Polymer Yearbook 18

18 Polymer Yearbook Editors: Richard Pethrick Gennady Zaikov Rapra Technology Limited Polymer Yearbook 18 Editors:...

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18

Polymer Yearbook

Editors: Richard Pethrick Gennady Zaikov

Rapra Technology Limited

Polymer Yearbook 18

Editors: Richard Pethrick and Gennady Zaikov

rapra TECHNOLOGY

Rapra Technology Limited Shawbury, Shrewsbury, Shropshire, SY4 4NR, United Kingdom Telephone: +44 (0)1939 250383 Fax: +44 (0)1939 251118 http://www.rapra.net

First Published in 2003 by

Rapra Technology Limited Shawbury, Shrewsbury, Shropshire, SY4 4NR, UK

©2003, Rapra Technology Limited

All rights reserved. Except as permitted under current legislation no part of this publication may be photocopied, reproduced or distributed in any form or by any means or stored in a database or retrieval system, without the prior permission from the copyright holder. A catalogue record for this book is available from the British Library. Every effort has been made to contact copyright holders of any material reproduced within the text and the authors and publishers apologize if any have been overlooked.

ISBN: 1-85957-383-5

Typeset by Rapra Technology Limited Cover printed by The Printing House, Crewe, Cheshire, UK Printed and bound by Rapra Technology Limited, Shrewsbury, UK

In Memorium

This book is dedicated to the memory of

Professor Karl S. Minsker 1929-2003

Karl Samoilovich Minsker (1929-2003)

On May 23rd, 2003 in the seventy-fourth year of his life a great scientist died. Professor KS Minsker was an expert in the field of chemistry of high molecular weight compounds, petrochemistry and technical chemistry. He was a doctor of chemical sciences, professor, and academician of the Academy of Sciences of the Republic of Bashkortostan. KS Minsker was a graduate in fine chemical technology from the Moscow Institute of MV Lomonosov. He started his working life in the town of Dzerginsk in the Nigegorodscaya area. From 1953 to 1967 he worked in the Dzerginsk Research Institute (nowadays NII of Chemistry and Technology of Polymers of the Academy of VA Kargin), where he rose from a young scientific employee to become the head of the laboratory. His first supervisor was GA Razuvaev. In 1968 he was invited to Ufa to organise the Faculty of High Molecular Weight Compounds of the Bashkir State University. Simultaneously from 1968 to 1983 he supervised the Laboratory of Ionic Polymerisation in the Institute of Chemistry of the Bashkir Academy of Sciences of the USSR. Professor Minsker set up and has headed the Research Laboratory of Destruction and Stabilisation of Halide Containing Polymers in Bashkir University. Under the supervision of KS Minsker, the quantitative theory of degradation of halide containing polymers was developed and a set of high performance chemical additives for polymers mainly those based on vinyl chloride were developed. The fundamental phenomenon of modifying Ziegler-Natta catalysts by electrodonor compounds for the first time was described by the polymerisation of olefines, that is now the classical method of regulation of activity and selectivity of catalytic systems for the polymer industry. The original theory about the mechanism of stereoregulation during polymerisation of olefines and dienes with Ziegler-Natta catalysts was developed by Minkser and colleagues. The important fundamental laws concerning the mechanism of cationic polymerisation of olefines were revealed. Professor Minsker developed the new division of chemical physics and theoretical technology concerning fast processes in turbulent flows that has allowed the creation and introduction in industrial production, of power and raw material saving technologies by using small-sized tubular turbulent reactors.

Among his students KS Minsker had 54 PhD candidates and 11 full professors. He has published more than 1100 papers/articles, including 16 monographs and books, 25 foreign patents and more than 300 copyright certificates and patents of the Russian Federation. KS Minsker was given the title ‘Man of the Year 1994-1995’ by the American Biographical Institute; he was the ‘International Man of the Year 1995-1996’ in the field of science and education (International Biographical Centre, Cambridge, UK). He was awarded with a medal for ‘Achievement in the 20th Century 1999-2000’ (International Biographical Centre, Cambridge, UK); was the winner of the State prize of the Republic of Tatarstan in the field of a science and engineering (2001) and the prize of academician V.A. Kargin of the Russian Academy of sciences (1999), multiple winner of the permanent exhibition of achievements in the USSR. The memory of Karl Samoilovich Minsker will be kept forever in hearts of his numerous students, colleagues and friends.

Professor Alexandr A. Berlin, Director of NN Semenov Institute of Chemical Physics, Russian Academy of Sciences, 4 Kosygin str., Moscow 119991, Russia Professor Gennady E. Zaikov, Deputy of Director of NM Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, 4 Kosygin str., Moscow 119991, Russia Dr. Vadim P. Zakharov and Dr. Rinat Akhmetkhanov – on behalf of Division of Highmolecular Compounds of Bashkirian State University, 32 Frunze str., Ufa 450074, Russia

Contents

Preface ................................................................................................................... 1 Contributors .......................................................................................................... 3 1

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) ...................................................................... 7 1.1

Abstract ................................................................................................. 7

1.2

Poly(perylenecarboximides) ................................................................... 7

1.3

Polyimides Based on Naphthalene-1,4,5,8-Tetracarboxylic Acid Dianhydride ................................................................................. 19

1.4

Polyimides Based on Non-condensed bis(Naphthalic Anhydrides) ....... 32

References ..................................................................................................... 42 2

Macromolecular Properties and Topological Structure of Lignin .................. 49 2.1

Introduction ......................................................................................... 49

2.2

Topological Structure of Lignin Macromolecules ................................. 50

2.3

Hydrodynamic Properties .................................................................... 57

2.4

Summary .............................................................................................. 67

Acknowledgements ....................................................................................... 68 References ..................................................................................................... 68 3

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems .......... 75 3.1

Introduction ......................................................................................... 75

3.2

Principal Groups of Lanthanide-Based Catalysts ................................. 75

3.3

Factors Affecting the Activity and Stereospecificity of Catalysts .......... 76

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Polymer Yearbook

3.3.1

Chemical Nature of Lanthanide ............................................... 76

3.3 2

The Nature of the Ligand ........................................................ 77

3.3.3

The Structure of Organometallic Component of Lanthanide Catalysts ............................................................... 78

3.3.4

The Nature of the Solvent ........................................................ 80

3.4

The Structure of Active Centres and the Mechanism of Stereoregulation in the Polymerisation of Butadiene ............................ 81

3.5

Role of the Structure of Diene in the Mechanism of Regioand Stereoselectivity ............................................................................. 86

3.6

The Role of Anti-Syn Isomerisation of the Terminal Unit of the Growing Polymer Chain ................................................................ 91

3.7

Conclusions ......................................................................................... 94

Acknowledgement ......................................................................................... 94 References ..................................................................................................... 95 4

Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion .................................................................. 101 4.1. Introduction ....................................................................................... 101 4.2

Experimental ..................................................................................... 103

4.3

Results and Discussion ....................................................................... 104 4.3.1

Discussion of Experimental Data and Formulating the Starting Position of the Kinetic Model ................................... 104

4.3.2

The Kinetic Model ................................................................. 109

4.3.3

Calculation - Results .............................................................. 120

4.4

Characterisation of the Peculiarities of the Linear Polymerisation of the Microheterogeneous System .................................................... 121

4.5

Conclusions ....................................................................................... 126

References ................................................................................................... 127 5

ii

Influence of Ultrasound on the Channels of the Forming Head in Extrusion Processes ..................................................................................... 131

Contents

Introduction ................................................................................................ 131 5.1

Construction of an Extrusion Head for Producing Polymers ............. 132

5.2

Investigation of the Hydrodynamic Performances of the Extrusion Head .................................................................................. 134 5.2.1

Investigation of Flow Characteristics of Polymer Melts ......... 135

5.2.2

Account of the Performance of Polymer Melts....................... 136

5.3

Results of a Study on High-Elastic Rating of a Polymer Melt Spray .... 136

5.4

Rating of Solid Properties of the Polymeric Items .............................. 137

5.5

Conclusions ....................................................................................... 139

References ................................................................................................... 139 6

Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain ................................................................................................... 141 6.1

Introduction ....................................................................................... 141

6.2

Experimental ..................................................................................... 142 6.2.1

Results and Discussion........................................................... 143

References ................................................................................................... 180 7

Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers ................................................................................. 185 7.1

Introduction ....................................................................................... 185

7.2

Thermo-oxidative Degradation of Polypyromellitimide, Poly(phenylquinoxaline) and Copoly(imidophenylquinoxalines) ......................... 186

7.3

Thermo-oxidative Degradation of Poly(alkane imide) ....................... 189

7.4

Thermo-oxidative Degradation of Polysulfones, Polyesterketones, Liquid-Crystal Copolyesters............................................................... 192

7.5

Thermo-oxidative Degradation of Polyesterimides, Polyamidoimides, Aliphatic-Aromatic Polyamides.......................................................... 198

References ................................................................................................... 204

iii

Polymer Yearbook

8

Fluorine-containing Polymers for Materials with the Complete Internal Light-reflection .............................................................................. 209 8.1

Introduction ....................................................................................... 209

8.2

The General Principle of Selecting Polymers for Polymer Optical Fibre Coating ..................................................................................... 210

8.3

Estimation of the Relative Activity of Fluoro-alkylmethacrylates in Block Radical Polymerisation and Copolymerisation with Vinyl Monomers and Structure of Macromolecular Chain of the Copolymers Obtained ........................................................................ 213 8.3.1

Kinetics of Block Radical Polymerisation of Fluoroalkyl(meth)acrylates .................................................... 213

8.3.2

Relative Activity of Fluorine-containing Methacrylates in Bulk Radical Polymerisation with Vinyl Monomers; Structure and Compositional Inhomogeneity of the Macrochain Copolymers Obtained ........................................ 221

8.3.3

Radical Polymerisation of Fluorine-containing Methacrylates in the Presence of Nitroxyl Radicals ...................................... 234

8.4

Some Properties of Fluorine-containing Polyalkyl(meth)acrylates and α-fluoroacrylates ......................................................................... 236

8.5

The New Fluorine Containing Copolymers - Prospective Materials for Covers of Optical Fibres............................................................... 243

References ................................................................................................... 244 9

Description of PMMA Molecular Orientation due to Clustering: Theoretical Model ....................................................................................... 251 9.1

Introduction ....................................................................................... 251

9.2

Model Considerations ........................................................................ 251

9.3

Results and Discussion ....................................................................... 253

9.4

Conclusions ....................................................................................... 257

References ................................................................................................... 257 10 The Fractal Analysis of Curing Processes of Epoxy Resins .......................... 259

iv

Contents

10.1

Introduction .................................................................................... 259

10.2

Experimental ................................................................................... 260

10.3

Results and Discussion .................................................................... 262

10.4

Summary ......................................................................................... 281

References ................................................................................................... 281 11 Fractal Analysis of Macromolecules ............................................................ 285 Abstract ...................................................................................................... 285 11.1

Introduction .................................................................................... 285

11.2

Modelling of Macromolecules......................................................... 293 11.2.1

Fractal Dimension ............................................................ 293

11.3

Polymer Fractal ............................................................................... 295

11.4

Statistical Fractal ............................................................................. 302

11.5

Experimental Determination of Fractal Dimensions ........................ 305

11.6

Levels of Fractality .......................................................................... 307

11.7

Fractal Characteristics of Macromolecules ...................................... 312

11.8

The Dimension of the Sections of a Macromolecule Between Topological Fixing Points ................................................................ 321

11.9

The Concept of Macromolecular Skeletons ..................................... 325 11.9.1

The Model of a Network Polymer ................................... 325

11.9.2

Scaling Representation of a Macromolecule ..................... 328

11.9.3

Estimation of Structural Parameters ................................. 332

11.10 Description of Molecular Mobility Using Fractal Characteristics .... 335 11.11 Conclusions..................................................................................... 339 References ................................................................................................... 339 12 Structural Aspects of Adhesion in Particulate-Filled Polymer Composites ... 349 12.1

Introduction .................................................................................... 349

v

Polymer Yearbook

12.2

Experimental ................................................................................... 350

12.3

Results and Discussion .................................................................... 352 12.3.1

Description of the Aggregation of Particles in the Framework of the Models of Irreversible Aggregation ....... 352

12.3.2

Effect of the Surface Structure of the Filler on Adhesion ...... 356

12.3.3

Interfacial Adhesion and the Strength of the Interfacial Layer ............................................................... 360

12.3.4

The Level of Interfacial Adhesion and Mechanical Characteristics of Composites .......................................... 364

Conclusions ................................................................................................. 368 References ................................................................................................... 369 13 Change of Microgel Structure on Curing Epoxy Polymers in Fractal Space ... 373 13.1

Introduction .................................................................................... 373

13.2

Experimental ................................................................................... 373

13.3


13.4

Summary ......................................................................................... 377

References ................................................................................................... 378 14 Levels of Fractality in Polymers ................................................................... 379 14.1

Introduction .................................................................................... 379

14.2


References ................................................................................................... 384 15 The Fractality of the Fluctuation Free Volume of Glassy Polymers ............. 387 15.1

Introduction .................................................................................... 387

15.2

Experimental ................................................................................... 387

15.3


15.4

Summary ......................................................................................... 390

References ................................................................................................... 391 vi

Contents

16 Rapid Method of Estimating the Fractal Dimension of Macromolecular Coils of Biopolymers in Solution ................................................................. 393 16.1

Introduction .................................................................................... 393

16.2

Theoretical Basis ............................................................................. 393

16.3

A Comparison of Calculated and Experimental Results .................. 395

References ................................................................................................... 399 Abbreviations and Acronyms ............................................................................. 401

vii

Polymer Yearbook

viii

Preface

The Polymer Yearbook is back. After a couple of years in which we were unable to publish the Polymer Yearbook, I am pleased to say that we are now once again in print. As you will be aware the publication is now being handled by Rapra and we hope that they will be able to sustain it for the next few years. Gordon and Breach Science Publishers who had been publishing Polymer Yearbook for almost seventeen years were sold out. The new publishers in their review of titles decided that Polymer Yearbook was too specialist a publication and indicated after some considerable delay that they would not continue its production. Rapra have kindly indicated that they feel it fits into their stable of publications and have agreed to continue its production. We hope that we will be able to work with them and over the next few years produce a product that will address the needs of the polymer community. In the previous publications we had included contributions from the former Soviet Union and also Japan. Unfortunately, we have not been able to continue the contributions from Japan for this issue, however we will be attempting to re-establish our contacts and hopefully expand the contributions to other areas of the world. Working with Professor Zaikov we have produced a volume that I trust will be of interest to many polymer scientists. The volume contains a broad spectrum of topics which we consider are of current interest. Polymer Yearbook 18 is a collection of articles that highlight some important areas of current interest in polymer science. Two of the articles consider progress which has been made into the synthesis of new materials: Advances in the synthesis of the poly(perylenecarboximides) and poly(naphthalenecarboximedes) and Key steps in the mechanism of stereochemical control in diene polymerisation using lanthanide catalytic systems. Both of these topic are of general interest and highlight specific aspects of the synthetic method. An article on the organosilicon copolymers with cyclosiloxane fragments in the side chain discusses the synthesis of these materials and also considers their application in the electronic industry. The electronic interest is extended in the article on polyfluoro(meth)acrylates for optical fibers coating: synthesis, general kinetic regularities of their formation and properties. Several of the articles deal with the kinetics of polymerisation: kinetic model of the bulk photopolymerisation of glycidyl methacrylate for high degrees of conversion and polyfluoro(meth)acrylates for optical fibers coating: synthesis, general kinetic regularities of their formation.

1

Polymer Yearbook Two of the articles examine the characterisation of polymer systems: hydrodynamic properties and structure of lignin and specific features of the thermooxidation of thermoresistant heterochain polymers. A connecting theme of this volume is the application of fractal analysis to a number of problems in polymer science. The topic is introduced in a general manner in the article: fractal analysis of macromolecules. A series of shorter articles illustrate the application of the method to a wide range of polymer situations and systems. These articles include consideration of the description of PMMA molecular orientation due to clustering; the fractal analysis of curing processes of epoxy resins, and the structural aspects of adhesion in particulate-filled polymer composites. The fractal theme is continued with consideration of the change of microgels structure on curing epoxy polymers in fractal space and an article that considers the various levels of fractality in polymers. The possibility of a connection between fractality of the thermal fluctuation and the free volume in glassy polymers continues this theme. An article on a rapid method of estimating the fractal dimension of macromolecular coils of biopolymers in solution illustrates the potential for this method for examination of biopolymer systems. Several of the earlier articles in the Yearbook also include consideration of the use of fractal analysis. An article entitled the influence of ultrasound on the extrusion processes in channels of the forming head as this topic is currently of considerable interest technologically. I would wish to acknowledge the help in the production of the volume from Helen Paton and Lesley Gilmore at the University of Strathclyde, who collected and collated the material. The volume would not have been produced had it not been for the help of Frances Powers and her colleagues at RAPRA, who arranged the continuation of the contacts and also has had a major role in the editing and checking of the material that appears in this volume. I would also like to thank the various authors who have contributed to the volume. Thank you for your patience and also for revising the documents that you originally submitted but did not get published. The publication would not exist without your support. I am hoping with Professor Zaikov to give the Polymer yearbook a new look in subsequent issues. We will be attempting to incorporate a broader authorship and also produce issues that will focus on specific topics. Lastly, may I thank the readers for their support of the publication and I trust that you will find the articles we have selected of interest. Professor Richard Pethrick University of Strathclyde September 2003

2

Contributors

Dr V.Z. Aloev Kabardino-Balkarian State Agricultural Academy, Nalchik – Tarchokov st. 1a KBR Russia Dr A.B. Bainova Buryat State University Ulan-Ude–670000 Smolina st., 24a Buryatiya Russia Dr A.A Bejev Kabardino-Balkarian State Agricultural Academy, 1a Tarchokov st., Nalchik - 360000 KBR Russia Dr A. Bratus Physical Chemistry and Technology of Combustible Minerals Department L.V. Pisarzhevsky Institute of Physical Chemistry, National Academy of Sciences of Ukraine 3a Naukova Str. 79053 Lviv Ukraine

Dr E. G. Bulycheva Nesmeyanov Institute of Organoelement Compounds Russian Academy of Sciences Ul. Vavilova 28 Moscow GSP-1 119991 Russia Dr I.V. Dolbin Kabardino- Balkarian State University Nalchik–360004 Chernishevsky st., 173, KBR Russia Dr L.B. Elshina Nesmeyanov Institute of Organoelement Compounds Russian Academy of Sciences ul. Vavilova 28 Moscow GSP-1 119991 Russia Dr G.L. Hafiychuk Physical Chemistry and Technology of Combustible Minerals Department V. Pisarzhevsky Institute of Physical Chemistry National Academy of Sciences of Ukraine 3a Naukova Str. 79053 Lviv Ukraine

3

Polymer Yearbook Dr K.Z. Gumargalieva N.N. Semenov Institute of Chemical Physics Russian Academy of Sciences 4, Kosygin str., Moscow 11991 Russia Dr E.V. Kalugina Research and Production Company ‘POLYPLASTIC’ 14a, General Dorokhov str. Moscow, 119530 Russia Dr A.P. Karmanov Institute of Chemistry, Komi Scientific Center Russian Academy of Sciences ul. Pervomaiskaya 48 Syktyvkar 167610 Russia Dr L. Khananashvili I Javakhishvili Tbilisi State University Chavchavadze Avenue 1 Tbilisi 380028 Georgia Dr O.F. Kiseleva The Ufa State Oil Technical University Pr. Oktyabrya 2 Sterlitamak 453118 Russia Dr G.V. Kozlov Kabardino-Balkarian State Agricultural Academy Nalchik – Tarchokov st. 1a KBR Russia

4

Dr A. Kytsya Physical Chemistry and Technology of Combustible Minerals Department L.V. Pisarzhevsky Institute of Physical Chemistry National Academy of Sciences of Ukraine 3a Naukova Str. 79053 Lviv Ukraine Dr M.B. Lachinov M.V. Lomonosov Moscow State University Vorobievi Gori 119899 Moscow Russia Dr N.G. Lekishvili Javakhishvili Tbilisi State University Ave. I. Chavchavadze 3 119899 Tbilisi Georgia Dr Yu.S. Lipatov Institute of Macromolecular Chemistry of the National Academy of Sciences of Ukraine 48 Kharkovskoje Shosse Kiev - 253160 Ukraine Dr Yu. Medvedevskikh Physical Chemistry and Technology of Combustible Minerals Department L. V. Pisarzhevsky Institute of Physical Chemistry National Academy of Sciences of Ukraine 3a Naukova Str., 79053 Lviv Ukraine

Dr S. Meladze Javakhishvili Tbilisi State University Chavchavadze Avenue 1 Tbilisi 380028 Georgia Dr K.S. Minsker N. Emmanuel Institute of Biochemical Physics Russian Academy of Sciences 4 - Kosygin Str. 117977 Moscow Russia Dr Yu.B. Monakov Institute of Organic Chemistry Ufa Scientific Center Russian Academy of Sciences pr. Oktyabrya 71 Ufa 450054 Russia Dr O. Mukbaniani Sukhumi State University L.Djikia Str. 12 Tbilisi 380087 Georgia Dr K. Müllen Max-Plank-Institut für Polymerforschung Ackermannweg 10 55128 Mainz Germany Dr V.U. Novikov Moscow State Open University Korchagin st. 22/2 129805 Moscow Russia

Dr T.N. Novotortseva Research and Production Company ‘POLYPLASTIC’ 14a, General Dorokhov str. Moscow, 119530 Russia Dr A.A. Panov The Ufa State Oil Technical University Pr. Oktyabrya 2 Sterlitamak 453118 Russia Dr A.K. Panov The Ufa State Oil Technical University Pr. Oktyabrya 2 Sterlitamak 453118 Russia Dr A.L. Rusanov Nesmeyanov Institute of Organoelement Compounds Russian Academy of Sciences ul. Vavilova 28 Moscow GSP-1 119991 Russia Dr Z.M. Sabirov Institute of Organic Chemistry Ufa Research Center Russian Academy of Sciences pr.Oktyabrya 71 Ufa450054 Russia Dr B.D. Sanditov Buryat State University Ulan-Ude – 670000 Smolina st., 24 a Buryatiya Russia

5

Polymer Yearbook Dr D.S. Sanditov Buryat State University Ulan-Ude – 670000 Smolina st., 24 a Buryatiya Russia Dr A. Turovski Physical Chemistry and Technology of Combustible Minerals Department L.V Pisarzhevsky Institute of Physical Chemistry, National Academy of Sciences of Ukraine 3a Naukova Str. 79053 Lviv Ukraine Dr V.N. Urazbaev Institute of Organic Chemistry Ufa Research Center Russian Academy of Sciences pr.Oktyabrya 71 Ufa 450054 Russia

6

Dr A. Zaichenko Organic Chemistry Department National University ‘Lvivska Polytechnika’ 12 Bandery Str. 79046 Lviv Ukraine Professor G.E. Zaikov N.M. Emanuel Institute of Biochemical Physics Russian Academy of Sciences 4 Kosygin Street Moscow117334 Russia

1

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) A.L. Rusanov, L.B. Elshina, E.G. Bulycheva and K. Müllen

1.1 Abstract The present state of the synthesis of poly(naphthalenecarboximides) and poly(perylenecarboximides) containing six-membered imide rings in the backbones is reviewed. Recent advances in synthetic approaches provide access to polymers exhibiting high thermal stability and chemical resistance, optical conductivity, and electrographic properties. The resulting polymers are high molecular-mass, soluble products that are easily processed by traditional methods. The increasing demand of high technologies for new materials offering advanced thermal and photochemical stability, optical conductivity, and electrographic and other special properties stimulates the growing interest in polymers containing condensed heterocycles. Furthermore, these polymers were found to possess valuable electrophysical properties [1-3]. At present, there exists a need for polymeric materials, which combine these properties with solubility in organic solvents and the capability of film formation. Major achievements have been attained in the synthesis of polyimides. This review is concerned with the synthesis of soluble polymers starting from compounds containing peryleneand naphthalenecarboxyimide rings and the systematisation of data available on the structure-property relationship.

1.2 Poly(perylenecarboximides) The published literature reveals that research in the field of soluble poly(perylenecarboxyimides) (PPI) has been carried out in the following directions: 1) Synthesis of polyimides directly from perylene-3,4,9,10-tetracarboxylic acid dianhydride (DPTA) [4, 5] using diamines as the nucleophilic comonomers which leads to improved solubility for the target polymers. 2) Synthesis of new imide-containing monomers bearing amine or acid chloride functional groups starting from DPTA, followed by the reaction of the resultant monomers with the appropriate compounds [6-8].

7

Polymer Yearbook 3) Modification of DPTA by incorporation of bulky substituents into a perylene fragment, thereby improving solubility of the resulting polymers [9, 10]. Little information is available on the synthesis of perylenecarboximide-containing polymers, because DPTA is a low reactive monomer. The low reactivity is explained by the fact that a six-membered anhydride ring has no strain [11]. In addition, DPTA has a poor solubility in organic solvents and the introduction of rigid perylene moieties into polyimides hampers the formation of high-molecular mass products. Attempts to prepare polyimides from DPTA and modified oligomers of caprolactam have led to the formation of an undesirable gel [12]. Nevertheless, some DPTA-based diimides are used as photosensitive materials, dyes, fillers in the photoactive films, and charge-generating coating in xerography and electrography [13]. Recently, direct synthesis of PPI from DPTA was reported [4]. The reaction between DPTA and 1,12-diaminododecane was performed in m-cresol at 200 °C in the presence of isoquinoline according to Scheme 1.1.

Scheme 1.1

The reaction produced a mixture composed of a dimer (2 wt% of the theoretical amount) soluble in chloroform and a polymer (94 wt %) with molecular weight = (2.4-2.6) × 104. The resulting PPI formed a solution in amide solvents (N,N-dimethylacrylamide: DMA and N,N-dimethylformamide: DMF) with a concentration of 10-3–10-5 mol/l. This polymer was also soluble in chloroform, pyridine, dimethylsulfoxide (DMSO), and acetonitrile. Although PPI contained long aliphatic fragments in the polymer chain and according to thermogravimetric analysis (TGA), it exhibited thermal stability up to 475 °C and had a softening temperature of 325 °C. It was shown that soluble PPI can be synthesised directly from DPTA and series of aromatic diamines containing flexible units, namely 2,2-bis[4-(3-aminophenoxy)phenyl]propane and 2,2-bis[4-(3-aminophenoxy)phenyl]hexafluoro-propane were reported (Scheme 1.2) [5]. Previously these diamines were used successfully in the synthesis of soluble polyimides starting from naphthalene-1,4,5,8-tetracarboxylic acid dianhydride [14].

8

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) When the reaction in Scheme 1.2 was carried out in p- or m-chlorophenol using benzoic acid and benzimidazole as effective catalysts, high-molecular-weight PPI, which were soluble in sulfuric acid and phenolic solvents, were obtained. Table 1.1, lists the properties of the resulting PPI.

Scheme 1.2

Later, it was established that rigid-chain PPI can also show solubility in organic solvents, such as p-chlorophenol. It was reported that soluble rigid-chain poly(naphthalenecarboximides) can be prepared under conditions similar to those mentioned previously [15]. Bulycheva and co-workers [5] synthesised PPI on the basis of 5-amino-2-(p-aminophenyl)benzimidazole (Figure 1.1). This polymer in Figure 1.1 showed solubility not only in sulfuric acid, but in p-chlorophenol as well, Table 1.1. According to thermomechanical measurements, the synthesised PPI, especially a polymer with benzimidazole units, possessed high heat resistance. This polymer did not soften until a temperature of intense degradation was achieved. Nevertheless, these PPI can be processed directly from the reaction solutions or solutions in phenolic solvents. Casting of the reaction solutions, followed by evaporation of the solvent, produced films showing a distinctive metallic (bronze) lustre and exhibiting a good adhesion to glass. After heating at 300 °C in vacuum over a period of two hours, the polymers lost their solubility in phenolic solvents, but remained soluble in a concentrated sulfuric acid. As demonstrated by the dynamic TGA, the resulting PPI show high thermal stability; temperatures corresponding to 5% weight loss are in the 400-500 °C range. All the polymers are characterised by high oxygen indexes (40-55%).

9

10 0.55

3.50

II

III

400 (483)

450 (466)

350 (326)

300 (287)

500

°C

°C

>480

T5%*

T g,

Note: The calculated data are given in parentheses; '+' is completely soluble. * Temperature of the 5% weight loss. ** Measured in a tetrachloroethane:phenol (3:1) mixture. ηred : reduced viscosity

0.68**

—R—

I

PPI

ηred (H2SO4), dl/g

+

+

+

H2SO4

Solubility

+

+

+

p-(m)chlorophenol

Table 1.1 Some properties of PPI of the general formula [5]

+

+

+

Tetrachloroethane:phenol mixture

Polymer Yearbook

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)

Figure 1.1

Among the synthesised PPI, the polymer bearing benzimidazole rings has the highest viscosity characteristics. On the basis of this polymer, high-strength and high-modulus films (flexural strength, σb = 315 MPa, elongation, ε = 8%, and Young’s modulus, E = 7500 MPa) were prepared. It appears that such high values of tensile strength and elastic modulus (E) are related to an enhanced chain rigidity of this polymer. Thus for this polymer, the calculated Kuhn segment is 350 Å, and the glass transition temperature (Tg), as indicated by DMA, is above 480 °C [5]. Information available on the synthesis of PPI, points to the fact that there exists a trend towards substitution of easily accessible DPTA, because of its low reactivity and poor solubility in organic solvents, by the other perylene-containing monomers. Karayannidis and co-workers [6] used DPTA to obtain a diacid dichloride that was allowed to react with various α,ω–alkanediols, containing from 4 to 12 methylene groups, to yield poly(ether perylenecarboximides) (inherent viscosity, ηlog=0.25-0.52 dl/g):

Scheme 1.3

11

Polymer Yearbook The solubility of the resulting polymers was not studied in detail, however it was found that they are soluble in a tetrachloroethane-phenol mixture. The differential scanning calorimetry (DSC) experiments did not confirm the existence of a liquid crystalline (LC) phase, but gave evidence of the crystalline structure of the PPI. Melting point temperatures for the synthesised polymers were in the 300-330 °C range; as the number of methylene groups in the polymer chain increased, the melting temperatures decreased. It should be noted that the long alkylene chains are responsible for the low thermal stability of such PPI. These polymers undergo degradation immediately after melting and show weight losses of up to 50 wt% in the temperature interval ranging from 350-500 °C. Alternating copolyimides soluble in m-cresol and having high viscosity characteristics ([η] = 0.50-0.88 dl/g) were obtained on the basis of a perylene-carboximide-containing diamine and various aromatic dianhydrides [7]. The polycondensation process proceeded at 200 °C in m-cresol under homogeneous conditions in the presence of a catalyst (isoquinoline) according to Scheme 1.4.

Scheme 1.4

The resulting PPI possessed low heat resistance (Tg = 170-210 °C), although these polymers exhibited thermal stability up to 410-486 °C. 12

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) The efforts of Ghassemi and co-workers were directed at the synthesis of new bis(Naminoimides) capable of reacting with aromatic dianhydrides (Scheme 1.5) [8].

Scheme 1.5 The reaction of hydrazine monohydrate with DPTA yielded the bis(N-aminoimide) that was allowed to react with the dianhydride of 2,2-bis[4-(3,4-dicarboxyphenoxy) phenyl]propane (dianhydride A) in m-cresol or o-dichlorobenzene to form a crystalline homopolymer (Scheme 1.6).

Scheme 1.6 This polymer showed solubility only in m-cresol and melted without decomposition. In the synthesis of copolymers, m-phenylenediamine or 4,4´-diaminodiphenyl oxide were added (Scheme 1.7). The reaction duration (3-9 days) can be shortened significantly if a more acidic and higher boiling p-chlorophenol is used as a solvent (Scheme 1.7). General properties of the PPI prepared in accordance with Scheme 1.7 are given in Table 1.2. Table 1.2 indicates that in a series of copolymers, solubility improves with a decrease in the fraction of perylenecarboximide units. A copolymer containing 20 mol% perylenecarboximide rings exhibits good solubility in chloroform, whereas a copolymer bearing 80 mol% of these

13

14

20:80

X

Chloroform

Tetrachloroethane

m-Cresol, tetrachloroethane

Chloroform

m:n ratio: ratio of copolymer blocks Ar: aromatic residue included in the molecule of the dianhydride A

80:20

50:50

20:80

VII

VIII

Tetrachloroethane

50:50

VI

IX

m-Cresol, tetrachloroethane

80:20

m-Cresol

V

—

100:0

Solubility

IV

—Ar—

m:n (%mol)

PPI

0.50

0.36

0.47

0.34

0.53

0.43

247

304

353

250

317

359

—

507

489

474

505

475

468

470

°C

°C (dl/g) 0.48

T5%,

Tg,

ηred,

Table 1.2 Some properties of copolymers of the general formula [8]

Polymer Yearbook


Scheme 1.7

units shows limited solubility in tetrachloroethane and is completely soluble only in m-cresol. Note that the homopolymer shows high solubility only in m-cresol. As shown by DSC, the Tg of copolymers synthesised using m-phenylenediamine are somewhat higher (359-250 °C), as compared to the copolymers derived from 4,4´-diaminodiphenyl oxide (353-247 °C). According to Ghassemi and co-workers, this finding is explained by the higher flexibility of an ether linkage [8]. X-ray diffraction analysis revealed that the homopolymer and copolymer containing 80 mol% perylene rings are crystalline compounds. As the perylene rings are substituted by mphenylenediamine or 4,4´- diaminodiphenyl oxide, the degree of crystallinity drops sharply. Although DSC investigation does not display any transition in the crystalline homopolymer, which decomposes above 450 °C without softening, thermomechanical analysis shows that Tg = 405°C. All the polymers possess high thermal stability in the temperature range from 453 to 507 °C. In our opinion, the most successful attempts at preparing PPI by polycondensation of DPTA and diamines were reported in [9, 10]. Homogeneous reaction was achieved when DPTA was modified by the incorporation of bulky substituents, namely phenoxy, 4-tertbutylphenoxy, and sulfophenoxy groups, into a perylene ring. The PPI, XI-XIV and XVI (Table 1.3) were prepared by polycondensation in m-cresol using catalysts (benzoic acid and isoquinoline) (Scheme 1.8).

15

16 +

+

+

XII

XIII

XIV

NMP +

—R′—

XI

—R—

solubility and molecular parameters of PPI ±

±

±

+

±

–

± +

±

Toluene +

THF +

+

CHCl3

Solubility

Table 1.3 Solubility and molecular parameters of PPI [9, 10]

34.1

64.1

46.9

22.6

Mw × 10-3

[9]

[9]

[9]

[9]

Reference

Polymer Yearbook

Note: — is an insoluble polymer, ± is a partially soluble polymer CHCl3: chloroform THF: tetrahydrofuran NMP: N-methylpyrrolidone

XVII

+

XVI

±

±

+

±

±

±

Toluene

THF

CHCl3

Solubility

Water soluble polymer

NMP +

—R′—

XV

—R—

Table 1.3 Solubility and molecular parameters of PPI [9, 10] continued

–

57.7

29.1

Mw × 10-3

[10]

[10]

[10]

Reference


17

Polymer Yearbook

Scheme 1.8

Polymer XV was prepared by the Yamamoto reaction [16, 17] in DMF at 60-65 °C using bis(cyclooctadiene)nickel (NiBr2Lm) as a catalyst (Scheme 1.9).

Scheme 1.9

18

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) For the PPI, the presence of a bulky substituent in a perylene fragment ensured solubility in organic solvents [(m-cresol, N-methylpyrrolidone (NMP)]. Dark-red transparent films were cast from these solutions. Table 1.3 shows that PPI solubility grows with an increase in the bulkiness of the side substituents. Analysis of polymer solubility in chloroform indicates that the solution of polymer XV shows a tendency toward precipitation. On the contrary, polymer XIV, bearing a more flexible diamine component, forms solutions up to a concentration of 0.2%, and polyimides XI-XIII are soluble up to a concentration of 0.5%. Water-soluble polymer XVII was produced by the selective sulfonation of PPI XVI which is soluble in organic solvents. As indicated by TGA, polyimides exhibit thermal and thermooxidative stabilities up to 350 °C.

1.3 Polyimides Based on Naphthalene-1,4,5,8-Tetracarboxylic Acid Dianhydride Another class of polyimides that are characterised by a higher chain flexibility, when compared to PPI, are based on naphthalene-1,4,5,8-tetracarboxylic acid dianhydride (DNTA). These polymers are of considerable interest due to their high heat resistance and thermal stability and due to easy accessibility of the starting monomers. DNTA is a widely available dianhydride showing the highest electrophilic reactivity among bis(naphthalene-tetracarboxylic anhydrides [18, 19]. Although some authors [20] state that poly(naphthalenecarboximides) (PNI) can be synthesised by the classical two-stage method, this approach seems to be ineffective in the synthesis of these polymers. Earlier investigations into the single-stage synthesis of PNI [21-29] revealed that the reaction of DNTA with m- and p-phenylenediamines, benzidine, 4,4´diaminodiphenyloxide, etc., yields only low-viscous products (ηlog = 0.05-0.15 dl/g), which precipitate from the reaction solution at early stages of the process because of their insolubility in organic solvents. When the polycondensation process was carried out in organic solvents (nitrobenzene, NMP, and m-cresol) at 180-210 °C and an effective catalyst (benzoic acid) was used, PNI having high viscosity characteristics and exhibiting film-forming properties were synthesised [3-36]. On the basis of ‘cardo’ diamines, such as 3′,3′′-bis(4-aminophenyl)phthalide and 9′,9′′bis(4-aminophenyl)fluorene [30, 32, 37, 38], homopolyimides that are soluble in m-cresol and a tetrachloroethane:phenol (3:1) mixture were prepared (Scheme 1.10).

19

Polymer Yearbook

Scheme 1.10

Block and statistical copolyimides (Figure 1.2) were obtained from DNTA and aromatic and aliphatic diamines [39].

Where:

R=

(CH2)n

,

n = 6, 8, 9, 12;

CX3 R′ =

C

, X = H, F;

CX3

,

,

O CO

CO

Figure 1.2

20

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) Film cast from solutions in a tetrachloroethane:phenol (3:1) mixture had a tensile strength of the order of 60-80 N/m2 and retained up to 50% of their initial strength upon heating to 200 °C. The high heat resistance and asymmetric structure of PNI hamper to the orientation of films made from these polymers. However, even a uniaxial orientation of PNI based on dodecamethylenediamine (ηlog = 0.81 dl/g) at 260 °C leads to an increase in the tensile strength σ from 60 to 160-200 N/m2 and in the elongation at break from 7 to 30% [40]. The use of another cardo monomer, namely 3,3-bis(4-aminophenyl)-quinuclidine (Figure 1.3) [41]:

Figure 1.3 made it possible to prepare DNTA-based high molecular weight polymers in the absence of a catalyst. Apparently, this is associated with the fact that a quinuclidine moiety contained in the monomer acts as catalyst. When the process was performed in the presence or in the absence of a catalyst (benzoic acid), under the conditions reported in [30, 32, 37, 38], PNI soluble in m-cresol and hexafluoropropanol and characterised by ηlog = 0.73 and 0.53 dl/g, respectively, were produced. The use of aromatic diamines with quinoxaline (Figure 1.4) [32, 33] and N-benzimidazole rings [34-36] as the nucleophilic monomer allowed the preparation of PNI soluble in phenolic solvents.

