223]. The studies combined optical microscopy and small-angle laser light scattering (SALLS) to characterize morphological patterns by the lamellar degree of organization. Five most typical Hv patterns, where the incident light is polarized vertically and the scattered light is polarized horizontally, are given in Figure 14 [224]. Patterns (a), (b) and (c) represent spherulitic structures with order deteriorating from (a) to (c). Pattern (d) is indicative of lamellae organized as rod-like aggregates. Pattern (e), which displays no angular dependence of the scattering, can be

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Figure 12 AFM images of development of axialites from the initial stages at room temperature for a random propylene 1-hexene with 25.1 mol% 1-hexene. The time is indicated. Reprinted with permission from Ref. [212]. Copyright 2005 American Chemical Society.

Phase Structure and Morphology

Figure 13 Top, plot of linear growth rates of poly(ethylene adipate) spherulites as a function of crystallization temperature for indicated molecular weight fractions. Spherulites shown correspond to the indicated range of temperatures. (A) Crystallization at the lower temperature range; (B) at intermediate temperatures; (C) crystallization at high temperatures. Reproduced with permission from Ref. [216]. Copyright 1956, John Wiley & Sons, Inc.

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Figure 14 Most characteristic small-angle laser light scattering patterns (Hv) observed with linear polyethylene fractions. Reproduced by permission of The Royal Society of Chemistry from Ref. [224].

attributed to rods whose breadth is comparable to their length (sheet-like structure) or randomly oriented lamellae. Optical microscopy can be used to distinguish sheet-like morphology (g) (plotted in Figure 15) from a collection of random lamellae (h) [222,224]. Controlling crystallization conditions, a morphological map was constructed that delineates the polyethylene molecular weight and crystallization temperature regions where structures of different types are formed. Such a morphological map is given in Figure 15. Clearly spherulite formation is not a universal mode of polymer crystallization, as confirmed in other studies [225,226]. In the region where spherulites are formed, the order decreases with increasing molecular weight. Rod structures (d) are formed at the lowest molecular weights and randomly oriented lamellae at high molecular weights (W1.6 105 g/mol). As the crystallization, or quenching temperatures increases, in the spherulite forming molecular weight range, there is a demarcation temperature above which rodlike scattering patterns Figure 14(d) are observed. If one takes well-organized spherulite (a) types as reference points, then the organized structures gradually deteriorate with increasing molecular weight and cooling rate. Except for the highest chain length, it is possible for a fixed molecular weight to develop different supermolecular structures by varying either the quenching or the isothermal crystallization temperature. As has previously been described, banded type spherulites form in the central region of the map [214]. Further studies in mixtures of polyethylenes of different chain lengths show that

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107

106 h

105

M

c

104

b

o 103

130

g Tc

d 102 -150

-100

-50

0

50

100

115

TEMPERATURE OF QUENCHING AGENT (°C) NON − ISOTHERMAL

Figure 15 Morphological map of linear polyethylene fractions. Plot of molecular weight against crystallization temperature. The types of supermolecular structures are represented by symbols. Patterns a, b and c represent spherulitic structures with deteriorating order from a to c. Patterns g and d represent rods or sheet-like structures whose breadth is comparable to their length g or display a different aspect ratio d. Pattern h represents randomly oriented lamellae. Neither h nor g patterns have azimuthal dependence of the scattering. Reproduced with permission from Ref. [223]. Copyright 1981 American Chemical Society. (See Ref. [223] for full details.) Note: the pattern ‘a’ is actually located as ‘o’ in the figure; this was an error on the original.

irrespective of the superstructures of the pure species, the morphological result for the blend corresponds to the pattern of the blend’s number average molecular weight [227]. Morphological maps for long-chain branched polyethylenes and random ethylene copolymers demarcating the formation of spherulites of different orders have been also constructed [228,229]. Thin-section electron microscopic studies of fractions of linear polyetheylene have shown systematic changes in the details of the lamellar crystallites that correlate quite well with the supermolecular structure as characterized by SALLS [222,230,231]. The change of lamellar patterns with increasing molecular weight vary in parallel with the observed supermolecular morphology as shown by the TEM micrographs of linear polyethylene fractions given in Figure 16. The staining reagent does not penetrate the crystalline regions, which appear as light

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Figure 16 Typical electron micrographs of quenched samples of indicated molecular weight fractions of linear polyethylene. Reproduced with permission from Ref. [231]. Copyright 1984, John Wiley & Sons, Inc.

regions in the micrographs. Dark areas correspond to non-crystalline regions. For low and modest molecular weights, the lamellae are straight and long and lead to well-organized stacked lamellae that correlate with the rod-like SALLS patterns. As the molecular weight increases, the lamellae become curved and shorter due to restrictions imposed by the higher entanglement density per chain, resulting in spherulitic structures continuously deteriorating. At high molecular weights the crystallites become highly segmented and arrange randomly. The crystalline morphology of poly(propylenes) is of interest due to the role of defect microstructure and crystallization temperature affecting the type of unit cell that develops and the homoepitaxial lamellar branching. The lamellar and crystallographic habits of the monoclinic (a) and orthorhombic (g) phases of poly(propylene) are unique among flexible chain molecules. For the a phase at the resolution level of the electron microscope, a three-dimensional array of nearly orthogonal ‘‘cross-hatched’’ lamellae is usually found [232–234]. The details of the molecular arrangement of the branching have been explained in terms of a homoepitaxial crystallization of transverse lamellae on the lateral 010 face of the parent ones [232–237]. This is possible by the near equivalence of the a and c axes of the unit cell and a good interdigitation of the methyl groups. The development of lamellar branching in homo poly(propylenes) is affected by

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isotacticity, undercooling and degree of transformation, and the impact on optical properties has been recently summarized by Lotz [238]. Positive, negative or mixed spherulites develop depending on the relative proportion of radial and transverse lamellae and on the orientation of the radial lamellae relative to the path of light. Spherulites with a negative character develop at the highest and lower undercoolings due to a reduced frequency of branching, while most often mixed spherulites develop at intermediate undercoolings. In some favorable conditions and with prolonged crystallization time, mixed spherulites acquire positive character due to branch infilling during secondary crystallization [239]. One consequence of the epitaxial lamellar crystallization (cross-hatching) in isotactic poly(propylenes) is the observation of two endothermic peaks that are obtained by conventional DSC [240]. A representative thermogram, obtained after isothermal crystallization at 1481C is given in Figure 17 for a Ziegler–Natta catalyzed isotactic poly(propylene) [241]. In a parallel experiment, the same polypropylene was crystallized in a microscope hot stage at the same temperature. Spherulites with mixed type birefringence were obtained. Subsequently, the temperature of the hot stage was raised to 1711C, a temperature just beyond the peak of the low temperature endotherm, and changes in the spherulites were followed with time. The change from mixed to negative birefringence is consistent with preferential melting of the transverse lamellae. It is then concluded that the low temperature endotherm results from the

Tc = 148

178.4°C 168.8°C

171.0°

(a) Tc = 148C, 2days

(c) 171C, 80min

140

150

160 170 temp (°C)

180

(d) 171C, 200min

190

(b) 171C, 10min

(e) 171C, 300min

Figure 17 Isothermal melting of Ziegler–Natta isotactic poly(propylene). (a) Spherulites with mixed birefringence at Tc ¼ 1481C. The top middle figure displays the melting for the same thermal history. (b) Subsequent to crystallization, the temperature was raised to 1711C; spherulites acquire negative birefringence. (c), (d) and (e) Isothermal melting at 1711C for 80, 200 and 300 min, respectively. Reproduced with permission from W.T. Huang, Dissertation, Florida State University, 2005. (See Color Plate Section at the end of this book.)

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cooperative melting of the branched or tangential lamellae. The high temperature one corresponds to the melting of the primary or radial lamellae. Furthermore, after 300 min, the whole structure is melted, indicating that isotactic poly(propylenes) melt with significant isothermal melting kinetics. This phenomenon requires the melting of the tangential lamellae so that the fusion of the epitaxial structure is not involved. What is involved is the melting of the radial lamellae devised of the epitaxy. The rate of isothermal melting depends on the location of the annealing temperature between the two initial endotherms. The isothermal melting kinetics has also been demonstrated by time resolved in-situ WAXS studies. The higher the annealing temperature is the faster the isothermal melting [242,243]. The structure of the unit cell of the g form of isotactic poly(propylenes) is unique to polymeric systems. It represents the first, if not the only one, observed to date where the chain axes are not parallel to one another. The gamma phase comprises non-parallel chains tilted at 40o to the lamellae normal and is favored in poly(propylenes) with short continuous isotactic sequences [244,245]. Defects of the stereo type or constitutional irregularities such as the 2,1 defect, the 3,1 defect or comonomers added to the iPP chain, disrupt the length of continuous crystallizable sequences (primarily isotactic placements), and enhance the formation of the g polymorph [246]. It was initially proposed by Lotz and Bru¨ckner that the development of a and g branching are intimately correlated as shown in the schematics of Figure 18 [245–249]. The morphological predictions from this model for iPP systems that undergo a change in polymorphic content (a/g ratio) were confirmed by AFM studies of a series of propylene ethylene copolymers made by a metallocene catalyst [246]. The content of stereo and 2,1 defects is fixed at 1.170.1 mol% in this series, hence the major crystallographic and morphological differences observed are due to the effect of the ethylene counit. As shown in Figure 19(a), at a fixed crystallization temperature, the g

Figure 18 Schematic model of a iPP and g iPP branching from a parent lamellae. The crystallographic axes are indicated. Adapted from similar schemes in Refs. [245,246], with permission of Elsevier; copyright 2004.

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PE 1.8, Tc = 110°C, ~ 40% γ

(a) 100

(b)

Gamma Content (%)

80

60

PE 3.4, Tc = 110°C, ~ 70% γ 40

PE 1.8 PE 2.8 PE 3.3 PE 3.4 PE 5.8 PE 8.7

20

0 80

90 100 110 120 130 Crystallization Temperature (°C)

140

PE 8.7, Tc = 110°C, ~ 100% γ

Figure 19 (a) Percentage of g phase vs. crystallization temperature,Tc, for metallocene propylene ethylene copolymers with ethylene content increasing from 0.8 to 7.5 mol%. (b) AFM phase images of selected copolymers with different content of g phase. The arrows indicate the radial direction of the spherulite. Reprinted from Ref. [246] with permission from Elsevier; copyright 2004.

content increases with increasing defects. The morphology for samples crystallized at 1101C, shown in Figure 19(b), reflects structural changes that parallel the schematic model for a/g branching. At this temperature the content of g phase changes from B40% (PE1.8) to B100% for PE8.7. Consequently, with increasing g content, iPP a lamellae that grow in the direction of the spherulite radius and branches thereon, are replaced in g rich copolymers with a dense array of short lamellae transverse or tilted to the main structural growth axis [246,250–254]. The images give evidence of systematic changes in the crystalline texture of random propylene copolymers with increasing comonomer content and crystallization temperature. The changes follow the variation in polymorphic content and the proposed growth models for epitaxial branching.

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2.1 Lamellar thickness The thickness of the ordered crystalline regions, termed crystallite or lamellar thickness (Lc), is an important parameter for correlations with thermodynamic and physical properties. Lc and the distribution of lamellar thicknesses can be determined by different experimental methods, including thin-section TEM mentioned earlier, atomic force microscopy, small-angle X-ray scattering and analysis of the LAM in Raman spectroscopy. Precise thickness measurements by TEM require sections transverse to the basal lamellar surface. Conversely, only lamellae that can be identified as untilted ‘‘edge-on’’ or ‘‘flat-on’’ in AFM images are suitable for thickness analysis. The average thickness obtained by these techniques is based on sampling microscopic areas and will only be correct if the morphology is uniform in the sample. Micrographs taken from different areas of the specimen are usually studied, and statistical analysis of histograms used for quantitative analysis [255,256]. SAXS is a major tool in characterizing lamellar structure. Direct application of Bragg’s law in a morphologically homogeneous system of stacks of lamellae provides the long period, which corrected with the crystallinity gives the lamellae thickness [257]. More elaborate procedures of analysis based on idealized models of alternating crystalline and non-crystalline regions include the one-dimensional electro-density correlation function [258–262] and the interphase distribution function [263,264]. Both are based on Fourier transformations of the scattering curve and yield quantitative information on the mean crystallite thickness, the most probable long spacing (or long period) and crystallinity within lamellar stacks or linear crystallinity. The results depend on the model assumed for the geometry of the lamellar stacks. If a model with diffuse interfaces is used, analysis of the SAXS data yields the thickness of the interfacial region [265]. The low-frequency LAM in Raman spectroscopy is a vibrational mode pertaining to ordered sequences in the chain direction. The mode frequency (Du) is inversely proportional to the ordered chain sequence length or to the crystallite thickness. This relation was given by Shimanouchi and co-workers [92,93] as:   m E 1=2 Du ¼ (11) 2cLc r Here m is the mode order (m ¼ 1,3,5 y, usually 1 for polyethylenes), c the velocity of light, r the density of the vibrating sequence (density of pure crystal) and E the Young’s modulus in the chain direction. The LAM band has been observed in many polymers and has been widely used in structural studies of polyethylenes [94–99,266], as well as other semi-crystalline polymers, such as poly (ethylene oxide) [267], poly(methylene oxide) [268,269] and isotactic poly(propylene) [270,271]. The distribution of crystalline thickness can be obtained from the width of the LAM mode, corrected by temperature and frequency factors [272,273] as:    hcDu fðLc Þ ¼ 1  exp (12) Du2 I obs u KT

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I obs is the observed intensity of frequency Du and K the Boltzman constant. u The displacement of the LAM peak frequency due to this correction is negligible for LAMs that appear at frequencies of 15 cm1 or higher and have half-width less than B5 cm1 [273]. These conditions are usually fulfilled by n-alkanes. However, for broad LAM modes, for example those displayed by ethylene copolymers, displacements to higher frequencies of Du by Equation (12) may exceed 5 cm1 or more. In addition, the thicknesses obtained from Equation (12) need a correction for the tilt angle (angle between the chain direction and the basal surface of the lamellae). Depending on crystallization temperature, tilt angles between 151 and 451 have been observed in polyethylenes [255]. As seen in the example of Figure 20, when the tilt angle is taken into account, the lamellar thicknesses obtained by Raman LAM were in good agreement with those obtained by TEM. The crystallite thickness distribution determined by thinsection TEM is compared in this figure with the distribution obtained from the LAM mode prior and after correction for the tilt angle for a narrow fraction of linear polyethylene. After the correction is made, the agreement between both techniques is excellent. The application of Equation (11) to obtain the lamellar thickness of polymeric crystallites requires knowledge of the Young’s modulus, E. In a study of n-alkanes, a value of E of 358 GPa was obtained [274]. However, it was later recognized that the LAM frequencies of the low molecular weight n-alkanes are raised by longitudinal forces at the chain ends [275]. Thus, E for low molecular weight n-alkanes is higher than the value corresponding to the chain devoid of ends. When these factors are considered, a value of E ¼ 290 GPa was obtained for high molecular weight polyethylene chains [275]. It has also been shown that the interaction between layers decreases with chain length [276]. Raman LAM, SAXS and TEM have been used to obtain the dependence of crystallite thickness with molecular weight under rapid crystallization as well as

Figure 20 Normalized frequency distributions of crystallite thickness for linear polyethylene fraction, Mn ¼ 76,700, Mw ¼ 80,800 crystallized at 118 1C; (9), electron micrograph histogram; (  ), smooth distribution from electron micrograph; (K), uncorrected Raman LAM distribution; (J), Raman distribution corrected for 301 tilt. Reproduced with permission from Ref. [256]. Copyright John Wiley & Sons, Inc., 1989.

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250

Thickness (Å)

200 La 150

Lc

100 50 Lb 0 1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

MW

Figure 21 Plot of thickness values as a function of molecular weight for linear polyethylene fractions quenched to 781C. (D), crystallite thickness, Lc; (J), interlamellar thickness, La; (K), interfacial thickness, Lb. Reprinted with permission from Ref. [277]. Copyright 1990 American Chemical Society.

for isothermally crystallized specimens. The crystallite thickness obtained by Raman LAM for rapidly crystallized polyethylene fraction remains constant at ˚ as molecular weight increases, as shown in Figure 21 [277]. Similar about 140 A constant thicknesses with chain length were obtained from TEM [255] and SAXS [278,279] of the rapidly crystallized fractions. Other polymers display the same trend [279–281]. It is, then, concluded that in general the lamellar thickness is independent of molecular weight for rapidly crystallized samples. Isothermally crystallized samples behave in a different manner. Lc was found to increase with increasing crystallization temperature for a narrow linear polyethylene fraction [282]. After rapid, non-isothermal crystallization a narrow ˚, size distribution is obtained. The crystallite thickness ranges from 120 to 150 A and is independent of the molecular weight in agreement with TEM data. After isothermal crystallization, there is a sharp increase in the crystallite thickness with crystallization temperature and a broad distribution develops. The increase in Lc with crystallization temperatures is not limited to polyethylene. Similar behavior has been obtained in poly(tetrafluoroethylene) [283], poly(ethylene terephthalate) [284], poly(aryl ether ether ketone) [285–287], poly(cis-isoprene) [288] and poly(ethylene oxide) [289] among others. It thus appears to be a general phenomenon. In summary, the structure and character of the lamellae formed by homopolymers and their thickness is strongly dependent on molecular weight and crystallization temperature. The structure can range from long, straight, stacked lamellae to ones that are short, curved and highly segmented. The lamellae thickness distribution also depends strongly on these variables.

3. CONCLUDING REMARKS The major components of the phase structure of semi-crystalline polymers and the most common techniques of characterization of the crystalline, amorphous

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and intermediate phases have been described in this chapter. Most properties of crystalline polymers depend to a large extent on the relative content of these phases, which can be varied over very wide limits and in a very systematic manner by changing molar mass, molar mass distribution, structural regularity of the chain and crystallization conditions. The morphology of organized crystalline entities at a level above the crystallographic unit cell is also described. These entities are polymeric lamellae that integrate the long-chain connectivity between crystalline and non-crystalline regions. The thickness and extension of the lamellae are a function of molecular variables (length and structural regularity) and crystallization conditions. Lamellae may aggregate in a large variety of supermolecular structures, or branch following homoepitaxial growth. Examples throughout this chapter are given primarily for two of the most simple, best studied semi-crystalline polymers, the polyethylenes and poly(propylenes).

ACKNOWLEDGEMENTS The author acknowledges funding by the National Science Foundation and the assistance of Dr. K. Jeon and URP student S. Warnock with some of the reproductions.

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CHAPT ER

8 Characterization of Molecular Orientation Thierry Lefe`vre, Christian Pellerin and Michel Pe´zolet

Contents

1. Introduction 2. Theory 2.1 The orientation distribution function 2.2 Biaxial distribution 2.3 Uniaxial distribution 2.4 Relationships between the order parameters and the shape of the ODF 3. Birefringence 3.1 Refractometry method 3.2 Compensation method 3.3 Transmission method 4. Infrared Linear Dichroism (IRLD) 4.1 Transmission IRLD 4.2 Reflection IRLD 4.3 Time-resolved IRLD 5. Raman Spectroscopy and Microspectroscopy 5.1 Conventional Raman spectroscopy (macro-Raman) 5.2 Spectromicroscopy (micro-Raman) 6. Fluorescence Spectroscopy 7. NMR Spectroscopy 8. X-Ray Diffraction and Absorption 9. Conclusion References

295 297 297 299 300 300 301 303 303 304 305 307 309 312 313 314 319 322 325 328 333 333

1. INTRODUCTION The physical properties of materials, especially their mechanical properties, are intimately related to their structural organization at all length scales. It is Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00408-X

r 2008 Elsevier B.V. All rights reserved.

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therefore of prime importance, from fundamental and practical viewpoints, to characterize the microstructure and crystallinity of the materials as well as their molecular conformation and orientation. The presence of molecular orientation in macromolecules leads to anisotropic physical properties. For instance, the modulus, toughness, electrical conductivity, etc., can widely differ along the longitudinal, transverse, or normal directions in highly oriented samples. Biomaterials made of fibrous proteins, such as collagen, keratin, or silk fibroin, often exhibit a multitude of anisotropic mechanical properties with important biological roles. These functions are related to a specific orientational and structural organization that has been optimized during thousands or millions of years of evolution. The dragline silk (the lifeline) of spiders, for instance, has a high strength, which is combined with a high extensibility, providing a toughness unmatched by any polymeric material. The biosynthesis of such biological materials is uniquely adapted because it allows precise specification of hierarchical order at all levels. For synthetic polymers, orientation is introduced during the processing operations such as molding, extrusion, drawing, rolling, or spinning. Kevlars (aramid fibers) and Dyneemas (polyethylene (PE) fibers) are examples of such highly oriented polymeric materials that are employed in different modern applications. Molecular orientation is also at the origin of the shrinkage phenomenon that can be observed for synthetic and natural fibers when subjected to a rise in temperature or relative humidity. The appropriate quantification of the degree of orientation has different motivations. First, it can provide a detailed knowledge about the structure of materials. In particular, the understanding of natural biopolymer organization is a basic paradigm to enable manufacturing biomimetic specimens with comparable properties. Quantitation of orientation can also provide knowledge about how and to what extent the orientation level relates to particular mechanical properties. There is also an important need, from a technological standpoint, to understand the influence of the processing method, temperature, strain rate, heat setting treatments, and cooling rate on the orientation level and final properties. Finally, many research activities are devoted to the investigation of the molecular disorientation occurring during the relaxation of polymeric chains in samples subjected to mechanical constraint because such molecular reorganization can compromise the sought anisotropic properties. The aim of this chapter is to describe how different physical techniques can provide useful quantitative data for the evaluation of molecular orientation and to emphasize their possibilities and limitations. The aim is not to present an exhaustive review on this subject. More details and applications can be found in the original articles and relevant books cited in the bibliography. The mathematical description of orientation will first be presented following the formalism introduced by Roe and Krigbaum [1,2] over forty years ago and nowadays commonly used in the scientific community. This formalism is based on the description of the orientation distribution function (ODF) as an expansion of weighted spherical harmonics, the weighted coefficients being the so-called order parameters. The methods most commonly used to study molecular orientation in samples having uniaxial or biaxial symmetry will then be

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presented in the order of increasing number of order parameters that can be determined by each technique. Based on this criterion, birefringence and infrared (IR) spectroscopy will be presented first. Indeed, they offer the simplest ways of obtaining the second moment of the orientation function. Polarized Raman spectroscopy and fluorescence spectroscopy that allow the determination of the second and fourth moments of the orientation function will then be presented. Finally, nuclear magnetic resonance (NMR) spectroscopy and X-ray diffraction, which are techniques that lead to the most detailed description of the ODF, will be presented. Both techniques allow the determination of higher moments of the ODF, X-ray diffraction providing the complete ODF of the crystalline phase of semicrystalline polymers.

2. THEORY 2.1 The orientation distribution function For most systems, the characterization of orientation essentially consists in the determination of the distribution of orientation of some structural units (crystallites, chain segments, chemical groups, etc.) dispersed within a sample. This problem reduces to the determination of the orientation of a local Cartesian coordinate system, Oxyz, linked to the structural unit, relative to a second macroscopic Cartesian coordinate system, OXYZ, linked to the sample. The first coordinate system can be related to the second using the Euler angles (y, j, c) as shown in Figure 1. The angles y and f, which represent the inclination and azimuth of the structural unit, respectively, allow specifying the orientation of the Oz-axis in the macroscopic coordinate system. To completely define the orientation of the structural unit, it is necessary to define the third angle, c, specifying its rotation about the Oz-axis. For fibers or samples with uniaxial symmetry, the OZ-axis corresponds to the axis of symmetry. For biaxial samples, OZ is the machine direction (MD) and OX the transverse direction (TD), OY being perpendicular to the plane of the film (normal direction, ND). When referring to polymer filming processes, the MD may be called the forward draw direction (FD) and the TD may be referred to as the sideways (draw) direction (SD). The orientation is not strictly identical for all structural units and is rather spread over a certain statistical distribution. The distribution of orientation can be fully described by a mathematical function, N(y, j, c), the so-called ODF. Based on the theory of orthogonal polynomials, Roe and Krigbaum [1,2] have shown that N(y, j, c) can be expanded as a series of generalized spherical harmonics that form a complete set of orthogonal functions, so that Nðy; j; cÞ ¼

1 X ‘ ‘ X X

u‘mn Z‘mn ðx ¼ cos yÞ eimj einc

(1)

‘¼0 m¼‘ n¼‘

The quantity Nðy; j; cÞ sin ydydjdc represents the fraction of structural units oriented in the generalized solid angle sinydydfdc, with the following

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Z 

z

x y 

Structural unit

O

Y 

X

Figure 1 Definition of the coordinate systems Oxyz and OXYZ and Euler angles y, j, and c.

normalization condition Z pZ

2p

Z

2p

Nðy; j; cÞ sin ydydjdc ¼ 1 0

0

(2)

0

The functions Z‘mn ðx ¼ cos yÞ are a generalization of associated Legendre functions and the coefficients of the series u‘mn are given by Z p Z 2p Z 2p 1 Nðy; j; cÞ Z‘mn ðx ¼ cos yÞ eimj einc sin ydydjdc (3) u‘mn ¼ 2 4p 0 0 0 The u‘mn coefficients are the mean values of the generalized spherical harmonics calculated over the distribution of orientation and are called order parameters. These are the quantities that are measurable experimentally and their determination allows the evaluation of the degree of molecular orientation. Since the different characterization techniques are sensitive to specific energy transitions and/or involve different physical processes, each technique allows the determination of certain u‘mn parameters as described in the following sections. These techniques often provide information about the orientation of a certain physical quantity (a vector or a tensor) linked to the molecules and not directly to that of the structural unit itself. To convert the distribution of orientation of the measured physical quantity into that of the structural unit, the Legendre addition theorem should be used [1,2]. An example of its application is given for IR spectroscopy in Section 4.