N H 2N

R

N R′

N

,

N

NH2, H2N

,

N

O

;

R′ = O

NH2 N

[32, 33]

Figure 1.4

21

Polymer Yearbook

Figure 1.5

The resulting polymers did not undergo softening before the onset of decomposition, except for PNI based on bis[(1-phenyl-2(3-aminophenyl)-benzimideazole-5-yl)] and bis[(1phenyl-2(3-aminophenyl)benzimideazole-5-yl)]-sulfone containing m-phenyl groups, which have a softening temperatures near 400 °C. As demonstrated by the dynamic TGA, the polymers under investigation showed 5% weight losses in the temperature range 520-545 °C. Polycondensation of DNTA with 1,3-bis[4′(4′′-aminophenoxy)cumyl]benzene in m-cresol yielded PNI of the Figure 1.6 [42]:

Figure 1.6

Although the diamine component contained ether linkages and isopropylidene groups, this polymer turned out to be insoluble in the organic solvents (chloroform or 1,2dichloroethane combined with trifluoroacetic acid, hexafluropropanol, or dichloroacetic acid); therefore, it was impossible to determine the viscosity characteristics of the polymer. The Kuhn segment length of this flexible-chain polymer was found to be 28.4 Å. According to X-ray diffraction analysis, the polymer did not form an LC-phase and did not exhibit any indications of the crystalline structure upon heating at 250 °C in vacuum for 48 hours. It has a Tg determined by DSC at 205 °C. 22

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) Synthesis of DNTA-based PNI that are soluble in phenolic solvents and in some other organic solvents is described in [14]. Optimal PNI structures were determined by computer-aided design. As a result, 4,4′-diamino(diphenyl ether of resorcinol), 2,2-bis[4-(4-aminophenoxy) phenyl]propane (diamine A), 2,2-bis[4-(3-aminophenoxy)phenyl]propane, and 2,2-bis[4-(4aminophenoxy)phenyl] hexafluoro-propane, were chosen as the DNTA comonomers. PNI were synthesised in phenol under heterogeneous conditions, polymer (XVIII) and homogeneous conditions using benzoic acid benzimidazole as the catalyst (see Table 1.4). Polymer XVIII (Table 1.4), whose diamine component contains two ether linkages and a m-phenylene fragment, shows solubility only in phenolic solvents and sulfuric acid. Poor solubility of PNI XVIII can be associated with its crystalline structure (X-ray diffraction analysis data). Polymer XX and XXI based on tetranuclear phenoxyamines with p-phenylene fragments are soluble in some organic solvents (NMP, DMA, DMF, and chloroform). This finding is explained not only by the chemical structure, but it also related to the amorphous state of the polymers. Synthesis of a high molecular weight PNI (XX; ηred = 4.26 dl/g) that shows solubility in chloroform permitted the preparation of films possessing fairly good gas-separation properties [43]. Contrary to the current notions that the rigid-chain PNI are insoluble in organic solvents and, consequently, it is impossible to prepare high molecular weight polymers, a high molecular weight poly(naphthylimidebenzimidazole) (PNIB) (Figure 1.7) based on 5(6)amino-2-(p-aminophenyl)benzimidazole was prepared by the catalytic condensation using new catalysts - carboxylic acids and nitrous heterocycles[15].

Figure 1.7

The resulting polymer was soluble in phenolic solvents and formed high strength films with the following characteristics: σ = 470 MPa, ε = 35%, and E = 5000 MPa. To achieve a further increase in the strength of film materials, a wide variety of high molecular-mass rigid-chain homo- and copoly(naphthylimides) containing benzimidazole rings were prepared (Scheme 1.11) [44, 45].

23

24 2.71*

3.94*

4.26

XIX

XX

—R—

XVIII

PNI

ηred (NMP), dl/g T5%*, °C

500 (470)

450 (470)

450 (470)

Tg, °C

410 (370)

350 (350)

290 (300)

+

+

+


---

-- -

-- -

NMII

---

---

---

DMA

Solubility

Table 1.4 Some properties of PNI of the general formula [14]

-- -

---

---

DMF

---

---

---

CHCl3

Polymer Yearbook

—R—

0.41

T5%* °C

440 (466)

Tg, °C

270 (260)

Note: The data given in parentheses were determined by calculation * Measured in tetrachloroethane: phenol (3:1) mixture

XXI

PNI

ηred (NMP), dl/g

+


+

NMII

+

DMA

Solubility

Table 1.4 Some properties of PNI of the general formula [14] continued

+

DMF

+

CHCl3


25

Polymer Yearbook

Where:

Scheme 1.11

The resulting polymers were soluble in sulfuric acid, and had high viscosities (ηred = 2.8-18.1 dl/g in 0.1% solution of H2SO4) and exhibited excellent thermal stability (T5% = 550-610 °C). Later, it was demonstrated that copolymers based on PNIB containing no less than 20-30 mol% rodlike fragments (Figure 1.8) offer the best tensile strength properties [45]. Great attention was paid to the polynaphthalenecarboximides containing sulfonic groups [46-61]. Such polymers which may be used for the preparation of protonoconductive membranes for fuel cells [62-64] are usually prepared by the interaction of DNTA with 4,4′-diaminobiphenyl-2,2′-disulfonic acid or a mixture of this sulfonated monomer with other aromatic diamines (Scheme 1.12).

26


Figure 1.8

Scheme 1.12

As well as 4,4′-diaminobiphenyl-2,2′-disulfonic acid [46-57], diamines such as sulfonated bis-(3-aminophenyl)phenyl phosphine oxide (Figure 1.9) were used for the preparation of sulfonated polyimides [58]:

27

Polymer Yearbook

Figure 1.9

3,3′-disulfonate-bis[4-(3-aminophenoxy)phenyl]sulfone (Figure 1.10) [59]:

Figure 1.10

9,9-bis(4-aminophenyl)fluorene-2,7-disulfonic acid (Figure 1.11) [61]:

Figure 1.11

It was shown [65], that a naphthalenecarboximide ring has a nonplanar structure. On the basis of the Kuhn segment length of a rigid-chain polymer (Figure 1.12) determined by diffusion (1200 ± 300 Å) and flow birefringence (1600 ± 400 Å), the authors [65] established that the following conformation fragments prevail in the polymer: boat (10-15% with a = 20° or 15-20% with a = 15°) (Figure 1.13) and chair (Figure 1.14) foams.

28


Figure 1.12

Figure 1.13 Chair form

Figure 1.14 Boat form

PNI with bulky N-naphthalenecarboximide ortho substituents, synthesised from bis[3amino-4-(p-aminophenoxy]arylenes [66] were allowed to react first with DNTA and then with a two-fold molar amount of naphthalic anhydride under the conditions ensuring high-temperature polycondensation (Scheme 1.13, method A). The resulting polymers showed high viscosity characteristics (ηred = 0.9-1.35 dl/g) corresponding to molecular weight (Mw) = (5.0-6.4) × 104. They were soluble in phenolic solvents, NMP, and tetrachloroethane. The Tg of the polymers ranged from 350 to 360 °C, while the temperatures of the 10% weight loss in air were between 510 to 530 °C. An alternative addition of mono- and dianhydrides yielded PNI with still bulkier N-(pphenoxy)naphthalenecarboximide ortho substituents. Thus PNI prepared (Scheme 1.13, method B) had Mw = (2.2-2.6) × 104 and, unlike PNI with N-naphthalenecarboximide ortho substituents, these polymers were partially soluble in chloroform. The softening temperatures of these polymers were in the 330-350 °C range, and the temperatures of the 10% weight loss ranged from 500 to 515 °C.

29

Scheme 1.13

Polymer Yearbook

30

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) Recently Hay and co-workers developed a method for preparing PNI that involves the use of a monomer containing imide rings [67]. The reaction of hydrazine with DNTA proceeds in a similar fashion to that in Scheme 1.4 and yields bis(aminoimide) that reacts with 2,2-bis([4-(3,4-dicarboxyphenoxy)phenyl]propane (dianhydride A) in an mcresol:o-dichlorobenzene mixture under the conditions of the single-stage polycondensation to produce poly(ether naphthalenecarboximide) (PENI) (Scheme 1.14):

Scheme 1.14

Copoly(ether imides) of the structures shown in Figure 1.15 were prepared using a mixture of dianhydride A with other aromatic tetracarboxylic acid anhydrides.

Figure 1.15

Only the reaction of the resulting monomer with dianhydride A made it possible to prepare high-molecular-weight homopolymers, while copolyimides were synthesised by the copolycondensation of bis(aminoimides) with dianhydride A and other dianhydrides.

31

Polymer Yearbook In the latter case, the molar ratio of reagents was 2:1. All the other polymerisation reactions produced low-molecular-weight, insoluble oligomers, which precipitated from the reaction solutions at the early stages of the process. Dianhydride A homopolymer is soluble in chloroform, while its copolymers show solubility in an m-cresol:o-dichlorobenzene mixture. The copolymers based on 2,2′bis(3,4-dicarboxyphenyl)hexafluoropropane are soluble only in a p-chlorobenzene:odichlorobenzene mixture. All the PENI, as demonstrated by DSC, have Tg above 340 °C; the copolymers derived from 2,2′-bis(3,4-dicarboxyphenyl)hexafluoro propane exhibit the highest heat resistance. TGA measurements demonstrated that fluoro-containing poly(ether naphthalene carboximide) possess the highest thermal stability. These polymers lose 5% of their original weight both in air and under nitrogen in the temperature interval extending from 495 to 526 °C, unlike dianhydride A-based polymers (445-465 °C). According to Hay and co-workers [67], the rigid naphthalenecarboximide fragments in the polymer chain and the restriction in rotation around an N—N bond are responsible for an increased Tg, whereas the dianhydride A groups and ether linkages impart flexibility and, consequently, solubility to the polymer. ULTEM (General Electric), one of the best commercial poly(ether imides), which is produced from dianhydride A and m-phenylenediamine, has a Tg of 215 °C [68]. When 50% of m-phenylenediamine was replaced by bis(aminoimide), a new copoly(ether imide) having Tg = 288 °C, and a temperature for the onset of degradation of 453 °C, was obtained. Its solubility was similar to that of ULTEM.

1.4 Polyimides Based on Non-condensed bis(Naphthalic Anhydrides) Another way of rendering PNI soluble is to use various bis(naphthalic anhydrides) of less condensed structure when compared with DPTA and DNTA [19, 21, 27, 69-82]. Interaction of bis(naphthalic anhydride) with 1,12-diaminododecane (Scheme 1.15) leads to the formation of PNI very soluble in methylene chloride and chloroform [69].

Scheme 1.15

32

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) Starting from 4,4′-diaminodiphenyl ether oxide and various dianhydrides of oxyaryleneand thioarylene-bis(naphthalic acids), PNI of the general formula shown in Figure 1.16 were synthesised [21, 70]. The polycondensation reaction proceeded under homogeneous conditions in m-cresol using quinoline or isoquinoline as the catalysts. PNI formed solutions in m-cresol up to a concentration of 15%.

Where:

Figure 1.16

However, their viscosity characteristics were low (ηlog = 0.15-0.30 dl/g), possibly due to the presence of electron-donating groups in the dianhydride component. The Tg of the resulting polymers varied in the range 253-317 °C. Higher molecular mass PNI were prepared by using bis(naphthalic anhydrides) bearing carbonyl electron-acceptor groups [70-73]. The reaction was carried out in m-cresol in the presence of benzoic acid as a catalyst. Polymers of the general formula shown in Figure 1.17 were soluble in phenolic solvents, while the polymers with the central ether and hexafluoroisopropylidene groups showed solubility in tetrachloroethane as well. The resulting PNI had softening temperatures ranging from 275 to 335 °C. The six-membered anhydride rings exhibit a lower electrophilic reactivity than their five-membered analogs, therefore, Sek and co-workers [74] investigated catalytic systems, which show the highest efficiency in the polycondensation reactions involving sixmembered anhydride rings. When studying the reaction of 1,4-bis(1,8-dicarboxynaphthoyl-4)-benzene dianhydride with 4,4´-diaminodiphenyl oxide, it was established that, depending on the viscosity of the

33

Polymer Yearbook

Figure 1.17

resulting polymers, the catalytic systems can be arranged in the following order: benzoic acid + isoquinoline > benzoic acid + quinoline > benzoic acid + imidazole > benzoic acid. Sek and co-workers [74] note that the polymer with the highest viscosity (ηred = 1.96 dl/g) was obtained using two catalysts: benzoic acid (2 mol), which was added to dianhydride (1 mol) at the beginning of the reaction, and isoquinoline (2 mol), which was introduced into the reaction mixture several hours later. In recent years, Sek and co-workers [75] managed to synthesise higher molecular weight PNI (relative to the polymers reported in [21, 70-73]), using the catalytic system composed of benzoic acid and isoquinoline. These authors used dianhydrides with both ketoaryleneand oxyarylene central fragments as shown in Figure 1.18. The polymers based on a dianhydrides with ether bonds and an unsubstituted central phenylene nucleus had somewhat higher viscosities as compared to the substituted structures. All the synthesised polymers were soluble in m-cresol, while the PNI bearing two substituents in ortho positions were also soluble in NMP, DMA, and DMSO. On the basis of the observation that the polymers derived from 4,4′-diaminodiphenyl oxide and 4,4′-diaminodiphenylmethane formed friable films, in contrast to a polymer based on 3,3-dimethylbenzidine, Sek and co-workers arrived at a controversial conclusion that the ortho substituents exert a stronger effect on the polymer flexibility than the bridging bonds between the phenylene nuclei [75]. It is doubtful whether applications for the resulting PNI can be found, because, for most of the polymers, no Tg were detected or, as in the case of PNI based on diamines with

34


Figure 1.18

alkyl substituents in ortho positions, the polymers possessed low heat resistance (Tg = 113-192 °C). The polymers exhibited similar thermal stability: the temperatures of the 10% weight loss varied in the 420-460 °C range; the polymers based on 4,4´diaminodiphenylmethane showed the lowest thermal stability. As a continuation of the studies aimed at improving the solubility of DNTA- and DPTAbased PNI [5, 14] tetranuclear phenoxyamines were also used in the synthesis of PNI starting from dianhydrides containing both ketoarylene and oxyketoarylene fragments (Scheme 1.16) [76] The previous reactions proceeded under homogeneous conditions. Table 1.5 summarises the calculated and experimental characteristics of the resulting polymers. The solubility of PNI based on 1,3-bis(1,8-dicarboxynaphthoyl)benzene dianhydride is almost identical to that of PNI prepared from 4,4´-bis(1,8-dicarboxynaphthoxy4)benzophenone dianhydride. Contrary to the DNTA-based PNI [14], para isomeric

35

Polymer Yearbook

Scheme 1.16

structures containing hinge groups in the dianhydride component are soluble in NMP and chloroform. However, among meta isomeric structures, only fluoro-containing PNI show solubility in DMA and DMF. Using chloroform solutions of high-molecularweight PNI, XXII and XXV, flexible, transparent films were prepared that can be used to make gas separation membranes [43]. Comparison of data presented in Table 1.5, demonstrates that the isomeric structure of the polymer unit affects the heat resistance of the polymers. For the identical chemical structures of the corresponding polymer pairs (XXII and XXV, XXIII and XXVI, and XXIV and XXVII), PNI containing meta isomeric fragments (see Table 1.5, polymers XXV, XXVI, XXIV, and XXVII) have lower Tg. Variation in the chemical composition of a polymer by substituting an isopropylidene group by a hexafluoroisopropylidene moiety made it possible to increase the PNI thermal stability. At the same time, the softening temperatures of the polymers became somewhat lower, thereby increasing the difference between the temperatures of softening and degradation. Moreover, the polymers with hexafluoroisopropylidene groups feature the lowered values (by 2-4 times) of reduced melt flow indexes (Table 1.5). Japanese researchers made an attempt to prepare soluble PNI from a silicon-containing bis(naphthalic anhydride) (Figure 1.19) [77].

36

+

XXIV

+ +

H

XXVI F

XXV

+

XXIII F

Meta-isomeric structures

+

H

XXII

Para-isomeric structures

X

PNI

Tetrachloroethane: phenol

+

+

+

+

+

-

-

-

-

-

-

-

-

-

-

NMP DMA DMF

Solubility

+

+

+

+

+

Chloroform

0.50

0.40

0.52

0.57*

2.08*

3.54*

dl/g

(NMP),

ηred

Table 1.5 Properties of PNI of the general formula [76]

°C

T5%,

250 490

260 470

280 470

290 500

270 420

°C

Tg,

320

320

-

-

-

2.0

4.0

8.0

-

-

-

Injection η eff moulding -5 temperature, × 10 , Pa.s °C


37

38 +

H

XXVII

XXVIII F

* Measured in a tetrachloroethane:phenol (3:1) mixture

+

X

PNI

Tetrachloroethane: phenol

+

+ -

-

-

NMP DMA DMF

Solubility

+

+

Chloroform

0.28

0.30

dl/g

(NMP),

ηred

°C

T5%,

250 500

250 480

°C

Tg,

Table 1.5 Properties of PNI of the general formula [76] continued

300

320

1.4

2.8

Injection ηeff moulding -5 temperature, × 10 , Pa.s °C

Polymer Yearbook


Figure 1.19

The resulting polymers (ηred = 0.10-0.24 dl/g) show a partial or complete solubility in m-cresol and NMP. The silicon content in PNI was dependent on the diamine structure, and with an increase in the silicon content, the polymer solubility was improved. For the thermal stability, the reverse trend was observed, namely as the silicon content in the polymer increased, the temperature of PNI degradation decreased and varied in the 455-475 °C range. PNI containing multiple phenyl side groups were prepared by the interaction of bis(naphthalic anhydrides) bearing eight phenyl substituents with aromatic diamines (Scheme 1.17) [78-80]. All highly phenylated polynaphthalenecarboximides thus obtained demonstrated very good solubility in various organic solvents combined with high thermal stability. Researchers involved in the synthesis of poly(ether imides) from diamines bearing imide rings [67] reported on the preparation of polymers of the general formula shown in Figure 1.20 [81] PENI synthesised under homogeneous conditions were soluble in m-cresol, odichlorobenzene, and NMP and showed film-forming properties. PENI were characterised by high Tg (307-406 °C), the Tg of the fluoro-containing polymers being 23-54 °C higher. As expected, these polymers also feature an enhanced thermal stability (507-521 °C), as demonstrated by the TGA data. Using the method developed by Rusanov and co-workers [66], PNI with bulky Nnaphthalenecarboximide ortho substituents were synthesised. These polymers were derived from bis[3-amino-4-(p-aminophenoxy)]arylenes [66, 82] that were allowed to react first with the dianhydride of bis[1-phenyl-2-(4,5-dicarboxynaphth-1-yl) benzimidazole-5-yl]sulfone and then with a two-fold molar amount of naphthalic anhydride under the conditions of high-temperature polycondensation (according to a scheme similar to Scheme 13, method A).

39

Polymer Yearbook

Scheme 1.17

40


Figure 1.20

The resulting polymers had ηred = 0.9-1.58 dl/g corresponding to Mw = (6.0-7.2) × 104 and were soluble in phenolic solvents, NMP, and tetrachloroethane. The Tg of the polymers were in the 330-340 °C range, and the temperatures of the 10% weight loss in air ranged from 480 to 505 °C. An alternative addition of mono- and dianhydrides led to PNI with N-(p-phenoxy) naphthalenecarboximide ortho substituents. PNI prepared by this method (Scheme 13, method B) had ηred = 0.27-0.40 dl/g [Mw = (2.2-3.0) × 104], and unlike PNI with N-naphthylimide ortho substituents, they showed a partial or complete, in the case of sulfur-containing polymers, solubility in chloroform. These polymers had Tg = 315-350 °C, and the temperatures of the 10% weight loss were in the 480-515 °C range. The experimental results presented previously demonstrate that considerable progress was achieved in the synthesis of polyimides bearing six-membered naphthylimide rings. Different synthetic approaches allowed for the preparation of soluble high-molecular-weight systems using processing by solution and thermal methods. It is expected that in the near future this rapidly developing field of polymer chemistry will witness remarkable new achievements.

41

Polymer Yearbook

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Polymer Yearbook 32. V.V. Korshak, E.S. Krongauz, S.V. Vinogradova, S. Vygodskii, N.M. Kofman, Kh. Raubakh, K.H. Frommel’t, D. Khain and B. Fal’k, Doklady Akademii Nauk SSSR, 1977, 236, 4, 890. 33. H. Raubach, H. Frommelt, D. Hein, V.V. Korshk, S.V. Vinogradova, E.S. Krongauz, J.S. Vygodskyj, N.M. Kofman, A.P. Travnikova, B. Falk and R. Bekker, Faserforschung und Textiltechnik, 1977, 28, 11-12, 611. 34. V.V. Korshak, A.L. Rusanov and I. Batirov, Doklady Akademii Nauk SSSR, 1978, 240, 1, 88. 35. I. Batirov, Yu.F. Milyaev and L.N. Balyatinskaya, Proceedings of the International Symposium on Macromolecular Chemistry, Tashkent, 1978, Volume 3, 34. 36. I. Batirov, Synthesis and Investigation of Organosoluble Polyimides based on Meterocyclic Diamines, Moscow Institute of Organoelement Compounds, USSR Academy of Science, 1978. [PhD Thesis] 37. S.V. Vinogradova, J.S. Vygodskyj and N.A. Churochkina, Vysokomolekulyarnye Soedin B, 1977, 19, 2, 93. 38. S.V. Vinogradova and Ja. S. Vygodskij, Faserforschung und Textiltechik, 1977, 28, 11-12, 581. 39. Ja.S. Vygodskii, V.V. Korshak, S.V. Vinogradova, Ya. G. Urman, S.G. Alekseeva, I.Ya. Slonim, G. Rainish, E.Bonatts, E. Yakab, F. Till and G. Rafler, Acta Polymerica, 1984, 35, 11, 690. 40. Ja.S. Vygodskii, Investigations in the Synthesis and Properties of Cardo Polimides, Moscow Institute of Organoelement Compounds, USSR Academy of Science, 1980. [DSc Thesis] 41. Ja. S. Vygodskij, N.A. Churochkina, T.A. Panova and Yu.A. Fedotov, Reactive Polymers, 1996, 30, 214. 42. G. Schwarz, S.I. Sun, H.R. Kricheldorf, M. Ochta, H. Oikawa and A. Yamaguchi, Macromolecular Chemistry and Physics, 1997, 198, 3123. 43. E.G. Bulycheva, L.B. Elshina, A.L. Rusanov, A.F. Alent’ev, Yu.G. Ishunina and Yu.P. Yampol’skii, Polymer Science, Series B, 1997, 39, 11, 390. 44. O.G. Nikol’skii, I.I. Ponomarev, N.S. Perov, V.A. Martirosov, V.P. Zhukov, E.S. Obolonkova, A.F. Bulkin, A.V. Zakharov, N.A. Skuratova and A.L. Rusanov, Polymer Science, Series A, 1993, 35, 9, 1226.

44

Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) 45. I.I. Ponomarev, O.G. Nikol’skii, Yu.A. Volkova and A.V. Zakharov, Polymer Science, Series A, 1994, 36, 9, 1185. 46. R. Salle and B. Sillion, inventors; Cemota Company, assignee; FR 2 212 356 A1, 1974. 47. S. Faure, R. Mercier, P. Albert, M. Pineri and B. Sillion, inventors; Cemota Company, assignee; FR 9 605 707, 1996. 48. S. Faure, N. Cornet, G. Gebel, R. Mercier, M. Pineri and B. Sillion, Proceedings of the Second International Symposium on New Materials for Fuel Cell and Modern Battery Systems, Montreal, Canada, 1997, p.818. 49. E. Vallejo, G. Pourcelly, C. Gavach, R. Mercier and M. Pineri, Journal of Membrane Science, 1999, 160, 127. 50. C. Genies, R. Mercier, B. Sillion, N. Cornet, G. Gebel and M. Pineri, Polymer, 2001, 42, 359. 51. C. Genies, R. Mercier, B. Sillion, R. Petiaud, N. Cornet, G. Gebel and M.J. Pineri, Polymer, 2001, 42, 5097. 52. S. Faure, R. Mercier, M. Pineri and B. Sillion, Proceedings of the 4th European Technical Symposium on Polyimides and Other High Performance Polymers, STEPI-4, Montpellier, France, 1996, Eds., M.J.M. Abadie and B. Sillion, p.414. 53. G.I. Timofeeva, I.I. Ponomarev, A.R. Khokhlov, R. Mercier and B. Sillion, Macromolecular Symposia, 1996, 106, 345. 54. Y. Zhong, M. Litt, H. Jiong, R.F. Savinell and J.S. Wainright, Proceedings of the 5th European Technical Symposium on Polyimides and Other High Performance Polymers, Montpellier, France, 1999, Eds., M.J.M. Abadie and B. Sillion, p.268. 55. Y. Zhong, M. Litt, R.F. Savinell, J.S. Wainright and J. Vendramin, Polymer Preprints, 2000, 41, 2, 1561. 56. H-J. Kim and M. Litt, Polymer Preprints, 2001, 42, 2, 486. 57. N. Ganduz and J.E. McGrath, Polymer Preprints, 2000, 41, 2, 1565. 58. H.K. Shobha, M. Sancarapandian, T.E. Glass and J.E. McGrath, Polymer Preprints, 2000, 41, 2, 1298. 59. Y-T. Hong, B. Emsla, Y. Kim and J.E. McGrath, Polymer Preprints, 2002, 43, 1, 666.

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Polymer Yearbook 60. V.A. Solomin, E.N. Lyakh and B.A. Zhubanov, Polymer Science, 1992, 34A, 3, 345. 61. X. Guo, J. Fang, T. Watari, K. Tanaka, H. Kita and K-I. Okamoto, Macromolecules, 2002, 35, 6707. 62. M. Rikukawa and K. Sanui, Progress in Polymer Science, 2000, 25, 1463. 63. J.A. Kerres, Journal of Membrane Science, 2001, 185, 3. 64. A.L. Rusanov, D.Yu. Likhatchev and K. Muellen, Russian Chemical Reviews, 2002, 71, 9, 761. 65. I.A. Ronova, I.I. Ponomarev and O.V. Shishkin, Polymer Science, Series A, 1997, 396, 10, 1122. 66. A.L. Rusanov and Z.B. Shifrina, High Performance Polymers, 1993, 5, 107. 67. H. Ghassemi and A.S. Hay, Macromolecules, 1994, 27, 3116. 68. V.V. Korshak, A.L. Rusanov, G.V. Kazakova, N.S. Zabel’nikov and G.S. Matvelashvili, Vysokomolekulyarnye Soedin A, 1988, 30, 9, 1795. 69. Z.Y. Wang, Journal of Polymer Science, Polymer Chemistry Edition, 1995, 33A, 1627. 70. G.A. Loughran and F.E. Arnold, inventors; The USA as represented by the Secretary of Air Force, assignee; US Patent 3 987 003, 1976. 71. A.L. Rusanov and E.G. Bulycheva, Proceedings of the 2nd European Technical Symposium on Polyimides and Other High-Temperature Polymers, STEPI-2, Montpellier, France, 1991, p.125. 72. D. Sek, P. Pijet and A. Wanic, Proceedings of the 3rd European Technical Symposium on Polyimides and Other High-Temperature Polymers, STEPI-3, Montpellier, France, 1993, p.121. 73. F.I. Adyrkhaeva, Synthesis and Investigation of Aroylene-bis (naphthalic anhydrides) and Polyheteroarylenes Synthesised from Them, Moscow Institute of Organoelement Compounds, USSR Academy of Science, 1982. [PhD Thesis] 74. D. Sek, P. Pijet and A. Wanic, Polymer, 1992, 33, 1, 190. 75. D. Sek, P. Pijet and E. Schab-Balcerzak, Journal of Polymer Science A, 1997, 35, 539.

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Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides) 76. A.L. Rusanov, A.P. Krasnov, E.G. Bulycheva, L.B. Elshina, N.A. Svetlova and Yu.E. Doroshenko, Polymer Science, Series B, 1997, 39, 11, 406. 77. Y. Yamada and N. Furukawa, High Performance Polymers, 1997, 9, 135. 78. M.L. Keshtov, A.L. Rusanov, A.A. Askadskiy, V.V. Kireev, S.V. Keshtova and F.W. Harris, Polymer Science, 2001, 43A, 3, 399. 79. M.L. Keshtov, A.L. Rusanov, N.M. Belomoina, A.R. Khokhlov, A.A. Kirillow, V.V. Kireev, A.N. Shchegolikhin and S.V. Keshtova, Proceedings of the 5th European Technical Symposium on Polyimides and Other High Performance Functional Polymers, STEPI-5, Montpellier, France, 1999, PL-19. 80. M.L. Keshtov, A.L. Rusanov and F.W. Harris, Proceedings of the Second International Symposium on Polyimides and Other High Temperature Polymers: Synthesis, Characterization and Applications, Newark, NJ, USA, 2001, Abstracts, 19. 81. H. Ghassemi and A.S. Hay, Macromolecules, 1993, 26, 5824. 82. A.L. Rusanov and Z.B. Shifrina, Polymer Science, Series A, 1995, 37, 2. 143.

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48

2

Macromolecular Properties and Topological Structure of Lignin A.P. Karmanov and Yu.B. Monakov

2.1 Introduction Experimental data on hydrodynamic properties of natural and biosynthetic lignins in dilute solutions are reviewed. The results of viscometric, translational diffusion, and sedimentation studies provide evidence for the macromolecules of lignin having a complex topological structure. The benefits and limitations of the theoretical approaches used to describe the topology of lignin macromolecular chains are discussed. The relationship between hydrodynamic characteristic and fractal properties of lignin is considered. During the long evolutionary period, through self-organisation and natural selection, nature has created a very complex multicomponent polymer composite, namely, wood. Structural organisation of lignin, which is one of the essential components of wood, controls the mechanical properties: compression and flexure, chemical resistance and thus lignin acts as an antioxidant and biological protection against pathogenic microorganisms [1, 2]. It is now accepted that the biosynthesis of lignin occurs by dehydrogenating free radical polymerisation of monolignols catalysed by a peroxidase hydrogen peroxide enzymic system [3]. The main monolignols are coniferyl, sinapyl, and p-coumaryl alcohols. Cinnamic aldehydes and acids that are biogenetic precursors to the monolignol can also take part in the biosynthesis. This chapter is concerned with the topological aspects of the structural organisation of lignin. Lignin is synthesised in plants from monomeric molecules, whose functionality varies from two to four. Thus, both branched chain and the crosslinked structure may be formed. In plant tissue, the polymer chains of lignin are surrounded by macromolecules of noncellulosic polysaccharides, with which they form an amorphous lignocarbohydrate matrix. The experimental methods that allow the study of the complex topology of macromolecules in a multicomponent solid composite are very limited. Therefore, most of the data are interpreted using theoretical methods developed from polymer chemistry. Because there are no effective experimental methods for the investigation of lignin in situ, the general approach adopted involves systematic studies of soluble samples isolated

49

Polymer Yearbook from wood. Structural studies of lignin chains are essentially similar to the investigation of synthetic polymers, although the specific features of lignin somewhat restrict the variety of experimental methods that can be used. Detailed investigation of the structure of lignin macromolecules was undertaken by Goring [4-6]. In his studies, Goring used sedimentation, translational diffusion, and viscometry measurements. Hydrodynamic studies are still one of the main sources of data about the structure of lignin macromolecules. However, these methods do not provide comprehensive information concerning the structure of lignin. Moreover, conventional approaches may be inadequate for the unambiguous characterisation of the macromolecular structure of this biopolymer. Quantitative assessment of the parameters of topological structure from experimental data on hydrodynamic properties often leads to controversial inferences. One of the natural causes of this situation is the absence of linear lignin analog. Generally, adequate description of the structure of macromolecules is a complex problem and not only in the field of lignin chemistry. In the chemistry of polysaccharides, this problem is not solved for complicated pectins either. In the absence of reliable data about the nature of branched junctions and the factors that control their distribution in a chain, quantitative assessment of the structure inevitably depends on the unavoidable assumptions made within the frameworks of various models. Presently, fractal concepts, which have grown out of the ideas introduced by De Gennes [7], have become common in the physical chemistry of polymers. It was established that a random walk without crossover, which describes the statistics of polymer chains with excluded volume, possesses a fractal structure. In recent years, the studies of lignin and its biosynthetic analogs has allowed significant progress to be made, which has resulted from the combined use of conventional methods and new approaches involving the application of fractal concepts and computer-aided studies. The results obtained offer a clue to a better understanding of the structure of macromolecules and indicate prospects for the future studies of the structural organisation of lignin.

2.2 Topological Structure of Lignin Macromolecules According to Erins [8, 9], the spatial structure of amorphous lignocarbohydrate matrix of wood is described by a superposition of three networks: a network of hydrogen bonds (H-network), which involves both lignin and carbohydrates; a network of lignocarbohydrate valence bonds (LCV network), and a lignin network. The concept of treating native lignin as a network structure has become popular, because this model makes interpretation easier of the complex processes that occur during the technological treatment of wood. The strongest argument in favour of the network model

50

Macromolecular Properties and Topological Structure of Lignin is presented by the insolubility of natural lignin in any ‘neutral’ solvent without previous chemical or mechanical degradation [3, 10]. The second argument relates to the high polydispersity of lignins isolated from plant tissue, because it is distinctly this kind of distribution that is expected to result from network fragmentation [5]. The physicochemical properties of lignin solutions and a rather high content of trifunctional monomer units in the lignin chains support this point of view [8]. Indeed, network polymers are insoluble in any solvents: they do not melt and they contain tri- or tetrafunctional units. At the same time, the fact that a polymer possesses these properties cannot unambiguously prove that it is a crosslinked polymer network. Indeed, some uncrosslinked polymers were also reported to possess these properties [11, 12]. According to an alternative viewpoint, lignin in situ exists as a polymer with a relatively low branched chain structure content. Within this framework, the insolubility of native lignin is explained by the fact that it is linked to polysaccharides by either valence and/or hydrogen bonds. For example, Evstigneev and co-workers [13] claim that the dissolution of lignin (delignification) must be preceded by functionalisation of the macromolecules of lignin, whose molecular mass distribution (MMD) has been completely specified at the instant of the biosynthesis in the cellular wall. Let us consider the results of the studies dealing with the topological structure of lignin. One of the approaches to solving the problems related to the formation of network topology involves statistical methods of the theory of branching processes, which are considered the most perfect form of statistical methods [12]. In [14], the parameters describing the gelation of lignin were determined. The known models for the macromolecules of lignin were represented by the graph tree in which the phenylpropane units are positioned at the tops, whereas the bonds between the monomer units are the branches of the tree in the graph. Using the theory of branching processes, the condition for gelation was verified and the mean molecular mass of the sol fraction was calculated. It was demonstrated that all theoretical lignin models (except for models of lignosulfonate from spruce) satisfy Flory’s critical condition for gelation, which, in terms of the theory of branching processes, is defined by the inequality: (∂F1/∂x)x=1 ≥ 1

(2.1)

where x is the variable, F1 is the generating function for the probability of the number of monomer ‘offspring’ in the first generation. The calculated molecular mass of the sol fraction (1.3 × 103 – 13.8 × 103) suggests that Braun’s lignin (low-molecular-mass lignin, which is isolated from wood by extraction with ethanol without heating or using catalysts) may be identified with the sol fraction of native lignin. Further development of the concept

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Polymer Yearbook of crosslinked lignin structure allowed the structure of network to be described in greater detail. Using the generating functions for probabilities, Gravitis and Ozol-Kalnin [15] calculated the statistical characteristics of lignin network: average chain length between the junctions, number of active chains in the gel fraction, length of active chain. Unfortunately, it is virtually impossible to assess whether the calculated parameters conform to reality. Only the distance between two branching junctions in a chain can be evaluated experimentally from hydrodynamic data, which are considered in Section 2.3 of this chapter. Recall that applicability of the theory of branching processes rests on two rather important assumptions: reactivities of reacting species are assumed to be independent (Flory principle) and intramolecular cyclisation is banned. According to [9], lignin polymer is a crosslinked system of microgel type, that is an heterogeneous network. Factors that account for the different network density involve the formation of lignin from monomers that contain functional groups of different reactivity [1, 3] and the fact that the polymerisation takes place in a carbohydrate environment, which is thermodynamically incompatible with the incipient lignin [16]. Heterogeneity of the structure of lignin is confirmed by the analysis of the mobility of a nitroxyl spin label [17]. Broad-line NMR spectra of lignin show broad and narrow components [18]; this feature was interpreted [17] as a manifestation of the different degrees of crosslinking, which results in different mobility of network chains. Theoretical treatment of the formation and the structure of lignin based on the regularities common for crosslinked polymers leads to the conclusion that it is hardly probable that a statistically uniform polymer network may form in different layers of a cell wall [19]. Several factors that give rise to topological heterogeneity of lignin may be: 1. Heterogeneity with respect to the molecular structure [20, 21]. One may assume that topological heterogeneity is predetermined genetically by the microstructure of chains. 2. An increase in probability of cyclisation as the molecular mass of macromolecule increases [22]. This factor follows from general considerations about the feasibility of intramolecular interaction between functional end groups during the growth of a branching tree [12]. 3. Microgelation. According to Bobalek and co-workers [23], formation of a crosslinked polymer can proceed via the formation of microgel. Data on the formation of supermolecular particles during the in vitro synthesis of model lignins support the assumption that lignification proceeds via microgelation [24]. Of the factors listed previously, only the last one may be related to the formation of a crosslinked structure, whereas the first two are not related directly to the topological nature of the polymer formed.

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Macromolecular Properties and Topological Structure of Lignin Ozol-Kalnin and co-workers [25] derived the kinetic equation that describes the polymerisation on assumption that the reaction proceeds via stepwise addition of the monomer of one kind. To describe the formation of a macroscopic network, the criterion for gelation, suggested previously for free radical polymerisation of unsaturated compounds: dN/dt = dN/dM=0

(2.2)

where N is the number of propagating polymer chains used. Within the framework of this concept, initiation of polymerisation initially leads to accumulation of the number of propagating chains and makes the dependence of the number of chains more profound. On the contrary, crosslinking reduces the number of chains, and, at the end of the process, the quantity dN/dt decreases to zero. This approach makes it possible to take into account the unsteady character of the polymerisation. However, because the mechanisms involved in the propagation of polylignol chains [3] are markedly different from the classical mechanism of free radical polymerisation, this variant hardly pertains to lignin formation. Information about the network structure may be acquired not only in the studies of growth processes, but also in the studies of the reverse process, degradation. This approach was first implemented by Szabo and Goring [26], who considered the fragmentation and dissolution of lignin in alkaline pulping as a reverse process to Flory-Stockmayer gelation. However, agreement between experimental and theoretical data was rather poor in spite of the assumption made that two types of gels, localised in different morphological elements of the cell wall, exist. More satisfactory results were obtained for sulfite delignification, which, according to Yan and co-workers [27, 28], involves the degradation of gel (and the concomitant formation of sol), which is reverse to the condensation of sol and post hydrolysis of bonds (resulting in the formation of low-molecular-mass ω-lignins). Studies by Bolker and Brenner [29] were also based on statistical methods. According to the theoretical notions of the authors, MMD of native lignin depends on the composition of lignin monomeric precursors. To find this quantity, one has to list all probable ways by which the molecular tree with a specified number of junctions and monomer compositions may be drawn. MMD of isolated lignin, i.e., sol, is defined by decomposition velocity of simple ether bonds. This problem was solved by Bolker for a particular case of a crosslinked system in which only the scission of crosslinkages formed by benzylether bond takes place. Summarising the studies using statistical approach to analysis of the structure and behavior of lignin, it is appropriate to note that it was assumed a priori that the distribution of all elements of the described by the most probable distribution. This is possible only if the

53

Polymer Yearbook processes that take place are at equilibrium. However, one cannot exclude that the polymerisation to lignin, which takes place in the open unsteady biosystem that is the cell wall [1, 30], is an essentially irreversible process leading to formation of dissipative structures. The formation of dissipative structure during the in vitro biosynthesis has been demonstrated [31]. The fractal properties of lignin [17, 32] and its biosynthetic analogs [33] that were recently discovered also support the important role of nonequilibrium in the biosynthesis of lignin. One of the promising methods for studying the topological structure of lignin involves computer simulation, which is advantageous over statistical methods in that there is no need to introduce any assumptions concerning the distribution of elements in the system and information about intramolecular cyclisation can be obtained from the modelling. Ozol-Kalnin and co-workers [34-36] simulated, using the Monte Carlo method, polymerisation of lignin macromolecules composed of 50 bi- and tri-functional monomer units. The simulation, which was performed on a cubic lattice, showed that the structure of the crosslinked macromolecule represented a hierarchic system of ring structures. Data on the size of rings and their number reveal that small rings usually prevail. On the basis of stereochemical considerations, the smaller ring in lignins is shown to contain four phenylpropane units. The curve that describes the size distributions for the rings in lignins is a rapidly declining function (Figure 2.1). An important characteristic of lignin topology is presented by the so-called bondedness of the rings, which is described by the degree of their condensation [35]. If the degree of condensation of the rings is equal to unity, the cycles of the graph are separated from each other. In all cases, the degree of condensation was found to be rather high (Figure 2.2), implying that the monomer unit of a ring is at the same time incorporated into several other rings. For a deeper understanding of the topology of lignin chains, computer-simulated fractal clusters present a topic of special interest. Analysis of the scaling properties of fractals that grow according to the model for branched clusters [37] demonstrate several factors. These are the role of the free path of particles, the probability of adding a particle on contact and of the space geometry on the structure (in particular, on the degree of intramolecular cyclisation [38] and the fractal dimensionality (df) [39] of a fractal macromolecule. This behaviour was demonstrated (Figures 2.3 and 2.4). The conclusions drawn from the computer simulation were to some extent confirmed in experimental studies of the properties of wood matter from various species [40]. At the same time, those studies revealed the drawbacks of computer-aided simulations related to the difficulties of making generalisations and limitations on the size of a polymer system, which must not be large.