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It should be noted that the functions Z‘mn ðx ¼ cos yÞ may assume the following normalized forms [1,2] Z p ðZ‘mn ðx ¼ cos yÞÞ2 sin y dy ¼ 1 (4) 0

For the non-normalized forms, the u‘mn coefficients have to be replaced by the coefficients hP‘mn i that differ by a numerical factor so that [3] 4p2 hP‘mn i ¼ u‘mn (5) N ‘mn with 2‘ þ 1 ðl þ mÞ! ðl  nÞ! 1 N 2‘mn ¼ (6) 2 ðl  mÞ! ðl þ nÞ! ½ðm  nÞ!2 The non-normalized forms are most commonly found in the literature and will be used throughout the rest of the chapter. The mathematical expression of N(y, j, c) is complex but, fortunately, it can be simplified for systems displaying some symmetry. Two levels of symmetry have to be considered. The first is relative to the statistical distribution of structural units’ orientation. For example, if the distribution is centrosymmetric, all the u‘mn coefficients are equal to 0 for odd ‘ values. Since this is almost always the case, only u‘mn coefficients with even ‘ will be considered herein. In addition, if the (X, Y), (Y, Z), and (X, Z) planes are all statistical symmetry elements, m should also be even otherwise u‘mn ¼ 0 [1]. In this chapter, biaxial and uniaxial statistical symmetries are more specifically considered. The second type of symmetry is inherent to the structural unit itself. For example, the structural units may have an orthorhombic symmetry (point group symmetry D2) which requires that n is even otherwise u‘mn ¼ 0 [1]. In this theoretical section, we will detail the equations of orientation for structural units that exhibit a cylindrical symmetry (cigar-like or rod-like), i.e., with no preferred orientation around the Oz-axis. In this case, the ODF is independent of c, leading to n ¼ 0. More complex cases have been treated elsewhere [1,4]

2.2 Biaxial distribution As seen above, the angle c takes random values (n ¼ 0) for structural units with cylindrical symmetry. The ODF is then defined by two angles and reduces to the following expansion in surface spherical harmonics  1 X ‘  1 X 2‘ þ 1 ð‘  mÞ! hP‘m iP‘m ðx ¼ cos yÞ cos mj; with ‘ even (7) Nðy; jÞ ¼ 2p ‘¼0 m¼‘ 2 ð‘ þ mÞ! P‘m ðx ¼ cos yÞ ¼ P‘m0 ðx ¼ cos yÞ are the associated Legendre polynomials and are given by the following expression [5] dm (8) P‘m ðx ¼ cos yÞ ¼ ð1  x2 Þm=2 m P‘ ðxÞ dx

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where the functions P‘ ðxÞ are the Legendre polynomials and are given, after the Rodrigue`s formula, by ‘ 1 d‘  2 P‘ ðxÞ ¼ P‘0 ðxÞ ¼ ‘ x 1 (9) ‘ 2 ‘! dx and Z p Z 2p hP‘m i ¼ Nðy; jÞP‘m ðcos yÞ sin ydydj (10) y¼0

j¼0

2.3 Uniaxial distribution In this case, the ODF is independent of j and c and simplifies into the following expansion in Legendre polynomials  1  X 2‘ þ 1 hP‘00 iP‘ ðcos yÞ; for ‘ even (11) NðyÞ ¼ 2 ‘¼0 Z

p

with hP‘00 i ¼ hP‘0 i ¼ hP‘ i ¼

NðyÞ P‘ ðcos yÞ sin ydy

(12)

0

The expressions of the first few non-normalized Legendre polynomials are given below hP000 i ¼ hP00 i ¼ hP0 i ¼ 1  1 3cos2 y  1 2

(14)

 1 35cos4 y  30cos2 y þ 3 8

(15)

hP200 i ¼ hP20 i ¼ hP2 i ¼ hP400 i ¼ hP40 i ¼ hP4 i ¼

  1  1  cos2 y cos 2f 4

(16)

  1  7cos4 y þ 8cos2 y  1 cos 2f 24

(17)

  1  4 cos y  2cos2 y þ 1 cos 4f 16

(18)

hP220 i ¼ hP22 i ¼ hP420 i ¼ hP42 i ¼

(13)

hP440 i ¼ hP44 i ¼

2.4 Relationships between the order parameters and the shape of the ODF The complete determination of the ODF requires the knowledge of all the hP‘m i coefficients. For each characterization technique, the measurable quantities that represent molecular orientation can be expressed as a function of a different number of order parameters. All techniques allow at least the measurement

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of hP2 i. Birefringence and IR spectroscopy, two techniques that are commonly used and relatively straightforward to implement (Sections 3 and 4), give access to hP2 i only. The boundary limits of hP2 i are 0:5  hP2 i  1 and the interpretation of the molecular orientation for the limiting hP2 i values in uniaxial systems is hP2 i ¼ 0:5 ) perfect orientation perpendicular with respect to the symmetry axis (OZ), hP2 i ¼ 0 ) isotropic system or perfect orientation at 54.71, and hP2 i ¼ 1 ) perfect orientation along the symmetry axis (OZ). For the ideal case where all the structural units have an identical orientational direction (i.e., a Dirac distribution), the angle of molecular orientation y0 can be calculated from the value of hP2 i by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 hP 2 i þ 1 y0 ¼ arcos (19) 3 One should be aware of the fact that orientation distributions with different shapes and/or widths can result in an identical hP2 i value. Determination of higher-order terms (hP4 i, hP6 i, etc.) of the ODF allows for distinguishing between these different possibilities [6]. Polarized Raman and fluorescence spectroscopies, NMR and X-ray diffraction allow the determination of at least hP2 i and hP4 i for uniaxial systems. This is a great advantage since the shape of the orientation distribution can then be estimated [7], even if not all the coefficients of the ODF’s expansion are known. While hP2 i has fixed boundary limits, those of hP4 i depend on the hP2 i value such as 3 35hP2 i2  10hP2 i  7 5 hP 2 i þ 7   hP4 imin ¼  hP4 i  hP4 imax ¼ 1 (20) 7 18 12 The limiting values of hP4 i are plotted as a function of hP2 i in Figure 2. For hP4 i ¼ hP2 i ¼ 0, the distribution is isotropic. If hP4 i ¼ hP4 imin , the ODF corresponds to a unimodal and infinitely narrow distribution centered at the angle y0 as given in Equation (19). If hP4 i ¼ hP4 imax , the distribution is infinitely narrow, bimodal, and centered at 0 and 901 with respect to the OZ-axis. Moreover, for certain values of hP4 i, the ODF is purely Gaussian (Figure 2) [8]. Finally, for intermediate values of hP4 i, the unimodal, bimodal, or Gaussian character of the ODF may be more or less pronounced.

3. BIREFRINGENCE Birefringence is one of the simplest methods for the characterization of molecular orientation in polymers. The polarizability of a structural unit is usually not equivalent in all directions, leading to three independent refractive indices along its principal axes. In an isotropic sample, a single averaged macroscopic refractive index is observed whereas birefringence or trirefringence is observed

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1.0

< P4 >min (unimodal, infinitely narrow) < P4 >max (bimodal, infinitely narrow) < P4 > (unimodal, Gaussian)

0.5 < P4 >

3/8

0.0

Isotropic

1/7 -0.5

0

0.5

1

-3/7

-0.5

< P2 >

Figure 2 Maximum and minimum values of hP4 i as a function of hP2 i and (hP2 i,hP4 i) curve for a Gaussian ODF.

if preferential orientation exists. Three birefringence indices, Dnij (i, j ¼ X, Y, or Z), can be calculated by measuring the refractive index, n, along the machine (Z), transverse (X), and normal (Y) directions: DnZY ¼ nZ  nY ;

DnZX ¼ nZ  nX ;

DnYX ¼ nY  nX

(21)

Only two birefringence indices are independent and necessary to describe the anisotropy of a biaxial system, while a single birefringence measurement is required for uniaxial samples because nX ¼ nY. Birefringence allows the determination of the second moment of the ODF with respect to a given axis as: Dn (22) Dn Dn1 is the intrinsic birefringence that would be observed if all chains were oriented along the reference axis. The magnitude and sign of Dn1 depend on the nature and physical state (crystalline or amorphous) of the polymer. It can be calculated from the polarizabilities using the Lorentz–Lorentz equation or from orientation values determined using an independent technique [3]. In addition to ‘‘orientation’’ birefringence, ‘‘form’’ birefringence due to the presence of anisotropic structures that possess a different refractive index can appear in multiphase polymer systems, including semicrystalline polymers. Its effect is generally neglected but it can be determined to obtain more accurate results [9]. The main limitation of birefringence is that it only provides an averaged orientation value without any discrimination between amorphous and crystalline phases, or between the components in polymer blends, copolymers, and hP 2 i ¼

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composites. Its experimental simplicity and its potential for time-resolved and imaging studies nevertheless make it the most widely used technique to study orientation in polymers. Only the most common experimental approaches to measure birefringence will be described.

3.1 Refractometry method Refractometry consists in the direct measurement of the three refractive indices (or only two in the case of uniaxial orientation) of the sample using a refractometer equipped with a polarizer [10]. Measurement along the ND can be challenging, especially for thin films. Tassin et al. have used this approach to study the orientation in films of poly(ethylene terephthalate) (PET) deformed under planar uniaxial conditions [11]. Figure 3 shows that, as stress is applied, the normal to the phenyl rings develops a negative orientation function with respect to the MD (expressed here as X1) because, as expected, the main chain of the polymer orients along the stretching axis. The orientation function is larger along the ND (X3) than the TD (X2), showing that orientation is not uniaxial with the phenyl groups being found preferentially parallel to the plane of the film.

3.2 Compensation method The compensation method is based on the phenomenon of optical retardation. The sample is placed between crossed polarizers set at 451 and +451 to the main axis, respectively. Because of the refractive index difference, the incident radiation will propagate at different speeds along the ordinary and extraordinary axes. The optical retardation, R, between the two components in the emerging beam is given by R ¼ dDn=l, where d is the thickness of the sample and l is the wavelength of the radiation. The sign and magnitude of R, and thus those of Dn and of hP2 i, can be determined by using many types of commercially available

Figure 3 Orientation of the phenyl rings in stretched PET films, with respect to the machine (X1), transverse (X2), and normal (X3) directions, as a function of applied stress, s0, at 901C. Birefringence results were obtained using refractrometry. Reproduced with permission from Lapersonne et al. [11]. Copyright Elsevier 1994.

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compensators. In the case of biaxial orientation, DnZY must be determined in addition to DnZX by tilting the sample around the Z-axis. The compensation method is highly sensitive and can detect birefringence as weak as 106 [12]. For instance, Abtal et al. have used a Babinet–Soleil compensator to study the overall orientation in blends of polystyrene (PS) and poly(vinyl methyl ether) (PVME) deformed above room temperature [13]. They observed similar behavior for birefringence and Young’s modulus during stretching, in agreement with the stress-optical rule. The compensation birefringence measurement is very easily coupled to optical microscopy in the transmission and reflection modes, thus allowing characterizing orientation with a spatial resolution of a few hundreds of nanometers [14]. Polarizing microscopes are widely available and are often used for birefringence studies even if spatial resolution is not required. Objectives specifically designed for cross-polarized microscopy are necessary to avoid artifacts.

3.3 Transmission method This technique is also based on the phenomenon of optical retardation. The transmission, T, of light transmitted through crossed polarizers depends on the birefringence of the sample as:   d (23) T  sin2 ðp RÞ ¼ sin2 p Dn l Such measurement provides the magnitude of birefringence, but not its sign. In addition, identical transmission values will be observed for multiple birefringence orders, that is, whenever the optical path difference, dDn, becomes a multiple of l. The main interest of this method arises from its excellent time resolution, below 1 ms, that is readily achieved using a low-power (e.g., 5 mW) continuous-wave laser and a photodiode. If the sample is initially isotropic, it is possible to follow the birefringence order to obtain quantitative results. For improved accuracy, a second (reference) photodiode or a beam chopper and a lock-in amplifier can be used. This technique has been employed to study the mechanical deformation of polymers [15,16] and the photo-induced orientation of azopolymers [17]. For instance, Messe´ et al. have followed in real time the deformation and relaxation of PS at different temperatures above its glass transition temperature (Tg) [15]. Figure 4 shows that hP2 i increases almost linearly during deformation but that lower values are obtained at higher temperatures, due to segmental relaxation during stretching. When deformation is stopped, orientation first decreases rapidly, with a characteristic relaxation time ranging from 13 s at Tg+51C to as little as 1 s at Tg + 201C, and then slowly decreases toward the isotropic state at long times. A method derived from the transmission technique, spectrographic birefringence, overcomes the problem of multiple birefringence orders [18]. It can be noted from Equation (23) that the transmission minima and maxima occur at a

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0.10

< P2 ( cosθ ) >Δn

0.08

0.06

0.04 Tg +5°C 0.02

Tg +10°C Tg +15°C Tg +25°C

0.00 0

100

200

300 time (s)

400

500

600

Figure 4 Evolution of the orientation during and after the deformation of PS films at different temperatures above Tg. Time-resolved birefringence results with up to a 2 ms time resolution were obtained using the transmission method. Reproduced with permission from Messe´ et al. [15]. Copyright Elsevier 2001.

different Dn value for different l. By replacing the laser by a broadband source and the photodiode by a spectrograph, it is thus possible to determine quantitatively the orientation of a sample without a priori knowledge of its birefringence order. A further development of the transmission technique for the study of biaxial systems consists in probing the sample at normal and tilted incidence simultaneously, allowing real-time characterization of both the inplane (DnZX) and out-of-plane (DnZY) birefringences. Ajji et al. have coupled this multiple incidence approach with spectrographic birefringence to study blown films and bottles, and biaxially tentered thick sheets [19].

4. INFRARED LINEAR DICHROISM (IRLD) IR spectroscopy is a powerful and readily available orientation characterization technique. It offers a high chemical selectivity since most functional groups absorb at distinct wavelengths (typically in the 2.5–25 mm range (4,000–400 cm1 range)), which often depend on their local environment. IR spectroscopy thus provides qualitative and quantitative information about the chemical nature of a sample, its structure, interactions, etc. The potential of IR spectroscopy for orientation characterization stems from the fact that absorption only occurs if the electric field vector of the incident radiation, E, has a component parallel to the transition dipole moment, M, of the absorbing entity. The absorbance, A, is given

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by A / ðM  EÞ2 ¼ M2 E2 cos2 g, where g is the angle between the transition dipole moment and the electric field vectors. The absorbance of an isotropic sample is thus independent of the polarization state, while an oriented sample preferentially absorbs radiation when g ¼ 01. In many cases, it is more interesting to describe the orientation of the polymer chain (the Oz-axis of Figure 1) with respect to the sample coordinate system rather than that of a specific chemical group. This is possible if the transition dipole moment of the measured band is at a fixed angle, b, with respect to the main chain of the polymer (i.e., the Oz-axis) and presents a cylindrical symmetry, that is, has no preferential orientation around the c angle. In this case, the Legendre addition theorem allows calculating the order parameters of the main chain, from the experimentally determined parameters for the transition dipole moment as hP2 ðcos yÞi ¼

hP2 ðcos gÞi ; P2 ðcos bÞ

where P2 ðcos bÞ ¼

3cos2 b  1 2

(24)

Because of the cos2g dependency, IR linear dichroism (IRLD) only provides the second moment of the ODF. It is often sufficient to describe the uniaxial and biaxial orientation in polymeric systems. However, the knowledge of hP2 i values alone does not allow discriminating between systems when its value becomes very close to unity, as illustrated below (see discussion on page 330 related to Figure 17). In addition, it does not provide information about the shape and the width of the ODF: one must assume a unimodal distribution, despite the fact that multiple ODFs can yield the same hP2 i value [6]. These limitations are nevertheless well compensated by the simplicity and availability of the technique, and by its selectivity that often allows the simultaneous measurement of the orientation of the different components in blends and copolymers, phases in semicrystalline systems, main chain vs. side-chain groups, etc. It should be noted that the cos2g absorption rule also applies to spectroscopies in the X-ray, ultraviolet (UV), visible, near-IR, and far-IR (terahertz) ranges, but those are less often used because of their more limited selectivity or strong overlap of bands. Exceptions are the frequent use of visible LD for the characterization of photo-oriented azopolymers [20], and that of near-IRLD for the study of millimeters thick polymer films [21]. Polarized IR spectra can be recorded using several sampling modes, depending on the coveted information and nature of the sample. Transmission IRLD is the most straightforward and common approach but its utility is limited to relatively thin films. In contrast, reflection techniques allow for studying thick or irregularly shaped samples and provide surface specific measurements, but are more complex and susceptible to artifacts. Polarized IR emission and photoacoustic spectra can also be measured but are seldom used, and will not be described here. A wire-grid polarizer is normally used to polarize the IR radiation. A typical degree of polarization value is 99.5% at 1,000 cm1, but it often decreases to less than 99% or 96% at 3,000 cm1 for holographic and mechanically grooved polarizers, respectively. These specifications can vary significantly between suppliers, in spite of similar groove densities and fabrication methods. The error on the orientation function is thus larger at higher frequencies due to polarization leakage.

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4.1 Transmission IRLD 4.1.1 Normal incidence Normal incidence transmission IRLD measurements are used to study thin films (typically 100 mm thickness and less, depending on the molar extinction coefficient of the bands) with in-plane uniaxial orientation. Two spectra are recorded sequentially with the radiation polarized parallel (p) and perpendicular (s) to the principal (machine) direction of the sample. The order parameter of the transition moment of the studied vibration is calculated from either the dichroic ratio (R ¼ Ap/As) or the dichroic difference (DA ¼ ApAs) as: hP2 ðcos gÞi ¼

R  1 DA ¼ R þ 2 3A0

(25)

Ap and As are the absorbances measured with p- and s-polarization, respectively,  and A0 ¼ Ap þ 2As =3 is the structural absorbance spectrum that would be measured for an isotropic sample. The order parameter of the main chain can be determined using the Legendre addition theorem (Equation (24)). In a classic series of articles, Monnerie and coworkers have used IRLD to study the effect of deformation on the orientation of a series of polymers and polymer blends [22,23]. For example, Figure 5 shows the p- and s-polarized

Figure 5 Polarized infrared spectra (s on top, p on bottom) recorded for an oriented 80/20 PS/PPO miscible blend using normal incidence transmission. Reproduced with permission from Lefebvre et al. [23]. Copyright Elsevier 1981.

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spectra recorded for a blend containing 80% of PS and 20% of poly(2,6-dimethyl1,4-phenylene oxide) (PPO) [23]. Because of IR selectivity, the orientation of both components could be followed independently. The 906 cm1 band, due to out-ofplane deformation of the phenyl groups, was used to quantify the orientation of PS. It shows parallel dichroism, as expected from its reported 351 b angle. In contrast, the PPO out-of-plane benzene mode at 865 cm1 shows negative dichroism because its transition dipole moment makes a 741 angle with the main chain. Deformation studies revealed that the hP2 i values for PS more than doubled with increasing PPO content from 0 to 25%. In contrast, the orientation of the higher-Tg PPO was not affected by composition over this range and was always larger than that of PS. Normal transmission IRLD can also be used to characterize polymeric fibers, although scattering can induce sloping baselines. Raman spectroscopy then becomes a convenient alternative. Rutledge et al. have recently probed the orientation in electrospun nanofibers composed of a core of Bombyx mori fibroin and an outer shell of poly(ethylene oxide) [24]. The orientation values were low, less than 0.1, as is often the case in electrospun fibers. Microscopic IRLD measurements can also be performed, either with a single element detector or with a focal plane array for direct imaging, providing a spatial resolution of a few to a few tens of micrometers. Specially designed objectives allow performing microscopy studies using the reflection techniques described below. Chalmers and Everall have presented several examples of the use of single detector IR microscopy to characterize industrial samples under various sampling modes [25], while Mendelsohn et al. have used polarized IR imaging to assess the orientation of collagen fibrils in different sections of articular cartilage [26]. While calculating the orientation function is the goal of several analyses, the presence of orientation in a sample can sometimes obscure other useful structural information obtainable by IR spectroscopy. For instance, the trans/gauche ratio of PET can be determined using conformationally sensitive bands, but the presence of molecular orientation makes direct determination impossible even with unpolarized light. In such cases, calculating the structural absorbance spectrum, A0, allows for extracting structural information from the spectra without any interference from orientation [27]. It should also be mentioned that, in several cases, it is not possible or even necessary to calculate the orientation function. It may often be sufficient to simply compare dichroic ratios, for instance, when comparing a series of samples from an industrial process. In other cases, the angle b is not known and the calculation of a hP2 ðcos gÞi may not yield more information. For instance, Bazuin and Fan used dichroic ratios to follow the development of orientation as a function of draw ratio for poly(ethyl acrylate) in ionically complexed blends of copolymers [28].

4.1.2 Tilted incidence Normal incidence measurements are sufficient for uniaxially oriented samples, but a third spectrum along the ND (Y) is necessary to describe the orientation in biaxially oriented samples or in the case of uniaxial anisotropy in the thickness

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of the film. This additional spectrum is also necessary to calculate the orientationindependent structural absorbance spectrum, which is given by A0 ¼ ðAZ þ AY þ AX Þ=3 for biaxially oriented samples. A tilted incidence transmission measurement can be performed to obtain the AY spectrum. The polarizer is set parallel to the Z-axis and the sample is rotated by an angle a around the X-axis. AY, is given by:  1=2 sin2 a Aa 1  2  AZ n AY ¼ þ AZ (26) sin2 a n2 Aa is the absorbance in the tilted geometry, AZ the absorbance measured in normal incidence geometry with light polarized along the Z-axis, and n the refractive index of the sample. The isotropic refractive index in the visible range is often used as a first approximation, but quantitative measurements require knowledge of the anisotropic refractive indices at the wavelength of interest [29]. The orientation along the different axes can be quantified using a series of orientation coefficients, fj: fj ¼

Aj =A0  1 ð3cos2 b  1Þ

(27)

where Aj is the absorbance along the j direction. For a system with uniaxial orientation and cylindrical symmetry, fZ simplifies to the usual hP2 i coefficient. Ajji et al. have used this technique and formalism to characterize the biaxial orientation in blown films of polypropylene/linear low-density polyethylene (PP/LLDPE) multilayers and blends [30]. The chemical specificity of IRLD allowed for independently determining the orientation coefficient of the c-axis of PP, as well as that of the a- and b-axes of the crystalline phase of PE. Tilted incidence IRLD was also used to probe biaxial orientation in films of polyamide-6 deformed under different conditions [31]. Structural absorbance spectra were also calculated to probe the amount of the different crystalline forms, in addition to their orientation.

4.2 Reflection IRLD 4.2.1 Attenuated total reflection (ATR) ATR is one of the most useful and versatile sampling modes in IR spectroscopy. When radiation is internally reflected at the interface between a high-refractive index ATR crystal (usually Ge, ZnSe, Si, or diamond) and the sample, an evanescent wave penetrates inside the sample to a depth that depends on the wavelength, the refractive indices, and the incidence angle. Because the penetration depth is typically less than 2 mm, ATR provides surface specific information, which can be seen as an advantage or not if surface orientation differs from that of the bulk. It also allows one to study thick samples without preparation and can be used to characterize highly absorbing bands that are saturated in transmission measurements.

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Four polarized ATR spectra can be recorded to characterize the threedimensional (3D) orientation of a sample. p- and s-polarized spectra are recorded with the sample clamped with its Z- and X-axes sequentially aligned perpendicular to the incidence plane (that is, parallel to the s-polarized electric field). The absorbance measured in these different configurations is related to the anisotropic absorption indices of the sample, kj, as As;Z ¼ K1 kZ ;

As;X ¼ K1 kX ;

Ap;Z ¼ K2 kX þ K3 kY ;

Ap;X ¼ K2 kZ þ K3 kY (28)

The parameters K1, K2, and K3 are defined by the refractive indices of the crystal and sample and by the incidence angle [32]. If the sample has uniaxial symmetry, only two polarized spectra are necessary to characterize the orientation. If the optical axis is along the plane of the sample, such as for stretched polymer films, only the two s-polarized spectra are needed to determine kZ and kX. These are then used to calculate a dichroic ratio or a hP2 i value with Equation (25) (replacing absorbance with absorption index). In contrast, a uniaxial sample with its optical axis perpendicular to the crystal surface requires the acquisition of spectra with both p- and s-polarizations, but the Z- and X-axes are now equivalent. This approach was used, through dichroic ratio measurements, to monitor the orientation of polymer chains at various depths during the drying of latex [33]. This type of symmetry is often encountered in non-polymeric samples, for instance, in ultrathin films of lipids or self-assembled monolayers. In contrast to the above cases, the spectra in the four geometries are necessary for samples showing biaxial orientation. The information along the ND is accessible because under p-polarization, the electric field has components both in-plane (Z or X) and out-of-plane (Y) with respect to the sample. Although the details are beyond the scope of this chapter, Everall and Bibby have shown how to determine directly the different hP2mn i values (m, n ¼ 0 or 2) by measuring the four absorbances of Equation (28) for two bands with different b angles [32]. It is important to stress that ATR absorbance is strongly affected by the sample/crystal contact. Quantitative results are thus difficult to obtain even if the contact is maintained during the sample rotation that is required to record all four polarized spectra. A reference band that does not show significant dichroism is thus most often used to normalize the polarized absorbances in order to obtain quantitative data. For instance, the 1,410 cm1 band of PET has often been chosen for that purpose, not only for ATR studies but also for specular reflectance (see below) and even transmission studies when the sample thickness is not uniform. It was shown that an appropriate normalization is possible even if no such reference band is available, by using a combination of two bands with orthogonal dichroism [34]. When performing ATR experiments, one should also make certain that the applied pressure does not create artifacts by affecting the structure of the sample. As an example, Cooper and coworkers have used polarized ATR spectroscopy to characterize the surface orientation of PET bottles [35]. They first confirmed the quantitative agreement between ATR and X-ray diffraction results, and then studied the molecular orientation of the bottles at 2 cm intervals.

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Figure 6 Chain orientation along the hoop, length, and thickness directions measured at different positions along the length of a standard PET bottle. Polarized ATR spectra were recorded for (a) the outer and (b) the inner surfaces of the bottle, respectively. Reproduced with permission from Smith et al. [35]. Copyright Elsevier 2006.

Figure 6 shows the biaxial orientation of PET on the inner and outer surfaces of the bottle, expressed in terms of the average squared cosine angles between the main chain of PET and the hoop, the length, and the thickness directions, respectively. These values are proportional to the orientation coefficients of Equation (27). Very small values are found in the thickness direction, indicating that the chains are almost exclusively in the plane of the bottle. The in-plane orientation varies significantly along the length of the bottle: for both surfaces, the chains are preferentially oriented along the length in the neck region and along the hoop closer to the base of the bottle, but the behavior at intermediate positions is quite different for the inner and outer surfaces. This information would have been lost with transmission measurements across the full bottle thickness.

4.2.2 Specular reflectance As for ATR, specular (front surface) reflection provides surface orientation and can be used to study thick samples or highly absorbing bands. In addition, because it is a non-contact technique, it enables the study of samples that cannot be held in close contact with an ATR crystal or that would be affected by pressure. In specular reflection, the polarized radiation is incident at an angle close to the normal, often 10–201, and only the light reflected at the front surface of the sample should be detected. This precludes the study of highly scattering samples and requires that the sample is ‘‘optically thick’’, meaning that it must be thick enough or that the bands are intense enough so that no light gets reflected from the second surface. In contrast with other methods, spectra recorded by specular reflection show dispersion-like shaped bands because both the refractive index (n) and the absorption index (k) contribute to reflection. These can nevertheless be separated

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by performing a Kramers–Kro¨nig transformation on the raw data using a processing tool implemented in most spectroscopy softwares [36]. The k values thus obtained are proportional to absorbance and can be used to calculate dichroic ratios and orientation coefficients using the procedures described in the previous sections. In some cases, surface imperfections and differences in polarized reflectivity can yield different k values for p- and s-polarized spectra even for an isotropic sample. The use of a reference normalization band is thus frequent. Specular reflection IR spectroscopy has been used by Cole and coworkers to study the orientation and structure in PET films [36,37]. It has allowed characterizing directly very highly absorbing bands in thick samples, in particular the carbonyl band that can show saturation in transmission spectra for thickness as low as 2 mm. The orientation of different conformers could be determined independently. Specular reflection is normally limited to uniaxial samples because the near-normal incident light does not allow measuring AY. However, it was shown that the orientation parameter along the ND can be indirectly determined for PET by using the ratio of specifically selected bands [38]. This approach was applied to the study of biaxially oriented PET bottles [39].

4.3 Time-resolved IRLD An interesting feature of polarized IR spectroscopy is that rapid measurements can be performed while preserving molecular information (in contrast with birefringence) and without the need for a synchrotron source (X-ray diffraction). Time-resolved IRLD studies are almost exclusively realized in transmission because of its compatibility with various types of tensile testing devices. In the simplest implementation, p- and s-polarized spectra are sequentially acquired while the sample is deformed and/or relaxing. The time resolution is generally limited to several seconds per spectrum by the acquisition time of two spectra and by the speed at which the polarizer can be rotated. Siesler et al. have used such a rheo-optical technique to study the dynamics of multiple polymers and copolymers [40]. A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a highfrequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to B400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pe´zolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The hP2 i values were determined

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Figure 7 Relaxation of orientation measured simultaneously for both components in miscible PS/PVME blends following a rapid deformation (1 m/s) to a draw ratio of 2 at Tg +151C. The time-resolved dichroic difference spectra were acquired using PM-IRLD. Reproduced with permission from Pellerin et al. [42]. Copyright 2000 American Chemical Society.

simultaneously using component specific C–H stretching bands. Larger orientations and slower relaxation rates were observed for PS as compared to PVME for all compositions. Nevertheless, the relaxation of both components was hindered by the addition of faster relaxing PVME, which was interpreted by the presence of nanoheterogeneities. Finally, an ultra-rapid-scanning FTIR spectrometer, which uses a continuously rotating wedged disk mirror rather than a standard reciprocating mirror, provides the fastest time resolution for polarized IR spectroscopy, but is limited to measurements with a single polarization. The cold drawing of PET was followed with a 10 ms time resolution, showing rapid gauche-to-trans conformational change and the development of very large trans conformers orientation upon necking [27].