54

Macromolecular Properties and Topological Structure of Lignin

Figure 2.1 Distribution of the rings with respect to size L. NL is the number of rings of length L, NS is general number of cycles. (1) All units are trifunctional; (2) 5% of the units are trifunctional and 95% are bifunctional [36].

Figure 2.2 Plots of the degree of condensation of the rings (K) versus fraction of bifunctional units C2. (1) Steric limitations are not taken into account; (2) steric limitations are taken into account, formation of tetrafunctional rings is forbidden [35].

55

Polymer Yearbook

Figure 2.3 Degree of intramolecular cyclisation, Y, as a function of the probability of addition P. The free path L = (1)1000, (2)100, (3)10, (4)5.

Figure 2.4 Fractal dimensionality, df, as a function of the particles free path L. The probability of addition P = (1)0.25, (2)0.5, (3)0.75, (4)1 [39].

56


2.3 Hydrodynamic Properties Depending on the procedure used to isolate them, soluble lignin polymers may be divided into three major groups [40]: ‘native’ lignins, for example, milled wood lignin (MWL) and dioxane lignin (DL), industrial lignins (sulfate or kraft lignin, lignosulfonate), and biosynthetic lignins [bulk dehydropolymer (DHP), bulk-DHP; end-wise DHP]. Present-day views on the structure of lignin macromolecules are mostly based on the studies of lignins from the first group. Naturally, lignins from different sources are subdivided according to their botanical origin. Lignins isolated from coniferous wood have been studied the most. Studies of biosynthetic lignins, (i.e., dehydropolymers synthesised in vitro under the conditions reproducing natural biosynthesis [41]), are important for understanding the factors that control the formation of lignin structure. Gardon and Mason [42, 43] who investigated industrial lignosulfonates in aqueous sodium chloride solutions first studied hydrodynamic properties of dilute lignin solutions. Based on the measurements of intrinsic viscosity [η] and translational diffusion coefficient D, they suggested that, at high ionic strength of solutions, the macromolecules of lignin acquire the conformation of a non-draining Gaussian coil. This conclusion was based on the values obtained for the exponents in the Mark-Kuhn-Houwink equation with bη = 0.47 and bD = 0.56: [η] = KηMbη

(2.3)

D = KD MbD

(2.4)

However, much lower values of these parameters were reported by Goring and co-workers [5, 44]: bη = 0.32, bD = 0.33. Detailed studies of lignosulfonates and other lignins led Goring to a model that treated a lignin macromolecule as a microgel particle [5, 26]. According to this model, the macromolecules of soluble lignins are identified with the fragments of the crosslinked structure of lignin in situ. Microgel particles, which may be of any shape including the irregular, possess hydrodynamic properties of slightly swollen spherical particles. This feature explains the low viscosity and the lower values of bη and bD as compared with those suggested by the model of a non-draining Gaussian coil. It is noteworthy that lignosulfonates are a rather special class of lignin polymers: lignosulfonates are polyelectrolytes. The presence of carboxyl and sulfo groups on the polymer chain and the concomitant ionic interactions give rise to abnormal hydrodynamic properties of ligno-sulfonates. Suffice it to say that calculations of the Tsvetkov-Klenin hydrodynamic invariant by using the equation: Ao=ηoDo (Mw [η])1/3 / T

(2.5)

57

Polymer Yearbook led, according [44], to values that are absolutely not typical of polymers: Ao = (5.2 ± 1.2) × 10-10 erg/(K mol1/3). Because of this, using lignosulfonates in the studies of the topological structure of natural lignin is rather limited. Alkali lignin, which is prepared by treating the wood with aqueous solutions of sodium hydroxide, in the presence of sodium sulfide (sulfate lignin) is a more appropriate object for structural studies. This polymer is not a polyelectrolyte and has a high molecular mass. In dimethylsulfoxide (DMSO), the macromolecules of sulfate lignin are compact particles, which are characterised by [η] varying from 7.4 (Mw = 1.3 × 103) to 13.3 cm3/g (Mw = 38.7 × 103) and the log [η] versus log Mw plot with the slope bη = 0.15 [45, 46]. Hydrodynamic properties of milled wood lignin (spruce) in pyridine were studied in [47]. The molecular masses of fractions isolated by preparative gel permeation chromatography on Sephadex were determined by sedimentation (according to Archibald) and from the diffusion and viscometric data (MDη). Logarithmic plots of [η], D, and S versus Mw are approximated by straight lines (Figure 2.5), with parameters bη= 0.115, bD = 0.39, and bS = 0.61, respectively. The diffusion coefficients were found to be concentration-independent; polyelectrolyte effects were not observed. The authors claimed that hydrodynamically lignin behaves as a rigid Einstein’s sphere. Obviously, this conclusion is not quite rigorous, because the experimental bη and bD values are quite

Figure 2.5 (1) log[η], (2) logS, and (3) log[η] versus log Mw for milled wood lignin fractions (pyridine as solvent) [47].

58

Macromolecular Properties and Topological Structure of Lignin different from those which are characteristic of hard globular particles. The average value of the hydrodynamic invariant A0 was 2.95 × 10-10 erg/(K mol1/3). Similar experimental results (Table 2.1) were obtained for milled wood lignin from pine [48]. Note only the higher value of the exponent bη than that reported in [47]. The fractions examined in this study spanned a broader interval of molecular masses; this usually allows a more reliable determination of hydrodynamic parameters.

Table 2.1 The hydrodynamic properties of lignin (MWL) fractions from wood (Pinus silvestris) [48]* Fractions

[η], cm3/g

Do × 107, cm2/s

So × 1013, s

k′

MDη

Ao × 1010 erg/ (K mol1/3)

1

15.5

2.10

1.67

1.07

64.1

3.54

2

8.1

2.65

0.875

2.08

61.0

2.67

3

8.0

2.80

0.704

1.92

52.4

2.57

4

7.8

4.20

0.528

1.21

15.9

3.04

5

7.2

5.60

0.396

1.86

7. 3

3.26

6

6.3

7.60

0.300

0.98

3. 3

3.48

7

5.9

7.70

-

0.97

3.4

-

8

3.5

17.20

-

0.56

0.5

-

9

3.4

18.70

-

0.66

0.4

-

10

2.7

21.10

-

2.22

0.4

-

11

2.2

22.40

-

4.33

0.4

-

12

2.0

31.40

-

5.33

0.2

-

MWL

4. 8

7.90

-

1.20

3.9

-

*Solvent – DMSO

The average value of Ao, as estimated from sedimentation (according to Svedberg) and viscometry was 3.1 × 10-10 erg/(K mol1/3). The data obtained suggest that [η], D, and S conform to cross correlation, which are characteristic of homologous polymers; this correlation is not confined to the routine test of the type⏐bD⏐= (bη+1)/3= 1 – bS, but involves more elaborate relationships between KS, KD, Kη and bD, bη, bS [38]. For lignin polymers with an obviously nonlinear chain topology, formulation of the concept of a homologous polymer may present a quite difficult task. At the current state

59

Polymer Yearbook

Figure 2.6 (1) log[η] and (2) logD versus log MDη for dioxane lignin fractions (DMSO as solvent) [38].

of knowledge of lignin structure, the fact that the hydrodynamic parameters fit the MarkKuhn-Houwink plots (Figure 2.6), suggests that the general pattern of the structural organisation of lignin does not change during the growth of its macromolecules. The principle of scaling invariance, which is a fundamental one for polymer science, is assumed to valid during the entire process. A relatively large number of publications [49-55] deal with dioxane lignins, which are prepared by mild acidolysis of plant tissue in a dioxane-water-HCl mixture. Pla with coworkers [51-54] elaborated on the effect of thermodynamic quality of solvents on the conformational characteristics of lignin macromolecules. These studies may provide valuable information about their structure. Pla and Robert suggested a number of θ-systems of the solvent-precipitant type: dioxane-hexane (100:0.5), tetrahydrofuran (THF)-hexane (100:6.8), THF-water (100:41.3 vol/vol) at 295.8 K. It was found that using dioxane, which is the most common solvent used in lignin chemistry, instead of the θ-solvent had little effect on the conformational parameters and hydrodynamic dimensions of lignin macromolecules (Table 2.2). A similar conclusion follows from the data reported in [38, 55], where the θ-temperature was evaluated for the dioxane lignin-dioxane system; it was found that, at T = 298 K, the Flory’s swelling coefficient is not greater than 1.05. Nevertheless, for the low-molecular-mass range characteristic of lignins, the steric effects related to thermodynamic quality cannot be very important. However, using dioxane as a solvent in the detailed studies of lignin structure is apparently justified because the measurements are conducted under conditions similar to θ-conditions. In practice, for polymers of complex topological structure, the definition of θ-point is ambiguous and requires a special discussion.

60


Table 2.2 Parameters of Mark-Kuhn-Houwink equation for different lignin preparations Lignin preparation

Source

Solvent

bη

-bD

bS

Refs.

2

3

4

5

6

7

MWL

Spruce

Pyridine

0.12

0.39

0.61

[47]

MWL

Pine

DMSO

0.25

0.43

0.57

[48]

MWL

Aspen

DMFA

0.47

0.61

[48]

DL

Pine

Dioxane

0.28

0.35

0.65

[49]

DL

Spruce

Pyridine

0.15

0.36

-

[50]

DL

Spruce

Pyridine

0.10

0.40

-

[5]

DL

Pine

Dioxane

0.18

0.39

-

[38]

DL

Pine

Dioxane

0.27

0.43

-

[38]

DL

Pine

Dioxane

0.11

0.37

-

[52]

DL

Spruce

Dioxane-ethanol

0.20

-

-

[52]

DL

Spruce

Dioxane

0.25

-

0.56

[54]

DL

Pine

DMSO

0.18

0.40

-

[66]

DL

Spruce

Dioxane-ethanol

0.23

-

-

[56]

Methanol lignin

Poplar

Dioxane-hexane

0.33

-

-

[56]

Methanol lignin

Poplar

2-Methoxy-ethanol

0.39

-

-

[56]

Alkali lignin

Spruce

Dioxane

0.12

-

-

[3]

Alkali lignin

Spruce

DMSO

0.15

-

-

[46]

Alkali lignin

Poplar

Dioxane-hexane

0.29

-

-

[56]

Alkali lignin

Spruce

0.1 M buffer

0.32

-

0.52

[4]

Lignosulfonate

Spruce

0.1 M NaCl

0.32

0.33

-

[44]

Lignosulfonate

Larch

0.5 M NaCl

-

0.56

-

[43]

Lignosulfonate

Larch

2 M NaCl

0.47

-

-

[42]

Bulk-DHP

Dioxane-water

0.13

0.35

0.41

[66]

Bulk-DHP

Dioxane-water

0.25

0.46

-

[33]

End-wise-DHP

Dioxane-water

0.78

0.58

0.45

[66]

1 ‘Native’ lignins

Industrial lignins

Biosynthetic lignins

Computer-simulated macromolecules F-1

-

-

0.26

0.42

0.58

[48]

F-2

-

-

0.18

0.40

0.60

[48]

DMFA: dimethylformamide

61

Polymer Yearbook It was found that the coefficients of translational diffusion and sedimentation coefficients for lignins are independent of concentration in the concentration range involved in analytical determinations [44, 47]. This fact was also reported in earlier studies [4, 5]. Dioxane lignins, as well as other lignin polymers except for lignosulfonates, are characterised by rather low intrinsic viscosities and exponential coefficients in the Mark-Kuhn-Houwink equations (note that bη is always smaller than bD). The lower limit of b η is 0.1, whereas the upper limit is 0.3. As demonstrated by the data on translational diffusion, for most polymers, the values of the exponent lie in a rather narrow range bD = 0.38 ± 0.05, that is, the characteristics of translational friction of the macromolecule are almost independent of the lignin source and the solvent used. There are almost no hydrodynamic data available on lignins isolated from leaves and the grass plants. The only publication [56] worth mentioning reported the properties of lignin isolated from the lint of Populus trichcarpa cotton by treating it with an aqueous methanolic solution of hydrochloric acid. This lignin was characterised by higher [η] and bη values than the coniferous lignins, however, the plot of log [η] versus log M was curvilinear. The Tsvetkov-Klenin invariant for coniferous dioxane lignins is usually not higher than 3 × 103 erg/(K mol1/3). According to [49], the value of Ao varied for some fractions in the interval (2.4-2.9) × 10-10 erg/(K mol1/3). Lignin polymers were found to show anomalous values of the Huggins parameter k′. In the region of low molecular masses, k′ varies from 1 to 3-5 units [48, 38]. At M > 1 × 104, the k′ values remain at a level of 1-1.5. Thus, analysis of hydrodynamic properties of native lignins reveals that their behaviour in dilute solutions is different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. Apparently, the macromolecules of soluble lignins are randomly branched chains. Branchings in a chain are known to reduce the hydrodynamic dimensions, (i.e., reduce [η]), and increase the diffusion mobility compared to the linear analog, theoretical value of bη in a θ-solvent is 0.25. The branching of the polymer also reduces the hydrodynamic invariant Ao by 15-20% compared to the ‘standard’ value 3.2 × 10-10 erg/(K mol1/3) and results in anomalous values of the Huggins parameter. As emphasised previously, an alternative approach treats the macromolecules of lignin as microgel particles that form as a result of fragmentation of the crosslinked natural lignin. Gravitis and Stoldore [57] analysed the hydrodynamic characteristics of lignin. Within the framework of the concept treating lignin as a crosslinked polymer, the g-factor for branching and the coefficient of bulk swelling q were calculated. The branching density of lignins, p, was compared with the theoretical branching density calculated on the basis of the existing molecular structures of lignin. It was found that the values

62

Macromolecular Properties and Topological Structure of Lignin calculated on the basis of Freudenberg’s structural scheme [3] agree well with the experimental values of the branching density. However, because neither the Freudenberg’s structural scheme nor later modifications comply with the topology of network polymers, the crosslinked structure of lignin macromolecules suggested in [57] seems to be arguable. Note that neither the branching density nor the swelling coefficient alone is obviously sufficient to identify the branching or the crosslinking of macromolecules, and take into account the lack of unambiguous relationship between the measured hydrodynamic parameters, the topology and the conformation of macromolecules. As noted above, studies of biosynthetic lignins obtained in vitro in a monolignolperoxidase-hydrogen peroxide system play an important role in gaining a deeper insight into the chemical structure of lignin. As monomeric lignin precursors, coniferyl alcohol [3], ferulic acid [24, 58], and isoeugenol [59] were used in model biosynthesis of coniferous lignin. Two synthetic procedures and correspondingly, dehydropolymers are most commonly used: end-wise polymerisation (implemented by continuous addition of monomer) and bulk polymerisation (conducted in batch mode). Recently, new procedures for in vitro biosynthesis of lignin have been suggested that model both the chemistry and the dynamics of the process [31, 60]. Depending on the conditions and the substrate used, dehydropolymers with different molecular mass distribution may be prepared, although in most cases oligomeric products prevail [61, 62]. Using ferulic acid as a monomer makes it possible to synthesise rather high molecular mass (Mw = 3 × 104 [63]) biosynthetic lignins. In [64, 65], a ferulic acid-based bulk polymer was studied. From the linear plots of log[η] versus log M and log D versus log M, coefficients of the Mark-Kuhn-Houwink equation were determined (Table 2.2). Hydrodynamic behaviour of bulk DHP was found to be similar to that of dioxane lignin. This is not the case with end-wise DHP [66, 67]. At an equal molecular mass, the end-wise DHP is described by a higher [η] and comparatively low sedimentation coefficient values. It was found that the exponents in the Mark-KuhnHouwink equations for D and [η] are greater than 0.5 (bη = 0.78, bD = –0.58). Sarkanen [3] suggested that the topological structure of lignin depends on the supply mode of the monomeric phenoxy radical into the reaction zone. In a continuous, endwise mode, formation of linear or slightly branched chains is more probable, whereas in the opposite case, because of the high initial concentration of phenoxy radicals, the formation of randomly branched macromolecules may be expected. In [66, 67], hydrodynamic properties of two model lignins, synthesised under identical reaction conditions but differing in the mode of monomer supply, were compared. In agreement with theoretical expectations, the end-wise DHP was found to be a linear polymer. The authors claimed that bulk-polymerisation led to a randomly branched polymer. It is noteworthy that the validity of this assignment is confirmed by the results reported by Tsvetkov and co-workers [68], who studied polymers with similar characteristics.

63

Polymer Yearbook In the physical chemistry of polymers, the degree of branching is described by the g-factor, which is defined as the ratio between the mean radius of gyration of the branched chain 〈R2〉br, and that of the linear chain of the same molecular mass 〈R2〉1: g = 〈R2〉br/〈R2〉1

(2.6)

A similar approach was introduced into lignin chemistry by Goring [4]. In the case of polymers, when there is no linear analog, in order to determine hydrodynamic parameters the specific approach is used. Acording to this approach, it was suggested that the value of [η] of ‘linear analog of lignin’ be determined by use of the equation [η]1 = KθM1/2, where Kθ is the parameter which characterises unperturbed sizes. This approach was verified for various lignin polymers. The Kθ value was determined by extrapolation according to a modified Stockmayer-Fixman equation [51-55] or by combining a number of similar equations [49]. Apparently, the most reliable value of this parameter, Kθ = 0.118 cm3/g, was obtained for dioxane lignin by Pla and co-workers [52-54], because they conducted the measurements in θ-conditions. However, in other publications, almost identical results were reported: 0.120 cm3/g for dioxane lignin in dioxane [55], 0.113 cm3/g for dioxane lignin in DMSO [49], 0.119 cm3/g for milled wood lignin in DMSO [49], 0.125 cm3/g for alkali lignin in 0.1 M buffer [4], 0.110 cm3/g milled wood lignin in pyridine [47], 0.119 cm3/g for alkaline lignin from cotton lint in θ-solvent [56] and 0.118 cm3/g for methanol lignin from cotton lint in θ-solvent [56]. It is a remarkable fact that Kθ is independent of the source and history of lignin. Evidently, this may mean that the topological structure of lignin macromo1ecules is rather uniform and is stable to the effect of various reagents. Plots of the g-factor versus the molecular mass of milled wood and alkali lignins reveal that at Mw > 6 × 103 the dependence reaches a plateau [14]. This was ascribed either to the existing distribution of units with respect to functionality [62] or to the specific features of the topological structure of lignin macromolecules [38]. A similar dependence was reported for dioxane lignins isolated from pinewood [49, 69]. Thus, after a certain molecular mass is attained, increasing the number of the side chains does not result in a significantly lower branching factor. Apparently, this situation may occur when the lengths of branches are different and decrease for the branches of later generations. Kogan and co-workers [70] suggested a model to describe the growth of randomly branched macromolecules. This model leads to the same dependence of g-factor on the molecular mass as that observed for lignins. Note that the basic assumptions of the Kogan-Gandel’sman-Budtov model comply with the modern understanding of the regularities of plant tissue lignification. It is important that this conformity is greater than that achieved within the frameworks of other models for macromolecular growth, the Zimm-Kilb model in particular. Calculations

64

Macromolecular Properties and Topological Structure of Lignin according to the Zimm-Kilb theory, which is valid for monodisperse randomly branched chains, demonstrate that each second-fifth phenylpropane unit must represent a junction. This is one of the contradictions between the results of numerical calculations and the model per se, which initially assumes that both the chains and the subchains are described by Gaussian statistics. Karmanov and co-workers [49] compared the branching densities obtained for dioxane lignins according to Zimm-Kilb and Kogan-Gandelsman-Budtov, The relationship between the branching factor, g, parameter a (which quantitatively describes the variation of branch chain lengths with the variation of ordinal number of generation j), and the number of junctions n is given by the following equation: g n = a − 1 / a + (a − 1)2 /[a2 (a n − 1)]−1 × {n +

n

∑ 1 /(a − 1)} i

j=1

As is seen from Figure 2.7, for dioxane lignin, the branching density (ρ = n/Mw) is approximately two times lower than the p value determined according to Zimm-Kilb. The branching density calculated for coniferous lignins according to the Zimm-Kilb model for polyfunctional branching is 0.3-0.4 [51-54] and tends to increase with molecular mass. According to interpretation of the hydrodynamic data suggested [56, 71], that the branching junctions of lignin macromolecules are tetrafunctional.

Figure 2.7 Branching density g as a function of the molecular mass of dioxane lignin fractions. (1) Zimm-Kilb model, (2) Kogan-Gandelsman-Budtov model [70].

65

Polymer Yearbook Analysis of hydrodynamic data for various lignins and their comparison with fractal theories led to a hypothesis [72-74] that considered the supermolecular structure of in situ lignins as a network of crosslinked fractal clusters. Within the framework of this hypothesis, the biosynthesis of lignin proceeds as a kinetically, unequilibrium, diffusion-limited aggregation of the particle-cluster type (Witten-Sander’s model) [75]. The fact that the fractal dimensionality df of milled wood lignin and dioxane lignin is on the average 2.5 [38, 76] confirms the validity of treating lignins as fractal clusters. The df values for lignin polymers were determined from hydrodynamic data according to [17, 38, 76]: d f = 3 (bη+ 1)-1 = (1 – bs) = bD-1

(2.8)

According to [17], in some cell wall regions, the crossover of the models describing the structure of lignin is possible (one mechanism of macromolecular growth changes to the other). In particular, a kinetic model of the irreversible growth of compact clusters of unit density (df is equal to the dimensionality of the growth space) cannot be excluded [62]. In [77], the hydrodynamic data were used to evaluate the fractal dimensionality of biosynthetic lignins (Table 2.3).

Table 2.3 Scaling characteristics of biosynthetic lignins and theoretical models Parameter

Experiment [77]

Theory*

Bulk-DHP

End-wise-DHP

RWCO

DLA-P-Cl

DLA-Cl-Cl

df

2.62 ± 0.27

1.66 ± 0.16

1.69

2.44

1.78

bη

0.13 ± 0.02

0.78 ± 0.02

0.78

0.23

0.68

0.38

0.60

0.59

0.41

0.56

νF**

*Simulated models: random walk without crossover (RWCO), diffusion-limited aggregation of particle-cluster (DLA-P-Cl) and cluster-cluster (DLA-Cl-Cl) types. **Flory’s critical parameter

It was demonstrated that for the branched dehydropolymers, df can be calculated by the relationship: gη ∼ 1/ Kθ [ M3/df -1.5]

(2.9)

Comparison of the fractal dimensionalities of lignins and the dehydropolymers revealed that the bulk DHP biosynthetic analog provides an adequate model of the topological structure and polymer properties of the native soluble lignins.

66

Macromolecular Properties and Topological Structure of Lignin Studies of natural lignin in the cell walls of wood (densitometric analysis of the micrographs) [38] revealed that the lignified secondary cell wall is characterised by fractal structure. This made it possible to suggest that, from the viewpoint of dynamics, the biosynthesis of lignin occur in the strange attractor mode. According to the definition [78], strange attractors comprise such solutions of the systems of differential equations that do not occupy the phase state compactly, but form a complex lacunar structure possessing fractal properties. In the studies of in vitro blosynthesis of lignin [60], several kinds of attractors, including the strange attractor, were discovered. Fractal nature of the dynamic processes of enzymic dehydropolymerisation of ferulic acid was established and some parameters of the random strange attractor in a two-dimensional pseudophase space were determined [79]. In particular, fractal self-similar dimensionality was found to be equal to 1.43 and informational dimensionality was equal to 1.61. Studies [76] of the dynamics of monolignol polymerisation demonstrate that the nature of fractal properties of lignin lies apparently beyond the concepts involved in diffusion models for the growth of self-similar structures.

2.4 Summary By using conventional methods of polymer science to analyse the topological structure of lignin polymers, a number of important parameters of this structure were reliably determined. These parameters include hydrodynamic characteristics of the macromolecules: intrinsic viscosity, diffusion coefficients, sedimentation coefficients, coefficients in the Mark-KuhnHouwink equations, hydrodynamic invariants. The analysis of hydrodynamic properties revealed that the behaviour of lignins in dilute solutions is markedly different from that of linear polymers, both flexible- and rigid-chain, in any of the known conformations. The microgel hypothesis of the structure of lignin macromolecules gained some popularity. According to this hypothesis, the macromolecules of lignin represent fragments of the crosslinked natural lignin, which are obtained by cleavage of the lignin network during the isolation procedure. At the same time, it is also possible that the macromolecules of lignin are common randomly branched chain molecules, thus, traditional approaches fail to give an unambiguous description of the topological structure of lignin. An important step towards a better understanding of the structure of lignin was made when fractal properties were discovered. It was found that a lignin macromolecule may be described as a fractal cluster of fractional dimensionality. Fractal dimensionality, df, describes the topological level of structural organisation. However, evaluation of df is only the first step in studying lignin as a fractal object. In reality, a spectrum of fractal dimensionalities, which serve the invariant measures of that topological characteristic

67

Polymer Yearbook must be determined. As is known, the concept of a fractal is closely related to the concepts of determinate chaos and the strange attractor. The discovery of random dynamics for the dehydropolymerisation of the monomer precursors of lignin in the strange attractor dynamic mode suggests that new procedures and parameters for the description of lignin structure may now be sought.

Acknowledgements This work is supported by the Russian Foundation for Basic Research, Project No. 0103-96402.

References 1.

J.F. Dean and K.E. Eriksson, Holzforschung, 1992, 46, 2, 135.

2.

Ya.A. Gravitis, A.G. Kokorevich and V.G. Ozol-Kalnin, Khimiia Drevesiny, 1986, 1, 107.

3.

K.V. Sarkanen in Lignins: Occurrence, Formation, Structure, Properties and Reactions, Ed., K.V. Sarkanen and C.H. Ludwig, Wiley-Interscience, New York, NY, USA, 1971.

4.

P.R. Gupta and D.A. Goring, Canadian Journal of Chemistry, 1960, 38, 2, 270.

5.

D.A. Goring, Pure and Applied Chemistry, 1962, 5, 1/2, 233.

6.

A. Rezanowich, W.Q. Yean and D.A. Goring, Svensk Papperstidning-Nordisk Cellulosa, 1967, 66, 141.

7.

P.G. De Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, USA, 1979.

8.

P.P. Erins, V.A. Cinite, Y.K. Jakobson and J.A. Gravitis, Journal of Applied Polymer Science: Applied Polymer Symposia, 1976, 28, 1117.

9.

P.P. Erins, Khimiia Drevesiny, 1977, 1, 8.

10. A. Maurer and D. Fengel, Holzforschung, 1992, 46, 5, 419. 11. V.R. Govariker, N.V. Visvanatkhan and D. Shridkhar, Polimery (Polymers), Nauka, Moscow, Russia, 1990, p.396. 68

Macromolecular Properties and Topological Structure of Lignin 12. V.I. Irzhak, B.A. Rozenberg and N.S. Enikolopyan, Network Polymers: Synthesis, Structure, and Properties, Nauka, Moscow, Russia, 1979. 13. E.I. Evstigneev, E.D. Maiorova and A.Y. Platonov, Khimiia Drevesiny (Wood Chemistry), 1990, 6, 41. (In Russian) 14. Y.A. Gravitis and V.G. Ozol-Kalnin, Khimiia Drevesiny (Wood Chemistry), 1977, 3, 24. (In Russian) 15. Y.A. Gravitis and V.G. Ozol-Kalnin, Proceedings of the Second Conference on Studies in Wood Chemistry, Riga, Zinatne, Latvia, 1978, p.56. 16. T.E. Skrebets, K.G. Bogolitsina and A.Y. Gur’ev, Khimiia Drevesiny (Wood Chemistry), 1992, 4/5, 3. (In Russian) 17. A.G. Kokorevich, Y.A. Gravitis and V.G. Kokorevich, Khimiia Drevesiny (Wood Chemistry), 1989, 1, 3. (In Russian) 18. H. Hatakeyama and J. Nakano, Tappi Journal, 1970, 53, 3, 472. 19. J. Gravitis and P. Erins, Journal of Applied Polymer Science, 1983, 37, 421. 20. A. Scalbert and B. Monties, Holzforschung, 1986, 40, 2, 119. 21. C. Lapierre and B. Monties, Holzforschung. 1984, 38, 6, 333. 22. A.P. Karmanov, V.D. Davydov and B.D. Bogomolov, Khimiia Drevesiny (Wood Chemistry), 1982, 2, 3. (In Russian) 23. E.G. Bobalek, E.K. Moore, S.S. Levy and C.C. Lee, Journal of Applied Polymer Science, 1964, 8, 2, 625. 24. B.A. Andersons, Reaction Ability of Lignification Phenolic Substrates and Macromolecular Properties of Dehydropolymers Synthesised on their Base, Institute of Wood Chemistry, Riga, Latvia, 1987. Candidate Science (Chemistry) Dissertation 25. V.G. Ozol-Kalnin, Ya.F. Gravitis and P.P. Erins, Khimiia Drevesiny (Wood Chemistry), 1978, 3, 57. (In Russian) 26. A. Szabo and D.A. Goring, Tappi Journal, 1968, 51, 440. 27. J.F. Yan, Science, 1982, 215, 1390.

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Polymer Yearbook 28. J.F. Yan, F. Pla, R. Kondo, M. Dolk and J.L. McCarty, Macromolecules, 1984, 17, 10, 2177. 29. H.J. Bolker and H.S. Brenner, Science, 1970, 170, 173. 30. T. Higuchi, Wood Science and Technology, 1990, 24, 23. 31. A.P. Karmanov and Y.B. Monakov, Khimiia Drevesiny (Wood Chemistry), 1994, 1, 62. (In Russian) 32. Y.A. Gravitis, Khimiia Drevesiny (Wood Chemistry), 1986, 5, 108. (In Russian) 33. A.P. Karmanov and Y.B. Monakov, Khimiia Drevesiny (Wood Chemistry), 1994, 2, 34. (In Russian) 34. V.G. Ozol-Kalnin, Y.F. Gravitis, F.G. Veide and A.G. Kokorevich, Khimiia Drevesiny (Wood Chemistry), 1984, 1, 108. (In Russian) 35. V.G. Ozol-Kalnin, A.G. Kokorevich and Y.F. Gravitis, Khimiia Drevesiny (Wood Chemistry), 1986, 1, 106. (In Russian) 36. V.G. Ozol-Kalnin, A.G. Kokorevich and Y.F. Gravitis, Vysokomolekuliaryne Soedineniya, Seria A, 1987, 29, 5, 964. 37. A.P. Karmanov, V.I. Rakin, S.P. Kuznetsov and Yu.B. Monakov, Proceedings of the First Meeting on Wood Chemistry and Organic Synthesis, Syktyvkar, Russia, 1994, p.75. 38. A.P. Karnanov, Structure and Properties of Natural Lignin and its Biosynthetic Analogues – Dehydropolymers, Institue of Organic Chemistry, Ufa, Russia, 1995. [PhD Thesis] 39. A.P. Karmanov and S.P. Kuznetsov, Problems of Wood Chemistry, Komi Science Centre Publishers, Syktyvkar, Russia, 1997, p.63. 40. D. Fengel and G. Wegener, Wood: Chemistry, Ultrastructure, Reactions, Walter de Gruyter, Berlin, Germany, 1984. 41. S. Guan, J. Mlynar and S. Sarkanen, 8th International Symposium on Wood and Pulping Chemistry, Helsinki, Finland, 1995, Volume 2, p.35. 42. J.L. Gardon and S.G. Mason, Canadian Journal of Chemistry, 1955, 33, 1477. 43. J.L. Gardon and S.G. Mason, Canadian Journal of Chemistry, 1955, 33, 1491.

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Macromolecular Properties and Topological Structure of Lignin 44. W. Yean, A. Rzanowich and D. Goring, Chemistry and Biochemistry of Lignin, Cellulose, and Hemicelluloses, Lesnaya Promyshlennost Publishers, Moscow, Russia, 1969. (In Russian) 45. B.D. Bogomolov, O.M. Sokolov, N.D. Babikova, G.G. Kochergina and E.V. Antonova, The Chemistry and Applications of Lignin, Eds., A.I. Kalninsh, V.N. Sergeeva and G.F. Zakis, Zinatne, Riga, Latvia, 1974, p.107. (In Russian) 46. O.M. Sokolov, Macromolecular Reactions of Lignin at Alkali Cookings, Polymolecular Composition and Hydrodynamic Properties of Slightly Decomposed and Industrial Lignins, Institute of Wood Chemistry, Riga, Latvia, 1988. 47. A.D. Alekseev, V.M. Reznikov, V.D. Bogomolov and O.M. Sokolov, Khimiia Drevesiny (Wood Chemistry), 1971, 7, 31. (In Russian) 48. A.P. Karmanov, L.S. Kocheva, V.Y. Belyaev and T.A. Marchenko, Proceedings of the Fifth European Workshop on Lignocellulosics and Pulp, Aveiro, Portugal, 1998, p.149. 49. A.P. Karmanov, V.Y. Belyaev and Y.B. Monakov, Polymer Science, Series A, 1995, 37, 2, 195. 50. A. Rezanowich, W. Yean and D. Goring, Svensk Papperstidning-Nordisk Cellulosa, 1963, 66, 141. 51. F. Pla and A. Robert, Cellular Chemistry and Technology, 1974, 8, 1, 3. 52. F. Pla and A. Robert, Holzforschung, 1984, 38, 1, 37. 53. F. Pla, P. Froment, B. Mouttet and A. Robert, Holzforschung, 1984, 38, 3, 127. 54. F. Pla and A. Robert, Holzforschung, 1984, 38, 4, 213. 55. A.P. Karmanov, V.D. Davydov and B.D. Bogomolov, Khimiia Drevesiny (Wood Chemistry), 1981, 4, 50. (In Russian) 56. F. Pla and J.F. Yan, Holzforschung, 1991, 45, 2, 121. 57. Y.A. Gravitis and I.A. Stoldore, Khimiia Drevesiny (Wood Chemistry), 1977, 2, 10. (In Russian) 58. A.P. Karmanov, V. Y. Belyaev and Y. B. Monakov, Khimiia Drevesiny (Wood Chemistry), 1991, 6, 73. (In Russian) 71

Polymer Yearbook 59. H. Elviya, Holzforschung, 1989, 43, 1, 61. 60. A.P. Karmanov and Yu. B. Monakov, Proceedings of the First Meeting on Wood Chemistry and Organic Synthesis, Syktyvkar, Russia, 1994, p.56. 61. O. Faix, Holzforschung, 1986, 40, 5, 273. 62. Y.A. Gravitis, Structural Organisation of Lignin, Riga, Latvia, Institute of Wood Chemistry, 1989. [PhD Thesis] (In Russian) 63. Y.A. Gravitis, B.A. Anderson, M.K. Yakobson, I.K. Duminya and P.P. Erins, Khimiia Drevesiny (Wood Chemistry), 1984, 5, 99. (In Russian) 64. A.P. Karmanov, V.Y. Belyaev and Y.B. Monakov, Khimiia Drevesiny (Wood Chemistry), 1992, 3, 25. (In Russian) 65. A.P. Karmanov, L.S. Kocheva, T.A. Marchenko and V.Y. Belyaev, Proceedings of the 11th Internation Symposium on Wood and Pulping Chemistry, Nice, France, 2001, p.7. 66. Y.B. Monakov, V.Y. Belyaev, T.V. Moskvicheva and A.P. Karmanov, Doklady Rossiiskaia Akademii Nauk, 1993, 333, 2, 200. 67. A.P. Karmanov, V. YU. Belyaev and Yu. B. Monakov, Proceedings of the 8th International Symposium on Wood and Pulping Chemistry, Helsinki, Finland, 1995, Volume 2, p.95. 68. V.N. Tsvetkov, S.V. Bushin, E.P. Astapenko, N.V. Tsvetkov, S.S. Skorokhodov, V.V. Zuev, R. Zentel and H. Potsch, Polymer Science, Series A, 1994, 36, 6, 983. 69. A.P. Karmanov, V.A. Demin and V.D. Davydov, Khimiia Drevesiny (Wood Chemistry), 1990, 3, 114. (In Russian) 70. S.I. Kogan, M.I. Gandelsman and V.P. Budtov, Vysokomolekulyaryne Soedineniya, Seria A, 1984, 26, 2, 418. 71. F. Pla, M. Dolk, F. Yan and J. McCarthy, Macromolecules, 1986, 19, 5, 1471. 72. V.G. Ozol-Kkalnin, A.G. Kokorevich and Y.F. Gravitis, Khimiia Drevesiny (Wood Chemistry), 1986, 5, 108. (In Russian) 73. V.G. Ozol-Kkalnin, A.G. Kokorevich and Y.F. Gravitis, Proceedings of the 8th All-Union Conference on the Chemistry and Applications of Lignin, Riga, Latvia, 1987, p.19. 72

Macromolecular Properties and Topological Structure of Lignin 74. Y.A.Gravitis, A.G. Kokorevich and V.G. Ozol-Kalnin, Proceedings of the 11th International Symposium on Wood and Pulping Chemistry, Nice, France, 2001, Volume 2, p.11. 75. T.A. Witten and L.M. Sander, Physical Review Letters, 1981, 47, 19, 1400. 76. A.P. Karmanov, V.I. Rakin, S.P. Kusnetzov and Y.B. Monakob, Proceedings of the 8th International Symposium on Wood and Pulping Chemistry, Helsinki, Finland, 1995, Volume 2, p.41. 77. A.P. Karmanov and Y.B. Monakov, Polymer Science, Series B, 1995, 37, 2, 63. 78. D. Ruelle and F. Takens, Communications in Mathematical Physics, 1971, 20, 167. 79. A.P. Karmanov, S.P. Kusnetzov and Y.B. Monakov, Doklady - Rossiiskaia Akademii Nauk, 1995, 342, 2, 193.

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74

3

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems Yu. B. Monakov, Z. M. Sabirov, V. N. Urazbaev and G. E. Zaikov

3.1 Introduction The distinctive feature of lanthanide and in particular Ziegler-Natta catalysts is that they allow one to synthesise polydienes with a high content of cis-1,4-units. In most cases, lanthanides are used in the form of blends and concentrates. About 50% of lanthanides consumed worldwide are used for the production of catalysts for various chemical processes. Using lanthanide catalysts in the manufacture of synthetic rubbers can increase the number of these processes. A large number of studies have been devoted to polymerisation of dienes with lanthanide catalytic systems. Many of these studies are concerned with the problems related to the mechanism that controls the microstructure of polydienes. Although not all aspects of stereoregulation have been clarified, many problems have been solved and possible explanations offered for some of the others [1-4]. The objective of this chapter is to examine the basic research on diene (butadiene, isoprene, and piperylene) polymerisation with the LnHal3⋅nL-AlR3 (Ln = lanthanide, Hal = halogen, ligand (L) = tributyl phosphate (TBP), AlR3 = triisobutylaluminum and diisobutylaluminum hydride) catalytic system. The chapter will analyse the role of such factors as the electronic and geometric structure of bimetallic active centres, anti-syn and π-σ-transitions of the terminal units of the growing polymer chains and the nature of the lanthanide, diene, and organoaluminum component in the mechanism of stereoregulation.

3.2 Principal Groups of Lanthanide-Based Catalysts Thus far, the attention of researchers has mainly been attracted to the family of ioncoordination lanthanide catalysts, by which cis-polydienes can be synthesised. These catalysts can be classified into several groups [3]. I.