5. RAMAN SPECTROSCOPY AND MICROSPECTROSCOPY Raman spectroscopy is an inelastic light scattering experiment for which the intensity depends on the amplitude of the polarizability variation associated with the molecular vibration under consideration. The polarizability variation is represented by a second-rank tensor, axyz , the Raman tensor. Information about orientation arises because the intensity of the scattered light depends on the orientation of the Raman tensor with respect to the polarization directions of the electric fields of the incident and scattered light. Like IR spectroscopy, Raman

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spectroscopy can provide qualitative and quantitative information relative to several chemical groups located in different parts of the macromolecules and that are often sensitive to molecular conformation, local environment, interactions, etc. The Raman tensor can be expressed in the coordinate system Oxyz of the molecule (Figure 1) with its principal components a1 , a2 , and a3 such as 0 1 0 1 a1 0 0 a1 0 0 B C B C axyz ¼ @ 0 a2 0 A ¼ a3  @ 0 a2 0 A; with a1 ¼ a1 =a3 and a2 ¼ a2 =a3 (29) 0 0 a3 0 0 1 For orientation measurements, this tensor also needs to be expressed in the ~ coordinate system OXYZ, aXYZ , using the matrix transformation axyz ¼ FaXYZ F, where F is a matrix whose elements are the direction cosines of the coordinate ~ is its transposed matrix [44]. axes and F

5.1 Conventional Raman spectroscopy (macro-Raman) The theory of orientation measurements by linearly polarized Raman spectroscopy has been developed in detail by Bower in 1972 [44]. The Raman intensity, I, is given by * + X 2 0 I ¼ I0 ‘i ‘j aij ; with i; j ¼ X; Y; or Z (30) i;j

‘i0 and ‘j are the direction cosines of the incident and scattered electric fields, respectively, I0 is a constant that depends on the number of scattering units, instrumental factors, and laser intensity, and the brackets indicate a mean value calculated over the distribution of orientation. In Equation (30), different quadratic quantities ha2ij i or haij apq i can be considered. They are related to the second and fourth moments of the ODF expansion. In particular, for uniaxial systems, knowledge of hP4 i indeed gives information about the shape of the distribution of orientation [7] and, moreover, allows the calculation of the most probable ODF using the information theory [45].

5.1.1 Uniaxial systems For a uniaxial sample, there are five independent quantities haij apq i or ha2ij i given by [44]     I 0 a2XX ¼ I 0 a23 ½ 3a21 þ 3a22 þ 3 þ 2a1 a2 þ 2a1 þ 2a2 =15   þ P2 3a21 þ 3a22 þ 6 þ 2a1 a2  a1  a2 =21   þ 3P4 3a21 þ 3a22 þ 8 þ 2a1 a2  8a1  8a2 =280     I 0 a2ZZ ¼ I 0 a23 ½ 3a21 þ 3a22 þ 3 þ 2a1 a2 þ 2a1 þ 2a2 =15   þ 2P2 3a21 þ 3a22  6 þ 2a1 a2  a1  a2 =21   þ P4 3a21 þ 3a22 þ 8 þ 2a1 a2  8a1  8a2 =35

Characterization of Molecular Orientation

    I 0 a2XY ¼ I 0 a23 ½ a21 þ a22 þ 1  a1 a2  a1  a2 =15   þ P2 a21 þ a22  2  4a1 a2 þ 2a1 þ 2a2 =21   þ P4 3a21 þ 3a22 þ 8 þ 2a1 a2  8a1  8a2 =280     I 0 a2ZX ¼ I 0 a23 ½ a21 þ a22 þ 1  a1 a2  a1  a2 =15   þ P2 a21 þ a22  2  4a1 a2 þ 2a1 þ 2a2 =42   þ P4 3a21 þ 3a22 þ 8 þ 2a1 a2  8a1  8a2 =70   I 0 haXX aZZ i ¼ I 0 a23 ½ a21 þ a22 þ 1 þ 4a1 a2 þ 4a1 þ 4a2 =15   þ P2 a21 þ a22  2 þ 10a1 a2  5a1  5a2 =42   þ P4 3a21 þ 3a22 þ 8 þ 2a1 a2  8a1  8a2 =70

315

ð31Þ

They represent a system of five equations with five unknowns, namely a1, a2, hP2 i, hP4 i, and I 0 a23 . Its complete resolution is the most general method to determine the molecular orientation of samples with uniaxial symmetry (referred to as the ‘‘general’’ method hereafter). As opposed to other methods (see below), it requires no assumption about the shape of the Raman tensor. Equations (31) have first been solved for oriented poly(methyl methacrylate) (PMMA) [46]. The method has later been extended by Pigeon et al. [47] to obtain the relevant spectra of Equation (31) using the backscattering and right-angle geometries. The ‘‘general’’ method is relatively complex from both mathematical and experimental viewpoints and requires the choice of initial conditions that are unfortunately not unique. Despite these difficulties, it has been successfully applied to quantify the orientation of various polymers. As an example, Figure 8 shows the five independent polarized spectra corresponding to Equation (31) for PE roll-drawn to a draw ratio of 11.7 [47]. The differences in the relative band intensities with polarization illustrate the strong   orientation of the molecules. The band at 1,130 cm1 measured in the I 0 a2XX spectrum (Figure 8) is assigned to the symmetric stretching mode of the C–C bonds and has been specifically used to determine the order parameters hP2 i and hP4 i for various draw ratios. The relative intensity of the 1,060 cm1 band (antisymmetric C–C stretching mode) with respect to that at 1,130 cm1 as a function of hP2 i and hP4 i is plotted in Figure 9. Such a calibration curve shows that some intensity ratios can be a good probe to estimate the orientation level of macromolecules. The method described by Pigeon et al. has been used to investigate PE foils [48], PET fibers [49] and films [50], and uniaxially oriented liquid-crystalline films of polyesters [51]. An approach simpler than the ‘‘general’’ method has been used by Bower and coworkers [52,53] and has proved to be useful to determine the order parameters of uniaxially oriented polymers. This approach, called ‘‘cylindrical’’ method, requires a smaller number of spectra that are easily measurable, but it assumes that the Raman tensor associated with the vibrational mode under study is cylindrical. In such case, a1 ¼ a2 ¼ a so that the depolarization ratio Riso of an

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Figure 8 Five independent spectra of a uniaxially stretched PE sample (draw ratio of 11.7). Reproduced with permission from Pigeon et al. [47]. Copyright 1991 American Chemical Society.

isotropic sample is given by ha2ij i   ð1  aÞ2 Riso ¼  2  ¼ ; iaj; with i; j ¼ X or Z 2 ð8a þ 4a þ 3Þ aii

(32)

Consequently, the measurement of three spectra and the determination of a from the isotropic sample allow calculation of hP2 i and hP4 i. This method has been applied successfully to PET [53] and rubber networks [52], and to study the

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Figure 9 Plot of the intensity ratio h1130/h1060 as a function of hP2 i and hP4 i of PE roll-drawn sheets for various draw ratios. Reproduced with permission from Pigeon et al. [47]. Copyright 1991 American Chemical Society.

photoisomerization of azobenzene polymer matrices [54] and liquid crystal elastomers [55]. Finally, Frisk et al. have proposed a third method, the ‘‘depolarization’’ method, that does not need the assumption of a cylindrical Raman tensor [56]. A randomly oriented sample is again necessary but the depolarization ratio takes the general form  2 2 a1 þ a22 þ 1  a1 a2  a1  a2  Riso ¼  2 (33) 3a1 þ 3a22 þ 3 þ 2a1 a2 þ 2a1 þ 2a2 The measurement of four independent spectra then leads to the complete resolution of the system, assuming that the depolarization ratio is the same for the oriented and isotropic samples. Frisk et al. have compared the three basic methods on the same poly(propylene terephthalate) (PPT) sample [56]. It appears that the assumption of a cylindrical Raman tensor may be too crude in some cases. Unless the hypothesis of a cylindrical tensor has been ascertained, the two other methods should be used. The ‘‘general’’ method is intrinsically the most accurate one but it

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suffers from experimental and mathematical complexity. The ‘‘depolarization’’ method is easier to implement but the assumption that the depolarization ratios of the oriented and isotropic samples are identical may not necessarily be true since the local environment may differ. Because the determination of the order parameters by Raman spectroscopy is not straightforward, some works have focused on using intensity ratios to evaluate the molecular orientation (see above). Frisk et al. [56],  in particular,   have shown that the simple parameter R0 ¼ 1  I XX =I ZZ ¼ 1  a2XX = a2ZZ can efficiently, although qualitatively, characterize orientation in polymers.

5.1.2 Biaxial systems Because of their relative complexity, few Raman studies have dealt with biaxial systems, although valuable structural information can be obtained. Assuming a cylindrical Raman tensor, it has been shown that there are six independent quantities I ij ¼ I 0 ha2ij i given by [3] I XX ¼ I 0 a23 ½A þ BðhP200 i  6hP220 iÞ þ Cð3hP400 i  60hP420 i þ 70hP440 iÞ I YY ¼ I 0 a23 ½A þ BðhP200 i þ 6hP220 iÞ þ Cð3hP400 i þ 60hP420 i þ 70hP440 iÞ I ZZ ¼ I 0 a23 ½A  2BhP200 i þ 8hP220 i I YZ ¼ I 0 a23 ½D  EðhP200 i  6hP220 iÞ  4CðhP400 i þ 15hP420 iÞ I YZ ¼ I 0 a23 ½D  EðhP200 i þ 6hP220 iÞ  4CðhP400 i  15hP420 iÞ I XY ¼ I 0 a23 ½D þ 2EhP200 i þ CðhP400 i  70hP440 iÞ with

  A ¼ 8a2 þ 4a þ 3 =15;   D ¼ 8a2  2a þ 1 =15;

  B ¼ 8a2  2a  6 =21;   E ¼  a2  2a þ 1 =15

ð34Þ   C ¼ a2  2a þ 1 =35 ð35Þ

The measurement of these six quantities with the knowledge of a ¼ a1 ¼ a2 leads to the determination of the six unknowns, namely I 0 a23 ; hP200 i; hP220 i; hP400 i; hP420 i; and hP440 i. Application of this method to unidirectionally drawn PET films reveals an orientation of the plane of the aromatic rings in the plane of the film and, surprisingly, a small overall orientation of the chain axes away from the plane of the film [3].

5.1.3 Orientation-insensitive spectra For oriented systems, the determination of molecular conformation is a complex problem because Raman spectra contain signals inherently due to both molecular conformation and orientation. To extract only the information relative to the conformation, one has to calculate a spectrum that is independent of orientation, in a similar way to the A0 structural absorbance of IR spectroscopy (Section 4). Frisk et al. [57] have shown that for a uniaxial sample aligned along the Z-axis, a spectrum independent of orientation (so-called isotropic spectrum), Iiso, can be calculated from the following linear combination of four polarized spectra [57] I iso ð3 þ 6Riso Þ ¼ I zz þ 2I xx þ 4I xz þ 2I xy

(36)

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The method has been successfully applied to PPT samples having different orientation levels. It is noteworthy that the factor (3+6Riso) is not a constant throughout the whole spectral range since Riso is a priori different for each band. This factor is then particularly important if one wants to compare the relative intensities of various vibrational modes. Sourisseau and Talaga [58] have expanded the theoretical expression of orientation-independent intensity sums for systems with biaxial symmetry by making use of the K2 Raman invariant.

5.2 Spectromicroscopy (micro-Raman) The advantage of Raman spectromicroscopy is that very small specimens can be studied while still allowing the determination of the second and fourth moments of the ODF. However, the expressions for the Raman intensities are more complex since the optical effects induced by the microscope objective have to be considered. Although the corrections may be small, they are not necessarily negligible [59]. This problem was first treated by Turrell [59–61] and later by Sourisseau and coworkers [5]. Turrell has mathematically quantified the depolarization of the incident electric field in the focal plane of the objective and the collection efficiency of the scattered light by high numerical aperture objectives. For brevity, only the main results of the calculations will be presented. Readers interested in more details are referred to book chapters and reviews of Turrell or Sourisseau [5,59,61]. The intensity in Raman spectromicroscopy is given by [59–61] Z Z D E ei a ej 2 dV dO I ij ¼ I 0 (37) V

O

where V is volume of scattering units and O is the solid angle of light collection, whereas the unit vectors ei and ej define the directions of the electric fields of the incident laser beam and scattered light, respectively (i, j ¼ X, Y, Z, Figure 1). In spectromicroscopy, the backscattering configuration limits to four the number of different accessible intensities (i, j ¼ X or Z). The four measurable intensities Iij are given by           I XX ¼ I 0 ð2C0 þ C2 Þ Aobj a2XX þ Bobj a2XY þ 4C1 Aobj a2YX þ Bobj a2YY      þC2 Aobj a2ZX þ Bobj a2ZY           I XZ ¼ I 0 ð2C0 þ C2 Þ Aobj a2XZ þ Bobj a2XY þ 4C1 Aobj a2YZ þ Bobj a2YY      þC2 Aobj a2ZZ þ Bobj a2ZY           I ZX ¼ I 0 ð2C0 þ C2 Þ Aobj a2ZX þ Bobj a2ZY þ 4C1 Aobj a2YX þ Bobj a2YY      þC2 Aobj a2XX þ Bobj a2XY           I ZZ ¼ I 0 ð2C0 þ C2 Þ Aobj a2ZZ þ Bobj a2ZY þ 4C1 Aobj a2YZ þ Bobj a2YY      þC2 Aobj a2XZ þ Bobj a2XY ð38Þ

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The constants Aobj and Bobj characterize the collection efficiency of the objective and originate from the integration over O. They are related to the numerical aperture NA of the objective so that   4 1  cos ym  cos3 ym Aobj ¼ p2 3 3 and Bobj ¼ 2p2



2 1  cos ym þ cos3 ym 3 3

 (39)

  with ym ¼ arc sin NA=n , n being the refraction index of the sample and ym the effective half-angle of the cone of the light scattered from the sample and collected by the objective. Typically, Aobj ¼ 3.759 and Bobj ¼ 0.737 for n ¼ 1.5 and for a 100 objective (NA ¼ 0.9). The coefficients C0, C1, and C2 represent the depolarization of the light by the objective and arise from the integration over V. They have to be calculated numerically but, since they roughly vary in the ratio 100/10/1, the expressions in Equations (38) can be simplified (see examples below). Based on two intensity ratios, R1 ¼ Izx/Ixx and R2 ¼ Ixz/Izz, and some assumptions, the order parameters can be determined.

5.2.1 Uniaxial systems The quantitative determination of molecular orientation by Raman spectromicroscopy was first applied to azobenzene holographic diffraction gratings [62]. These gratings are optically inscribed by the interference of two coherent laser beams having appropriate polarizations, taking advantage of the photo-induced orientation of the azobenzene moieties that are covalently bonded at side-chain positions of the polymer. This treatment leads to a B0.8–3.0 mm spatial period of the grating that can be suitably analyzed by Raman spectromicroscopy. In these studies, it was assumed that the Raman tensor is cylindrical and that a3 a1 ¼ a2 ða  1Þ. A detailed structural description of the surface relief gratings was obtained thanks to the characterization of molecular orientation. Silk fibers, a basic system with a uniaxial symmetry, have also been investigated by Raman spectromicroscopy [63] that is one of the rare techniques capable of providing molecular data on such small (3–10 mm diameter) single filaments. The amide I band of the silk proteins has been particularly studied to determine the molecular orientation using the cylindrical Raman tensor approximation. In this work, it was assumed that C0 C1 ; C2 and the a parameter was determined from an isotropic sample using the following expression of the depolarization ratio     1  a2  Aobj þ Bobj iso R ¼ (40) ð8a2 þ 4a þ 3Þ  Aobj þ ð1  a2 Þ  Bobj Figure 10 shows polarized spectra of two types of silks recorded by Raman spectromicroscopy: the dragline silk (the lifeline) of the spider Nephila edulis and the cocoon silk of a wild silkworm Samia cynthia ricini. The position of the amide I band at 1,668–1,669 cm1 for both threads is characteristic of the b-sheet

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Figure 10 Polarized spectra obtained by Raman microspectroscopy of (A) the dragline silk of the spider Nephila edulis and (B) the cocoon silk of the silkworm Samia cynthia ricini. Adapted with permission from Rousseau et al. [63]. Copyright 2004 American Chemical Society.

conformation. Since the IXX spectrum is the most intense, this shows that the carbonyl amide bonds are preferentially oriented perpendicular to the fiber axis, i.e., the b-sheets are basically aligned along the fiber direction. The comparison of the relative intensities of the polarized amide I bands also shows qualitatively that the cocoon silk is the most oriented. This is confirmed by the calculation of the order parameter hP2 i, which is 0.36 for the silkworm’s cocoon and 0.32 for the spider’s dragline.

5.2.2 Biaxial systems The biaxial orientation in photoaddressable azobenzene films has been observed recently by polarized Raman spectromicroscopy [64]. Here, IR spectroscopy has been advantageously used as a complementary technique to measure the order

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parameters hP200 i associated with five vibrational modes that are also Raman active, in particular the benzene n8a stretching mode at 1,599 cm1. From the measurement of the two intensity ratios R1 and R2, Raman spectromicroscopy has allowed the determination of the remaining unknowns, i.e., the fourthrank coefficients hP400 i, hP420 i, and hP440 i, assuming that C0 C1 ; C2 and that a3 a1 ¼ a2 . These measurements have provided an estimate of the overall distribution of orientation and showed that the chromophores have a preferential orientation in the plane of the films.

5.2.3 Orientation-insensitive spectra Finally, as in macro-Raman experiments, orientation-insensitive spectra can also be calculated for spectromicroscopy. A method has been developed recently for uniaxially oriented systems and successfully tested on high-density PE rods stretched to a draw ratio of 13 and on Bombyx mori cocoon silk fibers [65]. This method has been theoretically expanded to biaxial samples using the K2 Raman invariant and has proved to be useful to determine the molecular conformation in various polymer thin films [58].

6. FLUORESCENCE SPECTROSCOPY Like Raman scattering, fluorescence spectroscopy involves a two-photon process so that it can be used to determine the second and the fourth rank order parameters. In this technique, a chromophore, either covalently linked to the polymer chain or a probe incorporated at small concentrations, absorbs incident light and emits fluorescence. If the incident electric field is linearly polarized in the ei direction and the fluorescent light is collected through an analyzer in the es direction, the fluorescence intensity is given by   (41) I ¼ I 0 ðea :ei Þ2 ðee :es Þ2 where ea and ee are the unit vectors of the absorption transition dipole and the fluorescence emission dipole, respectively. I0 depends on the number of fluorescent molecules, incident light intensity, fluorescence quantum yield, and instrumental factors. Information about orientation results from the alignment of the chromophore moieties that absorb and/or emit light in preferential directions. Rewriting Equation (41), we have [44] DX DX 2 E 2  e 2 E I ¼ I0 ‘0i :f ai ‘j :f j ‘0i :‘j :f ai :f ej ¼ I0 ; with i; j ¼ X; Y; or Z (42) i;j

‘i0

i;j

and ‘j are the direction cosines of the incident and emitted electric where fields, respectively, and f ai and f ej are the direction cosines of the absorption and emission axes, respectively. Equation (42) is equivalent to the expression of the Raman intensity (Equation (30)) considering that Fij f ai  f ej are the elements a second-rank tensor similar to the Raman tensor a. The method to determine the order parameters [12,44,66] is then comparable to that of Raman spectroscopy, so it will not be developed here.

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Nobbs et al. [67] have performed a detailed fluorescence study of molecular orientation in PET tapes produced by melt spinning and subsequently uniaxially drawn at various temperatures and draw ratios. The instrument configuration was a straight-through geometry and the fluorescent probe was 2,2u(vinylene-dip-phenylene) bisbenzoxazole incorporated at 50–200 ppm. This study has established the usefulness and limitations of the technique, in particular by considering the fact that the absorption and emission axes do not necessarily coincide and by quantifying the effects of birefringence. An example of the determination of order parameters for a uniaxial system is given by Wolarz and Bauman [68] who studied the molecular orientation of a nematic side-chain liquid-crystalline polysiloxane using 4-dimethylamino-4unitrostilbene (DANS) as a guest probe. This polymer undergoes a nematicisotropic phase transition at TNI ¼ 348 K. Figure 11 shows the order parameters hP2 i and hP4 i of DANS as a function of the reduced temperature T ¼ T/TNI. They were deduced from two intensity ratios R1 and R2 measured for two positions of the sample differing by a rotation of 901 around the normal of the film, taking into account the angle d between the absorption and emission axes. R1 and R2 are given by I XX  I XZ I ZX  I ZZ R1 ¼ and R2 ¼ (43) I XX þ 2I XZ I ZX þ 2I ZZ

Figure 11 Order parameter hP2 i as measured by fluorescence emission (filled circles) and absorption dichroism (open squares) and order parameter hP4 i (open circles) of polysiloxane doped with DANS as a function of the reduced temperature T. Reproduced with permission from Wolarz and Bauman [68]. Reprinted with permission of John Wiley & Sons, Inc.

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Iij (i, j ¼ X, Y, Z, see Figure 1) is the fluorescence intensity with the incident beam polarized in the i-direction and with the polarization direction of the analyzer along the j-axis. The variation of the order parameters with T is characteristic of low molecular-weight nematic liquid crystals, but the absolute values are lower. This was attributed to limitations of the rotational and translational motions of the mesogenic segments attached to the rigid backbone of the polymer. This constraint would lead to the formation of clusters that display different orientations, thus reducing the hP2 i value. Figure 11 also presents the hP2 i values as measured by UV linear dichroism following Equation (25). The lower value observed for fluorescence emission than for UV absorption is common for low molecular-weight liquid crystals and is attributed to an intermolecular energy transfer, which can lead to depolarization of the emission. In fluorescence spectroscopy, the orientation distribution of the guest probe is not necessarily identical to the actual orientation of the polymer chains, even if it is added at very small concentrations (i.e., a probe with high fluorescence efficiency). As a matter of fact, it is generally assumed that long linear probes are parallel to the polymer main chain, but this is not necessarily the case. Nevertheless, if the relation between the distribution of the probe axes and those of the polymer axes is known, the ODF of the structural units can be calculated from that of the probe thanks to the Legendre’s addition theorem. Finally, the added probe seems to be mainly located in the amorphous domains of the polymer [69] so that fluorescence spectroscopy provides information relative to the noncrystalline regions of the polymeric samples. Problems related to the use of a guest dye can be reduced if the polymer contains a fluorescent chemical group. Gohil and Salem [70] took advantage of such intrinsic fluorescence to characterize the in-plane distribution of orientation in biaxially drawn PET films. In these experiments, the chain-intrinsic fluorescent label is due to the formation of dimers by two terephthalic moieties, exclusively within the noncrystalline regions. A comparison between sequential and simultaneous drawing along the MD and TD directions was undertaken for a fixed MD draw ratio of 3.5 and various TD draw ratios. The orientational order was characterized by two ‘‘orientation ratios’’ RMD and RTD such that RMD ¼

I MD I TD and RTD ¼ I MD þ I TD I MD þ I TD

(44)

Figure 12 shows the MD and TD orientation ratios as a function of the TD draw ratio after biaxial drawing of the film. The curves coincide for the sequential and simultaneous processes up to a TD draw ratio of 2.7, beyond which RMD and RTD deviate from linearity for the sequential drawing. The amount of oriented chains in the TD and MD is thus the same up to a draw ratio of 2.7 but, above 2.7, the sequential stretching involves a reorientation of the polymers in the TD after the molecules were initially aligned in the MD. At equal draw ratios in the TD and MD, the simultaneous drawing actually leads to an isotropic distribution in the plane of the film, whereas in the sequential drawing, the chains are preferentially aligned in the TD.

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Figure 12 Orientation ratios RMD (open symbols) and RTD (filled symbols) as a function of the TD draw ratio of PET films drawn for a sequential (circles) and simultaneous (triangles) process. Reproduced with permission from Gohil and Salem [70]. Reprinted with permission of John Wiley & Sons, Inc.

Recently, a formalism has been developed to determine the second and the fourth order parameters of films using polarized total internal reflection fluorescence (TIRF) [71]. Similarly to IR-ATR spectroscopy (Section 4), the experiment makes use of p- and s-polarized excitation, but the fluorescence emission (analyzed either in p- or s-direction) is detected normal to the substrate. Two approaches are developed based on the measurements of two intensity ratios. In the first one, the d angle has to be known experimentally or theoretically, and the order parameters hP2 i and hP4 i can be determined. In the second one, the order parameter hP2 i is obtained by another technique, for instance IR-ATR spectroscopy, which allows deducing the order parameter hP4 i and hcos2 di.

7. NMR SPECTROSCOPY NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR

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offers several ways to probe molecular order in oriented polymers. Since the detailed description of the available NMR techniques is outside the scope of this chapter and can be found elsewhere [72,73], only typical examples will be presented here. One problem with NMR spectroscopy of static polymer samples is the poor spectral resolution due to strong interactions in the solid state. Nevertheless, it has been shown that the hP2 i and hP4 i coefficients of the ODF can be determined for uniaxially oriented systems from the calculation of the second and fourth moments of resonance lines obtained by proton wide-line 1D NMR spectroscopy [72,73]. One way to increase the spectral resolution is by the isotopic labeling of some specific chemical groups so that one of the coupling tensors dominates in the 1D NMR spectra. Such strategy has been used successfully to study the distribution of orientation of polymer chains in highly oriented samples of deuterated PE [74] and PET [75] from the line shapes of 2H NMR spectra. Figure 13 shows the 2H NMR spectra of single-crystal mats and of a cold-drawn sample of PE with the magnetic field oriented either parallel or perpendicular to the preferred orientation axis. For both samples, the polymer chains in all-trans conformation are preferentially oriented along a single direction. When the external magnetic field, B0, is parallel to the chain direction, the C-2H bonds are perpendicular to B0, leading to a single doublet. The separation of these two lines depends on the angle between the C-2H bonds and the magnetic field. However, when B0 is perpendicular to the chain direction, the C-2H bonds are uniformly distributed in a plane forming an angle between 0 and 901 with B0, which leads to the characteristic spectrum with four singularities as seen in the right-hand side of Figure 13. For uniaxially oriented samples, the shape of this spectrum depends on the orientation distribution of the C-2H bonds and on the angle g between the magnetic field and the orientation direction. The quantitative line shape analysis as a function of g has shown that in both cases, the orientation distribution can be described as a simple Gaussian function with a width of 121 for the single-crystal

Figure 13 2H spectra of oriented polyethylene. Left, B0 parallel, right, B0 perpendicular to the orientation direction, respectively. Reproduced with permission from Hentschel et al. [74]. Copyright Elsevier 1981.

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mats and 2.81 for the drawn sample, in excellent agreement with X-ray diffraction measurements on the same samples [74]. This method is particularly effective for highly oriented systems. Site-resolved orientation measurements with high spectral resolution can be achieved without the need of isotopic labeling either by the 2D synchronized magic angle spinning (MAS) technique [76] or the multidimensional DECODER (Direction Exchange with Correlation for Orientation-Distribution Evaluation and Reconstruction) technique [73,77,78]. The MAS technique averages out second-rank tensor interactions in the solid state and provides well-resolved NMR spectra of solid samples. MAS spectra are composed of center bands at the isotropic chemical shift frequencies of individual resonances flanked by sets of rotational sidebands. If the sample is partially ordered with the orientation axis not parallel to the rotor axis, phase and intensity modulations of the center band and the sidebands are observed, which depend on the position of the rotor at the time the spectrum is excited. Therefore, by synchronizing data acquisition with the rotor position, a 2D sideband pattern can be obtained for each resonance, which is highly dependent on tensor orientation. This technique has been used successfully to determine chain order in semicrystalline PET fibers using 13C resonances for the glycolic ethylene (O-CH2) and carbonyl groups [76]. Due to the limited number of sidebands with appreciable intensity observed for a given rotor frequency, only the hP2 i and hP4 i coefficients of the ODF of the PET chains were calculated from hP‘ i-weighted subspectra (Table 1). However, the use of the DECODER technique has allowed the determination of hP‘ i coefficients up to hP10 i for the same sample. In the 2D DECODER exchange NMR experiment, the sample is macroscopically rotated as a whole during the mixing time of the pulse sequence, thus allowing the correlation of two frequencies for two different sample orientations [78,79]. Through this correlation, more information can be obtained than from 1D rotation patterns and the orientation of chemical groups around the equivalent of two Euler angles can be determined. As seen in Table 1, the hP2 i and hP4 i coefficients of the oriented PET fibers obtained by the sync-MAS and DECODER techniques are in very good agreement, but the higher angular resolution of the DECODER experiment has allowed for determination of higher hP‘ i coefficients and to reconstruct the orientation distribution of chain axes. The results have shown that the orientation distribution is at least bimodal with a broad component and a narrow component [77].

Table 1 Order parameters of OCH2 group of PET fibers from 2D-sync-MAS and 2D-DECODER 13 C-NMR experiments

a

Technique

hP2 i

hP4 i

hP6 i

hP8 i

hP10 i

sync-MASa DECODERb

0.55 0.60

0.55 0.47

– 0.37

– 0.26

– 0.17

From Harbison et al. [76]. From Chmelka et al. [77].

b

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8. X-RAY DIFFRACTION AND ABSORPTION Wide-angle X-ray diffraction (WAXD) is one of the most commonly used techniques for the determination of molecular orientation in semicrystalline polymers [12]. It is particularly powerful as it provides a direct measurement of the complete distribution of orientation N(y, j) of the crystal axes with respect to the macroscopic sample coordinate system (OXYZ, Figure 1). A WAXD study of the diffracted intensity from a crystal plane of Miller indices hkl, Ihkl, through the rotation of the w and c angles (Figure 14) at a fixed Bragg angle (2yB) gives a pole figure, which is a map of the density of the normal to the crystal plane in the sample coordinate system. In samples exhibiting axial symmetry around the reference MD, a complete pole figures analysis is not necessary and the measurement of the diffraction intensity as a function of the angle w (obtained by rotating the sample around the ND axis or by using a 2D detector) is sufficient to determine the distribution of orientation N(w)hkl. It is thus possible to calculate any hP‘ ihkl coefficients for a given hkl plane for the crystalline phase of the polymer by integration over every possible orientation [2,80]: R p=2 I hkl ðwÞPn ðcos wÞ sinðwÞdw hP‘ ihkl ¼ 0 R p=2 (45) I hkl ðwÞ sinðwÞdw 0 where Ihkl(w) is the intensity of diffraction (after background correction) at the azimuthal angle w. The distribution of orientation N(w) of a given reflection may be reconstructed by insertion of the hP‘ ihkl coefficients in the relation: 1 X NðwÞhkl ¼ ðn þ 1=2ÞhP‘ ihkl P‘ ðcos wÞ (46) n¼0

Figure 14 Angles w and c defining the position of the normal to a given hkl crystal plane in the sample reference system. Ix, incident X-ray beam; Ihkl, diffracted intensity; yB, Bragg angle. Adapted from Lafrance et al. [82]. Reprinted with permission of John Wiley & Sons, Inc.

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In the case of uniaxial cylindrical symmetry around the MD, the hP‘ ihkl values calculated from different crystal planes can be related to the hP‘ i coefficients of any of the three crystallographic angles using the Legendre addition theorem (see Section 4). For example, the hP‘ ic coefficients corresponding to the crystalline c-axis is given by [81] hP‘ ihkl hP ‘ ic ¼ (47) P‘ ðcos bhkl Þ where bhkl is the angle between the normal to the considered (hkl) plane and the c-axis. This relation is particularly useful to determine polymer chain orientation since reflections from planes that are perpendicular to the polymer chains (00l) are frequently absent or too weak to be analyzed with sufficient accuracy. In addition, in the case of unit cells with orthogonal crystal axes, geometrical consideration leads to the following expression for the second moments of the distribution of orientation (Herman’s orientation function) of the three crystal axes: hP 2 i a þ h P 2 i b þ h P 2 i c ¼ 0 (48) A nice example of the strength of WAXD to study molecular orientation in a semicrystalline polymer was given by Lafrance et al. [82]. In this work, WAXD was used to study the development of crystalline orientation in drawn ultrahigh-molecular weight PE films prepared by the gelation-crystallization method. Azimuthal profiles were measured to determine the presence of any preferred orientation of the crystals in the undrawn film (Figure 15). Scans measured with the incident beam perpendicular to the sample surface (A) show that the crystal a- and b-axes are randomly distributed around the ND.However, scans obtained with the beam parallel to the TD (B) show that the c-axis, and thus the PE chains, is oriented perpendicular to the surface of the film, the 002 reflection being centered at w ¼ 01. The average hP2 ic coefficient calculated from the 110, 200, 020, and 002 reflections is equal to 0.67 with respect to ND. Therefore, lamellar growth occurred in the plane of the film as the b-axis is that of the crystal growth for PE. Upon drawing, at 1301C, a change of the orientation of the PE chains from the normal direction to the drawing direction was observed. In addition, as shown in Figure 16, a marked decrease of the intensity of the Bragg peak for the 200 reflection relative to that of the 020 reflection was observed at low draw ratio (lo10). This variation, which occurs in the early stages of drawing, was assigned to development of double orientation during the transformation from the lamellar to the fibrillar morphology, with the a-axis oriented parallel to ND. Upon further drawing, the width of the azimuthal scans for different reflections was observed to decrease, indicating a narrowing of the distribution of orientation even at very high draw ratios. From these scans, hP‘ i coefficients were calculated using Equations (45) and (47). Although the hP2 i coefficient is a convenient index to characterize the orientation and is commonly measured by WAXD for semicrystalline polymers, it is only an average value and different distributions of orientation could give the same hP2 i coefficient (Section 2). It has been shown that higher hP‘ i coefficients are required to fully characterize the distribution of orientation [83]. This is

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Figure 15 X-ray intensity measured as a function of the polar angle w for an undrawn ultrahigh molecular weight PE film. Incident beam directed through the thickness of the film (A), and parallel to the plane of the film (B). Reproduced with permission from Lafrance et al. [82]. Reprinted with permission of John Wiley & Sons, Inc.

particularly important for highly oriented samples since hP2 i increases rapidly near its maximum value and remains constant afterward. This is clearly shown in Figure 17 where the hP2 ic , hP26 ic , hP60 ic coefficients were calculated from the 020 and 002 reflections as a function of the draw ratio. At draw ratios between 5 and 10, the hP2 ic values approach the theoretical limit of unity, showing that the crystal phase has already attained a high degree of orientation. At higher draw ratios, the hP2 ic coefficients show no additional significant variation because the secondorder Legendre polynomial is much broader than the narrow experimental intensity distributions. However, Figure 17 shows that higher-order coefficients of the polynomial series such as hP26 ic and hP60 ic can be used efficiently to follow the evolution of the orientation up to l ¼ 50. This example clearly emphasizes the

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Figure 16 Effect of l on the ratio of the 200/020 integrated intensities measured in the polar scans for a drawn ultra-high molecular weight PE film. Reproduced with permission from Lafrance et al. [82]. Reprinted with permission of John Wiley & Sons, Inc.

importance of using techniques that allow the determination of hP‘ i coefficients higher than hP2 i for highly oriented samples. For more complex morphologies showing biaxial orientation, a pole figure analysis involving the rotation of the w and c angles is necessary to fully characterize the orientation [84]. Near-edge X-ray absorption fine structure spectroscopy (NEXAFS), using linearly polarized synchrotron light, also provides a quantitative measurement of the direction and magnitude of orientation in anisotropic systems [85]. NEXAFS linear dichroism can also be recorded at high spatial resolution (o50 nm) using scanning transmission X-ray microscopy (STXM) [85]. Recently, STXM has been used for the first time to quantitatively map the level of orientation of the carbonyl bonds of the protein polypeptide chains in silkworm [86] and spider silks [87] at spatial resolution better than 50 nm. For these experiments, the absorbance of the 288.25 eV X-ray band due to the C 1s-p CQO transition of the protein peptide groups was measured with the electric field vector of the X-ray beam polarized parallel (Ap) and perpendicular (As) to the fiber axis, thus allowing one to calculate for each pixel the second moment of the orientation  function P2 ðcos gÞ as described for IR transmission measurements in Section 4. In this case, g represents the angle between the moment vector of the C 1s-p CQO transition and the fiber axis. An example of such orientation map obtained for a thin section of Nephila clavipes dragline silk fiber of about 3 mm in diameter is shown in Figure 18 [87]. Dragline silk presents a very fine microstructure in which small, highly oriented, domains are dispersed in a dominant, moderately oriented, matrix with several small unoriented domains.

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Figure 17 Values of the hP2 ic , hP26 ic , hP60 ic coefficients as a function of l for the 020 and 002 reflections for a drawn ultra-high molecular weight PE film. Reproduced with permission from Lafrance et al. [82]. Reprinted with permission of John Wiley & Sons, Inc.

Figure 18 Quantitative hP2 ðcos gÞi orientation map of a fiber reeled at 0.5 cm/s. Black areas correspond to unoriented regions, whereas bright areas correspond to more highly oriented regions. Reproduced with permission from Rousseau et al. [87]. Copyright 2007 American Chemical Society.

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Since the transition moment for the 288.25 eV band is perpendicular  to the plane of the protein peptide bond, the negative values of the P2 ðcos gÞ coefficient show that the peptide CQO groups are preferentially oriented perpendicular to the fiber axis. There is clearly an uneven spatial distribution of highly oriented (bright) domains (Figure 18), especially at the surface of the fiber where a skin B30–120 nm thick is present. These oriented domains are associated with the anti-parallel b-sheets formed by the repeating alanine sequences present in spider dragline silk. This example shows that STXM is a powerful technique to probe at high spatial resolution the microstructure of oriented polymer samples.

9. CONCLUSION As seen in this chapter, the theory and procedures for orientation measurements are well established, including for quantitative characterization. These methods can provide very accurate and useful information in the fields of synthetic, natural, and bio-inspired macromolecules. To this aim, researchers can make use of a wide range of techniques, each having its advantages and limitations. As judged from the recent literature, the studies devoted to the quantification and characterization of molecular orientation still represent a very dynamic research field and advances still continue to emerge. Further progresses in the development of new methods and new techniques to characterize orientational order are thus expected in the future.

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CHAPT ER

9 Polymer Networks: Elastomers B. Erman and J.E. Mark

Contents

1. Introduction 2. Structure of a Typical Network 3. Elementary and More Advanced Molecular Theories 3.1 Elasticity of the single chain 3.2 The elastic free energy of the network 3.3 The reduced stress and the elastic modulus 3.4 The affine network model 3.5 The phantom network model 3.6 More advanced molecular theories 3.7 Contribution of trapped entanglements to the modulus 4. Phenomenological Theories 5. Some Relevant Simulations 5.1 Gelation 5.2 Distribution functions and stress–strain isotherms 5.3 Crystallization 5.4 Filler reinforcement 6. Swelling of Networks and Responsive Gels 7. Enthalpic and Entropic Contributions to Rubber Elasticity: The Force–Temperature Relations 8. Multimodal Elastomers 8.1 General information 8.2 Bimodal networks 8.3 Trimodal networks 9. Liquid–Crystalline Elastomers 9.1 General information 9.2 Main-Chain liquid–crystalline elastomers 9.3 Side-Chain liquid–crystalline elastomers 9.4 Theory 10. Novel Reinforced Elastomers 10.1 Sol–Gel in-situ precipitated ceramic particles 10.2 Non-Spherical particles 10.3 Magnetic particles 10.4 Layered fillers 10.5 Polyhedral oligomeric silsesquioxanes (POSS)

Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00409-1

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10.6 Nanotubes 10.7 Porous fillers 10.8 Fillers with controlled interfaces 11. Further Comments on Some Characterization Techniques 11.1 Optical and spectroscopic techniques 11.2 Microscopies 11.3 NMR 11.4 Small-Angle scattering 11.5 Brillouin scattering 11.6 Pulse propagation Acknowledgement References

373 373 373 374 374 374 375 375 376 376 376 377

1. INTRODUCTION A network can be formed from a polymer by constraining pairs of its repeat units, typically by introducing cross-links between chains close to one another. The reaction is typically carried out in the isotropic, bulk state [1,2]. If approximately 1 repeat unit out of 10 along the chain backbone participates in this type of ‘‘cross-linking’’, then the result is an infusible, relatively hard material [3]. Examples of such materials are phenol formaldehyde resins and epoxy cements. If only approximately 1 out of 100 repeat units are involved in cross-links, however, then above its glass transition temperature the material has elastomeric properties similar to those of natural rubber, specifically high deformability with recoverability. They are therefore described as exhibiting ‘‘rubber-like elasticity’’ [4,5]. Both types of networks have been called ‘‘thermosets’’, but modern usage applies this term more to the very heavily cross-linked networks. The more lightly cross-linked, elastomeric materials are the focus of this chapter. More specifically, the rubber-like materials introduced above consist of relatively long polymeric chains having a high degree of flexibility and mobility, which are joined into a network structure [6,7]. The requirement of flexibility and mobility is associated with the very high deformability. As a result of an externally imposed stress, the long chains may alter their configurations, an adjustment which takes place relatively rapidly because of the high chain mobility. The requirement of having the chains linked into a network structure is associated with solid-like features, where the chains are prevented from flowing relative to each other under external stresses. As a result, a typical rubber may be stretched up to about 10 times its original length [8,9]. On removal of the external force, it rapidly recovers its original dimensions, with essentially no residual or non-recoverable strain. As a result of these unique mechanical properties,

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rubbers find important usages ranging from automobile tires to heart valves, and gaskets in jet planes, and space vehicles [10]. In ordinary solids such as crystalline or amorphous glassy materials, an externally applied force changes the distance between neighboring atoms, resulting in interatomic or intermolecular forces. In these materials, the distance between two atoms should only be altered by no more than a fraction of an angstrom if the deformation is to be recoverable. At higher deformations, the atoms slide past each other, and either flow takes place or the material fractures. The response of rubbers on the other hand is almost entirely intramolecular [4,5]. Externally applied forces transmitted to the long chains through the linkages let their extremities change the conformations of the chains, and each chain acts like a spring in response to the external stress. The molecular mechanisms relating to rubber-like elasticity were recognized in the early 1930s. Rigorous statistical mechanical theories describing the mechanical behavior of rubbers were given by Guth and James [11], Wall [12], Flory [13], and Flory and Rehner [14,15]. The present understanding of the molecular basis of rubber elasticity owes much to these early theories. They give an idealized picture of rubber elasticity, but at the same time form the basis of more advanced molecular theories of such elasticity, which describe the effects of intermolecular entanglements observed in real networks. Developments in the field from the beginning up to the present have been reviewed in several monographs (see, e.g., Treloar [16], Mark and Erman [4], and the more recent monograph by Erman and Mark [5]). In this chapter we first discuss the structural features of networks that contribute to the stress upon deformation. We discuss the simple classical models of elasticity and the departures from these simple models. Specifically, we differentiate between two classes of models, (i) the constraint models, which assume that the total elastic energy of the network equals the sum of the individual network chain energies, and (ii) trapped entanglement models, which assume that entanglements that are trapped during the cross-linking stage contribute additionally to the network elastic energy. We also give the molecular interpretation of coefficients obtained from the phenomenological theories. Some simulations relevant to rubber-like elasticity are then briefly described. This is followed by a discussion of swollen networks (‘‘gels’’), and responsive gels because of their increasing interest. We then discuss the thermoelastic (force– temperature) behavior of networks, followed by information on multimodal networks, liquid–crystalline elastomers, novel reinforcing fillers, and conclude with some further comments on characterization methods.

2. STRUCTURE OF A TYPICAL NETWORK As already mentioned, a network can be obtained by linking polymer chains together, and this linkage may be either physical or chemical. Physical linking can be obtained by (i) absorption of chains onto the surface of finely divided particulate fillers, (ii) formation of small crystallites, (iii) coalescence of ionic groups, or (iv) coalescence of glassy sequences in block copolymers.

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These physical cross-links are, in general, not permanent and may disappear on swelling or increase in temperature. The corresponding networks are referred to as ‘‘physical’’ or ‘‘thermoreversible’’ and are not considered in this chapter. The reader may refer to Burchard and Ross-Murphy [17–19] for further information on such materials. Chemical cross-links may be obtained by randomly joining segments in already formed chains, by random copolymerization, or by end-linking functionally-terminated chains. Sulfur cures, peroxide cures, and high-energy irradiations are familiar methods of random cross-linking [1,2]. Copolymerization of monomers where at least one type has three or more reactive sites also leads to randomly cross-linked networks. Formation of networks by end-linking individual chains by f-functional linkages is the most appropriate method of forming well-defined structures, where the functionality f of a linkage is defined as the number of chains meeting at the junction. A network is called perfect if its junctions have a functionality of at least three, it has no dangling chains (chains attached to the network only at one of their ends), and it has no loops (chains with both ends meeting at the same junction). Properties of perfect networks are discussed in this chapter. The reader may refer to Erman and Mark [5,20] and to the original work by Flory [21] and Flory and Erman [22] for the structure and properties of imperfect networks. The structure of a perfect network may be defined by two variables, the cycle rank x and the average junction functionality f. Cycle rank is defined as the number of chains that must be cut to reduce the network to a tree. The three other parameters used often in defining a network are (i) the number of network chains (chains between junctions) n, (ii) the number of junctions m, and (iii) the molecular weight Mc of chains between two junctions. They may be obtained from x and f using the relations x  n¼ 1  ð2=fÞ m¼

2n f

 1  ð2=fÞ rN A Mc ¼ x=V0

(1) (2)



(3)

where r is the density, V0 is the reference volume of the network, and NA is Avogadro’s number. The cycle rank completely defines the connectivity of a network and is the only parameter that contributes to the elasticity of a network, as will be discussed further in the following section on elementary molecular theories. In several other studies, contributions from entanglements that are trapped during crosslinking are considered in addition to the chemical cross-links [23,24]. The trapped entanglement model is also discussed below. In a typical elastomer, the number of skeletal bonds in a network chain range from about 100 to 700 [25]. Networks with chains shorter than 100 bonds have

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low extensibilities. Those having chains much larger than 700 bonds may have very high extensibilities but are too weak to serve as load-carrying materials. It is possible to prepare ‘‘bimodal’’ networks, however, by end-linking very short and very long chains to form networks of significant toughness, as described below and elsewhere [26,27].

3. ELEMENTARY AND MORE ADVANCED MOLECULAR THEORIES The basic postulate of elementary molecular theories of rubber elasticity states that the elastic free energy of a network is equal to the sum of the elastic free energies of the individual chains. In this section, the elasticity of the single chain is discussed first, followed by the elementary theory of elasticity of a network. Corrections to the theory coming from intermolecular correlations, which are not accounted for in the elementary theory, are discussed separately.

3.1 Elasticity of the single chain The chemical structure of a polymer chain determines its statistical properties, such as its average dimensions in space and its flexibility. These parameters, in turn, affect various properties of a network consisting of these chains. A detailed understanding of the single chain is therefore important in this regard. Using poly(dimethylsiloxane) (PDMS) [–Si(CH3)2O–]n as an example, the chain consists of silicon and oxygen atoms located in alternating order along the backbone, with the CH3’s on the Si atoms constituting the side groups. The lengths of the bonds and bond angles are approximately constant, but torsional rotations at angles f may take place relatively easily about the skeletal bonds. Large rotations may take place about the skeletal bonds, as a result of which the chain may take different spatial conformations, with varying values of the endto-end vector r of the chain. In most molecular theories of rubber-like elasticity, the individual chains are approximated by either the freely jointed or the freely rotating chain model. In reality, however, rotations about each bond are subject to potentials that arise from the intrinsic torsional potential of the backbone bond and from steric attractive and repulsive forces from neighboring atoms along the chain. The energy to which the bond torsional angle fi is subjected exhibits three minima, referred to as the three ‘‘isomeric states’’ or ‘‘isomeric minima’’. Of course, the numbers of isomeric states may be smaller or larger than three, depending on the chain architecture. In general, the three minima are approximately spaced at 1201 intervals and are referred to as the trans (t), gauche+ (g+), and gauche (g) states. The shape of a chain changes continuously and rapidly as each bond fluctuates about an isomeric minimum, with an amplitude of the order of 7601, and occasionally goes over the energy peak to another isomeric minimum. The rate of transition from one isomeric minimum to another, which is on the order of one per nanosecond at sufficiently high temperatures, depends primarily on the temperature and on the height of the energy barriers. These transitions determine

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the dynamics of the chain, and determine in part its glass transition temperature, Tg. Equilibrium properties of the chain, on the other hand, are influenced by the energy levels of the isomeric minima, as well as their locations. In the case of hydrocarbon polymers such as polyethylene, the t state in a randomly configured chain is more populated than the g+ and g states. The average number of bonds in the t, g+, and g states is determined according to the Boltzmann distribution of statistical mechanics [28–30]. According to statistical mechanical arguments, the number of each type of isomeric state in a chain remains essentially the same when the chain is stretched at its two ends. The change in the end-to-end vector takes place by the redistribution of the isomeric states along the chain. As the number of each type of isomeric state remains the same, the total internal energy of the chain remains constant during stretching. The elasticity of the chain resulting from redistribution of isomeric states is referred to as ‘‘entropic’’ elasticity, and a major part of the elasticity of a network is entropic. If part of the work done in deformation is used to change the relative populations of isomeric states, the bond angles, and the chain lengths, a change in internal energy takes place, which results in an ‘‘energetic’’ component of the elasticity. The relationship of the entropic and energetic components to molecular constitution in a network is discussed in the following sections. The vector r joining the two ends of the chain takes different values resulting from rotations about the individual bonds. For chains with more than about 50 skeletal bonds, the probability W(r)dxdydz that one end of r is at the origin and the other end is in an infinitesimal volume dV ¼ dxdydz is satisfactorily represented by the Gaussian function [31,32] !3=2 ! 3 3r2   WðrÞdxdydz ¼ exp   2  dxdydz (4a) 2 r 0 2p r2 0 Here, /r2S0 represents the average of the squared end-to-end vectors, and the subscript zero indicates that the chain is in the unperturbed or so-called theta state [21]. It is now well established that chains in the bulk undiluted state are in the unperturbed state. Equation (4a) represents the probability distribution of the vectorial quantity r. A less detailed form of representation is the distribution w(r) showing the probability that the magnitude r of r has a certain value irrespective of direction. Thus, the probability that the chain end-to-end length is in the range r to r+dr irrespective of its direction is !3=2 ! 3 3r2   WðrÞdr ¼ exp   2  4pr2 dr (4b) 2p r2 0 2 r 0 A schematic representation of the Gaussian function of Equation (4b) is given by the dashed curve in Figure 1. The abscissa is normalized by dividing the endto-end distance by the contour length of the chain, and the ordinate is made nondimensional (unitless) by multiplying w(r) by the contour length. For chains having fewer than 50 bonds, such as the short chains in a bimodal network, for example, the distribution departs markedly from the Gaussian limit.

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Figure 1 Distributions for the end-to-end distance of a PDMS chain having n ¼ 20 skeletal ˚ . The Fixman–Alben distribution (dotted curve) and that from a bonds of length l ¼ 1.64 A Monte Carlo simulation (solid curve) are compared with the Gaussian approximation (dashed curve).

Among various representations of w(r) for short chains are the Hermite series [31,32], the Fixman–Alben distribution [33], and Monte Carlo simulations [34]. The Fixman–Alben distribution is given by WðrÞdr / expðar2 þ b2 r4 Þ4pr2 dr

(4c)

where a and b are coefficients. This distribution and results of Monte Carlo simulations for a PDMS chain of 20 skeletal bonds are compared with the Gaussian approximation in Figure 1. The molecular theories of networks to be presented in the following paragraphs are based on the Gaussian picture of the individual network chains. With reference to the form of the distribution function, these theories are referred to as ‘‘Gaussian theories’’. The elastic free energy Ael of a Gaussian chain is related to the probability distribution W(r) by the thermodynamic expression [5] Ael ¼ CðTÞ  kT ln WðrÞ

(5)

where C(T) is a function only of temperature T, and k is the Boltzmann constant. Substituting Equation (4a) into Equation (5) leads to ! 3kT   r2 (6) Ael ¼ An ðTÞ þ 2 r2 0 Here, A(T) is a function of temperature alone. Equation (6) represents the elastic free energy of a Gaussian chain with ends fixed at a separation of r. The average force required to keep the two ends at this separation is obtained from the thermodynamic expression [28]   @Ael f¼ (7) dr T

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¼

! 3kT   r r2 0

(8)

where Equation (8) is obtained by substituting Equation (6) into Equation (7). The subscript T denotes differentiation at fixed temperature. Equation (8) shows that the single chain behaves like a linear spring, with spring constant equal to 3kT//r2S0.

3.2 The elastic free energy of the network The total elastic free energy DAel of the network relative to the undeformed state is obtained by summing Equation (6) over the n chains of the network [4] 3kT X 2  2  DAel ¼  2  r  r 0 (9) 2 r 0 n ! 3nkT r2   1 ¼ (10) 2 r2 0 where /r2S ¼ Sr2/n is the average square of the end-to-end vectors of chains in the deformed network. Substituting  2  2  2  2 (11) r ¼ x þ y þ z into Equation (10) and using the fact that chain dimensions are isotropic in the undeformed state  2  2  2  2 r 0 x 0¼ y 0¼ z 0¼ (12) 3 one obtains "  #  2  2 y z nkT x2   þ  þ  3 DAel ¼ (13) 2 x2 0 y2 0 z2 0 The ratios of mean-squared dimensions appearing in Equation (13) are microscopic quantities. To express the elastic free energy of a network in terms of the macroscopic (laboratory) state of deformation, an assumption has to be made to relate microscopic chain dimensions to macroscopic deformation. Their relation to macroscopic deformations imposed on the network has been a main area of research in the area of rubber-like elasticity. Several models have been proposed for this purpose, which are discussed in the following sections. Before that, however, we describe the macroscopic deformation, stress, and the modulus of a network.

3.3 The reduced stress and the elastic modulus The state of macroscopic deformation may be characterized by considering the deformation of a rectangular prism, with extension ratios lx, ly, lz, along the x, y,

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and z directions, respectively, as lx ¼

Lx Lx0

ly ¼

Ly Ly0

lz ¼

Lz Lz0

(14)

where Lx0, Ly0, Lz0 are the sides of the prism before deformation and Lx, Ly, Lz are the corresponding sides in the deformed state. For the sake of simplicity, we consider here dry networks, that is, networks in the absence of a diluent both in the state of formation and during deformation. However, we discuss effects of swelling later in Section 6. Also, we consider only the uniaxial case. The true stress t, that is, force per unit deformed area, resulting from a uniaxial force acting on a cross-section of the network sample is obtained by the Treloar relations [5,16] " ! !# 2 @DAel 2 @DAel 1 t ¼ 2V li (15)  lj @l2i @l2j T;V

where the subscript i denotes the direction of the applied uniaxial force and j denotes one of the other two directions on which only a hydrostatic pressure is acting. The expression in the brackets is evaluated at constant temperature and volume as identified by the subscripts T and V. The reader is referred to Treloar [16] and Ogden [35] for applications to other states of stress. The engineering stress s defined as the force per unit undeformed area follows from Equation (15) as t si ¼ (16) l The reduced force [ f ] is defined according to t ½ f n ¼ 2 (17) ðl  l1 Þ In the limit of small deformations, the reduced force equates to the shear modulus of the sample, that is, (18) G ¼ lim f n l!1

The expressions given in this section, which are explained in more detail in Erman and Mark [34], are general expressions. In the next section, we introduce two network models that have been used in the elementary theories of elasticity to relate the microscopic deformation to the macroscopic deformation: the affine and the phantom network models.

3.4 The affine network model One of the earlier assumptions regarding microscopic deformation in networks is that the junction points in the networks move affinely (linearly) with macroscopic deformation. It follows that chain end-to-end vectors deform affinely also, and  2    2    2   x ¼ l2x x2 0 y ¼ l2y y2 0 z ¼ l2z z2 0 (19)

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Substituting Equation (19) into Equation (13) in conjunction with Equation (1) leads to   1 f (20) DAel;affine ¼ xkTðl2x þ l2y þ l2z  3Þ 2 f2 A more rigorous statistical analysis [21] gives an additional volume term, mkT(V/V0) in Equation (20). This term does not appear in the simplified derivation presented here. The true stress for the uniaxial case is obtained by substituting Equation (20) into Equation (15) as   f xkT 2 t¼ ðl  l1 Þ (21) f  2 V0 The shear modulus Gaf of an affine network is obtained from Equations (17) and (18) as   j xkT nkT ¼ (22) Gaf ¼ j  2 V0 V0 where V0 is the volume during the formation of the network.