The initial compound of the lanthanide can be obtained by reacting its halide with the corresponding organic base [5]. The research is usually carried out with complexes containing various electron donor ligands, L, such as alcohols [6, 7], cyclic ethers [8], aliphatic esters of orthophosphoric acid [9-15], aliphatic, and cyclic sulfoxides

75

Polymer Yearbook [12, 14, 16]. Catalysts in which the initial lanthanide component, LnX3 does not contain a halogen make up group. II. The catalysts of this type include octanoates [17, 18], stearates [19-23], naphthenates [13, 18], acetylacetonates of trivalent lanthanides [19], and salts of di-2-ethylhexyl phosphoric acid [19, 20, 23]. In addition to LnX3 and AlR3, these catalytic systems must include halogen-containing components (one of the most frequently used compounds is AlR2Cl), the role of which is to halogenate the lanthanide by exchange reactions. Catalysts in which the initial halogen-containing compound of lanthanide has the Ln–C bond group. III. cis-Polymerisation of dienes can be catalysed, for example, by the system R´LnHal2 nTHF-AlR3 [24-28]. The synthesis of lanthanide compounds of this type is usually performed in tetrahydrofuran (THF) by conducting the reaction of the oxidative addition of R´Hal (triphenylmethyl chloride, benzyl chloride, phenyl bromide, allyl iodide) to zero-valent lanthanides [24, 25, 27, 29]. Chloride of oligoisoprene neodymium, which is not bound via solvation bonds to THF (THF/Nd < 3), catalyses cis-polymerisation of dienes even when no organoaluminum co-catalyst is present [30]. The use of the catalysts based on individual compounds of lanthanides of various structures may help to elucidate the nature of active centres. This explains the interest in the problems of synthesis and conversions of these compounds [31-40].

3.3 Factors Affecting the Activity and Stereospecificity of Catalysts 3.3.1 Chemical Nature of Lanthanide The activity of lanthanide-based coordination catalysts is strongly influenced by the chemical nature of the lanthanide component. Depending on the conditions of polymerisation, the relative activities of lanthanides can vary slightly. In all cases, however, with regard to the rates of polymerisation of dienes, lanthanides form the following series: LaDy>Ho>Er [11, 14]. In the polymerisation reaction of butadiene, the propagation rate constant changes as follows: for La - 10, for Ce - 40, for Nd - 140, for Gd - 130 and for Dy - 30 l/(mol min) [41]. A similar behaviour is observed for cis-polymerisation of isoprene [18] and piperylene [42]. Although the propagation rate constant depends on the chemical nature of lanthanide, in the case of polymerisation of butadiene, the degree of stereospecificity is approximately the same for all most active catalysts [41]. For polymerisation of isoprene, the content of 3,4-units in the cis-polymer decreases with a rise in the atomic number of the lanthanide (from 2.5 to 1%), whereas trans-1,4-units are not formed at all. The reaction of the addition of cis-1,4-units in

76

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems polymerisation of isoprene can occur via three different mechanisms. The data from 13C NMR indicate that only one of these mechanisms, namely, ‘head-to-head’ addition, is realised. This conclusion is also corroborated by the results of ozonolysis [43]. Thus, lanthanide catalysts can be used to synthesise polyisoprene with molecules almost identical to those of natural rubber. For the polymerisation of trans-isomer of piperylene, the microstructure of the polymer formed strongly depends on the nature of the lanthanine used as a catalyst [11]. It was found that for the lanthanides of the Ce subgroup, the content of cis-1,4-units in polypiperylene increases with an increasing atomic number. In contrast, in the Y subgroup, the number of cis-1,4-units decreases with a decreasing atomic number. The most stereoregular polypiperylene is formed when the polymerisation occurs on a gadolinium catalyst. For a neodymium catalyst, the polypiperylene chain consists 1,4- and 1,2-units. At the same time, a spectroscopic examination of polypiperylene synthesised on a neodymium catalyst gave no evidence of 3,4-units. The ozonolysis data show that 1,4units in this polydiene form ‘head-to-tail’ sequences [22].

3.3 2 The Nature of the Ligand It is known that the microstructure of polybutadiene synthesised with the use of catalytic systems on the basis of halides of elements with d-electron orbital depends strongly on the nature of the halogen. A special feature of catalysts on the basis of f-elements (lanthanides, uranium) is that they do not exhibit this dependence [44, 45]. Nevertheless, the effect of the chemical nature of halogen on the reactivity of active centres was observed for lanthanide-based catalysts. For polymerisation of butadiene, this was confirmed by the results of measurements of reaction rate constants [14]. For other types of polydienes, the influence of the nature of halogen can be seen from the microstructure of the polymers formed. In the series of catalysts containing chlorine, bromine, and iodine, the content of cis-1,4-units in polyisoprene slightly decreases, and the content of 3,4-units, correspondingly, increases [14]. The effect of nature of halogen is the strongest in polymerisation of piperylene [11]. Varying the ligand, L in the initial component LnHal3⋅3L does not change the microstructure of the polybutadiene formed [14]. Nevertheless, the analysis of propagation rate constants shows that active centres in catalytic systems on the basis of TBP and diamyl sulfoxide complexes of the same halide of lanthanide are different [14]. The correlation between the nature of the halogen and its presence in the catalyst, and the functioning of the active centres of the latter is very complicated and mainly depends on the nature of the ligands attached to the lanthanide. Polymerisation catalysed by compounds

77

Polymer Yearbook containing Ln-Hal bonds yields polydienes with a high content of cis-units. It was even thought that, in the absence of such bonds, lanthanide catalysts are not stereospecific. Systems on the basis of polynuclear complexes [(C6F5)3GeI7M2]Ln 3L-Al(i-C4H9)3, where M is either mercury or cadmium and Ln is either praseodium or neodymium (in the trivalent state), are catalytically active in the polymerisation of dienes [46]. For example, at 25 °C, these systems catalyse formation of polybutadiene with up to 90% of cis-1,4units. The products of ball-milling of lanthanide metals in aromatic hydrocarbons include active intermediates of carbene type (=CH-CH=CH-CH=CH-CH-Ln-) and initiate cis-1,4-polymerisation of butadiene and isoprene. It is assumed that the role of the electron acceptor ligand is played by the bulk of the metal or by its complex with a polyconjugated (polyacetylene) fragment. The latter is formed as a result of polymerisation of the solvent [40]. Polybutadiene and polyisoprene with 76-95% of cis-1,4-units can be obtained by using a combination of triisobutylaluminum with alcoholate or carboxylate of lanthanide chemically bonded to finely divided silica gel, on the surface of which compounds like (SiO2)-O-Nd(OR)2 are formed [47]. When the lanthanide has no electron acceptor groups, polymerisation yields transpolydienes. For instance, systems including alcoholate or carboxylate of lanthanide in combination with triisobutylaluminum have low activity, and give macromolecules with the content of trans-1,4-units up to 85% [48]. Organometallic derivatives of LnR3 type catalyse trans-polymerisation of dienes [30, 33, 36]. When butadiene and isoprene are polymerised on halogen-free ion-coordination catalytic systems on the basis of compounds of d-elements, polymers are obtained which contain 1,2- and 3,4-units, respectively. Lanthanide-based catalysts ensure ‘head-to-tail’ addition of monomers, i.e., formation of 1,4-units, even when the catalyst contains no halogen. These catalysts are characterised by high stereospecificity and, depending on the types of ligands bonded to the central atom, direct the polymerisation reaction so that the resulting polymer contains a majority of either cis-1,4 or trans-1,4-units. The only known case of when a lanthanide-based catalysts gave polybutadiene and polyisoprene macromolecules, which contained a mixture of cis- and trans-sequences and a considerable amount of 1,2- and 3,4-units, was that of phenylcarbin neodymium [31, 33].

3.3.3 The Structure of Organometallic Component of Lanthanide Catalysts The polymerisation of dienes occurs when the lanthanide catalyst contains an organometallic component (usually, trialkylaluminum or dialkylaluminum hydride). Systems LnHal3⋅nL-AlR2Hal do not reveal catalytic activity. Moreover, dialkylaluminum

78

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems halide acts as catalytic poison when added to systems LnHal3⋅nL-AlR3 [49]. A similar effect was observed when the content of dialkylaluminum halide in catalysts of the second group exceeded a certain optimum value [19]. The rate of polymerisation of dienes at 25 °C strongly depends on the structure of the organoaluminum component of the catalyst. Increasing the polymerisation temperature results in a levelling of the activities of such systems [14]. In addition, at a polymerisation temperature of 25 °C, the yield of polyisoprene on the catalysts of the type LnCl3•3TBPAlR 3, where Ln is Pr or Nd, decreases in the series Al(n-C10H21)3 >Al(n-C6H 13) 3 >Al(C2H5)3. Raising the temperature to 80 °C reverses the order in this series. This may be explained by the decomposition of associates at a higher temperature. The result of this decomposition is that the co-catalytic activity of AlR3 becomes consistent with its reactivity. Increasing the polymerisation temperature removes the anomaly in the dependence of the yield of polydienes versus the Al:Nd ratio. This anomaly is observed when the polymerisation is performed with organoaluminum co-catalysts that are able to form associates [49]. This fact shows that only the monomeric form of AlR3 can form active centres. The number of active centres in neodymium catalysts containing higher (6-8 carbons in the radical R) is about half that in catalysts with triisobutylaluminum [41, 50]. It was somewhat unexpected that the propagation rate constant depended on the nature of AlR3 for both butadiene and isoprene [18, 50]. That the reactivity of lanthanide active centres depends on the nature of AlR3 follows also from the microstructure of polydienes. Varying AlR3 component results in changes in the relative number of cis-1,4 and trans-1,4-units in polybutadiene. At the same time, the content of 1,2-units remains the same (about 0.6% at 25 °C). The only exception is a catalyst with diisobutylaluminum hydride, in which case, approximately a three-fold increase in the content of 1,2-units is observed. As the concentration of butadiene decreases ( toluene > xylene [11, 14, 26, 28].

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Diene Polymerisation Mechanism with Lanthanide Catalytic Systems

Table 3.1 Polymerisation of dienes in toluene and heptane at 25 °C in the presence of catalytic system NdCl3·3TBP-Al(i-C4H9)3 [3] Monomer

Solvent

cis-1,4-units (%)

Kp, l/(mol min)

*Cac, (%)

Butadiene

Toluene

95

140

7

Heptane

95

470

6

Toluene

95

80

9

Heptane

95

120

8

Toluene

64

14

9

Heptane

78

70

6

Isoprene Piperylene

Note: *Cac - concentration of active centres

3.4 The Structure of Active Centres and the Mechanism of Stereoregulation in the Polymerisation of Butadiene The main parameters of diene polymerisation with lanthanide-based catalytic systems are similar to those of polymerisation with ion-coordinated catalysts on the basis of dmetals. This can be seen from the following facts: polymerisation of dienes has an anionic coordinated character [18]: at polymerisation temperatures from 20 to 25 °C, the reaction is of first order with respect to the monomer and catalyst (this property is independent of the natures of catalyst and hydrocarbon solvent, the only exception to this rule being the system considered in work [18]) for most of catalysts studied [18, 21, 26, 28, 41] and, the apparent activation energy of the reaction of polymerisation of dienes is of the order of 33.5 kJ/mol [20, 41]. For lanthanide catalysts, the concentration of active centres is somewhat higher than for conventional Ziegler-Natta catalysts, e.g., for neodimiumbased catalysts their content varies from 6-10% [12, 41, 42, 50] to 15-20% [54-57]. It is generally accepted that, in the polymerisation of dienes on lanthanide catalysts, the growing chain is attached to the transition metal by an π-allyl bond and that the chain growth occurs by incorporation of the monomer via the metal-carbon σ-bond. In the case of neodymium catalysts, the delocalised π-allyl type structure of the terminal unit has been observed by spectroscopic methods [8, 26, 28, 58-60]. The results reported in these papers show that the relative contents of cis-1,4- and trans-1,4-units in polydienes depend on the type of solvent used, the polymerisation temperature, structure of diene monomer, and the composition of lanthanide-based catalysts. These data can be interpreted in terms of the concept of isomerisation equilibrium between anti- and syn-forms of πallyl terminal unit. One of the arguments in favour of the existence of this isomerisation

81

Polymer Yearbook equilibrium is that the content of cis-1,4-units in polydienes decreases at the cost of increase in the content of trans-1,4-units when the concentration of the monomer is reduced [10, 28, 54, 61-64]. More detailed information on the structure of the initial, terminal, and penultimate unit of polydiene chains, and, correspondingly, information on the mechanism of the formation of chains, can be derived from the results of investigations of polymer structure by nuclear magnetic resonance (NMR). Papers in this field are, however, not very numerous [65]. With regard to the operation of lanthanide catalytical systems, one of the most important questions is that of the nature of the bond responsible for the growth of the polymer chain. Both the traditional Ziegler-Natta catalysts and lanthanide catalysts contain bridge bonds of the chlorine, alkyl, or hydride type, between the metal atoms [64-69]. In view of this, it is usually assumed that the addition of molecules to the growing polymer chain occurs either via the metal-carbon σ-bonds (monometallic model of active centre) or via the bridge bond (bimetallic model of active centre). In the second model, the question arises as to whether the organoaluminum fragment constitutes a part of the active centre or not. Direct experimental investigation of the structure of active sites is extremely difficult. Therefore, attempts have been made to determine it indirectly. To this end, the effect of the structure of active centres on the kinetics of the corresponding reactions was investigated [70-72]. Polymerisation of butadiene with NdCl3⋅3TBP-AlR3 catalytic system, the reactivity of active centres and the dependence of the reactivity on the mechanism of introduction of AlR3 were studied [70] using ‘precipitated’ catalyst (precipitate of catalytic system multiplewash with purified toluene). It was found that the reactivity Kp and the stereoregulating properties of active centres in the system NdCl3⋅3TBP-AlR3 vary as the structure of AlR3 is changed. The reactivity of these centres is similar to the reactivity of active centres initially prepared in the presence of the organoaluminum compound, which is added to the ‘precipitated’ catalyst, Table 3.2. This result, in combination with the data on the effect of the structure component of the catalyst on the microstructure of polydienes and the asymmetry of active centres and reactivity ratios [16, 18, 50], suggests that the organoaluminum compounds constitutes a part of lanthanide active centre and that, in the catalytic system, there occurs an exchange reaction, which results in the substitution of the initial organoaluminum fragment (ligand) of the active centre by a new one. The assumption about the bimetallic bridge structure of lanthanide catalytic systems was made in many works [66-69]. Nevertheless, the possibility must not be ruled out that active centres contain both types of bonds (π-allyl and σ-bridge). It is important that these bonds may differ dramatically in reactivities. In order to answer the question concerning the possible coexistence of two types of bonds, the polymerisation of butadiene on catalytic systems NdCl3•3L-AlR3, where R is i-C4H9; Ln is Nd or Tb; L is TBP, prepared in the presence of a small amount of butadiene and piperylene [71, 72] was investigated, Table 3.3.

82


Table 3.2 Reactivity of active centres and microstructure of polymer in butadiene polymerisation with the precipitated catalyst with AlR3′ additives (starting system, NdCl3·3TBP-butadiene-AlR3; [NdCl3·3TBP] = 1 x 10-3, [AlR3′] = 1.5 x 10-2, [butadiene] = 1.5 mol/l, toluene, 25 °C. K p, l/(mol min)

cis-1,4, (%)

trans-1, 4, (%)

1,2 (%)

starting NdCl3·3TBPbutadiene-Al(i-C4H9)3 Al(i-C4H9)3 precipitated NdCl3·3TBPAl(i-C4H9 Al(i-C4H9)3

220

94.3

5. 1

0.6

210

94.5

4.8

0.7

45

93.5

4. 8

1.7

Starting NdCl3·3TBP butadiene- Al(i-C4H9)2H Al(i-C4H9)3 precipitated NdCl3·3TBPAl(i-C4H9)2H Al(i-C4H9)2H

50

93.4

4.8

1.8

200

94.3

4.9

0.8

50

93.5

5.0

1.5

Starting catalytic system

Additional AlR3′

Table 3.3 Dependence of Kp in butadiene polymerisation on the time of ageing for catalytic systems 3 and 4. That is, after adding the second portion of diene. Time of ageing catalyst, t, min

Kp, l/(mol min), system 3

Kp, l/(mol min), system 4

*

330 (1)

220 (2)

12

290

240

30

230

90 120

260 230

180

280

240

220

360

220

1440

220

300

System 1: NdCl3 3L-piperylene-AlR3; System 2: NdCl3 3L-butadiene-AlR3; System 3: system 1 + butadiene; system 4: system 2 + piperylene; [Al]/[Nd] = 30; [Nd] = 2, tprep = 120 min, AlR3 = Al(i-C4H9)3, toluene, 25 °C. *The values of rate constants for starting systems 1 and 2.

83

Polymer Yearbook It was shown that the initial reactivity of active centres in LnCl3⋅3L-butadiene-AlR3 (system 1) and in LnCl3 ⋅3L-piperylene-AlR3 (system 2) in polymerisation of butadiene is different. Addition prior to polymerisation of a small amount of butadiene ([diene]:[neodimium] =10) to system 2 and of the same amount of piperylene to system 1, and ageing the system for a certain time, results in the systems ‘forgetting’, as the residence time increases, what dienes were present during the preparation (formation) period. The reactivities of active centres of the two systems interchange, Table 3.4 and Figure 3.1. These changes in the reactivities can be due to the fact that active centres have bimetallic structure and include two metal-carbon bond, Ln-C (π-allyl) and Ln-C-Al (σ-bridge), via which the reaction of insertion of the monomer into the chain occurs. These bonds differ greatly in reactivity. The experimentally observed dependence of the reactivity of active centres of catalytic systems on the residence time can be explained by two reasons: (1) slow rate of chain growth when the propagation occurs via the least reactive bond, and (2) equilibrium reaction, (e.g., migration of organoaluminum fragment in the active centre), during which the bridge bond (Ln-Al-C) between the endgroup and the lanthanide converts to π-allyl bond and vice versa [71, 72]. It was also noted that some individual organometallic (or hydride) compounds of the type RLnCl2 lead to the formation of cis-polydienes even when the organoaluminum component is absent. However, these catalysts are much less active than LnCl3⋅nL-AlR3 [30, 38]. Complexes of these compounds with tetrahydrofuran (THF) do not catalyse polymerisation of dienes. At the same time, the addition of AlR3 gives an effective catalyst [24-28]. As shown by IR spectra, the addition of Al(i-C4H9)3 to (C6H5)3CNdCl2•THF (Al:Nd = 3-5) results in molecules of THF migrating from neodymium to the coordination sphere of aluminum atom [26-28]. In the reaction between LnCl3⋅nL and AlR3, alkylation of lanthanide should occur prior to the shift of the ligand coordination bond from L to AlR3, otherwise alkylation would be prohibited. It is of interest that the compounds of the type R2LnCl do not exhibit catalytic activity. This property remains whether AlR3 is present or not [24, 26, 28]. Active centres of lanthanide catalyst probably differ in reactivity. This conclusion was made on the basis that polydienes obtained with lanthanide catalysts have a broad molecular mass distribution [50, 55], the polydispersity index being in the order of three even when the reactions of chain termination and transfer do not occur [57]. Quantum-chemical calculations of the electronic structure of model active centres and analysis of their geometry is discussed in [70, 73-77]. It was established that anticonformation of model centres is less favourable, from the point of view of the total

84


Table 3.4 Electron bond populations in model complexes cis-C4H7-synC4H7NdCl2-Al(CH3)3 + C4H6 Electron bond populations

Complex in Figure

Nd-C1

Nd-C2

Nd-C3

Nd-C4

Nd-Ca

Ca-C4

1c

0.011

0.014

0.007

0.0

0.286

0.0

1d

0.043

0.047

0.030

0.008

0.096

0.235

1f

0.104

0.108

0.101

0.0

0.0

0.846

Figure 3.1 Basic stages of growing reaction by polymerisation of butadiene (R = R′′ = H), isoprene (R = H and R′′ = CH3) and piperylene (R = CH3 and R′′ = H) under the action of catalytic system NdCl3⋅3TBP-Al (iC4H9)3.

85

Polymer Yearbook electron energy, than syn-conformation. The total energy of centres with σ-bonds is smaller than the total energy of centres with π-bonds. The fact is that particular isomeric forms of the active centre exert little influence on the electron density on the Ln-Cα bond, it is via this bond that the growth of polymer chain occurs and suggests that the reactivities of different isomeric forms of active centre is about the same. In the lanthanide series, the variation of the electronic structures of active centres is very small. The calculation of the structure of complexes formed by the active centre with monomer showed that, for all lanthanides, the complexes which include cisoid conformers of dienes are energetically more favourable. In the lanthanide series, the preference for complexes with cisoid conformers with respect to similar complexes with transoid conformers changes from 4 to 7 kJ/mol. The preference is measured in terms of the difference in the total energy of formation of corresponding complexes. This means that, for cisoid conformers, the energy of complexation is from 19 to 23 kJ/mol larger than for transoid conformers. The results of quantum-chemical calculation also show that isomerisation transitions of active centres, anti-conformation-syn-conformation, are possible, in principle [73-77]. If the insertion reaction occurs only in the σ-type complexes, (i.e., only by the metalcarbon σ-bond), one should take into account the lifetime τ of those σ-form of the active centre that allow insertion of the monomer. This time, which is determined by the kinetics of the processes occuring in the complex, should be compared to the characteristic time τ1 of the elementary act of insertion. The role of the π-σ rearrangment in the mechanism of stereoregulation has been investigated works [78, 79]. It was established that in cases where the terminal unit of the growing polymer chain has the form of a stable π-allylic structure, (i.e., when the time spent by the terminal unit in σ- form is much shorter than the characteristic time of the elementary act of insertion), only the cisoid conformer of butadiene molecule can convert the terminal unit from π- to σ-form and then insert into the metal-carbon σ-bond. During the insertion, the active centre remains in the σ-form. This result does not depend on the overall geometry of the active centre, (i.e., whether it is octahedral, tetrahedral, etc.), and is explained exclusively by the presence of a stable, long lived π-allyl terminal unit. It has been assumed that it is the latter factor, i.e., the presence of a long lived π-terminal unit, that explains the fact that in some cases polydienes are formed with an exceptionally high content of cis-units [70, 79].

3.5 Role of the Structure of Diene in the Mechanism of Regioand Stereoselectivity The objective of this part of work was to study the role of the structure of the diene (butadiene, isoprene and piperylene) in the mechanism of regio- and stereoselectivity in polymerisation with the lanthanide catalytic system NdCl3⋅3TBP-Al(i-C4H9)3. To this 86

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems end, a quantum-chemical investigation of the electronic and geometric structures of the prereaction complexes of dienes (butadiene, piperylene, and isoprene) with an active centre and of the complexes that model the transition state in the reaction of insertion of dienes via the Nd-C σ-bond in the active centres was performed [80]. All calculations were made using the quasi-relativistic extended Huckel method [81]. It is known that, in diene polymerisation with cis-regulating systems, the terminal units of the growing polymer chains have delocalised π-allylic structure [8, 68]. High regioselectivity of the lanthanide catalysts in the polymerisation of nonsymmetric dienes implies that the active centres of single type, in which the delocalised terminal unit is linked to the penultimate unit according to ‘head-to-tail’ type, are predominantly formed during the polymerisation. This is shown for (P-cis-CH 2C γHC βRĆ αHR-antiCH2CγHCβRĆαHR-NdLL´ (see Scheme 3.1).

Scheme 3.1

where P is the polymer chain, L and L´ are the ligands determined by the initial composition of the catalytic system: R = CH3 and R´ = H in the polymerisation of piperylene, R = H and R´ = CH3 in the polymerisation of isoprene, and R = R´ = H in polymerisation of butadiene. The active centres formed in the polymerisation of dienes with the NdCl3⋅3TBP-Al(i-C4H9)3 catalytic system were modelled by the compound that took into account the two terminal units of the polymer chain: CH2HCγHCβRĆαHR-CH2CγHCβRĆαHR-NdCl2⋅AlR3. The necessity of including the organoaluminum component in the composition of active centres was substantiated in works [3, 82]. Because the reaction of insertion can proceed only via the metal-carbon σ-bond, at the first stage, the calculations were aimed at finding the manner in which the coordinating diene can stabilise the σ-structure of the active centre. The calculations of prereaction complexes showed that both piperylene and isoprene (like butadiene [79]) can stabilise the σ-form of the centre if they occupy the coordination site in the Nd sphere (Figure 3.1c), which becomes

87

Polymer Yearbook vacant upon the transition of the active centre from the π- to σ-structure (Figures 3.1a and 3.1b). The energies of this complex formation are 7.1, 8.5, and 9.2 kJ/mol for butadiene, isoprene, and piperylene, respectively. In the second stage, while retaining the centre in the σ-form, the diene can isomerise from the transoid to the cisoid conformation, due to the rotation of the -CH=CH2 double bond about the C-C ordinary bond. The driving force of isomerisation is that, in the cisoid conformation, the -C3H=C4H2 bond of the diene reacts with the Nd-Cα σ-bond. This is the beginning of the insertion of the diene into the chain (Figure 3.1d). The energy expended to accomplish the isomerisation is small and is equal to ∼12-15 kJ/mol, depending of the structure of diene. The complexes of cisoid isomers formed upon isomerisation have the energies of complex formation equal to 8.4, 9.7, and 10.5 kJ/mol, for butadiene, isoprene, and piperylene, respectively. Consideration of the possible structures of prereaction complexes shows that when the diene retains the transoid conformation, because of geometric reasons it cannot stabilise the σ-structure of the active centre and participate in the insertion at the same time. Thus, cis-stereospecificity results from π-allylic stabilisation of terminal unit of the growing polymer chain, when the lifetime of the terminal unit in the σ-state is not sufficient for the elementary event of insertion to take place. Otherwise, there is no need for σ-stabilisation of the centre by the formation of complex shown in Figure 3.1c, and the dienes directly attack the Nd-Cα bond with one of its double bonds. Naturally, the dienes take the conformation that is thermodynamically more advantageous in solution, that is, the transoid conformation. The occurrence of the reaction of insertion in complex c (Figure 3.1) necessitates that the diene further approaches the Nd atom; therefore a certain amount of energy is required to achieve the corresponding transition state. Taking into account that the structure of the active centre in the polymerisation of all dienes is similar and these complexes differ only by the presence and the arrangement of methyl substituents, the model structures of the transition states (Figure 3.1e) were assumed to be similar. The calculations showed that the energy expended to form the transition states depends slightly on the structure of diene and is equal to 49, 54, and 57 kL/mol for butadiene, isoprene, and piperylene, respectively. The analysis of electronic populations of the bonds of the atoms of dienes and active centres (Figure 3.1e, Table 3.4) indicates that the electronic structure of the transition complexes are characterised by delocalisation of the RHC1=C2R´ double bond and by incorporation into the complex of the diene linked to the Nd atom by the three carbon atoms C1, C2, and C3. The fourth carbon atom of the diene C4 begins to form the bond (C4-Cα) with the terminal carbon atom of the growing polymer chain. This implies that only a single double bond of the diene C3H=C4H2 is involved in the insertion via the Nd-Cα bond. The second double bond RHC1=C2R´ reacts only with the Nd atom. This offers the possibility for the subsequent formation of a π-allylic bond with the Nd atom. In the calculation of complexes modelling the final state in the reaction of insertion, the length of the Nd-Cα bond was greater than 4.0 Å; the plane of the molecule of the

88

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems inserted diene was brought closer to a distance of 2.6 Å. This distance corresponds to the equilibrium distance of the plane of the crotyl terminal group to the Nd atom, showing that the π-allylic bond of the newly forming terminal unit with the Nd atom takes place concurrently with the insertion. Table 3.4 shows that, in the final complex (Figure 3.1f), the Nd-Cα bond does not exist any longer, the new C4-Cα bond is formed, and the C3-C4 bond is ordinary, the population is 0.85. All these facts suggest that the insertion took place. The second double bond is delocalised, the electron populations of C1-C2 and C2-C3 bonds are close to 1.01 and the three carbon atoms C1, C2, and C3 form a π-allylic bond with the Nd atom. As for the regioselectivity, it is important that in the presence of lanthanide catalysts the dienes can enter insertion, upon isomerisation from the transoid to cisoid conformation, only via the double bond containing no methyl group. The reactions for this phenomenon are different for piperylene and isoprene. In the polymerisation of piperylene, when the CH2=CH(CH3) double bond of the diene comes closer to the Nd-Cα σ-bond, the steric repulsion between the methyl groups of the terminal unit and the piperylene molecule appears (Figure 3.2a). Therefore, it is necessary to alter significantly the orientation of the terminal unit of the growing polymer chain, for example, to turn it about the Nd-Cα bond to decrease the repulsion of the methyl groups. Naturally, these changes are extended in time and need considerable expenditure of energy. In our opinion, it is this factor that is responsible for the participation of only the unsubstituted double bond of piperylene in the insertion and ensures the regioselectivity, that is, the addition of 1,4-units only according to the ‘head-to-tail’ type. As for the problem why the cis-isomers of piperylene are not polymerised with cis-regulating lanthanide catalysts, note that among the four possible isomers of piperylene (cis-cisoid, cis-transoid, trans-cisoid, and trans-transoid), the cis-cisoid isomer is the least advantageous (according to the total electron energy) and this isomer apparently does not occur in the racemic mixture in solution [83]. To take part in the reaction of insertion, piperylene must isomerise from the transoid to the cisoid conformation. In this case, the cis-cisoid conformation appears, which is the least advantageous for piperyene. Therefore, this isomerisation may not take place. When the cis-cisoid isomer is involved in the insertion, the steric hindrances can appear, because at any orientation the methyl substituent turns out to be directed as if inwards into the centre (for example, see Figure 3.2b). All these facts predetermine the inactivity of the cis-isomer of piperylene in the polymerisation with cis-regulating lanthanide catalysts. Naturally, in the polymerisation initiated by the catalysts showing ‘mixed’ stereospecificity or trans-stereospecificity, the transition of piperylene from the transoid to cisoid conformation is no larger necessary and, for example, the cis-transoid isomer can enter the polymerisation.

89

Polymer Yearbook

Figure 3.2 Appearance of steric hindrances by piperylene polymerisation (a, b) and by isoprene polymerisation (c, d).

Also note that, in accordance with the calculated data, the energies of the σ-form of the ‘piperylene’ active centre, in which the Nd atom is linked to the Cγ atom, and the σ-form of the centre in which the metal atom is bonded to the Cα atom, differ slightly. The corresponding value of ΔE is maximal, when the terminal units are in the trans-cisoid conformation and is as low as 4 kJ/mol. In the models of the ‘butadiene’ centres, this difference is much greater (12.7 kJ/mol) [76], that is, in polymerisation of piperylene, the σ-structure of the active centre with the Nd-Cγ bond is realised more often than in the butadiene polymerisation. This accounts for why the total amount of 1,2- and trans-1,4units must be greater in the polymerisation of piperylene than in the polymerisation of butadiene, due to insertion via the Nd-Cγ bond and the anti-syn isomerisation of the terminal unit. This was shown experimentally [82]. In the polymerisation of isoprene, the arrangement of diene in the prereaction complex, as shown in Figure 3.2c, requires that the transition from the transoid to cisoid

90

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems conformation takes place via the rotation of the C(CH3) = CH2 substituted bond. The fact that the methyl group and the double bond are aligned in the opposite direction with respect to the ordinary C2-C3 bond (contrary to piperylene, when they are situated on one side of the C2-C3 bond) hampers the isomerisation. Upon rotation of the C(CH3)=CH2 group by 180 degrees, either the methyl or the =CH2 group approaches the Nd atom too closely. This sharply increases the energy barrier (to 76 kJ/mol), in contrast to butadiene and piperylene, when the barrier to rotation is 11.9 and 14.9 kJ/mol, respectively. This explains why the double bond of isoprene, which bears a methyl substituent, cannot participate in the insertion. Therefore, regioselectivity appears and polyisoprene presumably does not contain the trans-units. In fact, upon insertion of isoprene, the active centre is formed, whose σ-form, upon the formation of σ-bond with third carbon atom of the terminal unit, has a structure similar to that shown in Figure 3.2d. It is seen that, as in the case of complex 3.2c, the rotation of the -C(CH3)=CH2 group is necessary for the isomerisation of the terminal unit from cis to trans conformation to take place. It is the energy barrier of this isomerisation that is responsible for the absence of trans-1,4-units in polyisoprene, in contrast to polypiperylene and polybutadiene prepared with the same cis-regulating catalysts. Thus, the high stability of the terminal unit, which predominantly occurs in π-allylic state, leads to the participation of only the cisoid isomers of dienes in the reaction of insertion. In the polymerisation of piperylene regioselectivity, addition of 1,4-units according to ‘head-to-tail’ type, is caused by the fact that only the double bond of diene bearing no methyl substituent can react with the metal-carbon σ-bond of the active centre. Involvement of the double bond of piperylene bearing the methyl substituent in the reaction of insertion is considerably hampered because of the steric repulsion between the methyl groups of the terminal unit of the growing chain and the diene. The smaller difference in energy between the two possible σ-forms of the terminal unit in the polymerisation of piperylene, as compared to butadiene, is responsible for the increased lifetime of the active centre in the σ-form, in which the Nd atom is linked to the Cγ atom. This results in an increased content of trans-1,2- and trans-1,4 units in polypiperylene. In the polymerisation of isoprene, high regioselectivity and the absence of trans-1,4units in the polymer are related to the hampered rotation of the C(CH3)=CH2 double bond of isoprene incorporated into the complex with the active centre.

3.6 The Role of Anti-Syn Isomerisation of the Terminal Unit of the Growing Polymer Chain The possibility for the occurrence of anti-syn isomerisation was qualitatively estimated from the experimental dependence of the relative content of cis- and trans-units in the

91

Polymer Yearbook polymer on the monomer concentration in polymerisation with cis-regulating systems [4]. Similar dependence was also observed for lanthanide catalysts [84]. To obtain more detailed information on the reaction of isomerisation, a quantitative estimation of the kinetic scheme of the propagation reaction, which includes anti-syn isomerisation, for polymerisation butadiene and piperylene with the NdCl3⋅3TBP-Al(i-C4H9)3 system [72, 77, 85-89] was performed. According to the data of quantum-chemical studies, which indicates that the isomeric forms of active centres, in butadiene polymerisation, must not markedly differ by their reactivity, the following scheme of the reaction was analysed [85] (see Scheme 3.2).

AS + M

K1

AS⋅M

K

cis-1,4 -unit-AS +

K-1 K3

K5

K4 ASt + M

K1 K-1

K6 ASt⋅M

K

trans-1,4 -unit-AS

Scheme 3.2

where AS is the anti-structure of active centre, AS⋅M is a complex of active centre with monomer. The analogous designations are used for the syn-structure (ASt) of active centre. The meaning of the constants (K1, K-1, K3, K4, K5 and K6) can be deduced from the scheme. In accordance with this scheme it is possible to derive the following approximate expressions for chain propagation rate (V) and the ratio between cis-1,4- and trans-1,4unit formation rates (Vcis and Vtrans, respectively): V = KpCa[M]

(3.1)

Vcis/Vtrans = γ + [M]/(α2[M] + β2)

(3.2)

where Kp = 1/(α1[M] + β1); γ = K6/K5; β1 = (K + K -1)/KK1; α1 = 1/K; α2 = α1K5; β2 = K3[ α2 (1 + γ ) + β1 K1]/K1

(3.3)

This scheme takes into account that propagation is a two-stage reaction, coordination and insertion and that anti-syn isomerisation of the terminal unit of the growing chain

92


Table 3.5 The value of rate constants for elementary stages of propagation reactions and their ratios in polymerisation of butadiene with the catalytic systems NdCl3·3TBP-Al(i-C4H9)3 (I) and NdCl3·3TBP-Al(i-C4H9)2H (II) Catalytic system I II

Solvent

β1 = KK1/ (K + K-1), l/ (mol min)

α1-1 = K, min-1

α22 = K6/K, min-1

K3, min-1

K6, min-1

β2*, mol/l

γ

Heptane

267

8000

08

22

660

0.01

0.98

Toluene

0

-

04

80

-

0.09

0.97

Toluene

900

-

0.09

15

-

0.04

0.93

380

-

Note: *β2 ≈ K3(2α2/K1 + β1)

can occur both prior to diene coordination to the active centre and after formation of the complex between diene and the active centre. The meaning of the constants is clear from the scheme. Formation of 1,2-units in polybutadiene was not taken into account because in all experiments, their content did not exceed 1-3%. The value of γ, α2, and β2 parameters were determined by minimising the weighed sum of the squares of deviations of the experimental values of Vcis/Vtrans from the theoretical values determined from expression (3.2). Table 3.5 lists the experimental values of the constants for separate stages of chain propagation in butadiene polymerisation with the NdCl3⋅3TBP-Al(i-C4H9)3 system. As is seen, the nature of solvent most dramatically affects the stage of coordination (constant K1 in toluene is ∼3 times smaller than that in heptane) and the stage of isomerisation (constant K3 changes by ∼ 4 times on going from toluene to heptane). This may be associated with the fact that in toluene, the active centres not complexed with the monomer, form complexes (of the arene type) with aromatic hydrocarbon. The occurrence of aromatic hydrocarbon in the coordination sphere of Nd, first, hampers the coordination of the monomer (K1 decreases) and, second, favours the activation of π-σ transitions, (i.e., increases the rate of anti-syn isomerisation, which involved the σ-form of active centre). This is reflected in an increase in the magnitude of K3. For the centres complexed with the monomer, the isomerisation constant (K6) further increases, indicating that the monomer activates π-σ transitions to a greater extent than the solvent. Thus, in heptane, the isomerisation constant for the active centres complexed with the monomer (K6) is 30 times larger than the isomerisation constant for free active centres (K3).

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Polymer Yearbook

3.7 Conclusions The suggested mechanism of cis-regulation takes into account in an explicit form the kinetic factor, time of occurrence of the terminal unit in the π- and σ-structures and readily permits the following general conclusion to be drawn. In the case where the time of occurrence of the terminal unit in the π-structure exceeds the reaction time τ1, the stabilisation (fixation) of the σ-structure of active centre by the diene molecule would be no longer neccessary and the diene molecule can participate in the reaction regardless of its conformation (cis- or trans-). Naturally, this should imply the loss of cis-stereospecificity of active centre. On the other hand, if the system does not possess cis-regulating properties, (i.e., the time of occurence of the terminal unit in the σstructure exceeds τ1), the stabilising π-structures (for example, by introduction of halogenating agent) could lead to the emergence of cis-stereospecificity of active centres. Thus, the major components of active centres, such as terminal unit, bridging bond, organoaluminum component, lanthanide atom and its ligands, can decisively affect its stereospecificity. The role of each element manifests itself through different factors, and the possible mechanisms of their influence were discussed above. The key point determining the value of one or another factor in the mechanism of stereoregulation is the relationship between the following characteristic times: time of occurrence of the terminal unit in the π-state, time of occurence of the terminal unit in the σ-state, time of the elementary event of insertion, time of the elementary event of isomerisation, time interval between two successive additions of diene molecules to polymer chain. The interplay of these times can affect the microstructure of the resulting polydiene. Naturally, real active centres are markedly more complicated, and the mechanism of stereoregulation apparently includes many details, which are yet to be studied. However, account of the characteristic times for different stages of the complicated reaction of chain propagation will undoubtedly always be the necessary stage for both the study of all diverse possibilities of lanthanide catalysts and the development of new catalytic systems.

Acknowledgement We are grateful to the Russian Foundation for Basic Research (Grant no. 02-03-33315) for support of this research. We also thank our co-worker Dr. N. Marina for valuable discussions.

94


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10. Y.B. Monakov, N.G. Marina and G.A. Tolstikov, Chemia Stosowana, 1988, 32, 3/4, 547. 11. Y.B. Monakov, N.G. Marina, R.M. Khairullina, O.I. Kozlova and G.A. Tolstikov, Inorganica Chimica Acta, 1988, 142, 1, 161. 12. V.G. Kozlov, N.G. Marina, I.G. Savel’eva, Y.I. Murinov, Y.B. Monakov and G.A. Tolstikov, Inorganica Chimica Acta, 1988, 154, 2, 239. 13. V.I. Aksenov, V.B. Murachev, V.P. Ziborova and V.I. Anosov, Vysokomolekulyarnye Soedineniya Seriya B, 1988, 30, 6, 431. 14. Y.B. Monakov, N.G. Marina and G.A. Tolstikov, Polymery Tworzywa Wielkoczasteczkowe, 1989, 34, 6-7, 263.