3.5 The phantom network model The instantaneous vector r joining two junctions at the extremities of a network chain may be written as the sum of a time-averaged mean r¯ and the instantaneous fluctuation Dr from this mean, that is, r ¼ r¯ þ Dr

(23)

According to the phantom network model, the fluctuations Dr are independent of deformation and the mean r¯ deform affinely with macroscopic strain. Squaring both sides of Equation (23) and averaging overall chains gives  2  2   (24) r ¼ r¯ þ ðDrÞ2 The average of the quantity hr¯  Dri has been equated to zero in obtaining Equation (24) in as much as this quantity is equally likely to be positive or negative because of the fluctuating term Dr, and the average overall possible occurrences vanishes. Equation (24) is valid in both the deformed and undeformed states. It may be written in terms of lx, ly , and lz as ! l2x þ l2y þ l2z  2   2   r¯ 0 þ ðDrÞ2 r ¼ 3 " 2 # !  lx þ l2y þ l2z 2 2  2 ð25Þ ¼ þ r 0 1 f f 3

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Equation (25) is obtained by use of    2 2  2 r¯ 0 ¼ 1  r 0 f   2  2 r 0 ðDrÞ2 0 ¼ f

347

ð26Þ

These two relations result from the phantom network model, as shown in derivations given elsewhere [4,25]. Using Equation (26) in Equation (25) and substituting the resulting expression into Equation (13) leads to 1 DAel;phantom ¼ xkTðl2x þ l2y þ l2z  3Þ (27) 2 Comparison of the expressions for the elastic free energies for the affine and phantom network models shows that they differ only in the front factor. Expressions for the elastic free energy of more realistic models than the affine and phantom network models are given in the following section. The true stress for the phantom network model is obtained by substituting Equation 27 into Equation 15: t¼

xkT 2 ðl  l1 Þ V0

(28)

and the shear modulus Gph is obtained from Equations (17) and (18) as Gph ¼

xkT V0

(29)

Equation (29) shows that the modulus is proportional to the cycle rank x, and that no other structural parameters contribute to the modulus. The number of entanglements trapped in the network structure does not change the cycle rank. Possible contributions of these trapped entanglements to the modulus therefore cannot originate from the topology of the phantom network.

3.6 More advanced molecular theories The models presented in the previous section are of an elementary nature in the sense that they ignore contributions from intermolecular effects (such as entanglements that are permanently trapped on formation of the network). Among the theories that take account of the contribution of entanglements are (i) the treatment of Deam and Edwards [36] in terms of topological invariants, (ii) the slip-link model [37,38], (iii) the constrained-junction and constrainedchain models [39–43], and (iv) the trapped entanglement model [23,24,44]. The slip-link, constrained-junction, and constrained-chain models can be studied under a common format as can be seen from the discussion by Erman and Mark [5]. For illustrative purposes we present the constrained-junction model in some detail here. We then discuss the trapped entanglement models.

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The constrained-junction model was formulated in order to explain the decrease of the elastic moduli of networks upon stretching. It was first introduced by Ronca and Allegra [39], and Flory [40]. The model assumes that the fluctuations of junctions are diminished below those of the phantom network because of the presence of entanglements and that stretching increases the range of fluctuations back to those of the phantom network. As indicated by the second part of Equation (26), the fluctuations in a phantom network are substantial. For a tetrafunctional network, the mean-square fluctuations of junctions amount to as much as half of the mean-square end-to-end vector of the network chains. The strength of the constraints on these fluctuations is measured by a parameter k, defined as   ðDRÞ2 k¼   (30) ðDsÞ2 where /(DR)2S and /(Ds)2S denote, respectively, the mean-square junction fluctuations in the phantom network and in the entanglement domain. If the range of fluctuations decreases to zero because of entanglements, k becomes infinitely large. If the effect of entanglements is nil, then k ¼ 0. The k parameter is proportional to the number of junctions in the volume occupied by a given network chain. Thus,    3=2 m k ¼ I r2 0 (31) V0 where I is the constant of proportionality. For a network with tetrafunctional junctions, k may be written   !3=2  1=2   N A d 3=2 r2 0 x (32) k¼I 2 V0 M where d is the density of the network and M is the molecular weight of chains between two cross-links. The elastic free energy of the constrained-junction model is given by the expression ( ) 3 3 X 1 mX 2 ½Bi þ Di  lnð1 þ Bi Þ  lnð1 þ Di Þ DAel ¼ xkT ðli  1Þ þ (33) 2 x i¼1 i¼1 where Bi ¼ k2 ðl2i  1Þðl2i þ kÞ

Di ¼ l2i k1 Bi

(34)

The true stress for the uniaxial case is obtained from Equations (15) and (33) as

where

 

xkT m 2 2 2 1 t¼ ðl  l Þ þ lKðl Þ  l Kðl Þ V0 x

(35)



_ þ 1Þ1 þ k1 ðl2 B_ þ BÞðB þ kl2 Þ1 Kðl2 Þ ¼ B BðB

(36)

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@B B_ ¼ 2 ¼ B ðl2  1Þ1  2ðl2 þ kÞ1 @l The reduced force is given as    n xkT m lKðl2 Þ  l2 Kðl1 Þ f ¼ 1þ V0 x l  l2

349

(37)

(38)

The shear modulus of the constrained-junction model is obtained in the limit of small deformations as    m k2 þ 1 2 G¼ 1þ k (39) Gph x ð1 þ kÞ4 which shows that for nonzero values of the parameter k, the shear modulus of the constrained-junction model is larger than the phantom network shear modulus. For the affine limit, k-N, the shear modulus is   m f Gph G¼ 1þ (40) Gph ¼ x f2 Equation (40) shows that the small deformation shear modulus of an affine network increases indefinitely over the phantom network modulus as junction functionality approaches 2. The slip-link model incorporates the effects of entanglements along the chain contour into the elastic free energy. According to the mechanism of the slip link, sketched in Figure 2, a link joins two different chains which may slide a distance a along the contour of the chains. The elastic free energy resulting from this model is ( " #) 3 3 2 X X 1 N ð1 þ ZÞl s i Ael ¼ N c kT l2i þ þ logð1 þ Zl2i Þ (41) 2 N c i¼1 1 þ Zl2i i¼1

Figure 2 Schematic drawing of a slip link, with its possible motions along the network chains specified by the distances a, and its locking into position as a cross-link.

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where Nc and Ns are the number of chemical cross-links and slip links, respectively, and Z ¼ 0.2343. The first term on the right-hand side of Equation (41) is the contribution to the elastic free energy from the phantom network. The effect of entanglements enters as a further contribution and is proportional to the number of slip links. The elastic free energy of the constrained-junction model, similar to that of the slip-link model, is the sum of the phantom network free energy and that due to the constraints. Both the slip-link and the constrained-junction model free energies reduce to that of the phantom network model when the effect of entanglements diminishes to zero. One important difference between the two models, however, is that the constrained-junction model free energy equates to that of the affine network model in the limit of infinitely strong constraints, whereas the slip-link model free energy may exceed that for an affine deformation, as may be observed from Equation (41).

3.7 Contribution of trapped entanglements to the modulus As already mentioned, the cycle rank x of a network denotes the number of chains that have to be cut in order to reduce the network to a tree, and the moduli of the phantom, affine, slip-link, and constrained-junction models are all proportional to it. The cycle rank is independent of the number of trapped entanglements in the cross-linked system. A network in which chains are highly entangled has the same cycle rank as one with no entanglements. Therefore the models cited above categorically reject contributions from trapped entanglements to the modulus. However, a large body of experiments has shown that certain fraction of trapped entanglements contribute to the modulus [23,24,44]. The contributions to the modulus are given by the widely used Langley equation G ¼ Gch þ Te G0N

(42)

Here, the modulus G is given as the sum of the modulus Gch due to chemical cross-links and the trapped entanglement term TeG0N, where Te (called the ‘‘Langley trapping factor’’) is the fraction of trapped entanglements that contribute to the modulus, and G0N is the plateau modulus related to the molecular weight Me between entanglement by the expression G0N ¼

rRT Me

(43)

According to the arguments based on the constrained-junction model, the term Gch should equate to the phantom network modulus onto which contributions from entanglements are added. Experimental determinations of the contributions above those predicted by the reference phantom network model have been controversial. Experiments of Rennar and Oppermann [45] on end-linked PDMS networks, indicate that contributions from trapped entanglements are significant for low degrees of endlinking but are not important when the network chains are shorter. Experimental results of Erman et al. [46] on randomly cross-linked poly(ethyl acrylate)

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networks indicate that the observed high deformation limit moduli are within the predictions of the constrained-junction model.

4. PHENOMENOLOGICAL THEORIES The elastic free energy given by the elementary and the more advanced theories are symmetric functions of the three extension ratios lx, ly , and lz. One may also express the dependence of the elastic free energy on strain in terms of three other variables, which are in turn functions of lx, ly , and lz. In phenomenological theories of continuum mechanics, where only the observed behavior of the material is of concern rather than the associated molecular deformation mechanisms, these three functions are chosen as I 1 ¼ l2x þ l2y þ l2z I 2 ¼ l2x l2y þ l2x l2z þ l2y l2z

(44)

I 3 ¼ l2x l2y l2z DAel ¼ DAel ðI 1 ; I 2 ; I 3 Þ

(45)

The most general form of the elastic free energy may be written as a power series 1 X DAel ¼ Cijk ðI 1  3Þi ðI 2  3Þ j ðI 3  1Þk (46) i;j;k¼1

where Cijk are the phenomenological coefficients. The simple case of the phantom and affine networks is obtained as the first term of the series DAel ¼ C100 ðI 1  3Þ

(47)

The elastic free energy of the so-called Mooney–Rivlin solid is obtained from Equation (46) as DAel ¼ C100 ðI 1  3Þ þ C010 ðI 2  3Þ

(48)

The reduced force follows from Equations (15) and (17) as 2C2 (49) l where C1 ¼ C100/V0 and C2 ¼ C010/V0. For large deformations, the reduced force equates to 2C1, which may be identified with the phantom network model modulus. For small deformations, 2C2 may be obtained by equating Equation (49) to Equation (39) for the constrained-junction model. Thus, ½ f n  ¼ 2C1 þ

2C1 ¼ Gph   m k2 þ 1 2 2C2 ¼ k Gph x ð1 þ kÞ4

(50) (51)

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Further references to the phenomenological treatment may be found in Treloar [16], Ogden [35], Erman and Mark [5], and Mark [47].

5. SOME RELEVANT SIMULATIONS 5.1 Gelation The formation of network structures necessary for rubber-like elasticity has been extensively simulated by Eichinger and coworkers [48]. The basic approach is to randomly end link functionally-terminated precursor chains with a multifunctional reagent, and then to examine the sol fraction with regard to amount and types of molecules present, and the gel fraction with regard to its structure and mechanical properties (see also Chapter 2). The systems most studied in this regard [48] involve PDMS chains having end groups X that are either hydroxyl or vinyl groups, with the corresponding Y groups on the end linking agents then being either OR alkoxy groups in an organosilicate, or H atoms in a multifunctional silane [5]. There was very good agreement between theory and experiment [49]. The Monte Carlo method for simulating these reactions was used to generate additional information on the vinyl–silane end linking of PDMS [49,50]. The simulations gave a very good account of the extent of reaction at the gelation points, but overestimated the maximum extent of reaction attainable. The discrepancy may be due to experimental difficulties in taking a reaction close to completion within a highly viscous, entangled medium. If cyclic molecules of PDMS are present during the end linking, they are trapped within the network if they are large enough to be penetrated by any of the precursor chains [5]. This ‘‘incarceration’’ process has also been successfully simulated [51].

5.2 Distribution functions and stress–strain isotherms One novel approach to obtaining non-Gaussian distribution functions utilizes the wealth of information that rotational isomeric theory provides on the spatial configurations of chain molecules. Specifically, Monte Carlo calculations based on the rotational isomeric state approximation were used to simulate spatial configurations and thus distribution functions for the end-to-end separations [52]. The results obtained documented the expected fact that the Gaussian distribution is generally a very poor approximation for short chains, or for the high extensions that are of primary importance with regard to ultimate properties. Another example of this approach is to determine how an applied force can change the distributions for a chain that can undergo a coil-to-helix transition upon deformation [53]. These Monte Carlo distributions can be used in the standard three-chain model for rubber-like elasticity to generate, for example, stress–strain isotherms [5]. Non-Gaussian effects can cause large increases in modulus at high

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elongations, because of the limited extensibilities of the network chains [16]. Thus, it is very useful to identify chain structures and chain lengths giving the largest increases in stress without unacceptable decreases in extensibility. This will, of course, maximize the area under the stress–strain curve, which represents the energy for rupture or toughness of the material [50]. One of the most interesting applications of this approach is to PDMS elastomers which have a bimodal distribution of network chain lengths [54] and, correspondingly, very good mechanical properties [5,27]. The upturns in modulus observed at high elongations are thought to be due to the very limited extensibilities of the short chains in the bimodal structures, with the long chains increasing extensibility, and this seems to be supported by the simulated results [52,55]. Because of the improvements in properties exhibited by elastomers having bimodal distributions [5], there have been attempts to prepare and characterize ‘‘trimodal’’ networks [56]. The calculations suggest that adding a small amount of very high molecular weight end-linkable polymer could further improve mechanical properties.

5.3 Crystallization There is now considerable interest in using simulations for characterizing crystallization in copolymeric materials. In particular, Windle and coworkers [57] have developed models capable of simulating chain ordering in copolymers composed of two comonomers, at least one of which is crystallizable. Typically, the chains are placed in parallel, two-dimensional arrangements. Neighboring chains are then searched for like-sequence matches in order to estimate extents of crystallinity. Chains stacked in arbitrary registrations are taken to model quenched (Q) samples. Annealed samples, on the other hand, are modeled by sliding the chains past one another longitudinally to search for the largest possible matching densities. The longitudinal movement of the chains relative to one another, out of register, approximately models the lateral searching (S) of sequences in copolymeric chains during annealing [50]. One example [58] of such a study involved modeling random and semiblocky poly(diphenylsiloxane-co-dimethylsiloxane) copolymers. In this example, the chains were placed alongside one another in a two-dimensional array, with black squares representing dimethylsiloxane (DMS) units and white squares representing diphenylsiloxane (DPS) units [58]. ‘‘Like’’ squares neighboring each other in the same row are then viewed as coalescing into blocks the lengths of which are under scrutiny. It is thus possible to identify crystallizable DPS regions as distinct from non-crystallizable DMS component, or units of the crystallizable DPS component that were not long enough to participate in the crystallization [58]. A value of the degree of crystallinity L of a simulated sample can then be determined by counting the units involved in the matching sequences relative to the total number of units of all the chains. The crystallites thus identified presumably act as cross-linking sites and reinforcing domains,

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providing the additional toughness the semi-blocky copolymers have over their random counterparts. A similar approach was used for polypropylene (PP), a stereochemically variable hydrocarbon polymer. It is of particular interest since it can be prepared in the form of a thermoplastic elastomer in which there are alternating runs of blocks of isotactic and atactic sequences. The trick (which has been accomplished by some catalysts) is to make the isotactic runs long enough to give crystallites with enough stability to act as cross-links, without making their sizes and numbers so large that the material is highly crystalline rather than elastomeric [59,60]. Of greatest interest is the case where the isotactic lengths are kept at a constant relatively large value while the atactic sequences are increased in length, thereby decreasing the overall content [mmmm] of meso placements (replications of dextro or levo chiralities). The simulations were consistent with the presence of crystallinity at overall levels of PP isotacticity sufficiently low to give completely amorphous polymers had the structures not been blocky.

5.4 Filler reinforcement Monte Carlo computer simulations were also carried out on filled networks [50,61–63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64]. Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress– strain isotherms in elongation. In one application, a filled PDMS network was modeled as a composite of cross-linked polymer chains and spherical filler particles arranged in a regular array on a cubic lattice [65]. The filler particles were found to increase the nonGaussian behavior of the chains and to increase the moduli, as expected. It is interesting to note that composites with such structural regularity have actually been produced [66] and some of their mechanical properties have been reported [67]. In a subsequent study, the reinforcing particles were randomly distributed within the PDMS matrix [50]. One effect of the filler was to increase the extensions of the chains, at least in the case of relatively small filler particles. This is illustrated in Figure 3. These results on the distributions are in agreement with some subsequent neutron scattering experiments on silicate-filled PDMS [68]. The corresponding stress–strain isotherms in elongation are shown schematically in Figure 4. The substantial increases in stress and modulus with increase in filler content and elongation are in at least qualitative agreement with experiment. Non-spherical filler particles are also of considerable interest [50,69]. Prolate (needle-shaped) particles can be thought of as a bridge between the roughly spherical particles used to reinforce elastomers and the long fibers frequently

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P(r)

Unfilled

Filled

0.0

0.0

r/rmax

Figure 3 Sketches of radial distributions for two network chains as a function of the fraction of their full extension. The presence of filler particles is seen to increase the end-to-end separation of the chain.

[f* ]

Filled

Unfilled

0.0 0.5

1/α

1.0

Figure 4 Mooney–Rivlin isotherms for the two chains described in Figure 3, showing the resulting increases in modulus due to the chains being stretched by the presence of the filler particles.

used for this purpose in thermoplastics and thermosets. Similarly, oblate (disc-shaped) particles can be considered as analogues of the much-studied clay platelets used to reinforce a variety of materials [70–73]. In the case of non-spherical particles, their orientations are also of considerable interest.

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6. SWELLING OF NETWORKS AND RESPONSIVE GELS Throughout the preceding discussion, the networks were assumed to be formed in the dry state and tested in the dry state. In recent years, much emphasis has been placed on swelling of networks and their phase transitions under different activities of the network-solvent system. Large-scale volume transitions triggered by small changes in environmental variables directed attention to possible uses of swollen gels in the field of responsive materials technologies. The transition involves the gel-exuding solvent, for example, upon decrease in temperature. The resulting shrinkage (‘‘syneresis’’) is widely known as ‘‘gel collapse’’, and is shown schematically for such a temperature-induced change in Figure 5. In the following discussion, charged systems will be considered in particular because the presence of charges facilitates the volume phase transitions in swollen gels. The change in free energy of a network upon swelling is taken as the sum of the change in the elastic free energy, DAel, and the change in free energy of mixing, DAmix and the contributions from ionic groups DAi: DA ¼ DAel þ DAmix þ DAi

(52)

is where DAel may be taken as any of the expressions resulting from a model, DAmix the free energy of mixing, and DAi the contribution of the ionic groups on the chains. The total chemical potential Dm1 of solvent in the swollen network is obtained for the constrained-junction model as      Dm1 1 rV 1 m V1 v2 2 2 ¼ lnð1  v2 Þ þ v2 þ wv2 þ 1 þ Kðl Þ  in (53) l Mc x RT V0 N A v20 where v2 is the volume fraction of polymer, w the Flory interaction parameter, V1 the molar volume of solvent, Mc the molecular weight of a network chain, and l

Shrinkage

Wt % polymer in gel

Lightly swollen

Highly swollen Temperature

Figure 5 A gel exuding solvent upon decrease in temperature, with the shrinkage (‘‘syneresis’’) generally described as ‘‘gel collapse’’.

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the extension ratio, defined for the swelling case as  1=3   V n1 V 1 þ xV 1 n2 l¼ ¼ (54) V0 V0 Here, x is the number of repeat units in one network chain, n1 the number of solvent molecules, n2 the total number of network chains in the system, i the number of ionic groups on the chains, n the number of chains, and v20 the volume fraction of chains during the formation of the network. Equating the chemical potential to zero gives a relationship between the equilibrium degree of swelling and the molecular weight Mc. The relation for Mc,ph is obtained for a tetrafunctional phantom network model as Mc;ph ¼ 

1=2ðrV 1 Þðv2 =v20 Þ1=3 lnð1  v2 Þ þ v2 þ wv22  inðV1 =V 0 N A Þðv2 =v20 Þ

(55)

where v2 denotes the equilibrium degree of swelling. For the affine network model, the molecular weight between cross-links Mc,af is obtained as  1=3 rV 1 v2  ðv2 =2v20 Þ (56) Mc;af ¼  lnð1  v2 Þ þ v2 þ wv22  inðV 1 =V 0 N A Þðv2 =v20 Þ Alternatively, the chemical potential expression may be solved for v2, leading to a value for the degree of swelling of the network. The result shows that the degree of swelling increases as the chain length between cross-links increases. The dominant forces that operate in swollen uncharged gels are van der Waals forces, hydrogen bonds, hydrophobic forces, and forces resulting from chain entropy. When the network chains contain ionic groups, there will be additional forces that affect their swelling properties. Translational entropy of counterions, Coulomb interactions, and ion pair multiplets are forces that lead to interesting phenomena in ion-containing gels. These phenomena were studied in detail by Khokhlov and collaborators [74–77]. The free energy of the networks used by this group is DA ¼ DAmix þ DAel þ DAtrans þ DACoulomb

(57)

where DAtrans and DACoulomb are the contributions to the elastic free energy of the networks from the translational entropy of the counterions and the free energy of Coulomb interactions. Several interesting features of gels are obtained through the use of Equation (57). A network chain of a polyampholyte gel contains both positive and negative charges. The liquid phase in the swollen polyampholyte gel may contain additional counterions. The theoretical and experimental literature on such gels was reviewed recently by Nisato and Candau [78]. In ion-containing gels, when ion-containing groups are fully dissociated the gel swells excessively, because of the tendency of the free counterions to occupy as much space as possible. In the other extreme case, called the ionomer regime, counterions are condensed on oppositely charged monomer units, forming ion pairs followed by formation of multiplets. This decreases the osmotic pressure of the gel and results

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in its collapse. The conditions for ion pair formation and physical and chemical factors leading to gel swelling and collapse have been discussed by Khokhlov and Philippova [79].

7. ENTHALPIC AND ENTROPIC CONTRIBUTIONS TO RUBBER ELASTICITY: THE FORCE–TEMPERATURE RELATIONS The major component of elasticity of a network arises from the ‘‘entropic elasticity’’ of the individual chains. This was the basic assumption of the early molecular theories of rubber elasticity [5]. A closer consideration of the statistics of the single chain shows that the rotational isomeric states allowable to each torsion angle of the chain are not of the same energy, and stretching a chain or changing the temperature may move them from one isomeric minimum to a more favorable one. This results in an energetic contribution to the elasticity of a chain. Thus the total force acting on a network may be written as the sum of an entropic contribution, fs, and an energetic contribution, fe f ¼ fs þ fe

(58)

Force–temperature (‘‘thermoelastic’’) relations lead to a quantitative assessment of the relative amounts of entropic and energetic components of the elasticity of the network. In uniaxial deformation, the energetic contribution to the total elastic force [4,5,16,80–82] is given by the thermodynamically exact relation   fe @ lnðf=TÞ T (59) @T f L;V The subscripts L and V denote that differentiation is performed at constant length and volume. To carry out the differentiation indicated in Equation (59), an expression for the total tensile force f is needed. One may use the expression given by Equation (28) for the phantom network model. Applying the right-hand side of Equation (59) to Equation (28) leads to   f e Td ln r2 0 ¼ (60) f dT Equation (60) is important because the right-hand side relates to a microscopic quantity, /r2S0, and the left-hand side is the thermodynamic ratio of the energetic component of the force to the total force, both macroscopic quantities. It should be noted that Equation (60) is obtained by using a molecular model. Experimentally, the determination of the force at constant volume is not easy. For this reason, expressions for the force measured at constant length and pressure p or constant a and p are used. These expressions are   fe @ lnðf=TÞ bT T (61)  3 @T ða f  1Þ L;p

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Some typical values for fe/f

Elastomer

fe/f

Natural rubber cis-1,4-Polybutadiene Poly(dimethylsiloxane) Elastin

0.18 0.13 0.20 0.26

  fe @ lnðf=TÞ bT T  @T 3 f a;p

(62)

where b is the thermal expansion coefficient of the network. It should be noted, however, that both of these equations are derived on the basis of the equation of state for simple molecular models and therefore are not quantities based purely on experimental data. Values of the energetic contribution for some typical elastomers are given in Table 1.

8. MULTIMODAL ELASTOMERS 8.1 General information The main purpose of this section is to illustrate how manipulating the distribution of network chain lengths in an elastomer can give large improvements in its mechanical properties. The preparation of such networks of controlled structures obviously requires special cross-linking reactions. In fact, a variety of ‘‘model’’ networks can now be prepared using new synthetic techniques that closely control the placements of cross-links in a network structure [5,83,84]. Specifically, end-linking functionally-terminated chains, instead of haphazardly joining chain segments at random, controls the structure of the resulting network. The functionality of a cross-link is the same as the number of functional groups on the end-linking agent. More important in the present context, the molecular weight Mc between cross-links and its distribution are the same as those of the starting chains prior to their being end linked [85–87].

8.2 Bimodal networks 8.2.1 Background With regard to elastomers of controlled structure, those having unusual distributions of network chain lengths have been of particular interest [88,89]. The most novel elastomer of this type consists of a binary combination of unusually short network chains (molecular weights of a few hundred) and the much longer chains typically associated with elastomeric behavior (molecular weights of ten or twenty thousand). Such a network is sketched in Figure 6.

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Figure 6 A network having a bimodal distribution of network chain lengths. The short chains are arbitrarily shown by heavier lines than the long chains, and the dots represent the crosslinks, typically resulting from the end linking of functionally terminated chains.

As mentioned earlier, ‘‘bimodal’’ elastomers prepared by these end-linking techniques have very good ultimate properties, and for this reason there is currently much interest in preparing and characterizing such materials [88,90,91]. There is, of course, a long history of theoretical work in the area of rubber-like elasticity but almost all of it is based on monodisperse network chainlength distributions. Interest is now developing, however, in developing theoretical interpretations for the novel mechanical properties of bimodal elastomers [92–101].

8.2.2 Materials and synthetic techniques Most bimodal networks synthesized to date have been prepared from PDMS [88]. One reason for this choice is the fact that the polymer is readily available with either hydroxyl or vinyl end groups, and the reactions these groups participate in are relatively free of complicating side reactions. These ideas can obviously be extended to higher modalities (trimodal, etc., eventually approaching an extremely broad, effectively-unimodal distribution) [102–104]. The distribution of network chain lengths in a bimodal elastomer can be extremely unusual, and much different from the usual unimodal distribution obtained in less-controlled methods of cross-linking. In the important example, there is simultaneously a large number percent of short chains and a large weight percent of long chains. The major difference is the large amounts of both very short chains and very long chains in the bimodal network, which contrasts sharply with the small amounts of such chains in a typical unimodal distribution. The case where the short chains predominate numerically is of particular interest with regard to improvements in mechanical properties [5,27].

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8.2.3 Elongation results The great majority of studies of mechanical properties of elastomers of any type have been carried out in elongation, because of the simplicity of this type of deformation [5,89]. In the case of the bimodal materials, many of the stress–strain isotherms in elongation were obtained on PDMS elastomers in the vicinity of 251C, a temperature sufficiently high to suppress strain-induced crystallization. The results thus determined were of considerable interest since they indicated that the bimodal nature of the distribution greatly improved the ultimate properties of the elastomer [88]. This is illustrated schematically in Figure 7, in which the data are plotted in such a way that the area under a stress–strain isotherm up to the point of failure corresponds to the energy required to rupture the network. If the network consists entirely of the short-chain component, then it is brittle (which means that the maximum extensibility is small). Similarly, if the network consists of only the long-chain component, its ultimate strength is very low. As a result, neither type of unimodal material has a large area under its stress–strain curve and, thus, neither is a tough elastomer. As can readily be seen from Figure 7, the bimodal networks are much-improved elastomers in that they can have a high ultimate strength without the usual diminished maximum extensibility. This corresponds to high values of the energy required for rupture, which makes them unusually tough elastomers, even in the unfilled state. Apparently the short chains act primarily to increase the ultimate strength through their limited deformability, while the long chains somehow thwart the spread of rupture nuclei that would otherwise lead to catastrophic failure. If true, this could be analogous to what executives like to call a ‘‘delegation of responsibilities’’. It should be pointed out that there are three requirements for obtaining these improvements. The first is that the ratio MS/ML of molecular weights of the short (MS) and long chains (ML) be very small (i.e., that their molecular weights be very different). The second is that the short chains be as short as possible; for example, a network having network chain molecular weights of 200 and 20,000 g/mol

Bimodal

f*

Short-chain unimodal

Long-chain unimodal

α

Figure 7 Typical dependence of nominal stress against elongation for two unimodal networks having either all short chains or all long chains, and a bimodal network having some of both.

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would be expected to show much greater improvements from the biomodality than one having molecular weights of 2,000 and 200,000. Finally, there should be a large number concentration of the short chains, typically around 95 mol.%. Quantitative characterization of this limited chain extensibility requires, of course, a non-Gaussian distribution function [16] for the end-to-end separation r of the short network chains. One approach is based on the Fixman–Alben distribution [33], which was used [34] to calculate stress–strain isotherms in elongation for bimodal PDMS networks. Good agreement was found between theory and experiment. Other non-Gaussian distribution functions have also been successfully used for this purpose [5,105,106]. The experimental isotherms can also be interpreted using the van der Waals theory of rubber-like elasticity [5,107,108]. Another approach involves the Monte Carlo simulations described above. It utilizes the wealth of information that rotational isomeric state theory provides on the spatial configurations of chain molecules. In brief, Monte Carlo calculations based on the rotational isomeric state approximation are used to simulate spatial configurations and thus distribution functions for the end-to-end separations of the chains [20,55]. These distribution functions are then used in place of the Gaussian function in the standard three-chain model [16] in the affine limit to give the desired non-Gaussian theory of rubber-like elasticity. Stress– strain isotherms calculated in this way are strikingly similar to the experimental isotherms obtained for the bimodal networks [5,20,55]. The overall theoretical interpretations are thus quite satisfactory and would encourage other applications of these distributions, for example, to segmental orientation in networks containing very short chains. Such segmental orientation is of critical importance, for example, with regard to strain-induced crystallization. PDMS networks were found to be unsuitable for characterizing the effects of bimodality on strain-induced crystallization, because of their very low crystallization temperatures. The polymer chosen instead for these end-linked bimodal networks was poly(ethylene oxide), which has a relatively high melting point (B651C) and thus readily undergoes strain-induced crystallization [109]. The aspect of relevance here is the use of these networks to elucidate the dependence of strain-induced crystallization on network chain length distribution. Decrease in temperature was found to increase the extent to which the values of the ultimate strength of the bimodal networks exceed those of the unimodal ones [109]. These results suggest that bimodality facilitates strain-induced crystallization [5], possibly through increased orientation of the more easily crystallizable long chains, into crystallization nuclei. Similar conclusions have been reached in studies of elongated bimodal networks of poly(tetrahydrofuran) [110]. In practical terms, the above results demonstrate that short chains of limited extensibility may be bonded into a long-chain network to improve its toughness. It is also possible to achieve the converse effect. Thus, bonding a small number of relatively long elastomeric chains into a short-chain PDMS thermoset greatly improves both its energy of rupture and impact resistance [111–113]. Approximately 95 mol.% short chains give the maximum effect for the molecular weights involved. Lower concentrations give smaller improvements than can otherwise

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be achieved, and higher concentrations will convert the composite from a relatively hard material into one that is more rubber-like.

8.2.4 Results in other mechanical deformations Equi-biaxial extension results have been obtained by inflating sheets of unimodal and bimodal networks of PDMS [114,115]. Upturns in the modulus were found to occur at high biaxial extensions, as expected. Also of interest, however, are pronounced maxima preceding the upturns. Such dependences represent a challenging feature to be explained by molecular theories addressed to bimodal elastomeric networks in general. In shear measurements on some unimodal and bimodal networks of PDMS [116], the bimodal PDMS networks showed large upturns in the pure-shear modulus at high strains, which were similar to those reported for elongation and biaxial extension. Tear tests have been carried out on bimodal PDMS elastomers [117–119], using the standard ‘‘trouser-leg’’ (tear strength) method. Tear energies were found to be considerably increased by the use of a bimodal distribution, with documentation of the effects of compositional changes and changes in the ratio of molecular weights of the short and long chains. The increase in tear energy did not seem to depend on tear rate [117], an important observation that seems to suggest that viscoelastic effects are not of great importance in explaining the observed improvements. A subsequent series of shear tests [118] established the dependence of the tearing properties on the composition of the bimodal networks and the lengths of the chains used to prepare them. The observed increases in strength with decreases in the molecular weight of the short chains must eventually become decreases when the chains become too short to have any elastic effectiveness at all. Some viscoelasticity results have been reported for bimodal PDMS [120], using a Rheovibron (an instrument for measuring the dynamic tensile moduli of polymers). Also, measurements have been made on permanent set for PDMS networks in compressive cyclic deformations [121]. There appeared to be less permanent set or ‘‘creep’’ in the case of the bimodal elastomers. This is consistent in a general way with some early results for polyurethane elastomers [122]. Specifically, cyclic elongation measurements on unimodal and bimodal networks indicated that the bimodal ones survived many more cycles before the occurrence of fatigue failure. The number of cycles to failure was found to be approximately an order of magnitude higher for the bimodal networks, at the same modulus at 10% deformation [5]!

8.2.5 Results of non-mechanical properties Birefringence measurements have been shown to be very sensitive to bimodality, and have therefore also been used to characterize non-Gaussian effects resulting from it in PDMS bimodal elastomers [5,123]. The freezing points of solvents absorbed into bimodal networks are also of interest since solvent molecules constrained to small volumes form only relatively small crystallites upon crystallization, and therefore exhibit lower crystallization temperatures [124–126]. Some differential scanning calorimetry (DSC) measurements on

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solvent molecules constrained in the pores of PDMS elastomers gave evidence for several crystallization temperatures, which could be indicative of an unusual distribution of pore sizes. Calorimetric measurements on bimodal poly(ethylene oxide) networks indicated that the short chains seemed to decrease the amount of crystallinity in the unstretched state [127]. This is an intriguing result since they increase the extent of crystallization in the stretched state. A similar study on poly(tetrahydrofuran) did not show any decrease, however [128]. Additional insights into the dynamics and structure of bimodal elastomers have been obtained by dynamic light-scattering experiments [129], neutron scattering experiments [130] and calculations [131], dual cross-linking system experiments [132], non-affine swelling [133], and the computer simulations already mentioned.

8.2.6 Other materials in which bimodality might be advantageous There appear to be other cases where a bimodal distribution of chain length or some other physical property can be advantageous, possibly again through this idea of a ‘‘delegation of responsibilities’’ [5] (see earlier in Section 8.2.3). For example, in the area of thermosets, there seems to be an improvement in mechanical properties when the polymer being cured has a bimodal distribution of molecular weights [112]. In this case, the improvements may be due to different morphologies and degrees of inhomogeneity [113,134] resulting from the fact that the long chains in a bimodal distribution could have considerably lower solubilities than the short chains. Also, it is well known that the flow characteristics of a polymer during processing [135] can frequently be adjusted by the addition of a small amount of polymer of either very low or very high molecular weight. Another example is in the area of rubber-toughened thermoplastics in which an elastomer is dispersed as domains within the thermoplastic matrix to improve its mechanical properties [136,137]. It has been reported that a bimodal distribution of particle sizes gives the largest improvements [138–140]. Perhaps the small particles are most efficient at stopping one type of failure mechanism, and the large particles another type. In a related application, there is the possibility that a mixture of two chemically different particles, such as silica and titania [141], could have significant advantages in elastomer reinforcement, with one perhaps functioning best at moderate temperatures and the other at elevated temperatures. There is also interest in bimodal distributions of particle sizes in electrorheological fluids [142] and in stimuli-responsive films [143].

8.3 Trimodal networks 8.3.1 Experimental results Although there have been attempts to evaluate the mechanical properties of trimodal elastomers, this has not been done in any organized manner. The basic problem is the large number of variables involved, specifically three molecular weights and two independent composition variables (mol fractions); this makes it practically impossible to do an exhaustive series of relevant experiments. For this

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reason, the only mechanical property experiments that have been carried out have involved arbitrarily chosen molecular weights and compositions [102,103,144]. Perhaps, not surprisingly, only modest improvements have been obtained over the bimodal materials.

8.3.2 Results from theory and simulations Some recent computational studies [92], however, indicate that it is possible to do simulations to identify those molecular weights and compositions that should maximize further improvements in mechanical properties. Such simulations are being extended to search for optimum properties of trimodal networks, specifically: (i) the elastic modulus, (ii) maximum extensibility, (iii) tensile strength, and (iv) segmental orientability. Results to date [56] suggest that a trimodal network prepared by incorporating small numbers of very long chains into a bimodal network of long and short chains could have significantly improved ultimate properties.

9. LIQUID–CRYSTALLINE ELASTOMERS 9.1 General information In the phrase ‘‘liquid–crystalline’’, the ‘‘crystalline’’ adjective refers to the fact that these materials are sufficiently ordered to diffract an X-ray beam in a way analogous to that of normal crystalline materials. On the other hand, the ‘‘liquid’’ part specifies that there is frequently sufficient disorder for the material to flow like a liquid [145]. The disorder is typically in one dimension as is the case, for example, with rod-like molecules having their axes all parallel but out of register with regard to their lengths. Both low molecular weight materials [145] and polymers [146,147] can show liquid crystallinity. In the case of polymers, it frequently occurs in very stiff chains such as the Kevlarss and other aromatic polyamides. It can also occur with flexible chains, however, and it is these flexible chains in the elastomeric state that are the focus of the present discussion. One reason such liquid– crystalline elastomers are of particular interest is the fact that (i) they can be extensively deformed (as described for elastomers throughout this chapter), (ii) the deformation produces alignment of the chains, and (iii) alignment of the chains is central to the formation of liquid–crystalline phases. Because of fascinating properties related to their novel structures, liquid–crystalline elastomers have been the subject of numerous studies, as described in several detailed reviews [148–150]. The purpose here will be to mention some typical elastomers exhibiting liquid crystallinity, to describe some of their properties, and to provide interpretations of some of these properties in molecular terms. The types of liquid–crystalline phases of interest can be defined by the direction describing the preferred orientation (see Chapter 8). The limits are the usual completely ordered (crystalline) and completely disordered (isotropic) phases, with a nematic liquid–crystalline phase (‘‘mesophase’’) between them.

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Figure 8 Liquid–crystalline polymers in which the mesomorphic sequences occur in the sidechain (middle), in the chain backbone (top), or in both (bottom) (‘‘combination’’ structures).

The oriented parts can be entire molecules in the case of low molecular weight compounds, but only sequences along the chain backbone in the case of polymers. In the nematic case, the disorder is the already-mentioned sliding of segments relative to one another to place them out of register. There are also a variety of smectic liquid–crystalline phases, in which layers of molecules or chain sequences occur in layers that are disordered relative to one another. In contrast, cholesteric phases have layers of nematic arrangements that are stacked in rotated arrangements, and a similar stacking occurs in the case of the discotics. In the case of polymers, there can be liquid–crystalline arrangements that involve the side chains attached to the chain backbones. Figure 8 illustrates the three possibilities: groups that can form liquid–crystalline phases occurring in the backbones, in the side chains, and in both (in what are called ‘‘combination’’ structures) [20]. In the case of the side-chain structures, the length of the ‘‘spacer’’ connecting the group to the backbone is of great importance.

9.2 Main-Chain liquid–crystalline elastomers 9.2.1 Poly(diethylsiloxane) The polymer in this category that has been the most studied is poly(diethylsiloxane) (PDES) [–Si(OC2H5)2O–]n. Of greatest interest has been its formation of nematic liquid–crystalline phases, and relevant studies have covered a wide variety of its properties [20]. These studies have included structural changes during transitions [151], effects of stretching on the transitions [152], mechanical properties in general [153], characterization using atomic force microscopy (AFM) [154] or X-ray diffraction [155], and responses of guest chains in deformed PDES elastomers [156].

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One item of great interest with regard to these materials is the temperature at which the nematic liquid–crystalline phase becomes isotropic. Such isotropization (‘‘clearing’’) temperatures Ti have been reported for a variety of symmetric polysiloxanes polymers having repeat units [Si((CH2)mCH3)2–O–][20]. PDES elastomers show values of Ti that significantly decrease with decrease in molecular weight. In fact, the liquid–crystalline phase does not form at all if M is below approximately 25,000 g/mol. This is in sharp contrast to the behavior of low molecular weight liquid–crystalline molecules; many cholesterol molecules that show mesophases have molecular weights down in the hundreds [145]. Since stretching a PDES aligns the chains in the direction of the liquid– crystalline structures, the values of Ti should also increase with elongation, and this is indeed found to be the case [157].

9.2.2 Other acyclic polysiloxanes Symmetric polysiloxanes having m ¼ 29 have also been investigated, with some properties listed in several articles in a handbook [158], and elsewhere [20]. The isotropization temperatures reported in these studies show a very interesting increase with increase in the number m of methylene groups in the side chains [159]. As one interesting example, the results indicate that the predicted value of Ti for PDMS lies below its value of Tm (melt temperature). This means that PDMS does not show a liquid–crystalline phase because it crystallizes before it gets to the lower temperature required. Another interesting feature pertains to the melting points cited for the polymers having m ¼ 6–9. The side chains are now long enough to crystallize themselves, which is apparently the reason that formation of mesophases is suppressed. Such side-chain crystallization has also been involved in polysilane homopolymers [160], and chemical copolymers of polyethylene [161,162], the so-called linear lowdensity polyethylenes (see Chapter 4). In any case, such crystallization presumably could also interfere with formation of the mesophases that might otherwise occur.

9.2.3 Some polysiloxanes with cyclic groups in the backbone Polysiloxanes in this category typically contain cyclics of –Si(CH3)2–O– siloxane units of various sizes, or such siloxane units mixed with some carbosiloxanes (with additional –CH2– sequences) [163–165]. The cyclic portions can add considerable stiffness, resulting in isotropization temperatures above the polymers’ decomposition temperatures.

9.2.4 Polyphosphazenes A number of polyphosphazenes of repeat unit [–PRRuN–] also exhibit liquid– crystalline phases [166–168]. It is certainly intriguing that apparently the only classes of flexible chains that extensively exhibit liquid–crystalline phases are the polysiloxane and polyphosphazene semi-inorganic polymers.

9.2.5 Some mechanical properties in elongation One aspect of this type of behavior involves the already mentioned increase in the isotropization temperatures with increase in elongation [169–171]. Also of

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Lowest

f

High

Lower

0 α

Figure 9 Illustrative stress–strain isotherms for poly(diethylsiloxane), as a function of the amount of mesophase present.

importance, of course, are the stress–strain isotherms themselves. Some obtained for PDES as a function of degree of mesomorphic structure are shown schematically in Figure 9 [152]. The curves show yield points akin to those shown by partially crystalline polymers, and the overall shapes of the curve differ greatly with decrease in the amounts of mesophase present, either present initially or induced by the deformation. As is generally the case, formation of a second phase leads to irreversibility in the stress–strain isotherms [152]. The larger the elongation during the deformation, the larger the irreversibility (hysteresis) upon completing the retraction part of the cycle.

9.3 Side-Chain liquid–crystalline elastomers 9.3.1 Some general aspects In this category, the units giving rise to the liquid–crystalline behavior can be in the backbone (as already discussed), in the side chains, or in both [172]. Of considerable interest is the orientation of the mesogenic groups and the chain backbones to which they are attached [173,174]. Frequently-studied backbones include siloxanes and acrylates [175,176], but a variety of other structures have also been studied, including amphiphilics [177]. The side chains in these structures can rearrange into positions either parallel or perpendicular to the deformed chain backbone. [178]. The outcome depends particularly on the nature and length of the flexible spacer connecting the mesogenic groups to the chain backbone. As expected the physical properties can become strongly anisotropic [179]. It has been long known that some liquid–crystalline materials of this type could be oriented by imposing an electric or magnetic field [180]. The chains

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could also be aligned when these liquid–crystalline elastomers are deformed (generally in elongation but also in some cases in compression), and then crosslinked into network structures. The major focus in these experiments was how the mechanical deformation affected the nature of the mesophase (in particular its axial direction relative to the direction of the strain), and its isotropization temperature. The studies generally involved measurements of both stress and birefringence as a function of strain, and the ratio of the former to the latter (the ‘‘stress-optical coefficient’’). The mesogenic behavior of such networks obviously depends strongly on their structures. For example, the effects of degree of cross-linking, and composition in the case of copolymers, have been documented [181]. The phase transitions depend significantly on spacer length, as has been demonstrated, for example, for oligo-oxyethylene spacers [182]. Closer coupling between the mesogenic groups and the polymer backbone tends to make the system more sensitive to the mechanical deformation, at least in the case of methylene groups making up the spacer [183]. Cross-linking can generally be induced by gamma radiation or chemical means [184], and it has been observed that relatively high degrees of crosslinking can be introduced without destroying the liquid crystallinity [185]. Infrared (IR) spectroscopy and stress–strain measurements in extension indicated that relatively low strains may frequently induce significant organization. One relevant experiment involved two cross-linking procedures: the first cross-linking produced a network in which the mesogenic units could be oriented [186], while the second subsequently locked in the network anisotropy. Samples were found to be clear and to have X-ray diffraction patterns characteristic of a highlyordered nematic material. Also of interest was the fact that transitions from the isotropic phase to the nematic phase caused significant increases in length. Using one or two cross-linking agents in the presence of a magnetic field could also be used to prepare ‘‘Monodomain’’ nematics (in which the director alignment is claimed to be macroscopically uniform) [187]. The thermoelastic behavior of these materials has also been reported [188]. Such experiments resolve the nematic to isotropic transition into entropic and enthalpic contributions as already described, and provides values of the corresponding energetic and entropic parts of the force, fe and fs [175] (see Section 7).

9.3.2 Discotic, cholesteric, and smectic elastomers Considerably less work has been done on discotic liquid–crystalline elastomers [189,190] and cholesteric elastomers [191]. The same seems to be true for smectic elastomers [192,193], even though some of them have the additional interesting property of being chiral [194,195].

9.3.3 Ferroelectric and piezoelectric elastomers In addition, some liquid–crystalline elastomers are ferroelectric (possess spontaneous electric polarization) [196,197], or piezoelectric (become electrically

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polarized when mechanically strained, and become mechanically strained when exposed to an electric field) [198,199].

9.3.4 Photonic elastomers Finally, some liquid–crystalline elastomers exhibit interesting photonic effects [200,201]. Of particular importance are non-linear optical properties. These involve interactions of light with the elastomer in a way that some of the characteristics of the incident light change, specifically its phase or frequency (including frequency doubling or frequency mixing) [202,203].

9.4 Theory As would not be surprising, given the unusual properties cited in this overview, liquid–crystalline elastomers have been the focus of numerous theoretical investigations [148–150,204–207]. These theoretical treatments extend over a wide range of sophistication and rigor. The simplest physical picture of nematic elasticity can be visualized by the lattice theory, in which semi-flexible chains are assumed to be embedded in an isotropic lattice of solvent molecules. The semiflexible chains consist of rods of m freely jointed segments of length l, which determines their stiffness. Stretching of the chains orients the segments in a way that increases strongly with increasing stiffness of the chains. Calculations based on a lattice model [205] show an abrupt jump in the segmental orientation function at a finite stretch ratio, and this corresponds to the isotropic-nematic transition. Below the transition, the sample behaves close to isotropic Gaussian elasticity. At a fixed uniaxial force, the transition is marked by a sudden elongation, resulting from the abrupt alignment of the segments along the direction of the force during the transition. Above the transition point the segments are highly oriented along the direction of stretch, and the network is nematic.

10. NOVEL REINFORCED ELASTOMERS 10.1 Sol–Gel in-situ precipitated ceramic particles Some elucidation of the mechanism of elastomer reinforcement is being obtained by precipitating chemically-generated fillers into network structures rather than blending badly agglomerated filler particles into elastomers prior to their crosslinking. This has been done for a variety of fillers, for example, silica by hydrolysis of organosilicates, titania from titanates, alumina from aluminates, etc. [85–87]. A typical, and important, reaction is the acid- or base-catalyzed hydrolysis of tetraethylorthosilicate: SiðOC2 H5 Þ4 þ 2H2 O ! SiO2 þ 4C2 H5 OH

(63)

Reactions of this type are much used by the ceramists in the new sol–gel chemical route to high-performance ceramics [208]. In the ceramics area itself, the

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advantages are the possibility of using low temperatures, increased purity of the products, control of ultrastructure (at the nanometer level), and relative ease of forming ceramic alloys. In the elastomer-reinforcement area, the advantages include the avoidance of the difficult, time-consuming, and energy-intensive process of blending agglomerated filler into high molecular weight (highviscosity) polymer, and the ease of obtaining extremely good dispersions. In the simplest approach to obtaining elastomer reinforcement, some of the organometallic material is absorbed into the cross-linked network, and the swollen sample placed into water containing the catalyst, typically a volatile base such as ammonia or ethylamine [4,5,209–211]. Hydrolysis to form the desired silica-like particles proceeds rapidly at room temperature to yield the order of 50 wt.% filler in less than an hour. The particles formed are generally approximately spherical, and are well dispersed and essentially unagglomerated, which suggests that the sol–gel reaction within the elastomer may involve simple homogeneous nucleation. This is consistent with the fact that particles growing independently of one another and separated by cross-linked polymer would not agglomerate unless very high concentrations were reached. The particles appear to have a relatively narrow size distribution, with almost all of them having ˚. diameters in the range 200–300 A Such in-situ generated particles can increase the modulus by more than an order of magnitude, and the stress–strain isotherms show the upturns at high elongation that are the signature of good reinforcement [212]. As generally occurs in filled elastomers, there is considerable irreversibility in the isotherms, which is thought to be due to irrecoverable sliding of the chains over the surfaces of the filler particles. If the hydrolyses in organosilicate-polymer systems are carried out with increased amounts of the silicate, bicontinuous phases can be obtained (with the silica and polymer phases interpenetrating one another) [213]. At still-higher concentrations of the silicate, the silica generated becomes the continuous phase, with the polymer dispersed in it. The result is a polymer-modified ceramic, variously called an ‘‘ORMOCER’’ [214,215], ‘‘CERAMER’’ [216,217], or ‘‘POLYCERAM’’ [218,219]. It is obviously of considerable importance to determine how the elastomeric phase modifies the ceramic in which it is dispersed. The hardness of PDMS-SiO2 composites of this type can be varied greatly by changing the ratio of organic-to-inorganic character, as measured by the molar ratio of organic R groups to Si atoms. Low values of the R/Si ratio yield a brittle ceramic, and high values yield a reinforced elastomer. The most interesting range of R/Si values, in the vicinity of unity, gives a hybrid material that can be viewed as either a ceramic of reduced brittleness or an elastomer of increased hardness, depending on one’s point of view.

10.2 Non-Spherical particles Reinforcing fillers can be deformed from their usual approximately spherical shapes in a number of ways. For example, if the particles are a glassy polymer such as polystyrene (PS), then deforming the matrix in which they reside at a

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Figure 10 Deformation of spherical filler particles into prolate (needle-shaped) ellipsoids; see text for details.

temperature above the glass transition temperature of PS will convert them into ellipsoids. This is illustrated in Figure 10. Uniaxial deformations give prolate (needle-shaped) ellipsoids, and biaxial deformations give oblate (disc-shaped) ellipsoids [220,221]. Prolate particles can be thought of as a conceptual bridge between the roughly spherical particles used to reinforce elastomers and the long fibers frequently used for this purpose in thermoplastics and thermosets. Similarly, oblate particles can be considered as analogues of the much-studied clay platelets used to reinforce a variety of materials [70–73], but with dimensions that are controllable. In the case of nonspherical particles, their orientations are also of considerable importance. One interest here is the anisotropic reinforcements such particles provide, and there have been simulations to better understand the mechanical properties of such composites [86,222].

10.3 Magnetic particles Incorporating reinforcing particles that respond to a magnetic field is important with regard to aligning the particles to improve mechanical properties anisotropically [223–226]. In related work, some in-situ techniques have been used to generate electrically conducting fillers such as polyaniline within an elastomeric material [227].

10.4 Layered fillers Exfoliating layered particles such as the clays, mica, or graphite is being used to provide very effective reinforcement of elastomers at loading levels much smaller than in the case of solid particles such as carbon black and silica [228–231]. Other properties can also be substantially improved, including increased resistance to solvents, and reduced permeability and flammability.

10.5 Polyhedral oligomeric silsesquioxanes (POSS) These fillers are cage-like silicon–oxygen structures, and have been called the smallest possible silica particles. The most common structure has eight

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silicon atoms, each carrying an organic group. The particles on which none of the groups are functionally reactive can be simply blended into elastomers using the usual mixing or compounding procedures. In this case, the groups are chosen to improve miscibility with the elastomeric host matrix. In contrast, those particles having one reactive functional group can be attached to a polymer as side chains. Those with two reactive groups can be incorporated into polymer backbones by copolymerization, and those with more than two can be used for forming cross-linked networks [232–236].

10.6 Nanotubes Carbon nanotubes are also of considerable interest with regard to both reinforcement and possible increases in electrical conductivity [237–239]. There is considerable interest in characterizing the flexibility of these nanotube structures, in minimizing their tendencies to aggregate, and in maximizing their miscibilities with organic and inorganic polymers.

10.7 Porous fillers Some fillers such as zeolites are sufficiently porous to accommodate monomers, which can then be polymerized. This threads the chains through the cavities, with unusually intimate interactions between the reinforcing phase and the host elastomeric matrix [238,240], as is illustrated in Figure 11. Unusually good reinforcement is generally obtained. Also, because of the constraints imposed by the cavity walls, these confined polymers frequently show no glass transition temperatures or melting points [86,241].

10.8 Fillers with controlled interfaces By choosing the appropriate chemical structures, chains that span filler particles in a polymer-based composite can be designed so that they are either durable, breakable irreversibly, or breakable reversibly [242–245].

Figure 11 Schematic of threading polymer chains through a cavity by polymerizing monomer absorbed into a zeolite.

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11. FURTHER COMMENTS ON SOME CHARACTERIZATION TECHNIQUES 11.1 Optical and spectroscopic techniques An example of a relevant optical property is the birefringence of a deformed polymer network [246]. This strain-induced birefringence can be used to characterize segmental orientation, both Gaussian and non-Gaussian elasticity, and to obtain new insights into the network chain orientation (see Chapter 8) necessary for strain-induced crystallization [4,16,85,247,248]. IR dichroism has also been particularly helpful in this regard. Of predominant interest is the orientation factor S (1/2)(3/cos2bS1) (see Chapter 8), which can be obtained experimentally from the ratio of absorbances of a chosen peak parallel and perpendicular to the direction in which an elastomer is stretched [5,249]. One representation of such results is the effect of network chain length on the reduced orientation factor [S] S/(l2l1), where l is the elongation. A comparison is made among typical theoretical results in which the affine model assumes the chain dimensions to change linearly with the imposed macroscopic strain, and the phantom model allows for junction fluctuations that make the relationship nonlinear. The experimental results were found to be close to the phantom relationship. Combined techniques, such as Fourier-transform infrared (FTIR) spectroscopy combined with rheometry (see Chapter 8), are also of increasing interest [250]. Other optical and spectroscopic techniques are also important, particularly with regard to segmental orientation. Some examples are fluorescence polarization, deuterium nuclear magnetic resonance (NMR), and polarized IR spectroscopy [4,246,251]. Also relevant here is some work indicating that microwave techniques can be used to image elastomeric materials, for example, with regard to internal damage [252,253].

11.2 Microscopies A great deal of information is now being obtained on crystallinity, filler dispersion, and other aspects of elastomer structure and morphology by scanning probe microscopy, which consists of several approaches [254–256]. One approach is that of scanning tunneling microscopy (STM), in which an extremely sharp metal tip on a cantilever is passed along the surface being characterized while measuring the electric current flowing through quantum mechanical tunneling. Monitoring the current then permits maintaining the probe at a fixed height above the surface, and display of probe height as a function of surface coordinates then gives the desired topographic map. One limitation of this approach is the obvious requirement that the sample be electrically conductive. AFM, on the other hand, does not require a conducting surface. The probe simply responds to attractions and repulsions from the surface, and its corresponding downward and upward motions are directly recorded to give

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the relief map of the surface structure. The probe can be either in contact with the surface, or adjacent to it and sensing only Coulombic or van der Waals forces. There are numerous other types of scanning probe microscopy, including electrochemical STM and AFM, frictional force microscopy, surface force compliance, magnetic force microscopy, electric force microscopy, scanning thermal microscopy, and near-field scanning optical microscopy (NSOM). Some of these various techniques not only generate topographic relief images, but also provide the opportunity to transport separate individual atoms and molecules into nanoscale arrangements [85]. An example of an application to elastomers is the characterization of binodal and spinodal phase-separated structures occurring in model PDMS networks [257–259]. Another application of these microscopy devices involves attaching probes to the two ends of a single polymer chain and then stretching it to determine its equilibrium and dynamic mechanical properties. This is generally referred to as ‘‘single molecule elasticity’’ [260–264]. Some rather sophisticated equipment is required, such as ‘‘optical tweezers’’, and sensitive force-measuring devices. Most of the effort thus far has involved biopolymers, and mechanicallyinduced transitions between their various conformations. Although such studies are obviously not relevant to the many unresolved issues that involve the interactions of chains within an elastomeric network, they are certainly of interest in their own right.