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Polymer Yearbook 15. R.M. Khairullina, N.G. Marina, O.I. Kozlova, N.V. Duvakina, N.N. Sigaeva, Y.B. Monakov and S.R. Rafikov, Vysokomolekulyarnye Soedineniya Seriya B, 1991, 33, 6, 463. 16. Y.B. Monakov, N.G. Marina, O.I. Kozlova, F.Y. Kanzafarov and G.A. Tolstikov, Doklady Akademii Nauk SSSR, 1987, 292, 2, 405. 17. M.I. Lobach, I.A. Poletaeva, A.S. Khachaturov, N.N. Druz and V.A. Kormer, Polymer, 1977, 18, 11, 1196. 18. S.V. Bubnova, A.I. Tverdov and V.A. Vasil’ev, Vysokomolekulyarnye Soedineniya Seriya A, 1988, 30, 7, 1374. 19. S.R. Rafikov, Y.B. Monakov, Y.K. Bieshev, I.F. Valitova, Y. I. Murinov, G.A. Tolstikov and Y.E. Nikitin, Doklady Akademii Nauk SSSR, 1976, 229, 5, 1174. 20. Y.B. Monakov, Ya.Kh. Bieshev, A.A. Berg and S.R. Rafikov, Doklady Akademii Nauk SSSR, 1977, 234, 5, 1125. 21. Y.B. Monakov, N.G. Marina, N.V. Duvakina and S.R. Rafikov, Doklady Akademii Nauk SSSR, 1977, 236, 3, 617. 22. A.A. Panasenko, V.N. Odinokov, Y.B. Monakov, L.M. Chalilov, A.S. Bezgina, V.K. Ignatyuk and S.R. Rafikov, Vysokomolekulyarnye Soedineniya Seriya B, 1977, 19, 9, 656. 23. A.A. Berg, Y.B. Monakov, V.P. Budtov and S.R. Rafikov, Vysokomolekulyarnye Soedineniya Seriya B, 1978, 20, 4, 295. 24. I.N. Markevich, O.K. Sharaev, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1983, 268, 4, 892. 25. V.A. Yakovlev, E.L. Vollershtein, L.S. Cherezova, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1983, 268, 6, 1422. 26. O.G. Avdeeva, I.N. Markevich, O.K. Sharaev, G.N. Bondarenko, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1986, 286, 3, 641. 27. G.A. Gailyunas, R.Kh. Biktimirov, R.M. Khairullina, N.G. Marina, Y. B. Monakov and G.A. Tolstikov, Doklady Akademii Nauk SSSR, 1987, 295, 6, 1385. 28. O.G. Avdeeva, O.K. Sharaev, I.N. Markevich, G.N. Bondarenko, E.I. Tinyakova and B.A. Dolgoplosk, Vysokomolekulyarnye Soedineniya Seriya A, 1990, 32, 2, 367.

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Diene Polymerisation Mechanism with Lanthanide Catalytic Systems 29. B.A. Dolgoplosk, E.I. Tinyakova, I.N. Markevich, T.V. Soboleva, G.M. Chernenko, O.K. Sharev and V.A. Yakovlev, Journal of Organometallic Chemistry, 1983, 255, 1, 71. 30. E.L. Vollershtein, N.N. Glebova, S.B. Gol’shtein, E.N. Zavadovskaua, O.K. Sharaev, V.A. Yakovlev, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1985, 284, 1, 140. 31. I.Sh. Guzman, N.N. Chigir, O.K. Sharaev, G.N. Bondarenko, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1979, 249, 4, 860. 32. B.A. Dolgoplosk, E.I. Tinyakova, I.Sh. Guzman, E.L. Vollerstein, N.N. Chigir, G.N. Bondarenko, O.K. Sharaev and V.A. Yakovlev, Journal of Organometallic Chemistry, 1980, 201, 1, 249. 33. N.N. Chigir, I.Sh. Guzman, O.K. Sharaev, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1982, 263, 2, 375. 34. E.L. Vollershtein, V.A. Yakovlev, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1980, 250, 2, 365. 35. A.B. Nikitin, V.A. Yakovlev and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1986, 291, 2, 393. 36. E.N. Zavadovskaya, O.K. Sharaev, G.K. Borisov E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1984, 274, 2, 333. 37. E.N. Zavadovskaya, O.K. Sharaev, G.K. Borisov, Y.P. Yampol’skii, E.I. Tinyakova and B.A. Dogoplosk, Doklady Akademii Nauk SSSR, 1985, 284, 1, 143. 38. S.B. Gol’shtein, V.A. Yakovlev, G.N. Bondarenko, Y.P. Yampol’skii, E.I. Tinyakova and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1986, 289, 3, 657. 39. S.B. Gol’shtein, V.A. Yakovlev, A.I. Mikaya and B.A. Dolgoplosk, Doklady Akademii Nauk SSSR, 1989, 309, 5, 1129. 40. B.A. Dolgoplosk, V.A. Yakovlev, E.I. Tinyakova, S.B. Gol’shtein, G.M. Chernenko, E. V. Tzikhotzkaya and G.N. Bondarenko, Doklady Akademii Nauk SSSR, 1993, 328, 1, 58. 41. Y.B. Monakov, N.G. Marina, I.G. Savel’eva, V.G. Kozlov and S.R. Rafikov, Doklady Akademii Nauk SSSR, 1982, 265, 6, 1431. 42. S.R. Rafikov, V.G. Kozlov, N.G. Marina V.P. Budtov and Y.B. Monakov, Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, 1982, 4, 871. 97

Polymer Yearbook 43. V.A. Kormer, V.A. Vasil’ev, S.V. Bubnova and E.R. Dolinskaya, Kauchuk i Rezina, 1986, 1, 5. 44. T-C. Shen, C. Ouyan, F-S. Wang, C-Y. Hu, F-S. Yu and P-K. Chien, Journal of Polymer Science, Part A: Polymer Chemistry, 1980, 18, 12, 3345. 45. G. Lugli, A. Mazzei and S. Poggio, Makromolekulare Chemie, 1974, 175, 7, 2021. 46. N.G. Marina, Kh.K. Gadeleva, Y.B. Monakov, G.A. Tolstikov, M.N. Bochkarev and G.A. Razuvaev, Doklady Akademii Nauk SSSR, 1985, 284, 1, 173. 47. G.M. Chernenko, V.A. Yakovlev, E.I. Tinyakova and B.A. Dolgoplosk, Vysokomolekulyarnye Soedineniya Seriya B, 1989, 31, 8, 637. 48. N.N. Chigir, O.K. Sharaev, E.I. Tinyakova and B.A. Dolgoplosk, Vysokomolekulyarnye Soedineniya Seriya B, 1983, 25, 1, 47. 49. N.G. Marina, Kh.K. Gadeleva, Y.B. Monakov and S.R. Rafikov, Doklady Akademii Nauk SSSR, 1984, 274, 3, 641. 50. V.G. Kozlov, R.V. Nefed’ev, N.G. Marina Y.B. Monakov and S.R. Rafikov, Doklady Akademii Nauk SSSR, 1988, 299, 3, 652. 51. N.G. Marina, N.V. Duvakina, Z.M. Sabirov, V.S. Glukhovskoi, Y.A. Litvin and Y.B. Monakov, Polymer Science, 1997, 39B, 1-2, 34. 52. G. Lugli, W. Marconi, A. Mazzei, N. Paladino and U. Pedretti, Inorganica Chimica Acta, 1969, 3, 2, 253. 53. K.H. Thiele, R. Opitz and E.Z. Koehler, Zeitschrift fur Anorganische und Allgemeine Chemie, 1977, 435, 8, 45. 54. Y.B. Monakov, N.G. Marina, I.G. Savel’eva, N.V. Duvakina and S.R. Rafikov, Doklady Akademii Nauk SSSR, 1984, 278, 5, 1182. 55. V.S. Bodrova, E.P. Piskareva, S.V. Bubnova and V.A. Kormer, Vysokomolekulyarnye Soedineniya Seriya A, 1988, 30, 11, 2301. 56. S.V. Bubnova, E.P. Piskareva, V.K. Vasil’ev and V.A. Kormer, Vysokomolekulyarnye Soedineniya Seriya B, 1993, 35, 1, 18. 57. V.S. Bodrova, E.P. Piskareva and V.A. Kormer, Doklady Akademii Nauk SSSR, 1987, 293, 3, 645. 98

Diene Polymerisation Mechanism with Lanthanide Catalytic Systems 58. H.L. Hsieh and G.H.C. Yeh, Industrial & Engineering Chemistry Product Research & Development, 1986, 25, 3, 456. 59. X. Zhang, F. Pei and X. Li, Acta Polymerica Sinica, 1990, 8, 4, 391. 60. Y. Jin, X. Zhang, F. Pei and Y. Wu, Chinese Journal of Polymer Science, 1990, 8, 2, 121. 61. J. Wei and Y. Liao, Gaofenzi Tongxun, 1983, 5, 342. 62. Y.T. Jin, Y.F. Sun and Z. Liu, Fenzi Kexue Yu Huaxue Yanjju, 1984, 4, 2, 247. 63. X. Zhao and F. Tian, Kexue Tongbao, 1982, 27, 12, 731. 64. X. Zhao and F. Wang, Kexue Tongbao, 1983, 28, 6, 776. 65. K.D. Skuratov, M.I. Lobach, A.N. Shibaeva, L.A. Churlyaeva, T.V. Erokhina, L.V. Osetrova and V.A. Kormer, Polymer, 1992, 33, 24, 5202. 66. Y. Jin, X. Li and Y. Sun, Gaofenzi Tongxun, 1984, 5, 358. 67. Y. Jin, X. Li and Y. Sun, Kexue Tongbao, 1985, 30, 8, 1047. 68. C. Shan, Y. Lin, J. Ouyang, Y. Fan and G. Yang, Makromolekulare Chemie, 1987, 188, 629. 69. M.C. Throckmorton, Kautschuk und Gummi, Kunststoffe, 1969, 22, 6, 293. 70. Y.B. Monakov, N.G. Marina, Z.M. Sabirov, I.G. Savel’eva, O.I. Kozlova and N.V. Duvakina, Doklady Akademii Nauk SSSR, 1992, 327, 4-6, 524. 71. Y.B. Monakov, Z.M. Sabirov and N.Kh. Minchenkova, Mendeleev Communications, 1993, 3, 85. 72. Z.M. Sabirov, N.Kh. Minchenkova and Y.B. Monakov, Vysokomolekulyarnye Soedineniya Seriya B, 1991, 32, 2, 83. 73. Z.M. Sabirov and Y.B. Monakov, Doklady Akademii Nauk SSSR, 1988, 302, 1, 143. 74. Z.M. Sabirov, Y.B. Monakov and G.A. Tolstikov, Journal of Molecular Catalysis, 1989, 56, 1-3,194. 75. Z.M. Sabirov and Y.B. Monakov, Inorganica Chimica Acta, 1990, 169, 2, 221.

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Polymer Yearbook 76. Z.M. Sabirov, N.Kh. Minchenkova and Y.B. Monakov, Vysokomolekulyarnye Soedineniya Seriya A, 1990, 31, 11, 803. 77. Z.M. Sabirov, N.Kh. Minchenkova, I.I. Kazantseva, V.N. Urazbaev and Y.B. Monakov, Teoreticheskaya i Eksperimental’naya Khimiiya, 1991, 27, 6, 741. 78. Z.M. Sabirov, V.N. Urazbaev and Y.B. Monakov, Polymer Science, 1992, 34A, 5, 379. 79. Y.B. Monakov, Z.M. Sabirov and V.N. Urazbaev, Doklady Akademii Nauk SSSR, 1993, 332, 1, 50. 80. Z.M. Sabirov, V.N. Urazbaev and Y.B. Monakov, Polymer Science, 1997, 39B, 12, 22. 81. Z.M. Sabirov and A.A. Bagatur’yants, Uspekhi Khimii, 1991, 60, 10, 2065. 82. N.G. Marina, Y.B. Monakov and G.A. Tolstikov, Chemistry Reviews, 1994, 18, 4, 1. 83. D.A.G. Compton, W.O. George and W.F. Maddams, Journal of the Chemical Society, Perkin Transactions 2, 1977, 1311. 84. Y.B. Monakov and G.A. Tolstikov, Catalytic Polymerisation of 1,3-Dienes, Nauka, Moscow, Russia, 1990, 211. (In Russian) 85. Z.M. Sabirov, N.K. Minchenkova, V.N. Urazbaev and Y.B. Monakov, Journal of Polymer Science, Polymer Chemistry Edition, 1993, 31, 2419. 86. Z.M. Sabirov, N.K. Minchenkova, Y.B. Monakov, Inorganica Chimica Acta, 1989, 160, 1, 99. 87. Z.M. Sabirov, N.K. Minchenkova and N.A. Vakhrusheva and Y.B. Monakov, Doklady Akademii Nauk SSSR, 1990, 312, 1, 147. 88. Y.B. Monakov, Z.M. Sabirov and N.G. Marina, Polymer Science, 1996, 38A, 3, 232. 89. Z.M. Sabirov, V.N. Urazbaev, N.G. Marina, N.V. Duvakina, N.C. Minchenkova and Y.B. Monakov, Polymer Science, 1997, 39B, 1-2, 14.

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4

Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion Yu. Medvedevskikh, A. Bratus, G. Hafiychuk, A. Zaichenko, A. Kytsya, A. Turovski and G. Zaikov

4.1. Introduction The kinetics of glycidyl methacrylate block polymerisation have been investigated at high degrees of conversion with variations of photoinitiator concentration, temperature and the intensity of UV-illumination. The kinetic curves for the polymerisation process contains three characterised regions in the coordinates of ‘conversion – time’. The regions are, firstly, a practically linear dependence up to a conversion ≈ 0.5; the second region, describing an auto accelerated process and the third an auto deacceleration of the polymerisation process. An additional feature of such a polymerisation process is the poor reproduction of the kinetic measurements. This lack of reproduction does not correspond to instrumental error. Derivation of the kinetic model for block linear polymerisation has been carried out and is quantitatively in good agreement with the experimental data. The kinetics of mono- and multi-functional polymerisation investigated at high degrees of conversion are characterised by both the general and differential features of the process. Among the general features are: 1. an S-like shape to the kinetic curves, indicating the presence of auto acceleration and auto deacceleration processes; 2. a large post-irradiation effect, i.e., darkness after UV-illumination stopping the postpolymerisation process observed from the auto acceleration stage and 3. a high (up to 10-1 mole/m3) concentration of radicals discovered by ‘in situ’ electro paramagnetic resonance-spectroscopy investigations at the end of the polymerisation process [1-8]. Two main theories have been formulated with the aim of explaining the features observed when polymerisations are investigated at high degrees of conversion. The first is based upon the diffusion-controlled character of the elementary reactions described according to a classic kinetic scheme. It is assumed that the kinetic equations describing the initial

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Polymer Yearbook stage of the reaction process are used as a starting point in the diffusion-controlled reaction (DCR) approach. The selection of the parameters in this approach are influenced by the current state of our knowledge of monomer-polymeric solutions [9]. There are several variants of the DCR theory differing from one another by the way in which account is taken of the physical factors influenced by the diffusion control on the description of elementary reactions rate. As a rule, the main factor influenced is the bimolecular chain termination process. The constant rate of chain termination is considered as a function of the macroradical’s mobility, their length [9-14], free volume [12, 15-17] or characteristic viscosity of monomer-polymeric system. However, with the aim of explaining the auto deacceleration stage, the efficiency of initiation and constants of rate chain propagation are also considered to be functions of the macroradical’s mobility [12, 15, 18]. The second approach or microheterogeneous model [1, 19-22] is based upon the principle, that the kinetics of the reaction in its initial stage are not that of a homophase polymerisation in a liquid monomer-polymeric solution, but a heterophase one. The reaction proceeding at the boundary ‘liquid monomer - solid polymer’ microgranules surface under gel conditions. The microheterogeneity of the polymerising system, i.e., the presence of solid polymer micrograins within it, will limit the extent of conversion in the liquid monomeric phase or, after phase inversion, microdrops of liquid monomer distributed in solid polymeric matrix, and is demonstrated by both direct and indirect experimental methods. That is why, the effect of microheterogeneity on the polymerising system is not denied [2, 7, 10, 15] even in papers where DCR is assumed. Quite the reverse, this factor is taken into account in the explanation that the radicals at high concentration are stored via the polymerisation proceeding at the expense of their trapping [6] by the solid polymeric matrix. The factors controlling the polymerisation at high degrees of conversion can be explained by changing the chemical mechanism of chain termination, i.e., by a transition from a quadratic to linear dependence. This approach considers the physical elimination of active radicals through there being transformation into captured, ‘frozen’ or ‘locked’ into the solid polymeric matrix [5, 7]. From this point of view, the difference between microheterogeneous model and DCR approach consists only in the way that they consider or do not consider the microheterogeneity of polymerising system as an essential and important factor determining the main features of polymerisation process to the high degrees of conversions. Generally, the kinetic model of block 3-dimensional polymerisation of multifunctional monomers based upon microheterogeneity of polymerising system theory and especially the role of the interface layer of the boundary ‘liquid monomer - solid polymer’ has been

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Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion represented in theory [23-26]. The starting assumptions include that the observed rate of polymerisation is a sum of the rate of the homophase process proceeding in a volume of liquid monomer accordingly to classic kinetic scheme. This approach assumes quadratic chain termination and the heterophase process proceeding under gelation conditions. Clusters of solid polymer in the liquid monomeric phase and clusters of liquid monomer in solid polymeric matrix are characterised by the structure of mass fractals. The geleffect in the interface layer appears as a decrease in the rate of chain termination and a transition of control to the chain propagation rate. Linear chain termination plays the role of an active radical self-burial and is observed in computer simulation experiments as a self-avoiding walks [27, 28]. The kinetic equations obtained for stationary and non-stationary (so-called post polymerisation) processes [25, 26] qualitatively explain all the main features of block 3-dimensional polymerisation at high degrees of conversion. This feature has also been quantitatively proven on a wide range of experimental materials connected with the kinetics of photoinitiated polymerisation of dimethacrylates. This allows for the first time a numeric estimate of the rate constants for linear chain termination to be made [29]. In this study, the quantitatively kinetic model for linear block polymerisation up to a high degree of conversion is proposed on the basis of experimental material concerns to kinetics of photoinitiated polymerisation of glycidyl methacrylate (GMA) obtained over a wide range of variation of the available parameters.

4.2 Experimental Kinetics of glycidyl methacrylates (2,3-epoxypropylmethacrylate) photoinitiated polymerisation has been studied using laser interferometry in a thick layer (0.5 x 2) × 10-4 m in the presence of the photoinitiator 2,2-dimethoxy-2-acetophenone (ketal) C6H5-C(OCH3)2C(O)-C6H5 under the UV-illumination of a mercurial quartz lamp DRT-400. The experimental technique used is described in detail elsewhere [23]. Concentration of photoinitiator (0.5 × 3.0% by mass), temperature (10-30 °C) and power W0 of UV-illumination (37.4-65 W/m2) falling upon the surface of photocomposition layer have been varied. Selected experimental kinetic curves for the polymerisation of GMA are presented in Figure 4.2. As can be seen from the data, the instrumental error in the individual kinetic curve is relatively small. However, comparison of the individual kinetic curves with each other, (see Table 4.1) indicates a scatter of the characteristic parameters. The parameters are for example, the maximum rate W0 of the process in the auto acceleration region, conversion P0 and time t0 of achievement of W0, and also the rate W1 of the initial linear section of the kinetic curve. Such scattering essentially exceeds the error of individual

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Polymer Yearbook

Table 4.1 Characteristic parameters of GMA polymerisation kinetics at the photoinitiator concentration c0 = 0.5% (by mass), T = 283 K, E0 = 37.4 W/m2 and different thicknesses of the layer Thickness of layer, l × 104, m

Time of maximum rate coming, s

Conversion of maximum rate, P0

Maximum rate of process, s-1

Rate of the linear site, s-1

1

1.3

760

0.74

4.0

0.74

2

1.5

740

0.74

2. 7

0.89

3

1.8

780

0.80

4.5

0.83

4

2.0

720

0.72

3.4

0.81

5

2.3

720

0.75

4. 3

0.76

Number

experiment. At the same time, the scattering of characteristic parameters represented in Table 4.1 depends on the influence of the thickness of the layer l of photopolymerisation of the composition through the range of its change. The poor reproduction of the kinetic measurements or ‘whims’ of the process are well known [30, 31] and they are a result of the fluctual sensitivity of the polymerisation process, especially in the auto acceleration stage. That is why, the results consisting of 5-8 kinetic curves represented on Figure 4.2 have been obtained in a narrow limits of layer thickness with change of each set of variable parameters (concentration of photoinitiator, temperature and power of UV-illumination).

4.3 Results and Discussion 4.3.1 Discussion of Experimental Data and Formulating the Starting Position of the Kinetic Model The experimental data indicate one more general feature of linear and 3-dimensional polymerisation processes, namely: the bad reproducibility of the kinetic measurements does not correspond to the magnitude of the instrumental error. This proves the high fluctual sensitivity of these processes, especially on the auto acceleration stage. However, let us also identify the essential differences in the kinetics of linear and 3-dimensional polymerisation. In contrast to 3-dimensional polymerisation, the autoacceleration stage in the linear region begins only when higher degrees of conversion have been achieved, in this case at

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Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion P0> 1/2. As we can see from Figure 4.1 and Figure 4.2, this degree of conversion does not depend upon the photoinitiator concentration and the power of the UV-illumination and slightly increases (see Figure 4.1) with increase of the temperature. Up to a degree of conversion of P0ª 2, a practically linear section of the kinetic curve is observed, though according to classic kinetics the rate of polymerisation should be two orders of magnitude lower than observed. The inflection point of the kinetic curve or the degree of conversion P0, which corresponds to the maximum rate of the process, for a 3-dimensional polymerisation in dimethacrylates [24, 25] is less or equal to 0.5 for linear polymerisation P0 > 0.5. This occurs in the range of P0 = 0.7 to 0.75 and practically does not depend upon parameters of the process. The maximal rate W0 for the process of linear polymerisation depends less upon the concentration of photoinitiator than on the power of the UV-illumination for similar layers thickness, for the 3-dimensional polymerisation of dimethacrylates [24, 25]. The differences in the kinetics of linear and 3-dimensional polymerisation means, that the kinetic model of linear polymerisation cannot be a simple copy of kinetic model for 3dimensional polymerisation, but should contain in it some common factors. On the basis of the above, the kinetic model for linear polymerisation for high degrees of conversion is formulated as: 1. Up to a monomer concentration [Mv0], corresponding to conversion Pv0 = ([M0] – [Mv0]/[M0], where [M0] is an initial concentration of monomer in the block, the polymerising system is a monophase. This is represented by a solution of the polymer in the monomer and is named as the monomer-polymeric phase (MPPh).

Figure 4.1 Typical kinetic curves of GMA polymerisation for the photoinitiator concentrations: 1: 0.5%, 2: 1.5%, 3: 3.0% (by mass), T = 283 K, E0 = 37.4 W/m2

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Polymer Yearbook (a)

(b)

(c)

(d)

(e)

(f)

Figure 4.2 Comparison of the experimental data (thin lines) and calculated ones (bold lines) in accordance with Equations (4.61)-(4.64) of kinetic curves of GMA photopolymerisation in variants:

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Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion

Variant in Figure 4.2 Variant

a

b

c

d

e

f

Photoinitiator concentration, % (mass)

0.5

1.5

3.0

3.0

3.0

3.0

Power of UV-illumination, W0, W/m2

37.4

37.4

37.4

65

37.4

37.4

Temperature, K

283

283

283

283

293

303

In MPPh, the polymerisation process proceeds in accordance with the classic kinetic scheme with quadratic chain termination: k

pv ⎯ →R M + R ⎯k⎯

tv

R + R ⎯⎯→ products of reaction

(4.1)

The linear dependence of the degree of conversion upon time in MPPh is explained by partial diffusion control of the linear chain termination. 2. Once the degree of conversion has achieved a value Pv0, the monomer-polymeric solution becomes saturated relative to the polymer and a supersaturation of the new polymer-monomer phase (PMPh) is achieved. This is represented by the saturated solution of monomer in the polymer with the concentration of monomer [Ms0], which corresponds to a degree of conversion Ps0: Ps0 = ([M0] – [Ms0]) / [M0]. Concentrations of monomer [Mv0] in MPPh and [Ms0] in PMPh are functions of the nature of the monomer-polymeric system and the temperature. The supersaturation of MPPh disappears after the spontaneous creation of the PMPh phase. That is why the polymerisation process is accompanied by propagation within the new phase or micrograins of PMPh. 3. The photoinitiator is distributed non-uniformly between MPPh and PMPh, but is in equilibrium, i.e., in accordance with the law of partitioning between the two phases. Since PMPh is rather viscous, the effects of mixing inside of micrograins can be neglected, that is why the concentration of photoinitiator will be a variable that depends on the radius of micrograins. 4. In a case of a microheterogeneous system, polymerisation proceeds in the three reaction zones: in saturated monomer-polymeric solution, at the interphase layer of the boundary of MPPh and micrograins of PMPh, and in the ‘solid’ polymermonomeric solution.

107

Polymer Yearbook 5. In the MPPh, polymerisation proceeds in accordance with the same classic kinetic scheme (4.1), but at a constant concentration [Mv0] of monomer and viscosity of the solution. Only the concentration of the photoinitiator and volumetric part (ϕv) of MPPh are varied. 6. Polymerisation of the interphase layer of the boundary of MPPh and PMPh, proceeds accordingly to Scheme (4.1), but the constant rate of linear chain termination ktvs is different. This is because the ‘solid’ PMPh creates an ordered structure of the nearest reaction space, in which the translational movement and segmental mobility of macroradicals are significantly reduced. Let us assume that the concentration of monomer and photoinitiator in the interphase layer are equal or proportional to their concentration in MPPh. Volume and the volumetric part of interphase layer are the composite function of the propagation and aggregation process (stage of monolithisation [1]), respectively, of PMPh micrograins. The volumetric part of the interphase layer will be proportional to volumetric part ϕs of PMPh. Thus ϕvs ∼ ϕs only while ϕv t we have obtained β < 1, and amount of a monomer in a unit volume is equal to [Ms0]β. Via time dτ the d[Ms] of a monomer will reacted and remain in a non-glass transitioned part of unit volume [Ms0](β + dβ). It follows from this:

[ ] [ ] d[ Ms ] / dτ = [ Ms0 ]dβ / dτ d Ms = Ms0 dβ or

(4.27)

Comparing Equations (4.26) and (4.27) gives:

[ ]

dβ / β = −w sdτ / Ms0

(4.28)

Changing the level of the photoinitiator concentration as a result of its photodecomposition, we accept, that vis and ws in accordance with Equation (4.5) does not depend upon time in the interval τ – t after removing the given unit of PMPh volume. That is why, by integrating Equation (4.28) in accordance with condition β = 1 in a moment of time t for removal of PMPh, we obtain:

{

[ ]}

β = exp −w s ( τ − t ) / Ms0

(4.29)

The summary rate of polymerisation in removed unit dϕs of PMPh volume is equal to: −

[ ] dϕ

d Ms dτ

s

= w sβdϕ s

(4.30)

dϕ Substituting Equation (4.29) into Equation (4.30) and replacing dϕ s = s dt in its correct dt position, and integrating Equation (4.30) upon ϕs on the left and upon t on the right. Taking into account the fact, that in accordance with the mean-value theorem we have:

113

Polymer Yearbook

ϕs −

∫

[ ] dϕ

d Ms dτ

0

s

=−
ϕ

d Ms dτ

s

= ws ϕ s

(4.31)

we obtain:

ws =

1 ϕs

⎧ ⎫ ⎪ w ⎪ dϕ w s exp⎨− s ( τ − t )⎬ s dt 0 ⎪ Ms ⎪ dt 0 ⎩ ⎭ τ

∫

[ ]

(4.32)

It follows from this, that the rate contribution (dP/dt)s = <ws> ϕs / [M0] of the polymerisation process into PMPh in microheterogeneous system can be determined by expression: ⎛ dP ⎞ ⎜ ⎟ = ⎝ dτ ⎠ S

τ

⎧ ⎫ ws ⎪ w ⎪ dϕ exp⎨− s ( τ − t )⎬ s dt 0 M0 ⎪ Ms ⎪ dt ⎩ ⎭

∫[ ] 0

[ ]

(4.33)

The general kinetic equation of polymerisation in a microheterogeneous system at P ≥ Pv0 can be calculated as follows:

(

)

dP dϕ s = Ps0 − Pv0 + dτ dτ

τ

⎧ ⎫ ws ⎪ ws ⎪ dϕ τ − t )⎬ s dt exp⎨− ( 0 M0 ⎪ Ms ⎪ dt ⎩ ⎭

∫[ ] 0

[ ]

(4.34)

At this time we can write in accordance with Equation (4.5) the following:

[ ]

[ ]

(

w s / M0 = k3vis , w s / Ms0 = k3vis / 1 − Ps0

)

(4.35)

where:

[ ]

k3 = kps / kts M0

(4.36)

Equations (4.24) and (4.34) (taking into account that dt = dτ) represent by themselves the kinetic model of polymerisation in microheterogeneous system in the integraldifferential form. The integrated form of kinetic model will be obtained, if we rewrite: P = Pv0 (1 − ϕ s ) + Ps ϕ s

where is the average conversion in PMPh in the present moment of time t.

114

(4.37)

Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion As was shown previously, the amount of monomer in unit volume of PMPh when taken into account the share of β of its non-glass transitioned part is equal to [Ms] = [Ms0]β or: ⎧

[Ms ] = [Ms0 ] exp⎪⎨− ⎪ ⎩

ws

[M ] 0 s

⎫

(τ − t )⎪⎬

(4.38)

⎪ ⎭

By multiplying the left-hand side of the Equation (4.38) by dϕs, and the right-hand side dϕ s dt , and by integrating it by taking into account the mean-value theorem we obtain: by dt

[M ] [M ] = 0 s

s

ϕs

τ

⎧⎪ w s ⎫⎪ dϕ s t dt τ exp⎨− − ( ) ⎬ ⎪⎩ [ Ms0 ] ⎪⎭ dt 0

∫

(4.39)

It follows from this that: 1 − Ps0 Ps = 1 − ϕs

⎧ ⎫ ⎪ ws exp⎨− (τ − t )⎪⎬ ddtϕ s dt 0 ⎪ Ms ⎪ 0 ⎩ ⎭ τ

∫

[ ]

(4.40)

Thus, the integral kinetic model of polymerisation in microheterogeneous system can be notified in accordance with Equation (4.37) and Equation (4.40) as follows:

(

) (

P = Pv0 + 1 − Pv0 ϕ s − 1 − Ps0

⎧ ⎫ ⎪ w ⎪ dϕ exp⎨− s ( τ − t )⎬ s dt 0 ⎪ Ms ⎪ dt 0 ⎩ ⎭ τ

)∫

[ ]

(4.41)

The difference between the rates of initiation viv in a MPPh and vis in a PMPh is determined by an initiator distribution character between the two phases in the moment of PMPh removal from MPPh and also by the absence of mixing inside the grains of PMPh. We have obtained the distribution of the initiator at equilibrium as the following ratio: cs / cv = L

(4.42)

where L is a coefficient of distribution; cv and cs are the molar-volumic concentrations of the initiator in MPPh and removing PMPh, respectively, at the present time. Let us assume, that the initiator concentration in MPPh at the moment of time τ is equal to cv (1–ϕs). At the moment of time τ + dτ we shall obtain (cv + dcv)(1 – ϕs – dϕs); at this time the initiator concentration transported via time dτ in PMPh, is equal to csdϕs. It follows 115

Polymer Yearbook from this that: –cvdϕs + (1 – ϕs)dcv + csdϕs = 0. We have obtained Equation (4.43) by the replacement of cs = cvL. So: dc v / c v = (1 − L )dϕ s / (1 − ϕ s )

(4.43)

The concentration of initiator in MPPh will be equal to cv0 as a result of integrating Equation 4.43 under conditions so that the first portions of PMPh (ϕs = 0) are removed (ϕs = 0): c v = c 0v / (1 − ϕ s )

1− L

(4.44)

c s = Lc 0v / (1 − ϕ s )

1− L

(4.45)

So, the rates of initiation of thermal decomposition of the initiator in microheterogeneous system can be described as: viv = fiv kd c 0v / (1 − ϕ s )

1− L

(4.46)

vis = fiskd Lc 0v / (1 − ϕ s )

1− L

(4.47)

where kd is a constant rate of the initiator decomposition; fiv and fis are coefficients of initiation in MPPh and PMPh, respectively. Equations (4.24), (4.34)-(4.36) and (4.46), (4.47) represent by themselves the kinetic model of the thermally initiated polymerisation in a microheterogeneous system at P ≥ Pv0. The variation in the photoinitiated polymerisation is complicated, since it is necessary to take into account the presence of a gradient of the light exposure in the layer of the photopolymerising composition. This effect indicates that the rate of polymerisation and conversion are functions not only of time, but also of the coordinates of a layer x from an illuminated surface (x = 0), and appear, thus, in differential performances of the process in a layer x, x + dx. The transition from differential characteristics P(x, t) and ∂P(x, t) / ∂t to experimentally determined, P(t) and dP(t) / dt, is carried out via integrated transformations: l

1 P( t ) = P( x , t )dx , l

∫ 0

where l is thickness of a layer.

116

l

dP( t ) 1 ∂P( x , t ) = dx l dt ∂t

∫ 0

(4.48)

Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion Dynamics of the initiator decomposition in the homogeneous phase that takes into account the light illumination gradient is described by a system of nonlinear differential equations in partial derivatives: fc / ft = − γεcJ , fJ / fx = − εcJ

(4.49)

where J = J(x, t) and c = c(x, t) are light intensity and the photoinitiator concentration in the layer x, x + dx from an illuminated surface in time moment t; ε is molar factor of the photoinitiator extinction; γ – quantum yield of the initiator photodecomposition. The derivation of Equation (4.49) is well-known [34] and leads to the following expression of initiator photodestruction differential rate:

[

(

)]

fc ( x , t ) / ft = γεJ0 exp{γεJ0t − εc0 x} / 1 + exp{− εc0 x} exp{− εJ0t} − 1

2

(4.50)

where J0 is intensity of falling light upon surface of polymerising composition; c0 is initial concentration of the photoinitiator. However, Equation (4.50) in the full form can be used only for polymerisation in MPPh up to P = Pv0. That is why in the analysis of the kinetic models to high degrees of conversion, the simplifications used are invariant of the photoinitiated polymerisation. First of all, let us assume, that the characteristic time of the photoinitiator decomposition td = (γεJ0)–1 is considerably more than the time t of polymerisation, therefore we can neglect the polymerisation by changing the photoinitiator concentration via time (typical approximation for long-chain processes) taking c = c0. After integration, fJ / fx = –εc0J, we obtain the J=J0exp {–εc0x} and, after introduction of the latter into the left hand side of Equation (4.49) we obtain Equation (4.51):

[

]

− fc ( x ) / ft = γεc0 J0 exp{− εc0 x}

(4.51)

Third, allowing that the thickness of layer l for photopolymerising composition and its optical densities εc0l are small in our experiments. Let us also assume, that the kinetic model will be approximately adequate for photoinitiated polymerisation in a case when we use average rate upon layer instead of differential rate of photoinitiator decomposition according to Equation (4.51). Under the definition of average values of Equation (4.51) we obtain: ⎛ dc ⎞ − ⎜ ⎟ ⎝ dt ⎠

1/ 2

l

1 = ( γεc0 J0 )1 / 2 exp{− εc0 x / 2}dx l

∫

(4.52)

0

117

Polymer Yearbook

−

l

dc γεc0 J0 = dt l

∫ exp{−εc x}dx

1/ 2

1/ 2

(4.53)

0

0

therefore: ⎛ dc ⎞ − ⎜ ⎟ ⎝ dt ⎠

−

2 ⎛ γJ ⎞ = ⎜ 0⎟ l ⎝ εc0 ⎠

(1 − exp{−εc l / 2}) 0

dc γJ = 0 1 − exp{− εc0l} dt l

(

)

(4.54)

(4.55)

It follows from Equations (4.54) and (4.55), that at the small relative density of layer we will obtain: εc0l > 1, – = (2/l)(γεc0J0)1/2, – = γJ0/l. Thus, the observed order of photoinitiator at the quadratic chain termination can be varied from 0.5 to –0.5, and for the linear chain termination from 1 till 0 depending from thickness of layer l or its optical density εc0l. But, at the same time, the order upon UV-illumination intensity is always equal to 0.5 or 1. As we can see from the experimental data, the order of photoinitiator at the initial linear sections of kinetic curves is similar, but less than 0.5. It means, that the approximation of infinite thick layer εc0l Pv0 taking into account Equations (4.44) and (4.45) at the replacement of cv0 = c0 we will obtain: v1iv2 = ( γ v J0 )

12

(εc0 )m / (1 − ϕ s )m(1− L )

v1is 2 = γ s J0 (εc0L )

2m

(4.59)

/ (1 − ϕ s )

2 m(1− L )

(4.60)

where γv = fvγ and γs = fsγ are quantum yields of photoinitiation in MPPh and PMPh, respectively. By substituting the viv1/2 and vis in kinetic models (4.14), (4.24), (4.34) and (4.35) on their average analogs on layer (4.58)-(4.60), we have finally obtained the following equation for the variant of photoinitiated polymerisation in a homogeneous system at P ≤ Pv0, t ≤ tv0: 1/ 2 dP = k1 J10 / 2c0m (1 − P )(1 + aP ) dt

(4.61)

We have obtained the following expressions at Pv0 ≤ P, tv0 ≤ t for a microheterogeneous system: ⎡ 1/ 2 dϕ s 1 − P0 = 0 v 0 k1 ( J0 ) c0m ⎢ 1 + aPv0 dτ Ps − Pv ⎢⎣

(

(

)

1/ 2

+

⎤ 1− mα ϕ s ⎥(1 − ϕ s ) k1 ⎥⎦

k2

)

2m dP dϕ s + k 3 J0 (c0L ) U ( τ) = Ps0 − Pv0 dτ dτ

τ

U( τ ) =

∫ (1 − ϕ ) s

0

−2 mα

⎧ ⎪ k 3 J0 exp⎨− 0 ⎪ 1 − Ps ⎩

(4.62)

(4.63)

⎛ ⎞ c 0L ⎜ ⎟ ⎜ (1 − ϕ )α ⎟ ⎝ ⎠ s

2m

⎫ (τ − t )⎪⎬ ddtϕ s dt ⎪ ⎭

(4.64)

where α = 1 – L, and:

( )

0 k1 = k1γ 1v 2 ε m = kp γ 1v 2 ε m / ktv

12

(4.65)

k2 = k2 γ 1v/ 2 ε m = kp Fvskmkv γ 1v/ 2 ε m / (ktvs )

1/ 2

[ ]

k 3 = k3γ s ε 2 m = kp γ s ε 2 m / kts M0

(4.66) (4.67)

119

Polymer Yearbook Let us to rewrite the integral Equations (4.40) and (4.41) as follows:

[(

)

(

) (

Ps = 1 − 1 − Ps0 V ( τ) / ϕ s

]

(4.68)

)

P = Pv0 + 1 − Pv0 ϕ s − 1 − Ps0 V ( τ)

(4.69)

2m ⎧ ⎫ τ k 3 J0 (c0L ) ⎪ t V ( τ) = exp⎨− τ − )⎪⎬ ddtϕ s dt 2 mα ( 0 ⎪ 1 − Ps (1 − ϕ s ) ⎪ 0 ⎩ ⎭

∫

(

)

(4.70)

4.3.3 Calculation - Results The calculated kinetic curves when compared with the experimental data in Figure 4.2, show good agreement. The calculations have been done with the use of the constant parameters of a model represented in Table 4.2. Among these constant parameters part, for example k1, a, Pv0 and m, was simply estimated upon the initial sections of kinetic curves. Other values were selected ‘manually’ with the aim of obtaining satisfactory agreement between the experimental data and theory by variation of a range of the controlled parameters. As can be seen from Table 4.2, with the exception of a = 6.5 and m = 0.4, the other parameters of kinetic model are functions of temperature, but at the same time all of them do not depend upon the photoinitiator concentration and intensity of the illumination. The values of constants k1, k2 and k3 have been increased uniformly by 20% with the temperature increasing at 10 °C intervals corresponding to the effective activation energy of ≈ 12.6 kJ/mole. In accordance with the experimental data (see Figures 4.2c, 4.2e, 4.2f) the conversion Pv0 in the saturated MPPh with the increase of temperature is also increased, this can be considered as the polymer solubility propagation in monomer with the increase of

Table 4.2 Parameters of proposed kinetic model for the different temperatures Temperature, K

k1

k2

k3

Pv0

Ps0

a

L

m

283

0.020

0.50

2.40

0.50

0.80

6.5

0.50

0.4

293

0.024

0.60

2.87

0.53

0.76

6.5

0.55

0.4

303

0.029

0.72

3.45

0.57

0.73

6.5

0.60

0.4

120

Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion temperature. Similarly, we can expect the monomer solubility in polymer to increase, and that leads to the Ps0 decrease with increase of temperature. The factor of the photoinitiator distribution L between MPPh and PMPh is increased at the expense of the previous effect. Intensity of the illumination falling upon the surface of polymerising composition of UVillumination (J0) has been calculated by taking into account it’s power W0 (W/m2) (approximation), that it concentrated on the conditional wavelength λ = 340 nm: J0 = 2.83 × 10-6 W0 mole × quant/m2 × s. The starting concentrations of photoinitiator c0 = (% by mass) = ρm/Min and monomer in the block [M0] = ρm/Mm (where ρm = 1.04 × 106g/m3 – density of monomer, Min = 256 and Mm = 142 g/mole – the molecular masses of the initiator and monomer, respectively), expressed in the units mole/m3. The given choice of the dimensions J0, c0 also [M0] determines the numerical values, k1, k2 and k3, as represented in Table 4.2. From our point of view, taking into account the error in the experimental data, the agreement between them and the calculated ones can be considered as satisfactory. The proposed kinetic model quantitatively explains the main peculiarities of the photoinitiated linear polymerisation of the high conversions in the layers with small optical densities.