11.3 NMR Solid-state NMR methods have been much used to study the characteristics of the network chains themselves, particularly with regard to orientations [265], molecular motions [266], and their effects on the diffusion of small molecules [267]. Aspects related to the structures of the networks include the degree of cross-linking [268,269], the distributions of cross-links [270] and stresses [271], and topologies [272,273]. Another example is the use of NMR to clarify some issues in the areas of aging and phase separation [274]. Most elastomers require reinforcing fillers to function effectively, and NMR has been used to characterize the structures of such composites as well. Examples are the adsorption of chains onto filler surfaces [275], the immobilization of these chains into ‘‘bound rubber’’ [276], and the imaging of the filler itself [277].

11.4 Small-Angle scattering The technique of this type of greatest utility in the study of elastomers is smallangle neutron scattering (SANS), for example, from deuterated chains in a nondeuterated host [278–280]. One application has been the determination of the degree of randomness of the chain configurations in the undeformed state, an issue of importance with regard to the basic postulates of elasticity theory described earlier. Of even greater importance is determination of the manner in which the dimensions of the chains follow the macroscopic dimensions of the sample, that is, the degree of affineness of the deformation. This relationship

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Sensor 1 Excitation

Pulse amplitude

Δt

Sensor 2

Time t, secs

Figure 12 Pulse propagation results, showing measurement of the time Wt required for a pulse to pass downward through an elastomer from Sensor 1 to Sensor 2.

between the microscopic and macroscopic levels in an elastomer is one of the central problems in rubber-like elasticity. Some small-angle X-ray scattering (SAXS) techniques have also been applied to elastomers. Examples are the characterization of fillers precipitated into elastomers, and the corresponding incorporation of elastomers into ceramic matrices, in both cases to improve mechanical properties [4,85,213].

11.5 Brillouin scattering The application of Brillouin scattering to the characterization of elastomers [281–283] is an interesting extension of earlier work on polymers in general [284–287]. It should be quite useful for looking at glassy-state properties of elastomers at very high frequencies.

11.6 Pulse propagation One example of a relatively new technique for the non-invasive, non-destructive characterization of network structures involves pulse-propagation measurements [288,289]. In this technique, the delay Dt in a pulse passing through the network is used to obtain information on the network structure, for example, the chain length between cross-links or between entanglements. The technique is illustrated schematically in Figure 12 [282].

ACKNOWLEDGEMENT It is a pleasure to acknowledge the financial support provided JEM by the National Science Foundation through Grant DMR-0314760 (Polymers Program, Division of Materials Research).

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SECTION IV: Polymer Degradation

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CHAPT ER

10 Polymer Degradation and Oxidation: An Introduction John M. Chalmers and Robert J. Meier

Contents

1. Introduction 2. Standard Tests and Comparative Methods 2.1 Oxidative-induction time 2.2 Oxygen uptake 2.3 Carbonyl index 2.4 Wet chemistry/titration/staining 2.5 Melt flow index 3. Spectroscopic Techniques 3.1 Mid-Infrared spectroscopy 3.2 Raman spectroscopy 3.3 UV/fluorescence/phosphorescence/visible spectroscopy 3.4 Mass spectrometry 3.5 Nuclear magnetic resonance spectroscopy 3.6 X-ray photoelectron spectroscopy and secondary ion mass spectrometry 4. Thermal Methods 4.1 Differential scanning calorimetry 4.2 Differential photocalorimetry 4.3 Thermogravimetric analysis 5. Chromatographic Analysis 5.1 Gas chromatography 5.2 Liquid chromatography 6. Closing Remarks Acknowledgement References

Comprehensive Analytical Chemistry, Volume 53 ISSN: 0166-526X, DOI 10.1016/S0166-526X(08)00410-8

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1. INTRODUCTION As co-editors of this book, as with other chapters in this book, we would have liked to have featured a single chapter dealing with this specialised, important and very wide application area, but this proved difficult to realise because of the specialism of many of the researchers and practitioners in this field. So, as a compromise, we eventually commissioned two specific chapters detailing investigations using perhaps two of the less well-routinely publicised techniques, especially within industry; these are chemiluminescence (CL) and electron spin resonance (ESR), which are very well covered in the next two chapters and will therefore not be mentioned in this chapter, unless forming part of a multitechnique study. So this relatively concise chapter will provide an introduction to the molecular characterisation and analysis of the degradation and oxidation of polymers, and aim to provide information that complements the next two chapters. Reference sources on polymer degradation and oxidation are extensive and diverse, and most contain methods of molecular characterisation and analysis. Many cited in this chapter appear in the specialist journal Polymer Degradation and Stability (published by Elsevier Science B.V.). This chapter will not be a comprehensive review, but rather provide the reader with a snapshot of applications of many of the varied testing techniques or analytical tools that are brought to bear on investigating, studying and monitoring of the effects of polymer property and structure deterioration and alteration occurring as a consequence of degradation and oxidation mechanisms. The number of references in this chapter is also very far from exhaustive, examples having been selected merely to indicate an application type or area and most have been chosen from relatively recent publications; full referencing can be traced readily through the references cited within these references. Degradation means different things to different people: the polymer chemist might focus predominantly on the mechanisms of attack on and subsequent breakup of the polymer chain; the fabricator might recognise it initially through gel formation or processing properties; the consumer will likely complain about such as product discoloration, smell or increasing brittleness. Of course, these property changes and consequence are almost always interlinked. The properties of thermoplastic polymers are essentially the properties of long chains and so degradation can have a potentially profound effect. Polymer chains can be susceptible to breakage by a variety of mechanisms. Degradation can be oxidative, shear-induced, hydrolytic, by thermal scission, or by radiation attack from UV or other sources, or combinations of these or indeed other mechanisms. Chains may become oxidised; they may ‘unzip’, as, for example in the dehydrochlorination of poly(vinyl chloride) (PVC); or they may lose side groups. Each of these degradation processes impacts on the polymer properties (affecting such as processing conditions, mechanical performance, etc.) and product aesthetics (colour, smell, etc.). Degradation can be confined essentially to the surface of a polymer product, or it can be spread throughout the bulk. Usually the polymer chain is broken leading to smaller fragments. One or both of these ‘broken’ chain fragments may remain active long enough to take place in further reaction. The activity can be terminated internally leading to a shorter version of the original chain but with a different end grouping. It may also be possible for a still-active

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fragment to recombine with the main chain leading to a new permanent covalent bond. This may actually lead to a chain extension if the functionality at the chain end is favourable. A further alternative is that the active fragment may attack the main chain somewhere along its length resulting in a branched structure. If this happens repeatedly it may lead to hyperbranching and ultimately cross-linking. A useful concise source to a collective description of the processes of oxidative degradation of polymers and coverage of the analytical tools used to investigate and measure them is Chapter 14 in Ref. [1]. This reference also discusses the limitations of many of the techniques, and contains a more extensive list of references. In the discussions that follow, many of the application examples cited were undertaken using a variety of analytical techniques and tests, as is the norm, but for convenience here we have categorised them so that we may highlight application of a particular technique or methodology. In the descriptions of the examples, out of necessity, often only scant details are given in order to give a flavour of the investigation and technique used; of course, more complete details will be found within the cited reference(s). The natural tolerances of both surface and bulk properties are sometimes tested by such as outdoors weathering. However, the effectiveness of stabilisers and antioxidants in many polymer formulations means that in order to realistically evaluate their performance, accelerated ageing tests must be applied. The oldest and probably the most reliable thermal method is oven ageing. For outdoor applications the stability of polymers and polymer formulations must be assessed for against exposure to sunlight, UV radiation, etc., and for certain applications, for example some medical products or products to be used in harsh environments, it is also important to know how polymers behave in the presence of various other radiation sources, e.g., g-radiation from Co60. Although the majority of studies focus on the solid state, many applications focus more or additionally on the volatile products arising from polymer degradation. Evolved gas analysis (EGA) from thermal analysers and pyrolysers by spectroscopic and coupled chromatography–spectroscopy techniques can be particularly important from a safety and hazard viewpoint, since data from such measurements can be used to predict toxic or polluting gases from fires, incinerators, etc. Measuring the relative oxidative stability of polymers is important. Measurements can be used to determine dependencies on structural and molecular weight/weight distribution or the effectiveness of an antioxidant, or to perhaps assess the amount present in a polymer sample, etc. The preferred and commonest method consists in raising the sample temperature to a predetermined level, while in an inert atmosphere, then switching the atmosphere to air or oxygen. The time to the onset of exothermic reaction is measured. The measurement methods outlined in this chapter begin with what can be described as essentially comparative tests, many of them standard practices in common usage; the discussion then moves on to the role of spectroscopic methods in characterising degradation mechanisms and comparing relative levels of degradation, primarily in bulk samples; this is followed with a section covering the more surface-specific spectroscopic techniques; the chapter closes with, in sequence, discussions related specifically to thermal methods and chromatographic techniques, respectively.

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2. STANDARD TESTS AND COMPARATIVE METHODS 2.1 Oxidative-induction time The oxidative-induction time/oxidation induction time (OIT) test is described in standard test methods ISO 11357-6 [2] and ASTM D3895 [3]. OIT is expressed as the time to onset of oxidation in a polymer test sample exposed to oxygen [1,4]. The method was developed to specifically analyse polyolefin resins that are in a fully stabilised/compounded form. The method involves heating a polymer sample in a differential scanning calorimetry (DSC) instrument. The sample is heated in an open DSC pan under a purge of nitrogen gas from 501C to a test temperature (typically 2001C) at a fast heating rate; the instrument is then switched to isothermal mode and the sample exposed to an oxygen atmosphere, by switching the purge gas. The OIT is expressed as the elapsed time from the test sample’s exposure to an oxidising gas, usually oxygen, to the onset of oxidation at the isothermal test temperature. The time interval is determined from the DSC curve as the time-distance between the admission of oxygen and the point of intersection of the ‘tangent’ to the oxidation exotherm and the ‘baseline’ (see Figure 1). (The isothermal test temperature is usually selected to produce OIT values in the range 15–100 min.) The OIT test is used to assess the relative stability of a series of related polymer samples. It does however suffer from several limitations, which can include poor reproducibility and precision [1,5–7]. Some of the issues relate to:

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 Finding an optimum test temperature [1,5–7]. If the temperature is too high then undesirable side reactions may occur. Also, concerns about the realistic nature of the test for predicting performance at ambient conditions could arise. Too low a temperature will compromise the detection sensitivity and signal-tonoise ratio of the measurement [5].  Test specimen thickness [1].  Polymer structure and formulation. As an example, Woo et al. [7] measured OIT values for series of commercial PVC resins and polyester thermoplastic elastomers (TPEs). The researchers used the ASTM D3895-80 procedure, but substituted air as the oxidising gas instead of pure oxygen. A dependency on thermal processing history of the TPE film samples appeared to influence the measured OIT; in the PVC study, chemically different chain ends affected polymer stability and hence OIT values. In a study on the thermal and UV ageing of two commercial poly(oxymethylene) (POM) samples, one of which was a copolymer (see related study discussed later under Section 4.3, thermogravimetric analysis (TGA)), used in car interior applications, involving both DSC and TGA, isothermal OIT measurements were made at several different temperatures [8]. One conclusion from this study was that ‘‘extrapolation of the OIT data from high temperatures (molten state) to ambient temperatures in the solid state does not reflect effective antioxidant performance at room temperature’’, and thus measurements close to the melting point are not appropriate for reliable lifetime estimations. An oxidation induction time can also be determined by CL experimental methods, see Chapter 11 in this book. Fearon et al. [9] modified a commercial DSC instrument such that simultaneous measurements could be made of heat flow and light emission. In a study of unstabilised polypropylene (PP) over a series of temperatures (1201C, 1301C and 1351C), which were below the melting temperature of the polymer, a linear relationship between (CL intensity)1/2 and DSC heat flow rate in mW was obtained, although the plots had different gradients at each temperature, decreasing slightly with increasing temperature (see Figure 2(a)). The results were rationalised as giving support for the CL emission arising from a Russell-type mechanism (see Chapter 11), and the fact that while DSC effectively measures chain propagation, CL is measuring chain termination, and the kinetic chain length varies with temperature. The study also incorporated measurements of OIT from stabilised PP samples. Excellent agreement was established between the two measurements (see Figure 2(b) and (c)). In the same publication [9], simultaneous DSC and CL data were reported from a bottle-grade poly(ethylene terephthalate) (PET) sample (see Figure 3). Figure 3 shows that in a measurement from an oxidising sample, while endothermic and exothermic processes affect DSC measurements, the CL signal is not directly affected by these (although secondary effects may be caused by such as changes in sample geometry due to melting). In this study, the oxidation of the PET polymer accelerates rapidly around the crystal melting point. In the DSC trace, it can be seen that this is difficult to distinguish from both the baseline

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curvature and the phase transition at melting; in contrast, the CL gives a sharp, unambiguous onset. In OIT determinations, the test samples are flushed continuously with oxygen during the course of the measurement [1]. This is in contrast to oxygen-uptake measurements that are mostly undertaken in a static oxygen atmosphere (see below). Effects such as dynamic removal of volatile antioxidants in the OIT method can lead to these two methods yielding very different assessments of a polymer formulation’s stability [1].

2.2 Oxygen uptake Perhaps conceptually one of the simplest tests for comparing the stability of related polymer samples is that of measuring oxygen uptake. In such a measurement the amount of oxygen reacting with a polymer sample, at a particular temperature and over a specific time, can be measured either manometrically or volumetrically, by a relatively simple device [1], such as that illustrated in Figure 4 [10]. Whereas such a measurement may be made on solid samples, such as sheet, powder or film, in order to minimise errors, the measurement is preferably made on thin film samples. The technique of oxygen uptake is an absolute quantitative technique; it affords a direct measure of oxygen consumption during polymer degradation [11]. Whereas techniques such as OIT and melt flow index (MFI, see later) measure the stability of a polymer melt, oxygen uptake can, in principle, be undertaken at any temperature; it also uses larger sample amounts than OIT, generally leading to improved reproducibility. (As far as the authors can ascertain, there are no recommended ASTM or ISO procedures for this method; an ASTM method (D4478-85, ‘Test Method for Oxygen Uptake’) existed, but seems to have been withdrawn in 1994 and not replaced.)

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Figure 4 Schematic of an oxygen uptake device. 1, sample; 2, electrical oven; 3, Hg manometer; 4, intermediate vessel for pressure adjustment; 5, drying vessel; 6, control thermometer; 7, outlet to vacuum pump; and 8, inlet for gas feeding. Reproduced with permission from Zaharescu [10]. r Springer 2001.

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An extensive review of oxygen uptake techniques for measuring polyolefin oxidation was published in 1995 [11]. This listed the methods described in the literature over the period 1908–1991. Two categories of technique apparatus are used for measuring oxygen uptake; these operate under either isochoric or isobaric conditions. In the former, constant-volume (CV) type, there is no replacement of the oxygen consumed; in the latter, constant-pressure (CP) type, the volume of oxygen required to maintain isobaric conditions during polymer oxidation is measured. In this latter compensating-pressure approach, two strategies are employed: (i) the volume of the sample cell is decreased by raising a mercury levelling bulb or by the motion of a piston or bellows, or (ii) the consumed oxygen can be replaced by electrolysis or from a reservoir. Gijsman and Hamskog [12] reported recently on a study of stabilised and unstabilised PP in apparatus that enabled the simultaneous measurement of oxygen update (OU) and imaging CL, which enabled them to obtain comparable information on an oxidising area. Some conclusions from the study were (see Ref. [12] for full details):  The measurement of the induction time determined by CL and OU are, in general, comparable. However, at low temperatures, the OU induction time is shorter; this was postulated as being a decrease of sensitivity of CL at lower temperatures.  The CL curve is related to the amount of degrading polymer.  The OU and CL curves are not related to the kinetics of the degradation chemistry.

2.3 Carbonyl index The carbonyl index is not a standard technique, but is a widely used convenient measurement for comparing the relative extent and rate of oxidation in series of related polymer samples. The carbonyl index is determined using mid-infrared spectroscopy. The method is based on determining the absorbance ratio of a carbonyl (nCQO) band generated as a consequence of oxidation normalised normally to the intensity of an absorption band in the polymer spectrum that is invariant with respect to polymer oxidation. (In an analogous manner, a hydroxyl index may be determined from a determination of the absorbance intensity of a nOH band normalised against an absorbance band that is invariant to the extent of oxidation.) In the text following, two examples of multi-technique studies of polymer oxidation will be discussed briefly; each includes a measure of a carbonyl index. As part of a multi-technique investigation (see also discussion under midinfrared spectroscopy later), Corrales et al. [13] plotted the carbonyl index for films prepared from three grades of polyethylenes: a high-density PE (HDPE), a linear low-density PE (LLDPE) and a ‘metallocene’ PE (mPE) (see Figure 5). In this study, the data trend shown in Figure 5 correlated well with activation energies derived from the thermal analysis, which showed that the thermaloxidative stability followed the order LLDPEWmPEWHDPE, whereas the trend

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Figure 5 Left: thermo-oxidative carbonyl index vs oven ageing times at 901C. Right: photooxidative carbonyl index vs irradiation time after exposure to UV radiation (300–800 nm wavelength). In each case, the carbonyl index is based on the intensity of the mid-infrared absorption at 1,720 cm1 normalised against sample film thickness, d, which was 290 mm. Reprinted from Corrales et al. [13]. Copyright 2002, with permission from Elsevier.

for photo-oxidative stability was mPEWHDPEWLLDPE. The thermal-oxidative results were also in accord with CL measurements, although the CL data for the photo-oxidative series demonstrated a higher light stability for the LLDPE compared to HDPE and mPE, both of which exhibited CL emission below their melting points. In another fairly recent multi-technique study to investigate the influence of chemical modification on polymer degradation, oxygen uptake, UV-visible spectroscopy and a mid-infrared spectroscopy carbonyl index were used in association with viscometry and DSC analyses for characterising the thermooxidative degradation of a series of polystyrene (PS) copolymers containing different amounts (5%, 10% and 15%) of –CH2(CQO)CH2CH2– units in their backbone [14]. The OU measurements were undertaken during the thermooxidative degradation at 1501C. For other analyses, samples were taken at various times from a degradation experiment at 1501C carried out in a closed vessel filled with pure oxygen. The OU measurements showed that the rate of oxidation of the copolymers was higher than for the homopolymer PS, yet while the 15% copolymer was highest, it was not proportionally higher in relation to comonomer content throughout the measurement (see Figure 6(a)). The increase of UV absorbance at 400 nm was used to follow increasing degradation (see Figure 6(b)); samples were examined as solutions in THF. The observations were in line with the observed enhanced yellowing of the copolymer samples. As can be seen from the figure, the UV absorbance became distinctly more pronounced for the highest (15%) copolymer content sample with increasing time. This observation was in accord with the measurement of carbonyl index obtained from mid-infrared spectra recorded as KBr discs (see Figure 6(c)). The carbonyl index was calculated as the ratio of the nCQO absorption band profile maximum occurring at 1,725 cm1 (assigned to newly formed CQO groups) in a degraded sample compared with the absorption value at this position before degradation. Also shown in Figure 6 is a plot of the intrinsic viscosity, IV (see Figure 6(d)). The decreases in IV are related to lower molecular weight species

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Figure 6 (a) Oxygen uptake vs degradation; (b) UV absorbance at 400 nm vs degradation time; (c) changes in carbonyl index vs degradation time; and (d) intrinsic viscosity vs degradation time. PS (~), 5% copolymer (’), 10% copolymer ( ), and 15% copolymer ( ). Reprinted from Botelho et al. [14]. Copyright 2004, with permission from Elsevier.

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formed following chain scission; once again a more pronounced effect was observed for the 15% comonomer sample. The Tg (glass transition temperature) values determined from DSC measurements for the PS and 15% comonomer samples were very similar being 1021C and 981C, respectively; however, while for PS only a slight decrease occurred with degradation, when the 15% sample was studied, a large decrease of Tg was observed, again supporting the formation of shorter chain material.

2.4 Wet chemistry/titration/staining The formation and role of hydroperoxide groups, particularly in the early stages of polymer oxidation is well discussed in the introduction to the next chapter and also features in many of the references cited in this chapter. Their detection and quantification is therefore important. Although this can be done directly or implicitly through many of the instrumentation techniques discussed in this chapter, there are several tests that have been developed, some of which are still widely used, that are based more on chemical methods, titration or staining. The majority have been applied to polyolefins, especially polyethylene. The most widely used is the iodometric colorimetric method [1,15]. The test is based on measurement of the triodide anion, I 3 , formed by reaction with a polymer. The concentration of I formed may be determined by either titrimetry 3 or UV absorption spectrophotometry (usually about 350 nm). If P signifies the polymer chain, the reaction may be represented as: POOH þ 3I þ 2Hþ ! I 3 þ H2 O þ POH The method does not usually detect dialkylperoxides, POOP [16]. In applying the method, a known weight of sample will be refluxed in a mixture of isopropanol and acetic acid in the presence of sodium iodide. The reaction time is usually about 30 min. A detection limit of ca. 30 ppm of hydroperoxide has been reported [1]. Iodometric titration formed part of a multi-method analysis of the oxidative degradation of LDPE [17]. Although reasonable reproducibility was obtained within a series of powdered samples, consistent results could only be obtained from pellets or thick films when the polymer was completely dissolved rather than just swollen. The hydroperoxide formation goes through a maximum as they decompose to form other oxidised species, such as hydroxyl groups, which eventually become predominant. Figure 7 shows a correlation obtained between the hydroperoxide content estimated by the iodometric test and the normalised intensity of the 3,552 cm1 mid-infrared band, which is characteristic of the –OOH group (see later); the linearity is maintained as long as the band at 3,552 cm1 increases steadily, i.e., while the hydroperoxide groups remain essentially isolated, but is lost once associated groups become predominant. Another method is that based on the ferrous/ferric thiocyanate determination of hydroperoxides [1]. This exploits the ion-catalysed decomposition as shown by

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0.8 0.7

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Figure 7 Hydroperoxide index (HI) determined from mid-infrared spectroscopy (ratio of the integrated intensity of the 3,552 cm1 band to the integrated intensity of the band at 2,010 cm1) as a function of total hydroperoxide content measured by iodiometric titration. films (0.8 mm thick) thermally oxidised in air at 1601C for 0, 4, 5 and 10 min; K beads exposed to summer daylight for 2 months; ’ beads exposed to summer daylight and then thermally treated at 1201C for 0, 30, 60 and 90 min. Reprinted from Salvalaggio [17]. Copyright 2006, with permission from Elsevier.

7

the reaction: POOH þ 2Fe2þ þ 2Hþ ! 2Fe3þ þ H2 O þ POH The concentration of Fe3+ ions can be determined by titration with ferrous ammonium thiocyanate or spectrophotometrically by measuring the absorbance at 512 nm of the [Fe(SCN)6]3 complex [1]. In a recent study of the degradation of pre-aged (oven ageing and photooxidation) hydrocarbon homopolymers exposed to stimulated recycling, the ferric spectro-colorimetric method based on the stoichiometric of oxidation of Fe2+ ions to Fe3+ was used to determine hydroperoxide content [18]. The Fe3+ ions react with the thiocyanate to give an intense colour that is proportional to the hydroperoxide content; the study also involved use of DSC, MFI and tensile strength measurements. Figure 8 shows a plot of hydroperoxide formation in LDPE, which was unprotected by stabilisers, during oven ageing at 1001C. A similar behaviour was observed for high-impact polystyrene (HIPS) used in this study, whereas HDPE and PP remained very stable, even after 10 months oven ageing and no hydroperoxide formation could be detected. Another method of investigating the degradation levels of polymers involves staining in order to provide a greater sensitivity for spectroscopic/colorimetric techniques [1]. Staining can provide a very fast, low cost, simple to operate method of detecting/monitoring degradation in some polymers. Staining materials that have been used include: SO2, 2,4-dinitrophenylhydrazine (DNPH), dansyl hydrazine (DNSH: dimethylaminonaphthyl-5-sulfonylhydrazine),

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Figure 8 Hydroperoxide formation in LDPE granules during oven ageing at 1001C. Reprinted from Luzuriaga et al. [18]. Copyright 2006, with permission from Elsevier.

diphenyl-p-phenyldiamine, dansyl butyramide, iodine vapour, alkaline Procion black, Benedict’s solution and Tollen’s reagent, and Sudan III/methylene blue staining [1]. Aslanzadeh and Kish [19] recently used staining as part of a multi-technique (staining/colorimetric, scanning electron microscopy (SEM), mid-infrared and density) method of studying the photodegradation of thermalbonded PP non-woven fabric samples. The samples, commercial thermal-bonded non-woven fabrics manufactured from isotactic PP, were UV photo-degraded and then immersed in the stirred boiling staining solution for 15 min, then rinsed in isopropanol and distilled water, before drying. The staining solution was pure isopropanol saturated with Sudan III and methylene blue at room temperature, to which after a period of stirring extra pure NaOH was added, followed by more stirring. Figure 9 shows the changes in (a) redness and (b) blueness obtained from the colorimetric analyses. As can be seen, blueness increases linearly with POOH index (P ¼ polymer chain), while redness decreases with POOH index; the POOH index was determined from mid-infrared spectroscopic measurements (see Ref. [19] for full details).

2.5 Melt flow index Although essentially a bulk (rheological) property, the melt flow index (MFI) measurement is included here, since it complements the other techniques covered in this chapter and also is sometimes performed in parallel with these in investigations into polymer degradation, since oxidation/degradation can induce changes in the molecular weight distribution of a polymer. The measurement of MFI is a standard property method the procedure of which is described in ASTM D1238 [20] and ISO 1133 [21]; the two standard methods are essentially very similar in procedure. An alternative term for melt flow index is melt flow rate (MFR). The MFI test is a simple, low cost, rapid and convenient method for characterising the extent of degradation [1]; a decrease in MFI is indicative of a cross-linking mechanistic pathway; an increase in MFI indicates that chain

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Figure 9 Stained photo-degraded non-woven PP fabric samples (a) change in redness with POOH index, (b) change in blueness with POOH index. Reprinted from Aslanzadeh and Kish [19]. Copyright 2005, with permission from Elsevier.

scission has taken place. The first mechanism leads to a reduction in molecular weight (MW); chain scission leads to an increase in MFI. The MFI is most commonly applied to polyolefins. It is measured using a capillary melt viscometer. A schematic of a MFI apparatus is shown in Figure 10 [22]. The test consists of weight-loaded piston under the action of gravity forcing a heat-softened polymer through a rod die of specified dimensions [22]. A small amount of a sample, typically about 4–5 gm, is packed into the barrel, avoiding air pockets, which is then pre-heated for a specified time; for polyethylene this is 5 min at 1901C; for PP this is 6 min at 2301C. After this, a weight, usually 2.16 kg, is loaded onto the top of the piston. Three samples are then cut from the extruded melt at constant time intervals, which are each then weighed accurately, and the

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Weight (popular condition 2160 gms incl.piston) Mercury in Glass Thermometer

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Figure 10 Schematic of MFI apparatus. Reproduced from Hunt and James [22]. r with kind permission of Springer Science and Business Media.

MFI is reported as the number of grams of polymer/10 min of flow time. The flow rate will depend on the polymer and the conditions used; lower MW polymers will tend to flow through the die faster than higher MW polymers. A recent example of the use of determination of MFR in a polymer degradation study is that undertaken on the thermo-oxidative degradation of metallocene polyethylenes (mPEs) [15], which differed in their initial melt index, molar mass distribution, density and ash content. The degradation series of samples was prepared by processing (masticating) each sample in a torque rheometer open to air and operating at 10 rpm and a temperature of 225751C for differing lengths of time (15, 30, 45, 90 and 120 min). The MFI of these samples was determined by applying a standard weight of 10 kg at a melt temperature of 1901C, in accordance with ASTM D1238. Additional to the MFI measurements, transmission mid-infrared spectroscopy (see Section 3) was used to measure the level of vinyl and trans-vinylene unsaturated groups in each sample by examining a 200 mm thick compression moulded film prepared from each sample; mid-infrared spectroscopy was also used to measure the relative levels of carbonyl groups formed by measuring the normalised intensity of a band between 1,715 and 1,720 cm1. Also, an iodometric colorimetric test was

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undertaken to ascertain the levels of hydroperoxides formed. All the samples examined initially showed a large decrease in MFI with increasing processing consistent with a predominance of cross-linking reactions. One sample, from between 15 and 30 min mastication, showed a slight increase in MFI, indicating an increased proportion of chain scission taking place during this period. Differences in the rates of formation and relative changes in the levels of unsaturated, carbonyl and hydroperoxide groups were correlated with and used to rationalise the different behaviours observed in the mPEs as determined by the MFI measurements.