4.4 Characterisation of the Peculiarities of the Linear Polymerisation of the Microheterogeneous System The experimental data represented as a conversion dependence upon time does not permit selection of the separate components of the linear polymerisation process, to estimate their share into the rate of the process and to underline its characterised features. The kinetic model gives this possibility. Let us consider the most interesting stage of the polymerisation in the microheterogeneous system, i.e., from the moment of the polymer monomer phase extraction. The kinetic data of PMPh from MPPh extraction are represented in Figure 4.3 by calculation from (4.62) of the dependences ϕs and dϕs/dt upon time. The calculated results show, that the maximum rate (dϕs/dt)max of PMPh from MPPh extraction is observed practically at the same value ϕs(max) = 0.525 at all concentrations of the photoinitiator. From the analysis of Equation (4.62) for extremes of the function dϕs/dτ it follows that the maximum value dϕs/dτ should be observed at ϕs(max) ≤ 0.5; at equilibrium distribution of the photoinitiator between MPPh and PMPh, i.e., at L = 1. At this time a sign of equality is fulfilled under the condition k1 PES > polyesterestersulfone > PSF. Therefore, an initially linear macromolecule gradually transforms to a structured macroformation, partly losing the initial structure, but with new elements developing a system of conjugation blocks, which induces polymer yellowing (see Figure 7.4).

Figure 7.4 The fragments of structure formed as a result of degradation reactions

Beside the variant of typical radical-chain scheme development with future oxidation transfer to aromatic rings at H atom detachment in the chain propagation reaction, the possibility of direct attaching oxygen to aromatic rings with formation of endoperoxides of peroxyradicals is discussed for the mechanism of high temperature oxidation. Similar to previously considered APH, this reaction is probably accompanied by formation of a molecular complex of π-system with O2 and/or thermal transfer of the conjugated system to the electron excited state. This supposition seems quite real, keeping in mind that the red limit of electron absorption spectra of PES and PSF is located at 400-500 nm. This also corresponds to the high resistance of polymers containing –SO2– groups in the structure to thermo-oxidation. A strong electron-acceptor bridge –SO2– inhibits formation of molecular complexes with O2. An additional argument to confirm the mechanism suggested, is the highest stabilising efficiency of phosphorus-containing additives, taking into account the complex forming function of phosphorus. In the last 10-15 years, liquid-crystal aromatic polyesters (LCP) were of special interest, which above all was associated with the discovery of their ability to self-reinforce when melted. This enabled preparation of high accuracy and size stable articles with low coefficients of thermal shrinkage. Special interest in these polymers is stipulated by intensive progress in computer technology. In the last 5-10 years, a great list of publications concerning structure and properties of LCP was presented. However, there is little information on thermoresistance and specific features of LCP degradative behaviour. Authors have studied degradative transformations

195

Polymer Yearbook of LPC, based on p-oxybenzoic acid, dioxydiphenyl and terephthalic and isophthalic acids (TPA and IPA). Therefore, TPA/IPA concentration varied in the range of 100/0 - 0/100. Judging by kinetics of oxygen absorption at 350 °C (processing temperature) and data of dynamic TGA/DTA, thermo-oxidative stability of LCP with various concentrations of TPA/IPA decreases in the sequence: IPA-0 > IPA-25 ≥ IPA-50 > IPA-75 > IPA-100. In the absence of oxygen, LCP decomposition proceeds in one stage with formation of a significant (up to 40 wt.% at 700 °C) coke residue. Two endothermal heat effects were observed on DTA curves: a low peak in the melting area and a quite intensive one at polymer degradation. Value of the heat effect, associated with melting, is ΔH = 1-2.5 kJ/ mol. Shcherbakova and co-workers [39] who studied 4-hydroxybenzoic and 2,6hydroxynaphthoic acid copolymer by the differential scanning calorimetry (DSC) method, believe that the heat effect of about 1 kJ/mol relates not to the real melting, but to a change of ordering degree at the transition from a crystal to a mesophase. LCP thermoresistance in the air is much lower (~ by 25-30 °C) than in argon. According to dynamic TGA data in the air, mass losses of studied LCP are observed within the range of 350-800 °C. Decomposition proceeds in two stages: the first stage at 350-550 °C is accompanied by mass losses of up to 40 wt.%, and the second slower one in the temperature range of 550-800 °C proceeds practically to complete degradation of polymers. Coke content at 750-800 °C is 3-10 wt.%. Judging by DTA data, the stages of LCP degradation are accompanied by exothermal heat effects. In tests in the air, weak endothermal heat effect is absent in the ‘melting’ range, probably because of overlapping by exothermal effects accompanying degradative reactions. Increase of IPA concentration leads to a shear of the melting range to the area of low temperatures and reduction of LCP thermoresistance. Study of LCP phase transitions by the X-ray structuring analysis (RSA) in the temperature range of 20-400 °C showed that similar changes proceed in all LCP. Annealing at 300 °C causes an insignificant increase of the main crystal reflexive action. The ability of studied materials to transit into the so-called ‘liquid-crystal state’ displays their behaviour at processing temperature. In all polymers, a jump-like viscosity decrease is observed at softening temperature (depending on the structure, it falls within the range of 300-400 °C). Therefore, very strong threads are formed from the melt. This effect is explained [39] by cooperative orientation of large axes of macromolecules along the flow direction (viscosity anisotropy), which is realised only in LCP. It is common knowledge [7, 21, 39] that thermoresistance of polymers depends upon several factors: structure, molecular weight characteristics, content of macrochain defects, labile end groups (hydroxyl one, in the present case), low molecular organic admixtures (unreacted monomers residues) or inorganic ones (admixtures of metal ions appearing in a polymer from the raw material and equipment) in macromolecules.

196

Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers The composition of inorganic admixtures in monomers and LCP was studied by the inductively coupled plasma method. Nonequivalent influence of some metal admixtures on thermoresistance was shown by the TGA method using LCP KI-75. Introducing inorganic salts of an appropriate metal into the polymer increased the concentration of admixtures. The results obtained indicated different influence of metal admixtures on thermo-oxidative resistance of LCP. Aluminum and metals from the alkaline sequence, such as Ca, Na, K, do not practically affect thermoresistance in the studied range of concentrations. Fe, and Ca and Ni induce a negative effect in concentrations up to 10-310-4 wt.% which significantly increase thermoresistance of LCP. Composition and concentration of organic admixtures in LCP were studied by mass spectroscopy. In admixtures of phenol and dioxydiphenyl (m/e 94 and 186) – the hydrolysis product of the initial monomer (dioxydiphenyl diacetate), p-oxybenzoatedioxydiphenyl and oxydiphenyl acetate were identified. Total amount of organic admixtures in different samples did not exceed (1.0-2.0) × 10-2 wt.% – this had no effect on thermoresistance of polymers. Oxygen absorption kinetics is the two-stage process consisting of the first fast stage (2-3 hours long) with absorption of more than 1 mole of O2 per molecular unit and the second slow one with absorption of 0.2 mol/base-mol O2 during the next 7-8 hours of thermo-oxidation. Analogous dependencies are displayed by CO2 release kinetics – the main gas product of LCP degradation studied. Dioxydiphenol and p-oxybenzoic acid derivatives are present in the composition of heavy high-boiling degradation products, identified by NMR and MS: diphenylbenzoate, oxyphenylbenzoate, etc. The composition of these products is the same for all LCP studied and differs only by the ratio of the components. Analysis of the kinetic curves shows that thermo-oxidation rate is much lower at lower temperatures of 300 °C and 320 °C, near the melting point or at melting, than at 350 °C, when, judging by RSA data, the polymer completely transits into the isotropic melt. Beside the main CO2 gas product, hydrogen (in early stages of oxidation at exposure of 0.5-1.0 hour) and water (exposure longer than 4 hours) were identified at LCP thermo-oxidation in the studied temperature-time limits. Dynamics of the elemental composition change shows that hydrogen concentration decreases and carbon concentration increases in the sample containing IPA-75 during thermo-oxidation, i.e., a graphite-like structure is formed. This process proceeds intensively at 350 °C. IRspectroscopy data show that initial changes happen in the area of absorption of ester aromatic fragments: intensity of absorption bands decreases at νC=O = 1740 cm-1, νC-O = 1270 and 1160 cm-1, and νC=C = 1600 and 1500 cm-1, δC=C = 720 cm-1. Absorption bands of ether bonds, νC-O-C = 1080 cm-1, and aromatic structures are the only ones that remained at the maximal exposure (thermo-oxidation at 350 °C for 10 hours). Therefore, the spectrum noise decreases, which is also associated with formation of intermolecular crosslinks. At 350 °C, a large amount of oligomers, precipitated in the ampoule next to

197

Polymer Yearbook the reaction zone at ≅150 °C, formed into a melt. Structure and ratio of oligomers with p-oxybenzoate dioxydiphenyl (product a), oxydiphenyl (product b), p-oxybenzoic acid di- and trimers (product c) end groups in the mixture of oligomeric degradation products were identified with the help of 13C NMR. The amount of oligomers in the mixture was successfully determined by the ratio of signal squares with appropriate chemical shears of 11.5 and 115.82 ppm (product a), 115.43 ppm (product b) and 120.72 ppm (product c): product a – 15 mol.%, product b – 31 mol%, product c – ≅10-12 mol%. The fact that neighbouring p-oxybenzoic acid units were detected in the composition of thermo-oxidation products allows a supposition that, beside copolycondensation, homopolycondensation reactions of p-acetoxybenzoic acid also proceed. The output of free p-oxybenzoic acid is 3-4-fold higher, than its output in the linked state shaped as end groups in oligomers. Apparently, free p-oxybenzoic acid is formed as the result of thermal reactions at decomposition of labile bonds in structural p-oxybenzoic blocks. Analysis of kinetics and composition of LCP degradation products in the processing temperature range cleared up some general features in degradative behaviour of thermostable APH [40]: structure graphitisation, H2 release, thermo-oxidation resistance increase as additives of transition metals and PCA are introduced.

7.5 Thermo-oxidative Degradation of Polyesterimides, Polyamidoimides, Aliphatic-Aromatic Polyamides [7, 21, 40-43] Water is the main product (~0.3 wt.%), extracted from polyesterimide (PEI) based on dianhydride A (bisphenol A diaminodiphenolic ester) and m-phenylene diamine by thermooxidation in the temperature range of 320-340 °C at exposures up to 1 hour. The rest of the products give ~0.1 wt%. The following compounds were detected: CO, CO2, residues and transformation products of initial monomers, for example, bisphenol A. Increase of exposure duration and/or temperature up to 420 °C (initiation of intensive degradation by TGA) leads to deeper transformations of the polymeric structure and, consequently, to formation of greater amounts of products with different compositions. IR-spectroscopy data show that short-term thermo-oxidative effects cause loss of isopropylidene structure and p-substitution of aromatic rings at stability of phthalimide cycles. Gel permeation chromatography (GPC) data indicate that polymer structuring intensified with temperature or O2 content in the system. Temperature rises up to 420 °C cause Mz to increase by more than 30000, and increase of all moments of molecular mass and polydispersion from 2.3 to 3. The changes mentioned manifest themselves as a reduction of light transmittance of solutions and yellowing of PEI, and with other modifications – as a formation of insoluble

198

Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers gel-fraction, whose content increases proportionally to O2 absorption. The following compounds were identified in heavy (oligomeric), volatile (gaseous), solid and liquid products of PEI thermo-oxidation with the help of IR-spectroscopy, NMR, MS, highly efficient liquid chromatography (HELC) and gas chromatography (GC): H2, CO2, CO, CH2O, CH3OH, H2O, phenol and derivatives, bisphenol A, aromatic and ester-aromatic compounds with methyl, ethyl and isopropylidene groups. Judging by mass losses and melt viscosity stability, PCA display the highest thermo-oxidative efficiency in PEI. Judging by TGA data, thermo-oxidative resistance of polyamidoimide (PAIM), based on trimellitic acid anhydrochloranhydride and dianhydride A, is by ~10-20% lower than that of purely aromatic PAIM (based on trimellitic dianhydride and m-phenylene diamine). Similar regularity is observed in the study of thermo-oxidation in melts (higher thermoresistance for rigid-aromatic PAIM structure). Usual sigmoidal kinetics of O2 absorption and CO2 and CO release with fast first and slow second stages is typical of both polymers. Analysis of thermo-oxidative efficiency of numerous additives of various classes (amines, phenols, benzophenols, hydrazines, etc.), indicated the unambiguous advantage of PCA. As PCA is introduced, polymer yellowing at exposure in melt is reduced, mass losses are decelerated and melt viscosity is stabilised. Thermo-oxidation of polyphthalamides (PPA-1 and PPA-2) display the same regularities (kinetics of mass losses, oxygen absorption and release of the main volatile products, composition of volatile and heavy products relative to the polymer structure, oxidation inhibiting by adding PCA and transition metal compounds, etc.), which are described in detail for PAI, PPQ, polybenzoxazole (PBO), PEI, PI, PAIM, polyphenyl sulfide (PSP), PES and LCP. The degradation mechanism will now be discussed in more detail using PPA-1 and PPA-2 as examples (see Figure 7.5 and 7.6).

Figure 7.5 The structure of PPA-1

Figure 7.6 The structure of PPA-2

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Polymer Yearbook Structure of polyphthalamides PPA-1 and PPA-2 represents alternation of aliphatic and aromatic sequences. As thermo-oxidation develops statistically along the macromolecule, amide of terephthalic acid (TPA) formation (attack 1-2) is of the same probability as other fractures of the macrochain (attack 3-4) (Figure 7.7),

Figure 7.7 The sequence of an initial stage degradation - statistical disintegration of a sequence of a macromolecule

TPA amide is formed by thermo-oxidation in melt and at low-temperature solid-phase oxidation. Light yellow crystals of TPA amide and TPA mixture occur and accumulate on the surface of mould samples during accelerated heat ageing at temperatures of 150200 °C. TPA is a typical product of hydrolysis by macrochain ends. From our point of view, TPA amide product is of greater interest. Recall that analogous products (relative to polymer structure) were already observed in investigation of thermo-oxidative transformations of other APH. For example, pyromellite diimide, was identified in thermooxidation of PAI [7, 21] and classical polyimide ‘Capton’, and 2,2′-(1,4-phenylene)-bis(phenylpyrazine), is formed by poly(phenylquinoxaline) ageing [7]. From our point of view, a specific feature of thermo-oxidation of aromatic and aliphaticaromatic heterochain polymers is displayed in TPA amide formed during PPA thermooxidation. Unfortunately, this feature is insufficiently discussed in the literature yet. Three hypotheses were put forward in discussion of PDI formation at PAI thermo-oxidation: 1. Sequential burning of (oxidation) of aliphatic fragments from both sides of the imide cycle. 2. Formation of a molecular complex with oxygen [43]. 3. Macromolecule transition into an electron-excited state [11]. The first hypothesis is nonviable, because neither direct, nor indirect proofs were found for it. Kalugina and co-workers [21] confirmed the possibility of molecular complex

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Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers

Figure 7.8 Structure of pyromellite diimide

Figure 7.9 Structure of 2,2′-(1,4-phenylene)-bis-(phenylpyrazine)

with oxygen existence indirectly – on model compounds, and transition of macromolecules into the electron-excited state as the act of radical-chain process initiation was proved by quantum-chemical calculations of models and APH oligomers. Probably, formation of TPA amide, in products of PPA thermo-oxidation, as well as PDI in PAI and PI, can be explained by existence of two latter hypotheses. Introduction of additives is the common method of studying the mechanism of chemical reactions. Phenolic antioxidants, inhibiting oxidation in reactions with peroxyradicals RO2, in concentration of 10-2-10-3 mol/kg decelerate O2 absorption by PPA-1 and PPA2 at 150-250 °C (solid-phase oxidation). Kinetics of O2 absorption by PPA is characterised by absence of the induction period, e.g., critical concentration of antioxidant cannot be found. Concentration dependence of the antioxidant efficiency, determined from the relation of initial rate constants of O2 absorption by unstabilised and stabilised PPA-2, displays a clear optimum at concentration of 0.008 mol/kg. Although at phenol’s introduction antioxidant effects are not sufficiently high, probably due to high temperature of PPA processing, the fact of decelerating thermo-oxidation by itself (for example, at phenolic antioxidant introduction in concentration of 0.2%, O2 absorption by PPA-1 reduces by 10-20%) confirms once again contribution of the radical-chain process into PPA thermo-oxidative degradation. Some features of PPA thermo-oxidation do not fit in the traditional scheme. The supposition about molecular complexes with oxygen lead to PPA analogies with PAI, PI,

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Polymer Yearbook PPQ, and other APH, thermo-oxidation of which are decelerated by addition of Cu2+ [11] and PCA. For example, addition of anilidophosphoric acid diphenyl ether and CuSO4 was found the most effective in polyimide (PI) and poly(alkene imide) (PAI) [7, 21]. Use of PI and PAI as additives decelerate O2 absorption in PPA-2 at the solid-phase oxidation noticeably more effectively, than phenolic antioxidants. Efficiency of the additives is also noticeable at high temperatures, at which phenols are inefficient. The concentration dependence of Cu2+ adding efficiency passes through an extreme, as in the case of aliphatic PA. Even micro-concentrations of Cu2+ are quite effective for stabilising PPA. It is common knowledge that introduction of Cu2+ salts into PE destabilises the methylene chain at both low (solid-phase oxidation) and high (processing) temperatures. Comparison of Cu2+ additive effect, for example, in PPA, PAI, PSP and PE, points to a significant role of aromatic fragment in the oxidation. Flexible methylene chains, as any hydrocarbonic sequences, are the fragments most vulnerable for thermo-oxidation. Rigidity of the physical structure, the limitedness of molecular motions, in PAI is defined by the pyromellitimide fragment, and in PPA-1 and PPA-2 the terephthalic one. The presence of isophthalic acid (IPA) in PPA-1 also imparts a definite flexibility to the macromolecule (similar to the prviously considered LCP). To put it another way, reducing the molecular mobility of the macrochain, causes aromatic fragments to stimulate the physical mechanisms of methylene branching protection from thermo-oxidation. From positions of chemistry, if physical limits are neglected, the aromatic fragment increases reactivity of border methylene groups, which are more active in reaction with O2. Oxidation restrained in the solid phase develops violently in the polymer melt, touching upon aliphatic parts first and aromatic fragments in lesser degree. Some specific features of PPA-1 and PPA-2 thermo-oxidation are displayed at low temperatures on the background of the typical radical-chain process. Antioxidative effect of phenolic antioxidants is much weaker, than that of copper-containing additives and phosphates. Oxidation causes an ejection of TPA amide from macromolecule and an intensive crosslinking of macrochains. One may suppose participation of aromatic fragments in degradation, therewith, not only by α-bonds activation in the neighbouring flexible chain. Although there is no direct proof yet, the authors suggest that, beside classic initiation, for example, of the type shown in Figure 7.10:

RH + O2 → R• + RO2•, Figure 7.10 The sequence of a stage of initiation of process thermooxidation

202

Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers where RH is the methylene chain, thermo-oxidation is initiated with participation of aromatic phthalamide fragments. This can be the formation of a molecular complex of one or several O2 molecules with π-system of the fragment, or thermal transformation of the fragment into the triplet state with the help of O2 (similar to photo-oxidation). Probability or improbability of these facts will be discussed. No doubt that ‘for these polymers the classical radical-chain scheme of oxidation needs a significant supplement’. The following initiation reactions are possible: 1. Classic reaction:

2. Formation and degradation of molecular complex with O2:

3. Transformation into the electron-excited state:

The succeeding stages fit in with the radical-chain scheme and elementary acts of the chain transmission by end and middle alkyl radicals lead to formation of all detected volatile, low-volatile and polymeric products of degradation. In the applied aspect, the suggested scheme of PPA thermo-oxidative degradation, which to the authors’ point of view is applicable to all previously-mentioned APH, indicates two directions of antioxidative stabilisation – inhibition of the radical chain process and ‘destabilising’ function of the aromatic fragment. Therefore, the applied task is subdivided into two directions: antioxidative stabilisation during processing (temperature range of 300-350 °C, short-term) and stabilisation during exploitation (working temperatures within the range of 150-200 °C). The authors suppose that the account for features of thermo-oxidation gives grounds for optimisation of thermostabilising compounding of all ‘life stages’ of thermoresistant APH by combining antioxidants with compounds of alternating valence metals and phosphorus-containing substances.

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Polymer Yearbook

References 1.

A.B. Blumenfeld, A.L. Vdovina, K.A. Voloshchuk, N.S. Zabel’nikov and G.M. Tseitlin, Proceedings of the 15th Colloquium of Dunarea Countries on the Problems of Natural and Artificial Ageing of Polymers, 1982, Moscow, Russia, p.4142. (In Russian)

2.

A.L. Vdovina, A.B. Blumenfeld, N.S. Zabel’nikov and N.G. Annenkova, Vysokomolekulyarnye Soedineniya, 1984, 26B, 3, 223. (In Russian)

3.

A.L. Vdovina, A.B. Blumenfeld, N.G. Annenkova, A.P. Pleshkova, N.S. Zabel’nicov, O.V. Kachevskii and V.M. Ryaboi in Proceedings of the XXII AllUnion Conference on High-molecular Compounds, 1985, Alma-Ata, Kazakhstan, USSR, p.132. (In Russian)

4.

A.L. Vdovina, V.M. Ryaboi and A.B. Blumenfeld, Vysokomolekulyarnye Soedineniya, 1985, B27, 11, 808. (In Russian)

5.

A.B. Blumenfeld, A.L. Vdovina, A.P. Pleshkova and N.G. Annenkova, Vysokomolekulyarnye Soedineniya, 1986, B28, 7, 500. (In Russian)

6.

A.L. Vdovina, Thermal Transformations and Stabilisation of Polypyromettilimide, Poly(phenylquinoxaline) and Copoly(imidophenylquinoxalines), GS Petrov RIPM, Moscow, Russia, 1988. [Thesis on chemical sciences] (In Russian)

7.

G.M. Tseitlin, K.A. Voloshchuk and A.B. Blumenfeld, Vysokomolekulyarnye Soedineniya, 1989, A31, 2, 295. (In Russian)

8.

A.B. Blumenfeld, A.L. Vdovina and N.G. Annenkova in Polyimides and Other High-temperature Polymers, Eds., M.J.M. Abadie and B. Sillon, Elsevier Publishers, Amsterdam, The Netherlands, 1991, p.183-189.

9.

A.L. Buchachenko, L.L. Yasina, A.L. Vdovina and A.B. Blumenfeld, Izvestiya AN, Seriya Khimica, 1994, 8, 1402. (In Russian)

10. A.B. Blumenfeld, I.I. Levantovskaya and N.G. Annenkova, Itogi Nauki i Tekhniki, 1985, 20, VINITI, Moscow, Russia, p.143-211. (In Russian) 11. N.G. Annenkova, A.B. Blumenfeld, L.A. Vavilova, N.K. Pinaeva, M.E. Savina and A.G. Chernova in International Subject Collection: Polycondensational Processes and Polymers, 1985, Nal’chik, Russia, p.16-24. (In Russian)

204

Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers 12. I.M. Abramova, A.E. Azriel, L.I. Vavilova, V.A. Vatagina, A.G. Zezina, K.Yu. Zyisk, L.G. Kazaryan, N.K. Pinaeva, M.E. Savina, A.G. Sade and A.G. Chernova in Thermoresistant Materials, 1985, Niitekhim, Moscow, Russia, p.162-167. (In Russian) 13. Sh. Tuichiev, A.M. Kuznetsova and A.M. Mukhametdieva, Vysokomolekulyarnye Soedineniya, 1987, A29, 8, 1756. (In Russian) 14. E.V. Kalugina, A.B. Blumenfeld, N.G. Annenkova, D.V. Gvozdev, M.E. Savina and N.K. Pinaeva, Plasticheskie Massy (USSR), 1988, 7, 26. (In Russian) 15. E.V. Kalugina, A.B. Blumenfeld, N.G. Annenkova and B.M. Arshava in Proceedings of the VI All-Union Conference: Polymer Combustion and Creation of Limitedly Combustible Materials, 1988, Suzdal, Russia, p.64. (In Russian) 16. L.G. Kazaryan, A.E. Azriel, V.A. Vasil’ev, N.G. Annenkova, N.K. Pinaeva and A.G. Chernova, Vysokomolekulyarnye Soedineniya, 1988, A30, 3, 644. (In Russian) 17. E.V. Kalugina, A.B. Blumenfeld, N.G. Annenkova, M.E. Savina and B.M. Arshava, Proceedings of the 9th All-Union Conference: Synthesis and Efficiency Research of Chemicals for Polymeric Materials, 1990, Tambovs, Russia, p.49. (In Russian) 18. I.V. Sekacheva, I.N. Solynkin, N.K. Pinaeva, G.N. Koshel’, G.G. Kyukova, O.S. Kozlov and O.M. Smirnova in Collection of Works of the Yaroslav Polytechnical Institute, 1990. (In Russian) 19. E.V. Kalugina, A.B. Blumenfeld, N.G. Annenkova, B.M. Arshava, Yu.I. Kotov, M.E. Savina and A.G. Pleshkova, Plasticheskie Massy (USSR), 1991, 7, 48. (In Russian) 20. E.V. Kalugina, Thermal Transformations and Stabilisation of Some Thermoresistant Heterochain Polymers, 1992, GS Petrov RIPM, Moscow, Russia. [Thesis on Chemical Sciences] (In Russian) 21. E.V. Kalugina, A.B. Blumenfeld, N.G. Annenkova and M.A. Volkov, Plasticheskie Massy (USSR), 1993, 1, 30. (In Russian) 22. A.B. Blumenfeld, E.V. Kalugina, N.G. Annenkova, M.A. Volkov and M.E. Savina, Plasticheskie Massy (USSR), 1993, 1, 24. (In Russian) 23. E.V. Kalugina, A.B. Blumenfeld, N.G. Annenkova, M.A. Volkov, M.E. Savina, S.R. Rafieva, E.I. Markova and N.F. Janibekov, Plasticheskie Massy (USSR), 1993, 3, 30. (In Russian)

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Polymer Yearbook 24. E.V. Kalugina, A.B. Blumenfeld, M.E. Savina and V.M. Novotortsev, Plasticheskie Massy (USSR), 1996, 1, 14. (In Russian) 25. M.E. Savina, A.B. Blyumenfeld, A.G. Chernova, T.F. Vinogradova, E.V. Kalugina, N.G. Annekova and N.F. Miroshin, inventors; Institut Plasticheskikh Mass, IM GS Petrova, assignee; RU 2,028,337, 1995. 26. A.G. Chernova, M.E. Savina, N.K. Pinaeva, N.V. Sekacheva, L.P. Nekrasova, I.N. Solyankin, E.V. Kalugina and S.N. Nurmukhomedov, inventors; Institut Plasticheskikh Mass, IM GS Petrova, assignee; RU 2,069,670, 1996. 27. A.B. Blumenfeld, E.V. Kalugina, L.M. Bolotina and M.E. Savina, Plasticheskie Massy (USSR), 1993, 2, 21. (In Russian) 28. A.B. Blumenfeld, E.V. Kalugina and G.E. Zaikov, Polymer Yearbook, Volume 17, Ed., R.A. Pethrick, Harwood Academic Publishers, Amsterdam, The Netherlands, 2000, p.275-285. 29. L.A. Narkon, Research of Additives, End Groups and Molecular-Weight Characteristics Effect on Polysulfone Thermoresistance, 1984, G.S. Petrov RIPM, Moscow, Russia. [Thesis on Chemical Sciences], (In Russian) 30. I.I. Levantovskaya, A.L. Narkon, O.V. Ershov, V.V. Gur’yanova, L.I. Reiburd, M.P. Radetskaya, L.M. Bolotina, A.B. Blumenfeld, A.V. Pavlov and M.P. Motorina, Vysokomolekulyarnye Soedineniya, 1985, A27, 2, 362. (In Russian) 31. A.V. Pavlov, V.V. Gurjanova, O.V. Ershov, E.V. Kalugina and T.N. Prudscova in Proceedings of the Bratislava International Conference on Polymers, Bratislava, Czchoslovakia, 1990, p.55. 32. V.V. Gur’yanova, O.V. Ershov, G.S. Mednikova, I.A. Sharyigina and E.V. Kalugina, Plasticheskie Massy (USSR), 1990, 6, 82. (In Russian) 33. A.B. Blumenfeld, L.M. Bolotina, A.L. Narkon and E.V. Kalugina, inventors; RU 1,550,913, 1988. 34. A.L. Narkon, E.V. Kalugina, M.A. Volkov and P.A. Astakhov, Plasticheskie Massy (USSR), 1996, 3, 4. 35. E.V. Kalugina, T.N. Novotorzeva, M.B. Andreeva, V.A. Tochin, M.I. Gorilovsky, A.B. Blumenfeld, A.L. Narkon, K.Z. Gumargalieva and G.E. Zaikov in Ageing of Polymers, Polymer Blends and Polymer Composites, Volume 2, Ed., G.E. Zaikov,

206

Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers A.L. Bouchachenko and V.B. Ivanov, Nova Science Publishers, Inc., Hauppage, NY, USA, 2002, p.192-199. 36. E.V. Kulagina, T.N. Novotorzeva, M.B. Andreeva, V.A. Tochin, M.I. Gorilovsky, K.Z. Gumargalieva and G.E. Zaikov in Ageing of Polymers, Polymer Blends and Polymer Composites, Volume 2, Eds., G.E. Zaikov, A.L. Buchachenko and V.B. Ianov, Nova Science Publishers, Inc., Hauppage, NY, USA, 2002, p.175-190. 37. M.Y. Cao and B. Wunderlich, Journal of Polymer Science, Polymer Physics Edition, 1985, 23, 3, 521. 38. Liquid Crystalline Polymers, Ed., N.A. Plate, 1988, Khimia, Moscow, Russia. (In Russian) 39. T.S. Shcherbakova, L.I. Chudina, M.V. Myagkov and A.I. Semenova, Plasticheskie Massy (USSR), 1987, 7, 25. (In Russian) 40. M.B. Andreeva, N.V. Saratovskaya and E.V. Kalugina in Proceedings of the 2nd All-Russian Kargin’s Symposium: Chemistry and Physics of Polymers at Early 2000s, Moscow, Russia, 2000, p.20. (In Russian) 41. M.B. Andreeva, T.N. Novotorzeva and E.V. Kalugina in Proceedings of the 11th Symposium on Modern Chemical Physics, 1999, Tuapse, Russia, p.85. (In Russian) 42. E.V. Kalugina, T.N. Novotorzeva, M.B. Andreeva, A.B. Blumenfeld, Ya.G. Urman and V.V. Gur’yanova, Plasticheskie Massy (USSR), 2001, 1, 20. (In Russian) 43. A.L. Buchachenko, Complexes of Radicals and Molecular Oxygen with Organic Molecules, 1970, Nauka, Moscow, Russia. (In Russian)

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208

8

Fluorine-containing Polymers for Materials with the Complete Internal Light-reflection N.G. Lekishvili, M.B. Lachinov and G.E. Zaikov

8.1 Introduction The fluorine-containing polymers for materials with complete internal light-reflection are reviewed. The general kinetic control features for the synthesis of block polymerisation fluoroalkylmethacrylates (FMA), their copolymerisation with different vinyl monomers, their relative activity and the polymerisation of FMA in presence of nitroxyl radicals are discussed. The basic properties of the more frequently used FMA for materials with complete internal light-reflection, are characterised. The new optical transparent fluorine polymers, also containing per-fluorinated cyclobutane and aromatic fragments are reviewed. Data from the literature and original results are presented. Polymers have recently been used in a number of optical devices. The developments in the chemistry of the optical polymers have taken two directions: 1. The preparation of polymer materials based on carbochain polymerisation polymers: poly-alkyl(alkaryl)methacrylates and fluoromethacrylates, polynorbornene, polyvinylarylenes and their halogenderivatives, etc. 2. The preparation of polymer materials based on heterochain polymer polycarbonates (PC), polyethers, polyethercarbonates (PEC) or joint mixtures of polycondensational and polymerisational polymers [PC with polymethyl methacrylate (PMMA)]. Polycondensational polymers, such as PC, have high level intrinsic strength, high melting index and birefringence, difficult to control optical and mechanical properties, comparatively low water resistance, as well as a number of purity problems and a limited range of the available monomers. Compared to homopolymerisation, the method of copolymerisation, by successful choice of optical compatible monomer pairs, creates enormous difficulties in getting easily moulding thermoplastic polymer materials with the required definition of optical, physical-mechanical and technological characteristics. In spite of some of the shortcomings of industrial carbochain copolymers, such as high birefringence, a relative narrow working thermal interval and spectral range, a large shrinkage and composition heterogeneity, a large assortment of the thermoplastic polymer

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Polymer Yearbook optical materials have been produced. They are used as optical fibres (POF), prisms, lenses, contact disks, carriers for recording of information, the polymeric scintillation materials for registration of different types of ionisation. Among these applications optical fibres are especially important.

8.2 The General Principle of Selecting Polymers for Polymer Optical Fibre Coating For the further development of fibre optics it is necessary to fabricate a new optically transparent polymer (POF) with a better range of complex optical, physical-chemical and mechanical properties. As a rule POF are bi-component. They are composed of a core surrounded by a coating of polymer materials with complete internal lightreflection. These materials will require excellent transparency in the visible and near UV areas of spectrum, refractive index variation, mechanical and rheological properties, be easily mouldable, and show good light-, thermo- and moisture stability, etc. A large number of polymers for core materials are described in the literature [1-3]. POF coating polymers are rather few in number. The following groups of polymers are used for POF coating: I. Organic carbochain polymers and copolymers of poly-4-methylpentene-1 [4]; PMMA or methyl methacrylate (MMA) copolymers with other alkyl-(meth)acrylates (AMA) [1-3, 5]; poly(vinyl acetate); vinyl acetate copolymer with ethylene [4, 6-8] polymers of chlorine-containing olefins [9]. II. Elementorganic polymers and copolymers: copolymers of fluorinated olefins [1021]; poly(perfluoroalkylmethacrylates) and perfluoroalkylmethacrylates copolymers [1-3, 22-34]; poly(organosiloxanes) [25, 35]; fluorine-containing poly(organo siloxanes) [36]; fluorine-containing copolymers with side functional (hydroxy) groups [37, 38], and others [1]. III. Other polymers and copolymers which are more often used for POF core–MMA copolymer with styrene (azeotropic composition, for example, for polystyrene (PS) cover); MMA copolymers with alkylstyrenes [39, 40]. Selection of the coating polymer (Table 8.1) is often dictated by conditions of future application of POF and the core material itself [3]. The first polymer which was used as cover a POF for a PS core was PMMA. Optical fibres from this polymer are widely used. It is easily produced and processed; numerical aperture (NA) = 0.56. It also displays rather low light losses at λ = 670 nm (≤ 110 dB/km) [2]. However, (PMMA-PS) are not optimal due to some significant disadvantages of PS (low light resistance and light

210

Core Cover Cover Core

Cover Cover

1.480 1.480 1.525

1.590 1.586 1.42 1.370– 1.420 1.410

(PMMA)

(PMMA)

(PMMA)

Poly(methyl methacrylate)-D5

Poly(methyl methacrylate)-D8

MMA-S copolymer (azeotropic mixture)

Polystyrene (PS)

Polycarbonate (PC)

Poly(organosiloxane)

Poly(fluoromethacrylate)

TFE-VF copolymer

–

PMMA, PS, azeotropic mixture copolymer

PMMA, PC

–

–

–

Poly-α-styrene, PMMA, P(TFE-VF)

PMMA, PS, MMA-S copolymer, deuterated PMMA

–

Poly(fluoromethylacrylate)

TFE: tetrafluoroethylene; VA: vinyl acetate; VF: vinyl fluoride

Cover

Core

–

–

–

–

–

672

672

≥ 150 110

672

680, 780, 850

20, 25, 50 200– 300

565–546

672

672

655

522

672

568

Wavelength, nm

41–55

200– 300

110

200

63

> 129

85

Losses, dB/km

Poly(methylmethacrylate)


Core Core

PMMA


Poly-(MMA-S-azeotropic mixture), PC

PS

VA-ethylene copolymer

Poly(tetrafluoroethylene (plasma application)

Poly(organosiloxanes)


The second component recommended for PC

Core

Core

Core

(PMMA)

Core

Application (material type)

Core

1.470– 1.490

Refractive index

(PMMA)

Poly(methyl methacrylate) (PMMA)

Polymeric material

Table 8.1 Data illustrating possibility of selecting various polymers for POF components (core-cover) [24] (data for laboratory specimens)

Fluorine-containing polymers for materials with the complete internal light-reflection

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Polymer Yearbook transparency, especially in the range of short wavelengths, rapid ageing and plasticity decrease, etc). Moreover, the (PMMA-PS) couple displays low thermodynamic and rheological compatibility and possesses different temperatures of processing [2]. Due to these disadvantages, as well as in accordance with the limitations of selection of more suitable polymeric material for the core, PMMA was not widely used for the preparation of the POF coating. Researchers have used other organic polymers (poly-4-methylpentene-1, poly(vinyl acetate), etc., [4, 6, 7, 8, 41, 42]) and failed. Expanding application of PMMA and MMA copolymers with AMA as the POF core [39, 40], due to its low refractive index (nD = 1.48-1.49) led to the necessity to create polymeric materials possessing low refractive indices and an excellent set of physical-mechanical and optical properties. Such materials were found in the thermoand water-resistant polysiloxanes and some fluorine-containing carbochain polymers [2440, 43]. However, due to a number of valuable properties (high mechanical strength, resistance to aggressive media, relatively good compatibility with PMMA, MMA copolymers, etc.), fluorine-containing polymers were found the most useful of these polymers. The high strength of the C—F bond (EC-F = 468 kJ/mol) provides for its low polarisability. Despite the fact that fluorine atomic refraction differs insignificantly from hydrogen atomic refraction, molecular volume of monomers, obtained by substitution of hydrogen atoms, increased [1]. Application of the first industrial available fluorinecontaining polymer, polytetrafluoroethylene (PTFE), which has excellent properties of chemical resistance, high thermal resistance, low friction coefficient, excellent dielectric properties, etc., was found to be impossible to use due to its high crystallinity, leading to high attenuation of light, low adhesion to polymeric materials of the core and poor processing characteristics [17]. These disadvantages are not displayed by tetraflouroethylene (TFE) copolymers with other fluorine-containing and organic monomers, such as vinylidene fluoride (VDF), hexafluoropropylene (HFP), ethylene (ET), MMA, and others. These copolymers, as well as their three-component copolymer (VDF/TFE/HFP) [44, 45], preserve good optical properties over the long-term at temperatures above 80 °C and POF based on this copolymer are used as special purpose communication systems [3]. In most cases, obtaining fluorinated alkenes and polymers based on them demands special and often extremely complicated technologies [46]. That is why, these materials remain expensive and are used only when other polymeric materials cannot be substituted for them [2]. Asahi Garasu Co., Japan, has discovered an amorphous highly transparent fluorinecontaining polymer ‘CYTOP’, different from other fluorine-containing polymers [47, 48]. Its optical properties’ reflect a high degree of light transmittance in the visible spectrum, typical of a transparent PMMA polymer. In the UV spectrum, light transmittance of this polymer is also high.

212

Fluorine-containing polymers for materials with the complete internal light-reflection Due to good optical and rheological characteristics, homopolymers of fluorine-containing methacrylates and their copolymers with other methacrylates are more often used in fibre-optic practice [2, 20-24, 26-34]. But selection of a polymer with the best optical and mechanical properties requires establishment of the dependence of the structure and properties of the polymers on the structure and reactivity of initial monomers. To solve this problem the study of the kinetics of block polymerisation and copolymerisation process of fluoroalkyl-(meth)acrylates is desirable.

8.3 Estimation of the Relative Activity of Fluoro-alkylmethacrylates in Block Radical Polymerisation and Copolymerisation with Vinyl Monomers and Structure of Macromolecular Chain of the Copolymers Obtained 8.3.1 Kinetics of Block Radical Polymerisation of Fluoroalkyl(meth)acrylates Despite multiple investigations on the creation of (co)polymers and POF on based on FMA for optical materials with complete internal reflection, no full quantitative description of FMA polymerisation and their copolymerisation with other vinyl monomers is available. This slows down development of research of new optically transparent polymers and copolymers with the required properties, as well as the creation of new technologies for the creation of fibre optical materials [1, 3]. There are data available in the literature on the kinetics of homopolymerisation of FMA [24, 28, 49-53]. One of the most important among these papers was carried out in the early 1960s by Rostovskii and Rubinovich [51]. They have determined some general kinetic equations for the block radical polymerisation of a series of perfluoroalkyl methacrylates. It was found by investigation of the kinetics of the reaction that perfluoroalkyl methacrylates of the CH2=C(CH3)COOCH2(CF2-CF2)mH type [m = 2 (4FMA), 4 (8FMA), 6 (12FMA)], compared with alkyl methacrylates display higher reactivity, which is explained by the authors as being due to the induction effect of fluorine atoms on vinyl group of FMA. Later on, based on quantum-chemical investigations, it was proved [54] that structure of perfluoroalkyl alcohol radical and the amount of fluorine atoms in these radicals do really affect reactivity of the vinyl group of fluoromethacrylic monomer. Quantum-chemical calculations were performed based on semi-empirical MINDO-3 method. Standard Dewar parameters were obtained [55]. There are few data in the literature on spatial structure of perfluoroalkyl methacrylates, or the partial optimisation of the geometry of these molecules [54] (Figure 8.1). As the vinyl group is the main reaction centre of FMA, the attention of investigators has been generally attracted to consideration of parameters of this group with different investigators

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Polymer Yearbook

Figure 8.1 Distribution of charges on atoms of perfluoroalkyl (meth)acrylates and geometry of their molecules

at α-carbon (H, CH3). Table 8.2 shows general quantum-chemical characteristics of the previously mentioned monomers. When compared with the data on the quantum-chemical calculations of CH2=C(H)COOCH2(CF2)4H (4 FA) and MMA, CH2=C(CH3)COOCH2CF3 (3FMA), and 4FMA (with methyl substituents at α-carbon of the vinyl group), a significant difference in the electron structure and parameters of the vinyl group double bond were observed characterising its strength ( PCπ = C , PCfull , WC α -C β is the Weiberg index) and =C consequently the reactivity of the monomers [24]. The authors explain this fact [24] by the vinyl group being significantly affected by the methyl group at the α-carbon, despite the negative induction effects of the fluorine atoms, somewhat weakened by CH2-group. However, a definite influence of the concentration of fluorine atoms is observed [24].

214


Table 8.2 Some quantum-chemical parameters of perfluoroalkyl (meth)acrylates and methyl methacrylate [22, 49] qα

qβ

(Σ Σq)αCH2

PCπ = C

WCα-Cβ

EHOMO

ELUMO

MMA

-0.125

0.062

0.121

0.9455

1.8461

10.1747

0.4079

3FMA

-0.121

0.052

0.113

0.9462

1.8512

10.5657

-1.2796

4FMA

-0.120

0.050

0.101

0.9501

1.8660

-9.5259

-1.5622

4FA

-0.129

0.071

0.125

0.9050

1.8901

-9.2400

-1.3307

Monomer

qα, qβ

the charges on the a and b carbon atoms, respectively

(Σq)nCH2

total charge on CH2-groups of FMA

PCπ = C

p-bond order

WCα-Cβ

Weiberg Index

EHOMO

energy of the highest occupied molecular orbital

ELUMO

energy of the lowest non-occupied molecular orbital

Investigation of the kinetics of various FMA on the polymerisation has demonstrated the dependence of the reaction rate constants on the structure of perfluorinated alcohol radical [54]. Data on the molecular properties and structure of perfluoroalkyl methacrylates (CH2=C(R)COOCH2(CF2)mX, where R = H, X = H, or X = F; m = 2 (4FA), m = 4 (8FA), and m = 6 (12FA) were obtained using determination of dipole moments and Röentgen-phase analysis [55]. Comparison of values of the dipole moments of the fluorine-containing and hydrocarbon ethers of acryl acid (AC), displays a significant difference both in the absolute values of dipole moments and in the character of the change of the dipole moments on the number of carbon atoms. Dipole moments of fluorinated acrylates are significantly higher than appropriate values of their hydrocarbonic analogues (μFA = 2.41-2.91 D, and μAMA = 1.84 D (m = 4)) [56]. It is the authors’ opinion that such an increase of the dipole moment can be associated with a change of acrylate alcohol radical conformation that takes place on substitution of the hydrogen atoms by fluorine assuming formation of the preferred (polar) transconformation of the ester group [56]. Growth of the dipole moment in fluorine acrylate (FA) with the number m of CH2-groups testifies that a deviation from the plane structure and formation of a spiral conformation are observed in these monomers (especially for large m) [53]. Moreover, a decrease of the

215

Polymer Yearbook specific partial volume of perfluoroalkyl methacrylates with growth of m is observed that leads to an increase in their density. Apparently, large dipole moments (3D), as well as the conformation structure of higher FA homologues promotes the occurrence of their associates with the sacrifice of –CH…F– hydrogen bonds, as well as dispersion interactions of fluorinated alkyl radicals. Display of the FA molecule associates is confirmed by determination of the Kirkwood correlation parameter g (g < 1): g = μ 2eff μ 0 , where μeff is the efficient dipole moment, μ0 is the dipole moment of isolated monomer. X-ray study indicates that specificity of FA homologues structure is also displayed in the crystalline state. The reflex in diffractogram observed in the range of 2Θ = 18° (d = 4.9Å) confirms the presence of intermolecular packing of fluorocarbon chains [57]. Hence, conformation properties of fluoroalkylmethacrylates molecules define their specific behaviour in the condensed state. Large dipole moment of n-fluoroalkyl methacrylates molecules, as well as their affinity to associate in the condensed state are apparently, the determining factors in growth of polymerisation rate constants of these polymers comparing with alkyl acrylates analogous by structure [56, 57]. Lachinov and co-workers [52] have performed a more detailed study of the kinetics of block radical polymerisation of perfluoroalkylmethacrylates (FMA) in the solid state. The main method of investigation of the kinetics of FMA polymerisation was isothermic calorimetry [58]. Due to the absence of data on the heat effects of their polymerisation in the reference literature, these values were measured [52]. The values of ΔQ and glass transition point (Tg) of polymers formed are shown in Table 8.3. Obviously heat of polymerisation of monomers of the fluoroacrylate sequence is quite close to heat of polymerisation of non-substituted monomers of the AMA sequence [59], and a significant influence of the length of the fluoroalkyl radical on this parameter is absent [52]. In accordance with the Polyani-Semenov rule, the present result makes it possible to consider that chain propagation constant of FMA with the accuracy of the pre-exponential multiplicand being equal to each other [57]. The investigation has shown that for FMA polymerisation a linear part with a constant polymerisation rate is observed at the beginning of the reaction, followed by autoacceleration.

Table 8.3 Heats of polymerisation of perfluoroalkyl methacrylates, Tg, PFMA ΔQPM, kJ/mol

Tg, °C

ρ, g/cm3

4FMA

57.6 ± 0.3

75

1.4050

8FMA

56.0

35 – 70

1.6336

12FMA

58.6

–

1.6380

Monomer

216

Fluorine-containing polymers for materials with the complete internal light-reflection Therefore, initial polymerisation rates of these monomers (as in the case of AMA [60]) grows with length of fluoroalkyl radical, and degree of the gel effect display decreases. To obtain more precise information on kinetic parameters of FMA polymerisation, the dependencies of the transformation q-time, t degree (Figures 8.2-8.4) and the

Figure 8.2 Conversion versus time in polymerisation of (1) 4FMA, (2) 8FMA, and (3) 12FMA. [Benzoyl peroxide] = 5×10-3 mol/l, 60 °C

Figure 8.3 Conversion versus time in polymerisation of 4FMA. [Benzoyl peroxide]: (1) 5×10-2, (2) 1×10-2, and (3) 5×10-3 mol/l, 60 °C 217

Polymer Yearbook

Figure 8.4 Conversion versus time in polymerisation of 8FMA. [Benzoyl peroxide]: (1) 5×10-2, (2) 1×10-2, and (3) 5×10-3 mol/l, 60 °C.

transformation rate w, and transformation degree q (Figures 8.5-8.6) under initial concentrations of benzoyl peroxide (BPO) in the monomer [52]. As would be expected, initial polymerisation rates grow with the initiator concentration, and the total time of reaching the final transformation degree decreases [60, 61]. The initial polymerisation rates of 4FMA increase according to the 0.5 reaction order with respect to the benzoyl peroxide (BPO) concentration. Based on the experimental data obtained, several parameters for the elementary stages of FMA polymerisation were calculated. Determining the initiation rate of these monomers, one proceeded from the known value of the degradation constant of 1014exp(29,400/RT) = 5.09×10-6 s-1 at 60 °C [62]. From these calculations, values of the ratio k p k1t / 2 were determined for FMA polymerisation (Table 8.4). It is shown in Table 8.4 that the ratio k p k1t / 2 grows gradually at transition from 4FMA to 12FMA with regard to the supposition made about invariability of the initiation rate for these monomers [49]. Therefore, the value of k p k1t / 2 for 4FMA is approximately 1.5-fold greater than the appropriate value for MMA [52]. Comparison of curves of the dependence of the reaction rates for the three FMA mentioned above on the degree of transformation is shown in Figure 8.6. The rates obtained under the same conditions, indicates the general tendency of the change of reaction rates on initial stages of the transformation on the length of the perfluorinated FMA radical is similar to that observed polymerisation for alkyl methacrylates [62, 63]. This analogy in the kinetic behaviour of two sequences of monomers (FMA and AMA) enabled authors

218


Figure 8.5 The rate of polymerisation versus conversion in polymerisation of 8FMA. [Benzoyl peroxide]: (1) 5×10-2, (2) 1×10-2, and (3) 5×10-3 mol/l, 60 °C.

Figure 8.6 The effective rate of polymerisation versus conversion in polymerisation of (1) 4-FMA, (2) 8-FMA, and (3) 12-FMA. [Benzoyl peroxide] = 5×10-3 mol/l, 60 °C.

[49] to perform a series of additional kinetic calculations suggesting, in particular, that kp in the FMA sequence is constant, and to determine kp change for monomers studied. The constant of bimolecular termination at polymerisation of FMA sequence monomers naturally

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Polymer Yearbook

Table 8.4 Kinetic parameters of radical polymerisation of perfluoroalkyl methacrylates, at 60 °C during initial stages of transformation* Wa·10–5

kp/kt, (l/mol·s)0.5

kt·10–6, l/mol·s

ν

4FMA

2.8

0.175 ± 0.015

15.3

5,900

8FMA

3.6

0.25 ± 0.02

7.5

6,700

12FMA

4.6

0.31

4.9

7,500

Monomer

*It is supposed in calculations that initiation efficiency of BP and kp of the chain in the FMA sequence of monomers are constant and equal to f = 0.5 and k = 685 l/mol·s, respectively.

decreases with growth of methacrylate alcohol radical length. The length of kinetic chains in this sequence grows simultaneously, which confirms data on characteristic viscosities of polymers obtained on initial stages [52]. The similarity in the behaviour of the FMA sequence of monomers with that of the AMA sequence was observed that not only on the initial stages of the polymerisation, but also of the ones that followed. The onset of the gel-effect in the FMA sequence is shifted to the higher side of the degree of transformation (Table 8.5) with growth of fluoroalkyl radical length of the monomer, all other factors being the same. It has been shown in the case of 4FMA and 8FMA, that the degree of conversion of the onset of auto acceleration increases with initiator concentration in the monomeric mixture [52]. The latter result can be associated with a decrease of the molecular mass of polymers formed as the initiation rate is changed. The decrease in molar mass results in a higher degree of transformation being required in order to form an engagement network in the reaction mixture that leads to autoacceleration of polymerisation.

Table 8.5 Characteristics of kinetic stage of the gel-effect in polymerisation of monomers of the FMA sequence, at 60 °C [Benzoyl peroxide] = 5 × 10-3 mol/l Monomer

qa

Vmax/V0

(V/[M])max/(V/[M])0

4FMA

0.15 – 0.16

8.7

35

8FMA

0.23 – 0.25

4.0

25

12FMA

0.33 – 0.35

1.5

4

220

Fluorine-containing polymers for materials with the complete internal light-reflection Propagation of alkyl radical in the FMA sequence leads to a shift of the autoacceleration onset to the area of higher conversion, although length of kinetic chains and molecular mass do also increase [52, 60]. This can occur if the density of the engagement network in the FMA sequence decreases, and the distance between engagement crosslink points increases as happens in the sequence of non-substituted polymers [64, 65-72]. Reduction of the gel-effect intensity in the FMA sequence and characteristic viscosities of polyPFMA samples obtained on the complete transformation of monomers, confirms this suggestion [52]. Note that change of molecular mass on initial and border stages of the transformation proceeds antibatically and correlates with change of the constant of bimolecular termination suggested in the FMA sequence on different stages of polymerisation [52]. Note that the reaction rate of radical (co)polymerisation of fluorine-containing (meth)acrylates (with MMA) increases on substitution of CH3 groups and H by fluorine atoms at the αcarbon [49]. Therefore, the reaction is accompanied by excretion of a large amount of heat exceeding the heat effect of the block radical polymerisation of FMA [49, 52].

8.3.2 Relative Activity of Fluorine-containing Methacrylates in Bulk Radical Polymerisation with Vinyl Monomers; Structure and Compositional Inhomogeneity of the Macrochain Copolymers Obtained Influence of the structure on the reactivity of fluorine-containing methacrylates in the bulk radical copolymerisation with vinyl monomers, as well as the dependence of structure of macromolecular chain of copolymers obtained on these factors is not wellstudied [3]. There are data in the literature on the investigation of composite inhomogeneity by composition of macromolecules and the type of comonomeric units distribution in the macromolecular chain of FMA copolymers with MMA [22]. To determine the composition of copolymers by 1H-NMR method, signals of protons in –CH2CF2 and –CHF2 groups were used (δ 8.0-3.0) (Figure 8.7) [65]. To confirm the confidence of mi values determined by 1H-NMR spectroscopy method, they were compared with the composition data determined by analysis of the reaction mixture by the gas liquid chromatography (GLC). Good agreement of the values obtained is indicated (Figure 8.8) [65]. Using data of composition of copolymers and assuming that chain propagation reactions are described by classic kinetic scheme (in the frames of the ‘end unit’ model) by the Tudos-Kelen method [24, 66], copolymerisation constants are calculated (rij and rji). Values of rij and rji are shown in Table 8.6 [24]. Dependence of copolymer composition (mi) on content of monomers (Mi) in the initial mixture for systems MMA-4FMA, MMA-8FMA, 4FMA-S, 8FMA-S [66] corresponds 221

Polymer Yearbook

Figure 8.7 1H-NMR spectrum of copolymer based on MMA-8FMA system

Figure 8.8 Dependence of copolymer structure on composition of the initial mixture of monomers in 1: MMA-FA, 2: 4FMA-4FA, 3: MMA-4FMA systems (o - GLC, • - 1H-NMR method)

to that frequently observed, when both constants rij and rji are smaller than unity [24, 66]. This means that monomers participating in chain propagation reactions are more actively attached to an ‘alien’ radical, than to itself. This is the reason for the increased content of heterodyads, Figure 8.9 [66], in the total fraction of the 8FMA-MMA system, which exceeds 0.5 at MMA concentration in the initial mixture within the range of 30222


Table 8.6 Some parameters of compolymerisation of perfluoroalkyl methacrylates with MMA and styrene (S) in mixture (Treact = 70 °C, [BPO] = 0.001 mole per mole of monomer mixture) No.

Initial mixture of comonomers

r12

r21

r12·r21

1/r21

1/r12

Q of FMA

e of FMA

M1

M2

1.

4FMA

MMA

0.80 ± 0.04

0.85 ± 0.08

0.68

1.18

1.25

0.60

0.98

2.

8FMA

MMA

0.72 ± 0.04

0.53 ± 0.04

0.42

1.69

1.35

0.76

0.039

3.

3FMA

MMA

0.78 ± 0.03

0.74 ± 0.05

0.57

1.35

1.28

0.75

1.14

4.

4FA

MMA

0.23 ± 0.03

1.54 ± 0.06

0.35

0.65

4.34

0.34

1.47

5.

4FMA

S

0.19 ± 0.03

0.27 ± 0.042

0.553 1.261 1.422

0.69

-0.04

6.

3FMA

S

0.61 ± 0.03

0.49 ± 0.070

0.308

2.040

0.77

1.21

7.

8FMA

S

0.35 ± 0.024

0.78 ± 0.020

0.497 1.413 1.382

0.75

0.035

0.77

60 mol% [63]. The composition diagram, Figure 8.8 displays an azeotropic point. With the help of formula: Mi =

1 − rij 2 − rij − rji

(8.1)

obtained on the base of common Maio-Louis equation, in the limit of the ‘end unit’ model, appropriate azeotropic compositions of initial mixtures of comonomers are calculated. For example, for the MMA-4FMA system this ratio is 57.1:42.9 mol%, and for MMA-8FMA it is 40.6:59.4 mol% [24, 66]. The experiment performed confirms the correctness of these data, Figure 8.8. For MMA-4FMA and 4FMA-4FA systems, the copolymer is enriched by units of more active MMA and 4FA components, respectively, almost in the whole range of molar ratios of initial monomers (Figure 8.8, curves 1 and 2). Analysis of dyad distribution in macromolecular chain of copolymers of this system (Figure 8.9) shows increased concentration of homodyads [24, 66].

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Polymer Yearbook

Figure 8.9 Dependence of part of hetero- (1, 2, 3) and homodyads on composition of the initial mixture of monomers in systems: 1: MMA-FA, 2: 4FMA-4FA, 3: MMA-4FMA

For MMA-8FMA and MMA-4FMA systems, dependence of the reaction rate on composition of the monomeric mixture (Figure 8.10, curves 1 and 2) [66] is linear in the whole range of copolymers composition studied, and for 4FMA-4FA and MMA-4FA systems, dependencies (Figure 8.10, curves 3 and 4) possess an inflection point at concentration in the initial mixture of, for example, 4FMA and 4FA of 0.30-0.40 mol% and 0.45-0.50 mol%, respectively, which is typical of the case, when rij < 1 and rji > 1 (or vice versa). Therefore, the copolymerisation rate for these systems is lower (Figure 8.10) than, for example, for MMA-4FMA and MMA-8FMA systems [24, 66]. Experimental data obtained previously correlates well with data of quantum-chemical calculations (Table 8.7) [24, 66].

Table 8.7 Comparison of calculated quantum-chemical and some experimental parameters of niFMA at its copolymerisation with MMA (M1) Monomer

qβ

PCπ = C

PCcompl =C

r12

r21

1/r21

Q1

e1

3FMA

0.052

0.9462 1.8525

0.78

0.74

1.282

0.75

+1.14

4FMA

0.050

0.9051 1.8713

0.80

0.85

1.250

0.60

+0.98

4FA

0.071

0.9695 1.8955

1.54

0.23

0.649

0.34

+1.39

224


Figure 8.10 Dependence of copolymer structure on composition of the initial mixture of monomers in 1: MMA-FA; 2: 4FMA-4FA; 3: MMA-4FMA

For the 4FA-MMA system, the analogous situation also takes place in the case of fluorineoxygen-containing (meth)acrylates (FOAA) copolymerisation (Table 8.8) [52, 73]. Based upon the values of the copolymerisation constants of these systems, formation probabilities of various unit sequences in the macromolecules of the copolymers were calculated using the Wall and Medvedev formulae. Based on these data, as well as the

Table 8.8 Copolymerisation constants and activity factors at copolymerisation of fluorine-oxygen containing methacrylates (M1) with MMA (M2) [73] System

r 12

r21

1/r12

1/r21

Q1

e1

FOAA-1-MMA

0.20 ± 0.03

2.25 ± 0.03

5.00

0.44

0.95

1.08

FOAA-2-MMA

0.05 ± 0.01

2.65 ± 0.01

20.0

0.37

1.24

1.30

FOAA-2-MMA

0.10 ± 0.01

2.46 ± 0.02

10.0

0.40

1.26

2.12

FOAα-FA-MMA

0.15 ± 0.04

0.43 ± 0.03

6. 6

2.32

0.64

2.05

FOAA-1: CH2=CH-C(O)OCH2CF2OCF2CF2OCF3 FOAA-2: CH2=CH-C(O)OCH2CF2(OCF2CF2)2OCF3 FOAMA-2: CH2=C(CH3)C(O)OCH2(OCF2CF2)2OCF3 FOAα-FA: CH2=C(F)C(O)OCH2OCF2CF2OCF3

225

Polymer Yearbook value of average lengths of copolymer macrochains, it was found that in the case of FOAA-1 and FOAA-2 copolymerisation with MMA, Table 8.8, copolymers with the most regular structure can be obtained by keeping the initial monomeric mixture composition strictly to 95:5 mol%. In the case of FOAMA-1 and FOA αFA1 copolymerisation (Table 8.8) with MMA can be obtained at a constant ratio of 70:30 mol% composition of the initial mixture of monomers [73]. To estimate compositional inhomogeneity of synthesised copolymers, integral curves of the distribution by composition estimated by the Laury-Mayer method are calculated based on values of copolymerisation constants obtained, which confirmed that the compositional inhomogeneity decreased on approaching the azeotropic composition of the initial monomeric mixture [52, 65]. Based upon the previously mentioned data it is found that MMA-4FMA copolymers are the most homogeneous as defined by both structure of the macromolecules and type of units distribution in the chains and create compositionally homogeneous polymeric materials with the best optical characteristics [3]. As mentioned previously, special attention has been paid to optical polymeric materials obtained by radical copolymerisation of fluorine-containing methacrylates in mixture with various vinyl monomers [3]. Study of kinetics and mechanism of this reaction over a wide range of degrees of reaction remains one of the main problems of chemistry of polymerisational polymers as a whole, and synthesis of copolymers for optical purposes based on alkyl methacrylates, in particular. On the one hand, there is an increased interest in the studies of the mechanism during the initial stages of the radical copolymerisation [65, 66], and on the other hand, the processes occurring in specific comonomeric pairs, for the point of view of those which display the gel-effect and lead to systems with excellent optical characteristics [1, 3]. It is generally recognised that the main feature of the reaction proceeding in the area of autoacceleration is an alternation of the kinetic constants of some elementary reactions, which are untypical for the initial stages of the reaction. At the same time, it should be noted that questions about the nature and the mechanism of autoacceleration polymerisation still remain under discussion. The kinetics of homopolymerisation for high degrees of conversion have been studied for a broad list of monomers. At the same time, in copolymerisation possess, the self-reaction in the presence of other species has been much lesser studied. For example, a small number of papers [67-69] on this theme have been devoted to the study of an anomalous gel-effect associated with exhaustion of more active monomer long before the limit of the conversions occur. However, to display this effect, several conditions must be fulfilled (great difference in values of r1 and r2, kp1 and kp2, etc.) which can be realised for a small number of monomeric couples. Similar features observed in the high degrees of conversion caused by chemical effects only are specific for copolymerisation processes and are indisputably of definite interest

226

Fluorine-containing polymers for materials with the complete internal light-reflection for researchers for the carbochain polymers of optical purposes, obtained by radical polymerisation. However, more general features, typical of the kinetics of the radical polymerisation, defined by an increase of the role of the diffusion control of elementary reaction stage, bimolecular chain termination, were not studied systematically before in the case of copolymerisation. To solve these problems, the kinetics of the radical copolymerisation of the monomer couple of 1,1,3-trihydrotetrafluoropropyl methacrylate (4FMA) with MMA over the whole range of conversion and compositions of monomeric systems were investigated. Selection of the pairs of comonomers mentioned was caused by the fact that their copolymers are used in the creation of optical polymeric waveguides and other materials for optical purposes [1, 3]. At the same time, the kinetics of their copolymerisation was not studied. Values of the relative activities of these copolymerisation monomers are close and equal to r1 = 0.80 ± 0.04 and r2 = 0.85 ± 0.08 (Table 8.9) [24, 66]. This may simplify significantly the task of studying the kinetics of the process at high degrees of conversion, because no kinetic anomalies will be displayed in this case. On the other hand, it follows from the literature that copolymerisation of non-fluorinated n-alkyl methacrylates with significantly different length of side substituents allows changing of physical properties of polymeric solutions

Table 8.9 Methacrylates of fluorine-containing alcohols (CH2=C(CH3)COOR) for reflecting layers of polymeric waveguides Core

Reflecting layer based on FMA

Optical losses, dB/km

Wavelength, nm

P(MMA-D6)

Homopolymer

30

660

PMMA

Homopolymer

165

650

PMMA copolymer

Copolymer Homopolymer

240

650

CF3(CF2)7(CH2)2O

PMMA

Copolymer

19 0

650

H(C2F4)CH2O

PMMA

Copolymer

65

566

H(C2F4)CH2O

PMMA

Copolymer

122

650

1.427

(CF3)2CHO

Copolymer

Copolymer

–

–

1.40

(CF3)2CHCH2O

Copolymer

Copolymer

110

840

CF3CF2CH2O

Polycarbonate

Copolymer

100

770

H(C2F4)CH2O

Polycarbonate PMMA

Copolymer Copolymer

200 150

770 650

R CF3CH2O CF3CF2CH2O

n 20 D

1.417

227

Polymer Yearbook over a wide range and changes the diffusion characteristics of the macromolecules. In their turn, these changes must affect the kinetic behaviour of the copolymerisational systems in the area of the polymerisation auto-acceleration, where the kinetics of the process are defined almost completely by diffusion controlled chain termination. It should be noted that in the latter case, both the mean composition of macromolecules accumulated and the immediate composition of macroradicals formed in the stage of auto-acceleration should be of importance. It would appear reasonable that the former, will define properties of interlocks network in the case of its formation in the reaction mixture, and the latter mobility of the polymeric chains terminating at a given moment. To measure copolymerisation kinetics, the method of isothermal calorimetry was also used [58, 69] that enables continuous recording of the absorption or heat elimination during endo- and exothermal processes, respectively. To recalculate experimental curves of heat elimination into kinetic curves of copolymerisation, it was necessary first to determine heat of chain crossed propagation. This value was calculated from total copolymerisation heat effects for monomeric systems of various compositions [4FMA (1)-MMA (2), ΔH11=57.6 ± 0.3; ΔH22=56.8 ± 0.2; /2=52.7 ± 0.2]. Dependence of the total heat effect of copolymerisation on composition of the initial monomeric mixture for copolymerisational system studied is shown in Figure 8.11 [69]. Note that values were obtained experimentally using no additional suggestions about the mechanism of the elementary stage of chain propagation. Clearly total heat effect of 4FMA-MMA copolymerisation depends upon the ratio of monomers in the reaction

Figure 8.11 Dependence of the total heat effect of (co)polymerisation on the composition of the initial monomeric mixture

228

Fluorine-containing polymers for materials with the complete internal light-reflection mixture and is shaped as a curve possessing a minimum at equimolar composition of the monomeric mixture. Heat of crossed propagation was calculated to be 52.7 ± 0.12 kJ/mol, i.e., it is significantly different from heats of homopolymerisation of both comonomers, Figure 8.11. A significantly lower value of the heat of cross-chain propagation in the system of 4FMA-MMA (compared with the systems of MMA-butylmethacrylate and of MMAlaurylmethacrylate, studied earlier [70, 71]), is apparently, associated with H substitution by F and, consequently, obtaining a less stable structure of a heterounit in the copolymer chain. It is also necessary to note that the shape of the curve showing the dependence of on the monomer mixture composition allows one to assume that, according to the rule of Polyani-Semionov, even the dependence of the effective constant of the chain propagation will deviate from the additive scheme due to possible effect of pre-end chain segment in the system 4FMA-MMA [68]. Integral and differential kinetic curves for homo- and copolymerisation of 4FMA and MMA were calculated for different ratios of monomers in the initial monomeric mixtureat initiation of benzoyl, lauryl and azo-bis-(isobutyronitrile) peroxides with the help of known values of heat effects of MMA and 4FMA homopolymerisation and the value of heat of crossed propagation obtained from experimental dependencies of heat elimination rates on the reaction time. Typical kinetic curves in the ‘transformation degree-time’, Figures 8.12 and 8.13 [69] and ‘reaction rate-transformation degree’ Figures 8.14 and 8.15 [69] coordinates are shown for some compositions of monomer mixtures used for reaction in the presence of PB and AIBN. Analogous kinetic curves are also typical of 4FMA reaction with MMA initiated by thermal degradation of lauryl peroxide (LP). As seen from Figures 8.12 and 8.13, a linear growth of the transformation degree with reaction time is observed on integral kinetic curves at the beginning of the reaction, after which polymerisation is autoaccelerated. Tangent of the initial part and shape of the curve on the stage of polymerisation autoacceleration depend upon initial composition of the monomeric mixture. Dependence of the initial rate of 4FMA-MMA copolymerisation on composition of the monomeric mixture [72] indicates growth of the polymerisation rate at transition from MMA to 4FMA. Therefore, a tendency to saturation in the systems at approaching 4FMA is observed. To analyse reasons of change of copolymerisation rate, the rate equation is used, which is true for the case of homopolymerisation: v = k p [ M](Vini / k t )

1

2

(8.2)

where kp and kt are the effective constants of chain propagation and termination, respectively; vini is the initiation rate; [M] = [M1] + [M2] is the total concentration of comonomers in the reaction mixture.

229

Polymer Yearbook

Figure 8.12 Dependence of transformation degree on (co)polymerisation time for monomeric systems: 1: MMA; 2: 4FMA-MMA (50:50); 3: 4FMA ([BP] = 5×10-3 mol/l)

Figure 8.13 Dependence of transformation degree on (co)polymerisation time for monomeric systems: 1: MMA; 2: 4FMA-MMA (50:50); 3: 4FMA ([Azobis(isobutyronitrile); AIBN] = 5×10-3 mol/l)

230


Figure 8.14 Dependence of (co)polymerisation rate of transformation degree for monomeric systems: 1: MMA; 2: 4FMA-MMA (50:50); 3: 4FMA ([BPO] = 5×10 -3 mol/l)

Figure 8.15 Dependence of (co)polymerisation rate of transformation degree for monomeric systems: 1: MMA; 2: 4FMA-MMA (50:50); 3: 4FMA ([AIBN] = 5×10-3 mol/l)

231

Polymer Yearbook It was shown preliminarily that a change of the initiation rate of polymerisation of the monomeric systems of different composition cannot lead to the change of polymerisation rates observed in the experiment. It is common knowledge that copolymerisation initiation rates are determined by the additive scheme from homopolymerisation initiation rates of appropriate monomers. The experiment has shown that at transition from MMA to 4FMA the rate of initiation decreases a little. Neglecting the possible reduction of the initiation rate at this transition and assuming it is constant for monomeric systems of various compositions, the change of the effective ratio k p k1t / 2 was calculated from the equation for the polymerisation rate shown. Results of the calculation of k p k1t / 2 ratio dependence on composition of the monomeric mixture for three initiators used in the work have shown that the value of k p k1t / 2 grows regularly with fluorine methacrylate content in the monomeric mixture, and all points fall on to the general straight line independently of the nature of the initiator. The latter confirms the truth of the assumption made about the absence of a noticeable contribution of the initiation rate change into the initial polymerisation rate for monomeric systems of various compositions [69, 70]. The question about reasons of change of the ratio of effective chain propagation and termination constants with change of the monomeric mixture composition on the initial stage of 4FMA-MMA remains unanswered and requires future investigation. However, based on the data obtained previously on homopolymerisation kinetics of different fluoroalkylmethacryl monomers it is possible to assume that the k p k1t / 2 ratio change along variations of the composition of the monomer mixture at copolymerisation is connected, first of all, to the decrease of the constant of the bimolecular termination of the that, itself, is caused by the decrease of the segmental mobility of the propagating chains when the ratio of fluorine-substituted monomer increases. Analysing polymerisation kinetics of the monomeric couple studied (4FMA-MMA) in the range of transformation degrees after the initial stage, it is of interest to study the process in the conversion interval, where the process rate increases, i.e., there, where the reaction transits to the autoacceleration regime, and the gel-effect occurs. In this connection, quantitative analysis of kinetic regularities of 4FMA-MMA copolymarisation in the area of the gel-effect onset was performed [70, 72]. The value of degree of transformation corresponded to the inflection point on lg(V/[M]) dependencies on q after the initial stationary part was used for quantitative characterisation of the onset of copolymerisation autoacceleration [61, 73]. Such method of determination of (qa) is quite often used [70, 74]. Nevertheless, the physical sense of this value demands some explanation. Since the very onset of polymerisation, the elementary stage of bimolecular termination remains unchanged up to some conversion, qa. As this

232

Fluorine-containing polymers for materials with the complete internal light-reflection transformation degree is reached, conditions are formed in the reaction mixture abruptly decreasing the diffusion rate of macroradicals and the rate of their termination. It was shown [70] that these conditions correspond to a formation of the so-called topological interlocking network in the reaction mixture. Therefore, from the kinetic point of view, the character of diffusional control of termination is changed. If the segmental diffusion of propagating chains was the limiting stage of termination at the beginning of the reaction, then after reaching the qa level translation of macroradicals as the whole becomes the limiting stage. In its turn, this stipulates for occurring a dependence of the termination constant on chain length, i.e., leads to a distortion of the Flory principle, basic in kinetics of polymerisation processes. Equality of lengths of kinetic chains and the distance between interlocks of the networks forming in the reaction mixture can be considered as the kinetic condition of the onset of autoacceleration, or VR(qa) = ie/q2 [63]. On the other hand, as the polymer solution concentration increases, the distance between interlocking contracts according to the relation ie = ie0/q2 (where ie is the distance between interlocks in the polymer melt). Termination of a propagating chain at polymerisation of methacrylic monomers proceeds mostly by the mechanism of disproportionation that enables one, finally, to give the approximate equality VR ≅ Pn as: qPn0.5 = i0e0.5

(8.3)

The experiment confirmed the feasibility of using this equation to study the conditions of the gel-effect onset at polymerisation of some monomers and above all for MMA polymerisation [59, 69]. At the same time, the exponent of this equation at Pn appeared smaller than 0.5 for polymerisation of other monomers. For example, in the AMA sequence this index regularly decreases from 0.5 down to 0 as the size of the monomer alkyl radical increases from MMA up to cetyl methacrylate. In the latter case, qa does not depend at all on the polymerisation degree of forming molecules. At polymerisation of such monomers, the diffusional control does not change the type, transition to autoacceleration is rather unclear, and the gel-effect itself is rather weakly expressed. The reason is the growth of diffusional limitations of segmental mobility of propagating chains on contraction of the free volume of a polymerisational system as the degree of monomer transformation into polymer increases (phenomenon of a pseudo gel-effect). It was also shown [52] that at radical homopolymerisation of monomers from the fluoroalkyl methacrylic sequence in mixture conversion of the autoacceleration onset increases, and intensity of the gel-effect display decreases as the length of fluoroalkyl radical of the monomer increases.

233

Polymer Yearbook As two monomers, 4FMA and MMA, are copolymerised that leads to formation of polymers with a different density of interlocking network, a dependence of autoacceleration onset, firstly, on composition of the initial monomeric mixture can be expected and, secondly, on molecular masses of reaction products formed. The dependence of the autoacceleration onset on composition of the initial monomeric mixture was studied in the presence of various initiators. Autoacceleration is observed at different ratios of monomers in the mixture [69, 75]. However, in the range of the same concentration of initiators in the system, autoacceleration of the reaction is displayed at higher conversions of 4FMA and is significantly lesser intensive than in the case of MMA polymerisation. Therefore, the onset of copolymerisation autoacceleration falls between appropriate values of homopolymerisation. Clearly the experiment has shown that conversion of the onset of autoacceleration at 4FMA-MMA copolymerisation depends on composition of the initial monomeric mixture and grows linearly with the part of fluorine-substituted comonomer [69]. It is typical that on initial stages of transformation, molecular mass of PMMA and P4FMA homopolymers grow slightly in the same direction. That is why, the change of conversion, qa, observed at copolymerisation can be associated just with reduction of the interlocks network density at the transition from PMMA to poly-FMA [69]. The decrease of autoacceleration and the maximal reaction rates observed on the geleffect stage with growth of the molar part of 4FMA in the monomeric mixture confirms the supposition made about a change of interlocks network density at transition from MMA to 4FMA [69, 72]. Note that nature of the initiator applied does not cause an effect either on heat effects values, or on the type of kinetic curves changing at transition from 4FMA to MMA. Note also that characteristic viscosities of copolymers obtained at the end of the reaction at copolymerisation of monomeric systems of various compositions increase with the molar part of MMA in the initial monomeric mixture [70]. Molecular masses of copolymers obtained must increase in the same direction. This result also fully corresponds to a change of the copolymerisation gel-effect intensity as the initial composition of the monomeric couple studied changes [69, 70].

8.3.3 Radical Polymerisation of Fluorine-containing Methacrylates in the Presence of Nitroxyl Radicals Radical polymerisation of fluoroalkyl methacrylates CH2=C(CH3)COOCH2-(CF2-CF2)mR, where R = H (I) or CH3 (II), m = 1, 2, 3, in the presence of stable iminoxyl radicals was studied [76]. Study of the induction stage indicates that secondary inhibition observed is performed by the catalytic mechanism without using the secondary inhibitor effects

234

Fluorine-containing polymers for materials with the complete internal light-reflection and possesses a stoichiometric inhibition coefficient much greater than two. One of the most demonstrative arguments for the benefit of catalytic inhibition mechanism is high (from 6.5 for m = 2 up to 8.2 for m = 3) total stoichiometric effective inhibition coefficient (μ), values of which are calculated by this equation [77]:

)(

(

(

1

))

μ = 2Wn / kdegr [ X]0 1 − exp −kdegr / t − (2W /[ X]0 ) γ 2 (t)dt

∫

(8.4)

0

where t is the experiment duration; kdegr is the initiator degradation constant; [X]0 is the initial inhibitor concentration; Wn is the initiation rate; γ is the deceleration coefficient (relationship between initial polymerisation rates of inhibited and uninhibited processes). Investigation of radical polymerisation kinetics of fluoroalkylmethacrylates under the previously described conditions [in the presecence of 2,2,6,6-tetramethylpiperidine-1oxyl (TMPO)] indicates that the process does really proceed with secondary inhibition [77, 78]. A kinetic equation is deduced for describing polymerisation proceeding after the induction period for the case of catalytic secondary inhibition, which is of this form:

(

ln( W /[ M]) = ln k* / k p + ln ( Wn )0 /[ X]0 − kdegr / t *

)

(8.5)

where kdegr and kp are the constants of initiator degradation and chain propagation, respectively; k* is the effective constant of secondary inhibition; [X]0 is the initial concentration of inhibitor; Wn is the initiation rate. Relations k*/kp and k*/kt0.5 were determined from the expressions (γ1exp(–kdegrτ) – γ) – [X]/[I]0.5 and ln(W[M]) – t, the values of the former being changed from 1.8 ± 0.2 (n(CF2) = 2) to 1.5 ± 0.3 [n(CF2-CF2) = 3] (I) for k*/kp and from 0.26 ± 0.02 [n(CF2-CF2) = 1] to 0.38 ± 0.02 [n(CF2-CF2) = 3] for k*/kt0.5 [77] (k0 are constants of square R• + R• termination); k* is the effective constant of catalytic inhibition: k* = 1/(1/kx + 1/ky), where kx and ky are the rate constants of expense and formation of the catalyst [76]. Influence of the monomer type and structure of nitroxyl radicals on the value of secondary inhibition was also studied [77]. It was established that: a) For the series of fluoroalkyl methacrylates selected, the induction period precedes polymerisation. b) The rate of polymerisation after the induction period end (W/[M]) in the presence of TMPO radicals is always lower than without inhibitor. The regime of complete inhibition (γ < 0.3) is reached at polymerisation of the previously-mentioned methacrylates with the end –CF2H group in the presence of TMPO. Moreover, the gel-effect is completely degenerated for the same monomers. Note that as the end

235

Polymer Yearbook group of the fluorine-containing alcohol radical – CF2H is substituted by a CF3group, the effect of secondary inhibition on their copolymerisation in the presence of free stable radicals is decreased abruptly which is apparently associated with a decrease of associative nature of fluoroalkyl methacrylates with the end CF3-group of alcohol radical [56, 78, 79]. Free-radical polymerisation inhibitors possess some advantages before usual molecular ones – the constant of monomolecular chain termination is very high for them (about 104 – 105 m3/kmol·s or l/mol·s) [80]. In this case, probability of regeneration is almost equal to zero. That is why, they are used for preventing spontaneous polymerisation during the monomer (or polymerising composites) storage between initiator injection into composite and its application, as well as for regulating the polymerisation rate and molecular mass of the polymer formed [80]. Note that inhibitors of spontaneous polymerisation must as soon as possible exhaust their effect during the induction period, for polymerisation to proceed somewhat in the absence of an inhibitor. Several of these inhibitors can also preserve monomers from oxidation in air [80]. Based on the results of kinetic study the more successful pairs (couples) of FMA-MMA were selected and the optimal technological regimes of their polymers were obtained [3, 63].