3. SPECTROSCOPIC TECHNIQUES 3.1 Mid-Infrared spectroscopy1 The mechanisms of oxidation in the degradation of polymers is well described in Chapter 11 co-authored by Richly´ and Matisova´-Rychla´, and will not be repeated here; suffice it to say here that one of the most informative and sensitive techniques to observe functional groups associated with oxygen is infrared (IR) spectroscopy, and many researchers have used mid-infrared spectroscopy to study and investigate degradation reactions and processes in polymers. As expected, many of the early reported fundamental studies focused on polyolefins, in particular polyethylene [23,24] in which many of the effects of oxidation and degradation may be readily observed. As explained in Chapter 11 by Rychly´ and Matisova´-Rychla´, one of the key early steps in the oxidation processes is the formation of hydroperoxide groups; these give rise to a distinctive absorption band in the mid-infrared spectrum of polyethylene that may be observed at 3,555 cm1 [23] (see, e.g., Figure 11(a)). Further oxidation leads to a variety of carbonyl groups with characteristic absorption bands in the region 1,800–1,675 cm1; these may be variously assigned to species such as esters (1,740 cm1), aldehydes (1,730 cm1), ketones (1,720 cm1), acids (1,705 cm1), peracids (1,785 cm1) and peresters (1,763 cm1) (see Figure 11(b)). Also generated are absorption bands due to hydroxyl species; these occur in the region 3,600–3,200 cm1 (see Refs. [25] and [26] and references therein). As such, the sensitivity of mid-infrared spectroscopy is especially useful for characterising the consequences of thermal, thermal-oxidative, photo, photo-oxidative and radiation-induced degradation, not only in the regions associated with oxygenated functional groups, but also those associated with unsaturated olefinic groups. For example, in low-density branched polyethylene photooxidation tends to lead to an increase in the level of the bands characteristic of the vinyl (–CHQCH2) end group, which is characterised by a pair of bands occurring at 990 and 910 cm1, whereas thermal-oxidation tends to lead to a reduction in relative intensity of the band attributed to vinylidene (WCQCH2) 1

While most of the references tend nowadays to use FT-IR/FTIR (Fourier transform infrared) to denote the use of mid-infrared spectroscopy, we mostly use the more precise phrasing of mid-infrared (mid-IR) spectroscopy.

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unsaturation that occurs at 888 cm1 [26]. Observation of variation in intensity of all these absorption bands may form part of a basic study into a polymer or polymer formulation stability study, or they may form part of an investigation into a product failure or deterioration; the latter often being undertaken using FTIR microscopy. As discussed earlier under Section 2.3, Carbonyl index, in one relatively recent comparison of the photo-oxidative and thermal (oven-aged) degradation behaviour of different polyethylenes, additive free grades of a metallocene (mPE), an HDPE and a linear low-density PE (LLDPE) were analysed by a combination of mid-IR spectroscopy, TGA and CL [13]. The mid-IR

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measurements were used to provide a carbonyl index (see earlier); also determined were relative changes in free (3,555 cm1) and associated (3,410 cm1) hydroperoxides, hydroxyl (3,371 cm1) esters (1,743 cm1), aldehydes (1,733 cm1), ketones (1,720 cm1) and acid (1,712 cm1) groups, and chain branching level through measurement of the dCH3 absorbance band at 1,378 cm1. (Second derivative UV spectra were used to estimate the initial concentration and evolution of vinyl groups.) Activation energies determined from TGA experiments were shown to decrease during thermal degradation in the order HDPEWmPEWLLDPE, whereas under conditions of photo-oxidation they followed the order mPEWHDPEWLLDPE. The rates of oxidation as indicated by the mid-IR determined carbonyl index correlated with the respective changes in activation energies (see also figures and discussion under Section 2.3, Carbonyl index). A microscope hot-stage, fitted with barium fluoride windows, inserted into the beam of a FTIR spectrometer was the apparatus of choice for a study of the kinetics and mechanisms of the thermal degradation of poly(methyl methacrylate) (PMMA) leading to char formation [27]. Thin films (ca 1 mm thick) were degraded in an atmosphere of argon (to avoid oxidation) isothermally at temperatures between 3401C and 4201C. To complement these mid-IR studies, TGA was also carried out under similar conditions on selected samples. An advantage of using mid-IR for the study was that it could be used to provide information about the chemical changes that occurred in the polymer residue. In the temperature range 340–3851C, mid-IR spectra were recorded at 10 min intervals; at 4001C they were recorded at 2 min intervals; at 4201C they were recorded at 1 min intervals. One series of samples analysed was of a monodisperse PMMA with peak molecular weights, Mp, between 12,700 and 1,520,000; each chain was terminated at one end by a hydrogen atom and at the other by a 2,2-diphenyl hexyl group. Selected figures reported from this study [27] are shown in Figure 12. Figure 12(a) shows a stack plot of some typical changes observed in the mid-IR spectra at 3701C. The band at 1,550 cm1 that develops with increasing degradation was assigned to a conjugated unsaturation band, and developed in part through the mechanism proposed in Figure 12(e). The build up of this band with time at 3701C for the different Mp polymers can be seen in Figure 12(f), in which the ratio c/m represents the absorbance of the band at 1,550 cm1 divided by the initial height of the nCQO carbonyl band (1,730 cm1). Figure 12(b) show the mid-IR spectrum of the final residue (PMMA char) remaining after isothermal degradation at 4201C. The spectrum is dominated by the intense band at 1,550 cm1, formed mainly by side-group elimination by scission of the C–C bond of the methoxy-carbonyl side group [27]. Figure 12(c) shows the change (% conversion) of selected mid-IR absorbance bands of the lowest Mp polymer at 3701C. Up to 20% conversion, first-order rate plots from the bands at 1,730, 1,234 and 1,139 cm1 showed good linearity (see Figure 12(d)). Above 20% conversion, those samples with a lower initial degree of polymerisation, D, produced relatively more conjugation. This was attributed to either ‘‘a greater number of unsaturated end-groups, as CQC from previous scission or from activation by the 2,2-diphenyl hexyl group, joining with unsaturated groups from the side-chain elimination, following depropagation’’

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(see Figure 12(g)). From the combined mid-IR and TGA study, some of the overall conclusions reached were that:  thermal degradation was initiated by a mixture of chain end and chain scission processes,  at lower degradation temperatures, this was followed by depropagation, and first-order termination,

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Figure 12 (a) Mid-IR absorbance spectra recorded from the thermal degradation of PMMA (Mp ¼ 12,700) (under argon) at 3701C. (b) Mid-IR absorbance spectrum of the final residue (char) produced on thermal degradation of PMMA (Mp ¼ 12,700) (under argon) at 4201C. (c) Change in absorbance of some mid-IR bands of thermally degraded PMMA (Mp ¼ 12,700) (under argon) at 3701C. (d) First-order rate plot for loss of absorbance of bands at 1,730; 1,234 and 1,139 cm1 for PMMA (Mp ¼ 12,700) (under argon) at 3701C. (e) Proposed mechanism of side-group elimination in thermally degraded PMMA. (f) Buildup of conjugation band at 1,550 cm1 with time for PMMA samples thermally degraded at 3701C. (g) Proposed mechanism for end-group contribution to the intensity of the mid-IR band at 1,550 cm1. Reprinted from Holland and Hay [27]. Copyright 2001, with permission from Elsevier.

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Figure 12 (Continued)

 at higher temperatures, initiation was followed by depropagation mostly to the end of the polymer chain,  under the conditions used, thermal degradation of PMMA eventually produces a char; the amount of char being dependent on molecular weight and temperature. Hot-stage FT-IR spectroscopy has also been employed monitoring chemical changes in nylon 6 and nylon 6,6 undergoing isothermal degradation (under an argon atmosphere) at temperatures in the range 350–3701C [28]. Complementary data was supplied from measurements by TGA, DSC and solution viscosity. The mid-IR results showed that the thermal degradation led to formation of an aromatic-conjugated structure indicated by development of a new band at 1,590 cm1; also noted was the appearance of a band at 2,190 cm1 indicative of a keteneimine formed from the dehydration of an amide linkage. Chemical changes leading to formation of volatile products, cross-linking, formation of an

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aromatic-conjugated material and eventual formation of a black char residue, are a consequence of the thermal degradation at these temperatures. The thermal(under nitrogen) and thermo-oxidative (under oxygen) degradation in an environmental chamber of nylon 6 and nylon 6,6 at 2001C were also the subject of an earlier in situ FT-IR investigation [29]. At these temperatures, under a nitrogen atmosphere, the majority of observed spectral changes could be associated with crystallinity or crystalline-phase changes; under an oxygen atmosphere the trends observed were a decrease in intensity of all absorbance bands related to amide groups accompanied by growth of other carbonyl and hydroxyl species. Coleman and Sivy also used an infrared transmission cell to undertake degradation studies under reduced pressure on a series of poly(acrylonitrile) (ACN) copolymers [30–33]. Thin films prepared from a polymer were mounted in the specially designed temperature-controlled cell mounted within the infrared spectrometer. The comparative studies were made on ACN copolymers containing vinyl acetate [30,32], methacrylic acid [30,31] and acrylamide [30,33]. The species monitored was the production of the cyclised pyridone structure. This was characterised in part by loss of CRN stretch (nCRN) intensity at 2,240 cm1 accompanied by the appearance and increase in intensity of a doublet at 1,610/1,580 cm1. Many of the carbonyl and hydroxyl species that are formed as a consequence of oxidation have fundamental absorption bands that severely overlap; this sometimes makes discriminating between particular species difficult. This limitation can sometimes be overcome, or at least partially, through the use of chemical derivatisation [34]. For example, alkali treatment of oxidised polyethylene can be used to convert acid carbonyls to carboxylate salts; this results in a shift in the band position, since the carbonyl band of a saturated carboxylic acid occurs at ca. 1,710 cm1, whereas the antisymmetric stretch of the carbonyl band of the carboxylate salt occurs at ca. 1,610 cm1. Another possibility is treatment with SF4; this converts the carboxylic acid to and acid fluoride, thereby shifting the band from ca. 1,710 to ca. 1,840 cm1 [1]. In a study of the thermo-oxidative degradation of heterophasic ethylene/propylene copolymers and their fractions, both NH3 and SF4 were used to convert carboxylic acids to the ammonium salt or acyl fluoride, respectively [35]; the latter treatment was preferred since while the ammonium salt formation was quantitative, the bands formed are very broad. More distinct information was available through formation of the acyl fluoride, which created the disappearance of two bands in oxidised isotactic PP, one at 1,710 cm1, the other at 1,760 cm1, which were assigned as originating from carboxylic acids in different environments, one from dimers and one from an associated form between a carboxylic acid and a non-carboxylic acid hydroxyl group, respectively. In LLDPE, however, only the conversion of the typical dimeric acid group was observed. Additionally in this study, derivatisation using NO was particularly helpful for elucidating mechanisms in the thermo-oxidation of the ethylene/propylene copolymers, since it reacts with hydroperoxides and alcohols to give nitrates and nitrites with characteristic absorption bands, respectively. SF4, NH3 and NaCl treatments were all used in an investigation of the photo-oxidation of anhydride-cured epoxies [36]. SF4-derivatisation reaction

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has also been employed to aid mid-IR identification of photo-products on photooxidised films of bisphenol-A-polycarbonate in a combined analysis involving mid-IR, mass spectrometry (MS) and UV spectroscopy [37]. Whereas SO2 has been used more simply as a staining technique (see earlier) to monitor hydroperoxide formation, it has also been used to characterise oxidised polyolefins [38] in order to gain insight into the sites of oxidative attack. Reaction of SO2 with PE that was expected to have been oxidised to a low level confirmed that hydroperoxide formation probably takes place in the b-position to a pendant methylene (vinylidene) group (a defect structure in PE) (Figure 13). Figure 13 shows that negligible differences were observed in the mid-IR spectra of a control LDPE and a PE oxidised to a low level until they were treated with SO2. These samples were part of a study into storage in a silo of PE granules arising from a bulk property deterioration complaint. Melt flow measurements had indicated that the stored material was subject to setting up. However, preliminary IR examination of the ‘oxidised’ complaint sample revealed no sign of absorptions due to hydroperoxide or carbonyl groups. Assuming that the complaint sample was more oxidisable, the samples were heated in an air oven to

Figure 13 Left: FTIR absorbance spectra of a control LDPE sample and difference spectra, (A, as received; B, after SO2 treatment; C, heated at 1001C for 18 h; D, heated at 1001C for 18 h then SO2 treated.) Right: FTIR absorbance and difference spectra of ‘oxidised’ sample, (A, as received; B, after SO2 treatment; C, heated at 1001C for 18 h; D, heated at 1001C for 18 h then SO2 treated.) Reproduced from Henman [38]. r, with permission from Elsevier.

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enhance the differences between the complaint and the control sample, as indeed was the case (see Figure 13). As can be seen in the figure, reaction with SO2 resulted in a loss absorbance at 888 cm1 of vinylidene unsaturation in the complaint sample, which was enhanced after the heat treatment, whereas no such loss could be detected in the control sample. In addition to transmission spectroscopy finding extensive use as a sampling technique for studying the bulk degradation effects on such as polymer films, the surface layer specific sampling technique of attenuated total reflection (ATR), also referred to as internal reflection spectroscopy, finds extensive use for interrogating the surface layer of oxidised/degraded/irradiated polymer films and products. Depending on the experimental conditions employed, the ATR approach will probe a surface layer of between ca. 0.3 and 5 mm over the range 4000–400 cm1 [26]. A limitation of the technique is that the depth probed is wavenumber dependent, being greater towards lower wavenumber, so that in any ATR measurement the surface layer probed varies over the spectral range examined. Unlike X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectrometry (SIMS), see later, ATR mid-IR is not a surface-specific technique, but may be regarded rather as a surface layer-specific technique. One method of promoting the adhesive properties of some polymer films is exposure of their surfaces to corona discharge in air. This introduces oxidised polar groups on the film surface, which may be investigated by mid-IR ATR spectroscopy (and, of course, XPS and SIMS techniques, see later). The surface oxidised species on isotactic PP films generated as a consequence of corona discharge were identified by mid-IR ATR spectroscopy and a carbonyl index plotted as a function of corona discharge treatment time (Figure 14 [39]). The 1.4 1.2

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Figure 14 Carbonyl index as a function of corona discharge treatment of PP film. Reproduced with permission from Sellin and Campos [39].

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mid-IR results were complemented by topographic images obtained by atomic force microscopy (AFM) and wettability (contact angle). With increasing generation of lower molecular weight surface oxidised groups, and decrease in contact angle with water, the film adhesion property improves. ATR-FTIR spectroscopy alongside electron spin resonance imaging (ESRI, see Chapter 12 in this book) was employed in a spatial resolution study of the effects of photo- and thermo-oxidation processes in stabilised polystyrene (PS) and PP plaques exposed to accelerated photo- or heat-ageing [40]. The samples examined were cylindrical samples (3 mm diameter, 6 mm length) that had been bored out from the plaques after exposure for different time periods. (The cylindrical samples were more appropriate for the ESRI examinations.) ESRI, the primary technique in this investigation, was used to determine concentration profiles of nitroxides along the cylinder axes coinciding with the direction of irradiation in the weatherometer. The main supporting role of the ATR FT-IR measurements was to compare the relative amounts of WCQO and –OH existing on unexposed and exposed surfaces from both aged and unaged samples and the surface formed by cutting the exposed samples in the middle of their thickness. It was found that the relative intensity of WCQO bands formed on irradiation was much higher for PS than PP, it being greatest on the irradiated PS surface; the extent of formation of WCQO groups was approximately equal on both the irradiated and unexposed surfaces of the irradiated PP sample. In a novel application, ATR mid-IR was used for studying the thermal degradation of chlorosulfonated polyethylene (Hypalons) glove samples [41]. The glove samples were aged in circulating air in temperature-controlled ovens. A main use of Hypalons gloves is as gloves for glove-box use, because of the material’s resistance to alcohols, strong acids and bases. The ATR spectra recorded from aged series of samples were subjected to multivariate data analysis using a multivariate curve resolution technique (MCR), using an alternative least squares (ALS) algorithm. The loadings from such an analysis are related to component spectra, the scores of which are related to concentration. From this data analysis, the dominant degradation pathways were deduced to be formation of –CQC– via dehydrochlorination, loss of –SO2 functionality, oxidation to form ketones, and cross-linking. The scores from the extracted MCR factors as functions of time showed the onset and duration of a particular mechanism. The correlation of the deterioration of polymer properties with degradation, such as mechanical performance and lifetime, is key to many areas, and has ever increasing importance in areas such as biodegradability, waste disposal and recycling. Jansson et al. simulated a recycling processing step on a series of unstabilised PP samples, which had been previously aged at 701C for differing lengths of time [42]. Following a second compression moulding it was found that the hydroperoxide content, determined by an iodometric test, decreased by rapidly transforming to additional carbonyl groups (Figure 15). The implication of this observation is that in order to maintain mechanical property performance, the polymers must be re-stabilised before recycling. The variation in carbonyl and hydroxyl species type and concentration were monitored using mid-IR spectroscopy on series of g-sterilised polyolefin film samples that had been

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0.8 1750 cm-1

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Figure 15 IR absorbance spectra of PP films after ageing in air at 701C (dashed curve) and after ageing at 701C and re-processing (solid curve). Reprinted from Jansson et al. [42]. Copyright 2004, with permission from Elsevier.

subjected to composting and fungal (microbial) culture environments [43]. Changes in viscosity and surface morphology (by SEM) were also monitored. The series comprised samples of isotactic PP, HDPE and ethylene/propylene (E/P) copolymers. It was concluded that pre-treatment by g-irradiation (sterilisation) accelerated significantly the biodegradation of the polymers. PP was found to be more susceptible to microbial attack than HDPE; comonomer composition and distribution were found to affect the behaviour of the E/P copolymers. Mid-IR spectroscopy, alongside gravimetric and molecular weight determinations, has also been used to analyse the biodegradation by a thermophilic bacterium (isolated from soil) of an LDPE film [44]. The mid-IR studies were undertaken using the ATR sampling technique on control samples, samples that had been UV irradiated, and samples that had been UV irradiated then incubated with bacteria. The study showed that the particular bacterial strain was capable of utilising standard and photo-oxidised polyethylene as the sole carbon source. FTIR microscopy, in which a FTIR spectrometer is coupled to an optical microscope, enables mid-IR spectra with a lateral spatial resolution of ca. 10 mm to be recorded from samples. (Higher lateral spatial resolution spectra suffer significantly from diffraction effects.) The attributes of FTIR microscopy can be successfully employed to probe the depth of degradation into a polymer product. The procedure involves analysing a cross-section slice microtomed in a plane perpendicular to the axis of irradation/degradation [34] (see, e.g., Figure 16(a)). A profile of the degradation products through such as a polymer film may then

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Figure 16 (a) Schematic for obtaining a thin microtomed cross-section for FTIR microscopy analysis. (b) Oxidation profile for a polyamide film based on the absorbance at 1,715 cm1. The thickness of the microtomed layer was 30 mm. The sample had been artificially aged for 75 h at 601C. Reproduced with permission from Gardette [34]. r John Wiley & Sons Ltd., 2002.

be obtained by recording spectra from successive localised areas along the film thickness axis (see e.g., Figure 16(b)). As Figure 16(b) shows, only the outermost portion of the sample has been photo-oxidised in to a depth of ca. 40–60 mm; the core (bulk) of the polyamide film sample remains unaffected, as detected by FTIR microscopy. In addition to characterising the effects of degradation by recording spectra related to solid-state changes, FTIR spectroscopy (like MS, see later) can also be used to detect the evolved volatile products from such as a pyrolysis or TGA experiment (see Section 4.3 on TGA later). In one such study, the CO2 generated from a series of TiO2-pigmented LDPE films was monitored by FTIR spectroscopy; the apparatus (cell) used allowed for in situ UV exposure under controlled temperature, reaction atmosphere and humidity conditions, and mid-IR detection of the off gases [45]. Ranking of the samples according to either the rate of carbonyl development in the film samples or rate of CO2 evolution were identical. On-line analysis of the volatile products from the pyrolysis (under nitrogen) over the range 1,073–1,273 K of nylon 6,6 has been reported [46]. Such information can be useful in predicting the formation of nitrogen oxides during incineration of plastic wastes. Among the evolved gases detected were HCN, CO, NH3, CO2 and light hydrocarbons. Two competing mechanisms were deduced, one at low temperature that yields carboxylic acid and amines that release NH3, and one at high temperature that leads to formation of nitriles (see Figure 17). The primary volatile products evolving from the pyrolysis in the range 220–6001C of poly(3-hydroxy butyrate) (PHB) were passed through a gas chromatogram for separation prior to their identification by on-line FTIR spectroscopy [47]. The pyrolysis/gas chromatography (GC)/FTIR analysis was accompanied by weight loss determinations from TGA measurements (see later). Figure 18(a) shows the Gram–Schmidt chromatogram (reconstructed from the total mid-IR absorbance variation with time) obtained at four pyrolysis

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Fuel N coversion yield (%)

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Figure 17 Conversion of fuel nitrogen to HCN and NH3. Furnace temperature: top, 1,073 K; bottom, 1,273 K. Reprinted from Leichtnam et al. [46]. Copyright 2000, with permission from Elsevier.

temperatures. Figure 18(b) shows the infrared spectrum recorded from the peak 2 that eluted at ca. 20 min. As can be seen in the insert it features two carbonyl bands. These occur at 1,770 cm1 and 1,759 cm1, and are associated with S-trans and S-cis conformations of 2-butenoic acid, respectively. Peak 1 had contributions from both evolved CO2 and propene; peaks 3 and 4 were identified as essentially dimer- and trimer-type structures of 2-butenoic acid, each containing an a,bunsaturated ester group and an acid functionality, with peak 3 containing additionally a saturated ester group. The two-step degradation of commercial ethylene-vinyl acetate (EVA) copolymers has been investigated using TGA coupled with FTIR detection of the pyrolytic products evolved [48]. Acetic acid was evolved from the first

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1 600°C

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Figure 18 (a) GC-FTIR Gram–Schmidt chromatograms from evolved gases from PHB at pyrolysis temperatures of 2201C, 3001C, 4001C and 6001C. (b) FTIR spectrum recorded from peak 2 in chromatogram, identified as 2-butenoic acid. Reprinted from Gonzalez et al. [47]. Copyright 2005, with permission of Elsevier.

decomposition (360–4501C); gases identified from the second decomposition (450–5501C) were: 1-butene, ethylene, methane and CO2. The merits of TGA-FTIR for studying polymer degradation were reviewed in 1999 by Wilkie [49].

3.2 Raman spectroscopy The sensitivity of Raman spectroscopy to CQC species is clearly demonstrated in its application to the study of PVC degradation. As PVC unzips and

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100 090 080 ABSORBANCE

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Figure 19 Example of a UV-visible absorption spectrum recoded from a typical thermally degraded PVC sample. Reprinted with permission from Gerrard and Maddams [50]. Copyright 1975 American Chemical Society.

dehydrochlorinates (loses HCl) conjugated polyenes are formed in the polymer backbone, which give rise to chromophores that absorb in the UV-visible region (see, e.g., Figure 19 [50]). Once the number of double bonds in the conjugation sequence reaches 6, this electronic absorption occurs in the visible region, giving rise to discolouration of the polymer. Using a Raman spectroscopy excitation laser that is in coincidence (or near coincidence) with the maximum absorption wavelength of one of these chromophores will give rise to a resonance Raman spectrum, in which the Raman scattering bands due to the conjugated species causing the chromophore will be enhanced by several orders of magnitude, such that the Raman spectrum may be dominated by the n2 (CQC) and n1 (C–C) bands (see Figure 20 [50,51]) and there is little evidence of the normal Raman bands expected from PVC. Consequently, different conjugation sequence lengths may be probed using different excitation laser wavelengths. By taking advantage of the sensitivity of the resonance Raman effect, low levels of degradation may be detected enabling such as the early stages of weathering to be monitored [26,51]. The polyenes may be detected at levels of o0.00001%. However, on solid samples, one must be careful about laser power densities used in a study; if the laser power is too high or the exposure time to the laser too long then one may obtain false results [52]. Another valuable advantage of Raman spectroscopy, which is unique, is its capability of being used to characterise carbon species, in particular graphitic and amorphous carbon; this can be of value to many degradation and pyrolysis studies. Perfectly ordered graphite is characterised by a Raman-active vibrational mode that occurs at 1,575 cm1; this band is usually referred to as the ‘G’ band. With increasing disorder in the carbon, a new band, the ‘D’ band, appears at

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Figure 20 Raman scattering from PVC thermally degraded at 801C. The excitation laser was 514 nm; the degradation time in minutes is indicated above each spectrum. Reproduced form Everall [51]. r, with kind permission of Springer Science and Business Media.

ca. 1,330 cm1 (because of resonance effects, the position of the band maximum of the D band may be shifted, and its half bandwidth change). In a study of the structural and conductivity changes during the pyrolysis of polyaniline (PANI), Trchova´ et al. [53] used both mid-IR and Raman spectroscopies to examine PANI samples that had been exposed in air to temperatures between 1001C and 1,0001C for 2 h. Figure 21 shows the progression of a PANI sample (1.5 g) to carbonaceous graphite-like material as it was exposed in a porcelain crucible in ambient atmosphere for 2 h to elevated temperatures in a furnace. In another joint vibrational spectroscopy study, in combination with X-ray diffraction (XRD), both Raman and infrared spectroscopies were used to characterise the formation of carbonaceous materials derived from polyparaphenylene (PPP) in argon gas for increasing treatment times (up to 6 h) at 7001C [54]; also studied was the effect of different atmospheres. The Raman spectra of the most degraded samples resembled that of weakly graphitised carbon, and a progression to this end through the series of examinations made, whereas, little change was observed in the XRD patterns after initial loss of crystallinity within 0.5 h. In the FTIR spectra recorded from KBr discs a quasi-total disappearance of all bands due to PPP was observed in the spectra of PPP pyrolysed at 7001C for 6 h. Both XRD and Raman spectroscopy were also used in a complementary study of the formation of glassy- or amorphous-like carbon materials as a consequence of the carbonisation of a cured resol-type phenol-formaldehyde resin [55]. In one other example, Raman spectroscopy was employed along with FTIR spectroscopy, XPS, elemental analysis, TGA, SEM and transmission electron microscopy (TEM) to follow the compositional and structure variations of polymethylsilsesquioxane samples pyrolysed at different temperatures in an atmosphere of nitrogen [56]. At 9001C the main product was silica, with formation too of some silica oxycarbide and amorphous carbon, with Raman spectroscopy showing complementary evidence for presence of both the minor species.

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Raman spectra (488 nm)

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Figure 21 488 nm excitation Raman spectra of PANI exposed to elevated temperatures for 2 h. Reprinted from Trchova´ et al. [53]. Copyright 2006, with permission of Elsevier.

Raman microscopy offers a much higher lateral spatial resolution than that attainable with FTIR microscopy; 1–2 mm lateral spatial resolution may be achieved with Raman microscopy. In addition, Raman microscopes, because of their confocal capability, have the capability to undertake depth-profiling measurements [57]. Confocal Raman microscopy was one of the tools used in a study of the natural photo-ageing of LDPE [58]; DSC and AFM were the other techniques employed. Raman spectroscopy was used to highlight differences between the surface and sub-surface morphology (crystalline vs amorphous character of the regions). Kim et al. [59] used Raman microscopy to investigate the electrical degradation of triarylamine-based light-emitting polymer diodes. A gradual irreversible oxidation of the blue-emitting conjugated polymer was indicated by the spectral evolution. A study of the degradation of a biodegradable composite periodontal membrane was the subject of investigations using both Raman and mid-IR

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spectroscopies by Taddei et al. [60,61]. The formulation consisted of a commercial biodegradable poly(e-caprolactone)-poly(oxyethylene)-poly(e-caprolactone), PCL-POE-PCL, block copolymer composite membrane containing hydroxyapatite (HA). The in vitro degradation (weight loss) was undertaken in alkaline and physiological solutions [60]; enzymatic degradation has also been followed [61]. The researchers established that in all media the POE undergoes degradation preferentially, and that bands attributed to the HA component decrease with time, and that the HA is removed faster than the polymer by the degradation media.

3.3 UV/fluorescence/phosphorescence/visible spectroscopy These techniques, all of which involve transitions between electronic energy levels, have to greater or lesser extents, as appropriate, found uses in monitoring the effects of degradation and oxidation on polymers. The high sensitivity of UV (and visible) spectroscopy to chromophores involving p-electron systems makes it particularly sensiti