8.4 Some Properties of Fluorine-containing Polyalkyl(meth)acrylates and α-fluoroacrylates High value of C-F bond energy in molecules of perfluorinated methacrylic monomers stimulates increased thermal stability and bad wettability of polymers and copolymers on their base. The substitution of all the hydrogen atoms in polymer C-H groups leads to increasing of the value of the dipole moment (μ) and to change of the basic absorption frequency by 8 μm. Simultaneously with decreasing of refractive index of polymers via substitution hydrogen atoms by fluorine atoms the reflection and scattering losses are decreased [81]. Structure, length of hydrocarbon chain, location [26] and amount of fluorine atoms in fluoroalkyl radical significantly affect properties of appropriate methacrylic polymer (see Table 8.9). Increasing the content of fluorine atoms in the polymer, increases the chemoresistance, thermo- and heat resistance and water absorption decreases. It should be noted that the fluorine atom in the ω-position in fluoroalkyl radical leads to a decrease of the surface tension, which is also the the reason for poor adhesion of the fluorinecontaining polymer to the core and water absorption. In the α-position, the heat resistance and other properties of polymers obtained on this basis are presented in Table 8.10 [25].

236

91 90 91 86 91 91 90

Poly(1,1,3-trihydroperfluoropropyl-α-fluoroacrylate)

Poly(1,1,5-trihydroperfluoroamyl-α-fluoroacrylate)

Poly(1,1-hydroperfluoroethyl-α-fluoroacrylate)

Poly(pentafluorophenylα-fluoro-acrylate)

Poly(1,1,3-trihydroperfluoropropyl methacrylate)

Poly(1,1-dihydroperfluoroethyl methacrylate)

Poly(perfluorohexyl methacrylate)

Poly(methyl methacrylate)

2.

3.

4.

5.

6.

7.

8.

9. 90

91

Poly(methyl-α-fluoroacrylate)

1.

K, %

Polymer

No.

1.491

1.346

1.416

1.400

1.467

1.385

1.379

1.398

1.459

20 nD

113

62

76

50

174

123

77

95

140

Tmix, °C

77

Undetermined

48

–

56

63

18

54

96

σb, MPa

33.3

Undetermined

2.0

–

3.1

12.5

24

66

4.6

ε, %

180

Undetermined

180

–

Undetermined

220

Undetermined

230

240

Tg, °C

Table 8.10 Properties of some polymers based on MMA and fluorinated ethers (meth)acrylic acid


237

Polymer Yearbook Most of these polymers possess rather low Tg, and some of them exist in the high elastic state at room temperature already. Comparing with polyalkyl(meth)acrylates, temperatures of their transitions to the high elastic state are shifted to higher temperatures. Mass losses at heating of fluorine containing polymers reduce with growth of length of side perfluoroalkyl radical [3]. As the carbonic chain of the alkyl group propagates, Tg of the polymer decreases. For fluorinated polymers, Tg is 30 °C higher than for non-fluorinated analogues. Poly-α-fluoroacrylates were studied and compared with the appropriate characteristics of their organic analogues [82]. Using experimental data [82], it was shown that polymethyl- and polyperfluoroalkyl-α-fluoroalkylates possess a series of advantages over methacrylate polymers, in particular, low values of the refractive index, higher softening points and thermooxidative stability and resistance to atmospheric ageing, Table 8.10. However, as perfluoroalkylmethacrylates homo-polymers are used, their comparatively low temperatures of thermal deformation should be taken into account [83]. As the temperature was increased above 220 °C (at POF moulding from the melt), adhesion of the cover material to the core deteriorates; on the stage of moulding and future treatment of light transmitting fibre, cracks occur on the cover-core interface that causes a negative effect on stability of light transmittance and its reliability, which is the reason of occurrence of definite difficulties in their application for the above-mentioned aims [2]. Some of these disadvantages can be eliminated by two pathways: 1. Copolymerisation of known fluoroalkyl acrylates and methacrylates with various vinyl and (meth)acrylic monomers; 2. Synthesis of new fluoroalkyl (meth)acrylates with a ‘nontraditional’ structure, Table 8.11 and their copolymerisation with known vinyl and (meth)acrylic monomers. Perfluoroalkyl methacrylates copolymers with MMA [25], butyl acrylate [1], triallylcyanurate [83], methacrylic acid [22, 83], etc., are described, which are synthesised by the method of block radical copolymerisation. Their optical and operating properties were studied compared with properties of nonfluorinated polymethacrylates [83]. Refractive indices (nD) of synthesised fluoromethacrylic copolymers (FMC) are much lower than nD values of organic analogues and fall within the range of 1.3605-1.4290. It is found that the most of FMC exceed PMMA and MMA copolymers with AMA by light transmittance (possess better light transmittance comparing with MMA and AMA copolymers) in UV and visible spectra and are characterised by higher stability of mechanical and optical indices, including under conditions of atmospheric ageing. The list of fluorine-containing carbochain polymers [24, 49, 73, 84, 85] can be broadened by synthesising new fluoroalkyl methacrylates with a nontraditional structure of alcohol

238


Table 8.11 General characteristics of fluorine-oxygen containing monomers Structure and name of monomer

Tboil, °C/kPa

d 420 , kg/m3

n 20 D

CH2=CH-C(O)O-OCH2CF2OCF2CF2OCF 1,1-dihydro-3,6-dioxaperfluoroheptyl acrylate (FOAA-1)

31/2.5

1.378

1.3062

CH2=CH-C(O)O-OCH2CF2(OCF2CF2)2OCF3 1,1-dihydro-3,6-dioxaperfluorodecyl acrylate (FOAA-2)

50/2.5

1.463

1.2907

CH2=C(CH3)-C(O)O-OCH2CF2OCF2CF2OCF3 1,1-dihydro-3,6-dioxaperfluoroheptyl methacrylate (FOAMA-1)

51/2.3

1.422

1.3206

CH2=CF-C(O)O-OCH2CF2(OCF2CF2)OCF3 1,1-dihydro-3,6,9-trioxaperfluorodecyl methacylate (FOAMA-2)

80/2.5

1.470

1.3017

CH2=CF-C(O)O-OCH2CF2OCF2CF2OCF3 1,1-dihydro-3,6-dioxaperfluoroheptyl-αfluoroacrylate (FOAaFA-1)

49/2.1

1.526

1.3155

CH2=CF-C(O)O-OCH2C2(OCF2CF2)2OCF3 1,1-dihydro-3,8,9-trioxaperfluorodecyl-αfluoroacrylate (FOAaFA-2)

69/2.1

1.582

1.2970

radical, in particular, containing atoms of oxygen between CF2-groups, Table 8.11. Copolymers of these (meth)acrylates with MMA are obtained; their properties are shown in Tables 8.11, 8.12 and 8.13. It is found that presence of oxygen atoms in alcohol radical leads to improving of flexibility and oleophobic properties, increase of adhesion of copolymers on their base to core materials [73, 84, 85]. Moreover, it is found that synthesised polymers compared with MMA are more thermostable than PMMA, and can stand higher temperatures than organic methacrylates during both processing and exploitation, Table 8.14 [73, 85]. They are capable of preserving good optical characteristics at relatively increased temperature [85]. The study of kinetics of thermodestruction in the temperature range of 427-517 °C indicated that as the part of fluorine-oxygen-containing copolymers in the initial monomeric mixture increases, the rate of thermodestruction decreases significantly (Table 8.11), and is lower than for MMA homopolymer [85]. It must also be noted that as the content of fluorine-oxygencontaining monomeric units in the composition of copolymeric chain increases, Tg decreases, and the fluidity point rises [73].

239

Polymer Yearbook

Table 8.12 Molecular-mass characteristics of FOAMA-1 copolymer with MMA α

lgS

lg[η]*

lgMSn

1.

1.22

0.19

5.72

526,500

2.

1.17

0.08

5.57

375,200

3.

1.09

-0.02

5.87

4.

1.07

-0.07

5.28

193,700

5.

0.97

-0.13

5.17

149,800

No.

K·10–4

5.64

0.5

MSn

238,200

* For [η]=5.64·10 ·M (by the Mark-Kuhn-Houwink equation), the segmentation coefficient S0 = 5.56·10–10·M0.5. –4

0.5

Table 8.13 Dependence of properties of fluorine-containing (meth)acrylate copolymers on their composition Copolymer composition M1, mol%

Refractive index,

Softening point, °C

Density ρ, kg/m3

M2, mol%

n 20 D

26.0

74.0

1.416

10 0

1,283

26.0

64.0

1.395

91

1,347

49.0

51.0

1.382

92

1,391

339.0

41.0

1.361

74

1,457

28.0

72.0

1.395

109

1,271

37.3

62.7

1.378

97

1,335

80.6

49.4

1.357

86

1,408

57.2

42.8

1.348

77

1,462

FOAMA-1-MMA

FOAαFA-1-MMA

Interesting results were obtained by Iwata and co-workers [50] by synthesising fluorine copolymers with zero birefringence using MMA as the monomer with negative birefringence and 2,2,2-trifluoroethyl methacrylate (3FMA) as the monomer with positive birefringence. These monomers with radical random copolymerisation display almost the same activity – the values of copolymerisation constants rij and rji do not differ significantly from each other and are close to unit, Table 8.15. 240


Table 8.14 Thermal degradation parameters of MMA and FOAA copolymers under dynamic mode* Temperature, °C

Content, mol% Comonomer

Maximal rate of thermodegradation

Activation energy, kJ/mol

MMA

Comonomers

Onset of Degradation

Mass loss by 10%

86.0

14.0

230

320

330

20.5

75.0

25.0

240

332

347

20.5

42.0

58.0

250

350

380

20.5

FOAA-2

77.3

22.7

220

324

334

28.4

FOAM-1

41.3

58.7

240

367

375

39.0

FOAA-4

74.9

25.1

230

350

360

58.4

FOAαF-1

42.0

58.0

250

364

371

68.1

FOAαF-2

79.3

20.7

250

359

370

98.6

PMMA

100

0

288

300

342

–

FOAA-1

*Heating rate is 10 °C/min.

Table 8.15 Value of copolymerisation constants r12 and r21 for MMA and 3FMA and activity factors in reaction of their block radical copolymerisation Qi

ei

Copolymerisation constant

MMA (Mi)

0.74

0.40

r12 = 0.83

3FMA (Mj)

1.13

0.98

r21 = 0.85

Comonomers

It is shown that as the MMA:3FMA ratio (mol%) is 45:55, copolymers obtained possess no birefringence, and light losses in appropriate materials do not exceed 65.9 dB/km [50]. The study of physical-mechanical properties is attracting a lot of attention from researchers of PFMA [24, 31, 53, 73, 82, 86-91]. Interesting results are described in [8], where the dynamic mechanical Young’s modulus of a series of poly-fluoroalkyl(meth)acrylates were characterised. The data for poly-3FMA, however, was limited to temperature-dependent storage modules at one frequency, and no secondary transitions were observed. Also, the dielectric properties of poly-FMA and poly-α-FMA were investigated in [87], but the α 241

Polymer Yearbook and β relaxation were not separated and the dielectric strength analysis was limited to γ transition region [86, 87]. The mesomorphic character of poly-FMA were investigated (Xray analysis and colorimetric method) [89]. The dielectric permittivity was also determined [91]. Dielectric analysis was used [86] to characterise the response of dipoles to an electric field as a function of temperature. Mechanical properties were determined via dynamic mechanical analysis and stress relaxation measurements. Relaxation behaviour was interpreted in terms of intermolecular and intramolecular mechanisms. Discounting anomalous effects encountered in poly-FMA and poly-α-FMA due to the overlap of α and β transitions, the secondary transition behaviour indicated that fluorinated polymers have lower secondary transition temperatures and lowered activation energies for these transitions than for the respective non-fluorinated polymers. These secondary relaxations are intramolecular in nature and steric effects, due to fluorination, are not as pronounced as those noted in the glass transition regions [86]. The results of comparing of optical, physical-chemical and mechanical properties of fluorinated and non-fluorinated methacrylates is given in Table 8.16.

Table 8.16 Comparison of optical, physico-chemical and mechanical properties PMMA, PTFE and PFA Characteristic

PTFE

PFA

PMMA

Note (conditions of measurement)

Refractive index, nD

1.35

1.35

1.49

Abbe refractometer

Nontransparent

Semitransparent

93

Visible spectrum

327

310

250 – 160

2.14–2.20

2.12–2.17

1.19–1.20

0.01

0.01

0.3

140–330

280–320

680–730

200–400

280–300

3–5

Flow limit, kGs/cm

110–160

140–150

650

Elasticity modulus, kGs/cm2

4,000

5,800

3·104

Light transparency, % Glass transition temperature, °C Density, g/cm3 Wetting angle by water, degree Strength at break, kGs/cm2 Elongation, % 2

242

Water, 60 °C, 1 week


8.5 The New Fluorine Containing Copolymers - Prospective Materials for Covers of Optical Fibres In Sections 8.1-8.3 the optical transparent carbochain polymers for materials with the complete internal light-reflection based on fluorine-containing vinyl and (meth)acryl monomers were discussed. These are described in literature as the new type of principal amorphous heterochain fluorine polymers containing the stable perfluorinated cycloalkane and aromatic fragments in the main chain of macromolecules [92]. The authors reported studies on the characterisation of various random polyfluorocyclobutene (PFCB) copolymers of new type of monomers F 2C=CF–O–Ar–O–FC=CF2 (Ar, see Figure 8.16). These monomers were prepared from their corresponding phenolic precursors and have been described previously in paper [93]. Perfluorinated polycyclobutane copolymers were obtained by Smith and co-authors [92], using the method of thermal step-growth cyclopolymerisation at temperatures of 150200 °C, under an inert atmosphere, according to the scheme shown in Figure 8.16.

F

F

F

F

F

F

F

F Δ

+ F

O

Ar O

F

F

Ar ′ O

O

F

F

F

F

F

F

F

F

F

F

F

F

O

O

O

O

Ar

x

F

Ar ′

y

z

Random PFCB Copolymer CH3

?

For Ar or Ar =

CF3 CF3

F O

F

1

2

3

165 °C

130 °C

F Homopolymer Tg =

>350 °C

Figure 8.16 The reaction scheme of cycloalkanes. The polymers were characterised by 19 F NMR and MALDI-TOF MS [91]. They have variable indices of refraction (from 1.45-1.52) and Tg from 310-350 °C

243

Polymer Yearbook The polymers were characterised by 19F NMR and matrix assisted laser desorption/ ionisation-time of flight MS (MALDI-TOF MS) [92]. They have variable indices of refraction (from 1.45-1.52), Tg from 265-350 °C, and long-term thermal stability at 623 K. The dependence of refractive index on wavelength were also measured and the constants of copolymerisation reaction were determined [92]. End-group analysis has been a reliable asset in PFCB chemistry and in particular for copolymerisation studies [92]. The synthesised polymers show great potential for low loss photonic application. They are recommended for use in optical telecommunication devices [92]. They could also be successfully used as a thermo-stabile and heat-resistence cover materials for POF, capable to work in extreme conditions.

References 1

L.P. Asatiani, N.G. Lekishvili, G.M. Rubinstein and W.S. Chagulov, Functional Classification of Optically Prepared Polymeric Materials, Tbilisi University Publishers, Tbilisi, Georgia, 1990, [In Russian].

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V.M. Levin and A.C. Chegolya, Proceedings of the 4th International Symposium on Man-Made Fibers, Kalinin, Russia, 1986, 76.

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N.G. Lekishvili, G.M. Rubinstain and L.P. Asatiani, Polymer Waveguides: Obtained, Possibilities, Perspectives, Tbilisi University Publishers, Tbilisi, Georgia, 1994, 131.

4.

A. Tanaka, H. Sawada and W. Noboru, Fujitsu, Science and Technology (Japan), 1987, 23, 3, 166.

5.

Specialty Fiber Optic Systems for Mobile Platforms and Plastic Optical Fibers, Eds., L. Figueroa, M. Kitazawa, N.E. Lewis, R.E. Steele and D. Varshneya, Proceedings of the SPIE, Volume 1799, Bellingham, WA, USA, 1993.

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T. Kaino, M. Fujiki and S. Nara, Japan Applied Physics, 1981, 52, 12, 7061.

7.

I. Sasaki, K. Nishida, M. Morimoto and T. Yamamoto, inventors; Mitsubishi Rayon Company Ltd., assignee; US 4693553, 1987.

8.

S. Yamamoto and H. Kobayashi, inventors; The Furukawa Electric Co., Ltd., assignee; US4744632, 1988.

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Fluorine-containing polymers for materials with the complete internal light-reflection 9.

D.R. Zuccaro, inventor; Board of Regents, University of Texas System, assignee; US4576348, 1986.

10. T. Kaino, K. Jinguiji, S. Nara, K. Ishhvari, A. Ohmori, N. Tomihashi and S. Yuhara, inventors; Nippon Telegraph and Telephone Public Corporation and Dalkin Kogyo Co., Ltd., assignee; EP 0101048A2, 1984. 11. Y. Ueba and S. Miyake, inventors; Japan Sumitomo Electric Industries, Ltd., assignee; US4681400, 1987. 12. N. Isikava and E. Kobaiasi, Fluorine: Chemistry and Applications, Mir Publishers, Moscow, Russia, 1982, [In Russian]. 13. M. Kazuhiko and K. Akira inventors; Central Glass Company Limited, assignee; GB2171706, 1988. 14. H. Fitz, inventor; Hoechst AG, assignee, DE3617005, 1987. 15. J. Dumoulin, inventor; Solvay & Cie, assignee; US4524194, 1985. 16. A.A. Khan, inventor; EI DuPont de Nemours and Company, assignee; US4524197, 1985. 17. R.D. Youssefyeh, J.W. Skiles, J.T. Suh and H. Jones, inventors; USV Pharmaceutical Corporation, assignee; US4686295, 1987. 18. Y. Koike, T. Ishigure, and E. Nihei, Journal of the Lightwave Technology, 1995, 13, 7, 1475. 19. K. Toshio, T. Isao, Y. Takashi and N. Yukitoshi, inventors; Central Glass Company Limited (Japan), assignee; GB 2161954A, 1986. 20. Y. Ueba and S. Miyake, inventors; Sumitomo Electric Industries, Ltd., Japan, assignee; US 4 505 543, 1985. 21. Y. Ueba and S. Miyake, inventors; Sumitomo Electric Industries, Ltd., Japan, assignee; US 4 681400, 1987. 22. L. Machova, H. Kalinova and L. Dvozanek, Collection of Works on Polymers, High School, Prague, Czechoslovakia, 1986, p.33-45. 23. W.C. Chen, I.H. Chen, S.Y. Yang, J.J. Chen, Y.H. Chang, B.C. Ho and T.W. Tseng in Photonic and Optoelectronic Polymers, Eds., S.A. Jenekhe and K.J. Wynne, ACS Symposium Series No. 672, Washington, DC, USA, 1997, Chapter 6, p.71-77.

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Polymer Yearbook 24. N. Lekishvili, L. Asatiani T. Guliashvili and L.M. Khananashvili, International Journal of Polymeric Materials, 1995, 27, 3-4, 163. 25. B.B. Troitskii and L.C. Troitskaya, Plasticheskie Massy, 1987, 4, 54. 26. Fluorine Compounds: Modern Technology and Applications, Ed., N. Ishikawa, Mir Publishers, Moscow, Russia, 1984, [in Russian, translated from Japanese). 27. H.A. Deckers, T. Dittmer, R.W. Fuss and R. Stern in Proceedings of Fluoropolymer Conference, Manchester, UK, 1992, Paper No.12. 28. T. Kaino in Polymers for Lightwave and Integrated Optics, Ed., L.A. Hornak, Marcel Dekker, New York, NY, USA, 1992. 29. T. Yamamoto, K. Nishida and A. Tateishi, inventors; Mitsubishi Rayon Co., Ltd., assignee; US4593974, 1986. 30. J. Gaynor, G. Schueneman, P. Schuman and J.P. Harmon, Journal of Applied Polymer Science, 1993, 50, 1645. 31. S. Koizumi, K. Tadano, Y. Tanaka, T. Shumidzu, S. Kutsumizu and S. Yano, Macromolecules, 1992, 25, 6563. 32. A. Ohmori, N. Tomihashi and T. Kitahara, inventors; Daikin Kogyo Co., Ltd., assignee; US4557562, 1985. 33. P.P. Resnik and W.H. Buck in Modern Fluoropolymers: High Performance Polymers for Diverse Applications, Ed., J. Scheirs, Wiley, New York, NY, USA, 1997, p.397. 34. T. Koishi, I. Tanaka, T. Yasumura and Y. Nishikawa, inventors; Central Glass Company, Limited, assignee; US 4687295, 1987. 35. S. Oikava, M. Fujiki and Y. Katayama, Electronics Letters, 1979, 15, 25, 829. 36. O. Poleta, Chemishe Techni, 1988, 40, 11, 459. 37. N. Lekishvili, L. Asatiani, T. Guliashvli, M. Kezherashvili and N. Grdzelidze, Proceedings of the Academy of Sciences of Georgia, Chemistry Series, 1993, 19, 1-2, 193, [in Georgian]. 38. N. Lekishvili, T. Guliashvli, L. Asatiani, N. Andguladze and G. Lekishvili, International Journal of Polymeric Materials, 1998, 39, 237.

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Fluorine-containing polymers for materials with the complete internal light-reflection 39. L.A. Korotneva, The Polymerisation of Plastics, NIITEKhim, Moscow, Russia, 1984, [in Russian]. 40. V.S. Chagulov, Quantum Electronics, 1982, 9, 2431, [in Russian]. 41. L-R. Allemand, J. Calvet, J-C. Cavan and J-C. Thevenin, inventors; Commissariat a l’Energie Atomique, assignee; US4552431, 1985. 42. Y. Otsuka, Oputoronikyusu, Optronics (Japan), 1986, 5, 2, 67. 43. C. Emslie, Journal of Materials Science, 1988, 23, 7, 2281. 44. L.P. Asatiani, N.G. Lekishvili, G.M. Rubinstein and W.S. Chagulov, Functional Classification of Optically Prepared Polymeric Materials, Tbilisi University Publishers, Georgia, 1990, [in Russian]. 45. Y. Tatsukami, Y. Kato and S. Wake, inventors; Sumitomo Chemical Company, Ltd.; assignee; EP 0 097 325 A2, 1984. 46. V.A. Braginskii, Plasticheskie Massy, 2001, 8, 36, [in Russian]. 47. M. Nakamura, Kobunsi, 1989, 38, 364. 48. M. Nakamura and G. Kozima, Purastikkucu Edzi, 1988, 34, 236. 49. L.E. Boguslavskaya, I.U. Panteleeva, T.V. Morozova, A.V. Kartashev and N.N. Chuvatkin, Uspekhi Khimii, 1990, 59, 9, 1555, [in Russian] 50. S. Iwata, H. Tsukanara, E. Nihei and Y. Koike, Japan Journal of Applied Physics, 1995, 35, 3896. 51. E.N. Rostovskii and L.D. Rubinovich, Vysokomolekuliarnie Soedinenia, 1963, 4, 141, [in Russian]. 52. M.B. Lachinov, N.P. Chkheidze, T.T. Guliashvili, N.G. Lekishvili, Polymer Science, (Russia), 40A, 2, 88. 53. L.D. Budovskaia, Synthesis and Polymerization of the Vinyl and Methacryl Esters with the w-H-Perfluorinealkyl Groups, Leningrad Institute of Macromolecular compounds, Academy of Sciences of the USSR, 1968, [In Russian]. [PhD thesis] 54. N.G. Lekishvili, T.T. Guliashvili, D.G. Khuroshviliand, L.P. Asatiani and M.G. Kezherashvili, Bulletin of the Academy of Sciences of Georgia, 1994, 148, 234, [In Russian].

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Polymer Yearbook 55. R.C. Binghem, M.J.S. Dewar and D.H. Lo, Journal of the American Chemical Society, 1975, 97, 1285. 56. T.P. Stepanova and L.L. Burstein, Zhurnal Fisicheskoi Khimii (USSR), 1984, 58, 8, 1949, [in Russian]. 57. C.W. Bunn and E.O. Howell, Nature, 1954, 174, 4429, 549. 58. S.I. Kuchanov and M.I. Gelfer, Vysokomolekuliarnie Soedinenia, 1991, 33A, 12, 2667, [in Russian]. 59. E.I. Cherep, M.B. Lachinov, V.P. Zubov and B.A. Kabanov, Vysokomolekulyarnye Soedineniya, 1986, 28B, 165, [in Russian]. 60. E.A. Sidorovich, Vysokomolekulyarnye Soedineniya, 1995, 37A, 12, 2020. 61

N.T. McManus and A. Penlidis, Journal of Polymer Science: Polymer Chemistry Edition, 1995, 34, 2, 237.

62. A.V. Tobolsky and B. Baysal, Journal of Polymer Science, 1953, 11, 471. 63. V.A. Ivanov, V.A. Kaminskii, E.B. Brun, B.A. Korolev, M.B. Lachinov, Vysokomolekuliarnie Soedinenia, 1991, 33A, 1, 1442, [in Russian]. 64. G.I. Litvinenko and V.A. Kaminski, Progress in Reaction Kinetics, 1994, 19, 139. 65. S.S. Ivanchev, Radical Polymerisatsion, Khimia, Leningrad, Russia, 1985, p.279. 66. N.G. Lekishvili, B.B. Zaitseva, S.B. Tkachuk, N.S. Sanadze, V.S. Chagulov and L.P. Asatiani, Bulletin of the Academy of Sciences of Georgia, 1990, 139, 3, 513. 67. M.B. Lachinov, R.A. Simonian, T.G. Georgieva, V.P. Zubov and V.A. Kabanov, Journal of Polymer Science: Polymer Chemistry Edition, 1979, 17A, 2, 613. 68. M.B. Lachinov, N.G. Lekishvili, N.P. Chkheidze, L.P. Asatiani and T.T. Guliashvili, Russian Polymer News, 1999, 4, 1 27. 69. M.B. Lachinov, N.G. Lekishvili, N.P. Chkheidze, L.P. Asatiani and T.T. Guliashvili, Proceedings of the USSR Academy of Sciences, Chemistry Series, 1999, 25, 1-2, 125, [in Russian]. 70. D.V. Trachenko, M.B. Lachinov, Vysokomolekulyarnye Soedineniya, 1996, 38A, 7, 1093, [in Russian].

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Fluorine-containing polymers for materials with the complete internal light-reflection 71. D.V. Trachenko, M.B. Lachinov, Vysokomolekulyarnye Soedineniya, 1997, 39A, 1, 109, [in Russian]. 72. H.C. Bogdasarian, Teoria Radicalnoi Polimerisatii, Nauka Publishers, Moscow, 1966, [in Russian]. 73. S.S. Sharakhmedov, Synthesis and Properties of the Copolymers of Ffluorinealkylacrylates with Methylmethacrylates, Tashkent Institute of Chemistry and Physics of Uzbekistan Academy of Sciences, 1994, [in Russian]. [PhD Thesis] 74. R. Radicevich, L. Korugich, D. Stoikovich and S. Jovanovich, Journal of the Serbian Chemical Society, 1995, 60, 5, 347. 75. S.I. Kuchanov, M.I. Gelfer, Vysokomolekulyarnye Soedineniya, 1991, 33, 4, 286, [in Russian]. 76. A.A. Ilin and B.R. Smirnov, Vysokomolekulyarnye Soedineniya, 1992, 34A, 1, 53, [in Russian]. 77. B.R. Smirnov and A.A. Ilin, Vysokomolekulyarnye Soedineniya, 1993, 35A, 6, 591, [in Russian] 78. A.A. Ilin, B.R. Smirnov, I.V. Golikov and M.M. Mogilevich, Vysokomolekulyarnye Soedineniya, 1993, 35A, 6, 597, [in Russian]. 79. M.D. Goldfain and G.P. Gladishev, Uspekhi Khimii, 1988, 58, 11, 1888, [in Russian]. 80. Entsiklopedia Polymerov, Ed., V.A. Kargin, Sovetskaia Entsiklopedia, Mocow, Russia, 1974, [in Russian]. 81. Fluorine Compounds: Modern Technology and Applications, Ed., N. Ishikawa, Mir Publishers, Moscow, Russia, 1984, p.26, [in Russian, translated from Japanese]. 82. L.E. Boguslavskaia, A.V. Samarina, B.N. Lebedeva, I.U. Panteleeva, T.V. Morosova, N.N. Chuvatkin, A.V. Kartashev and A.P. Sineokov, Plasticheskie Massy, 1988, 12, 15, [in Russian]. 83. E.L. Karagina, V.N. Serova and E.V. Kuznetsov, Proceedings of the 5th all USSR Meeting On Optical Polymer Materials, Leningrad, Russia, 1991, p.27, [in Russian].

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Polymer Yearbook 84. F.M. Mukhametshin, A.A. Iulchibaev and S.S. Sharakhmedov, Plasticheskie Massy, 1990, 9, 31, [in Russian]. 85. A.A. Iulchibaev and A. Filaleev, Collected Works of The Gorki State Institute of the Applied Chemistry, Gorky State University of Applied Chemistry (GIPKH), Russia, 1988, p.52. 86. P.R.H. Bertolucci and J.P. Harmon in Photonic and Optoelectronic Polymers, Eds., S.A. Jenekhe and K.J. Wynne, ACS Symposium Series, No. 672, Washington, DC, USA, 1997, Chapter 7, p.79. 87. K. Ishvari, A. Ohmori and S. Koizumi, Nippon Kogaku Zasshi, 1985, 10, 1924. 88. T. Shimizu, Y. Tanaka, S. Kutsumizu and S. Yano, Macromolecules, 1993, 26, 6694. 89. L.D. Budovskaia, V.N. Ivanova, I.N. Oskar, S.V. Lukasov, Y.G. Baklagina, A.V. Sidorovich and D.M. Nasledov, Vysokomolekulyarnye Soedineniya, 1990, 32A, 561. 90. C.P. Jariwala and L.J. Mathias, Macromolecules, 1993, 26, 5129. 91. M.W. Victor, M. Saffariannour and J.R. Reynolds, Journal of Macromolecular Science, 1994, A31, 6, 721. 92. D.H. Smith, A.B. Hoeglund, H.V. Shah, C. Langhoff, J. Ballato, S.F. Macha and P.A. Limbach, Polymer Preprints, 2000, 41, 2, 1163. 93. D.W. Smith, Jr., H.W. Boone, R.Traiphol, H. Shah and D. Perahia, Macromolecules, 2000, 33, 4, 1126.

250

9

Description of PMMA Molecular Orientation due to Clustering: Theoretical Model V.Z. Aloev and G.V. Kozlov

9.1 Introduction This chapter discusses the independent determination of parameters for a cluster entanglement network enabling the accurate description of the experimental data on the molecular orientation in polymethyl methacrylate. This confirms the validity of the earlier proposed structural model for the polymer amorphous state [1, 2]. Due to the significance of materials produced from oriented polymers, the properties of such polymers have always been studied with great attention. Semicrystalline polymers are more advantageous for applications than amorphous ones [3]. Indeed, the former orients much more easily than the latter, resulting in a higher draw ratio and, therefore, in better properties. This follows from the difference between supermolecular structures of the polymer classes [4]. Still, the properties of oriented amorphous polymers have not been investigated. It is possible to obtain the relationship between the properties and the degree of orientation and, by using the structure of amorphous polymers, which are free from crystallinity and therefore easier to deal with. Two deformation schemes are commonly used to account for molecular orientation. These are the so-called ‘affine’ and ‘pseudoaffine’ schemes whose description, along with their applicability to real polymers, it given in a series papers [5, 6]. However, it turns out that the behaviour of the real polymers (amorphous as well as the semicrystalline ones) differs essentially from these schemes, entailing numerous modifications [5, 6]. The main principle of all these modified and unmodified deformation schemes is the presence of a molecular entanglement network [7, 8].

9.2 Model Considerations Several approaches to the description of molecular entanglements in polymers are available at present. A brief outline will be given here. The best known is the version of the binary hook [9, 10] with some network features. At temperatures (T) exceeding the temperature of glass transition (Tg) for the polymer, the network density Vbh is usually determined in the framework of the rubber-like elasticity, while for T < Tg, Vbh is assumed to be a constant. The existence of such entanglement network is proven both theoretically and

251

Polymer Yearbook experimentally [10-13]. Another approach deals with a cluster network of macromolecular entanglements, whose junctions compose a set of collinear, densely packed segments of various macromolecules (analogue of crystallite with stretched out chains). There are three distinctions of the entanglement cluster network, in comparison with the network of binary hooking, which are important in the following: 1) The junctions of the cluster network have definite sizes (the length of the cluster segment is assumed to be equal to that of the polymer statistical segment [1]. 2) The density of cluster network junctions Vcl is a function of temperature, which decreases as temperature increases. This network decay, is complete at T = Tg. The increasing of Vcl (the density of the entanglement of the cluster network) caused by decreasing of temperature, is slowed down drastically for T ≤ Tg = – 223 °C. 3) The density of Vcl exceeds that of the macromolecular binary hooking network by, approximately, an order of magnitude. It is worth mentioning that the influence of the regions of local order, i.e., clusters, on the orientation behaviour of amorphous polymers has been discussed previously [14, 15]. Finally, a version of a ‘temporal’ molecular network, which has the high density of Vtemp and which is caused by the electrostatic interaction of the chain units, was proposed [7]. A number of features of the behaviour of the oriented polymers, that fits weakly to the version of macromolecular entanglement network, has been revealed during detailed revision of some results of [5-9, 14, 15]. Thereby, the direct application of the two deformation schemes mentioned previously is prohibited. These features are: 1) Molecular orientation depends on the draw ratio λ, which is qualitatively different at temperatures above and below Tg. 2) The value of Vtemp is practically constant at temperatures less than ~ 52 °C. 3) Variation of the shrinkage force at temperatures above Tg shows the presence of the permanent ‘residual’ network. 4) The only mechanism, implying the variation of entanglement density as the temperature and strain varies, is assumed to be enough to describe the molecular orientation. 5) The orientation in poly(ethyleneterephthalate) is believed [5] to result from formation of microcrystallites, whose dimensions are equal or less than the wavelength in Brillouin light scattering. 6) The values of n (number of statistical segments between the entanglement junctions) are small enough to enable high values of network density.

252

Description of PMMA Molecular Orientation due to Clustering: Theoretical Model

9.3 Results and Discussion All the previously mentioned inconsistencies have resulted in a series of modified deformation schemes. One of them can be described by [7]: Δn = CV0α(λ2 − λ1 ) exp(−kλ)

(9.1)

where Δn is the path difference in birefringence measurements, characterising the degree of molecular orientation; V0 is molecular network density; α is the difference between parallel and perpendicular polarisiabilities relative to statistical segment axis; λ is draw ratio; k determines the rate of breakdown of the network. The constant C is defined as [8]: C=

2π ⎡ (n 2 + 2)2 ⎤ ⎢ ⎥ 45 ⎢⎣ n ⎥⎦

(9.2)

where n is the mean refraction index. Botto and co-workers [6], Equation (9.1) describe the experimental data at T < Tg well, but the agreement becomes poor at T > Tg. They put forward the following modification of Equation (9.1):

(

)(

Δn = αC Vp + Vtemp exp( −k(λ − 1)) λ2 − λ−1

)

(9.3)

that implies the existence of two molecular entanglement networks namely ‘permanent’ ones with Vp and Vtemp densities, respectively. In spite of the successful application of Equation (9.3) to the description of experimental data of poly(methyl methacrylate) (PMMA) both for T < Tg and T > Tg [6], two comments must be made. First, the values of Vp, Vtemp and k have been obtained by experimental data regression analysis and the lack of independent methods of Vp and Vtemp estimations does drastically reduce the value of the Equation (9.3). Second, the values of Vtemp an order of magnitude exceed that of Vbh. As we know, the variant with network of electrostatic origin [7] was not used elsewhere, although the absence of the influence of such a dense macromolecular network upon other properties of polymers is unlikely to be correct. The cluster model of the structure of polymer amorphous state [1] is the general model, describing mechanical [16-18], thermophysical [19, 20] and other [2] properties of polymers. The value of Vcl can be estimated independently from the mechanical testing of unoriented polymers [1, 2, 21]. So the aim of this chapter is to demonstrate using PMMA, that this model can describe the molecular orientation.

253

Polymer Yearbook

Figure 9.1 Dependence of birefringence |Δn| on the macroscopic draw ratio λ at T = 135 °C for PMMA. 1: experimental data [6]; 2: calculation by Equation (9.3); 3: calculation by Equation (9.7). In the insert: dependence of density of entanglement cluster network Vcl on the temperature T for PMMA.

One can determine the density of entanglement cluster network Vcl from the value of Poisson’s ratio μ by means of the following approximation [21]: μ = 0.5 − 4.87 × 10 −13 ( Vcl )

12

(9.4)

μ as a function of temperature has been tabulated from the data in [22]. The insert in Figure 9.1 contains Vcl versus temperature for PMMA, as described previously. The cluster model [1] doesn’t prohibit simultaneous existence of the molecular binary hooking network in the polymer. Its density Vbh can be determined from the relationship [23]: Vbh =

ρN A M bh

(9.5)

where ρ is the density of polymer (ρ = 1.20 g/cm3 for PMMA), NA is the Avogadro number, and Mbh is molecular mass of the chain fragment between the entanglement

254

Description of PMMA Molecular Orientation due to Clustering: Theoretical Model junctions. Mbh values of PMMA from different references [10, 23, 25, 26] differ drastically and vary from ~ 6.2 [23] to 15.5 mg/mole [26]. We have selected for our present estimations the latter one, and from Equation (9.5) we have obtained the value Vbh ≅ 0.47 x 1026 m-3. The molecular network density equals (Vcl + Vbh) at T < Tg and Vbh at T ≥ Tg. It is evident from points 1 to 6 in Section 9.2, that there are discrepancies in the molecular orientation behaviour. Macromolecular network densities obtained by regression of experimental results from [6, 8], have been compared with those, obtained by independent methods [21]. Both have been listed in Table 9.1.

Table 9.1 The structural parameters of PMMA Reference [6]

T, °C

Reference [4]

This chapter

V bh

K

Vp

Vtemp

k

Vcl

Vbh+Vcl

k

30

15.1

1.42

-

-

-

9.23

9.7

2.0

90

8.4

1.22

0.38

4.70

0.89

3.83

4.3

2.0

100

6.4

1.18

-

-

-

1.33

1.8

1.3

115

2.4

0.58

-

-

-

-

0.47

-

135

-

-

0.31

0.31

0.61

-

0.47

-

Table 9.1 shows that V0 (Vtemp) from [6, 8] differ by almost a factor of two. At the same time Vp values from [6] and Vtemp as well as Vbh and Vcl are in good agreement. In essence, the present study and the paper [6] have thereby utilised the same model of two networks, but in the former one a precise physical identification and independent determination of these network densities have been given. A comparison of both calculated from Equation (9.3) and experimental |Δn| values as a function of λ for PMMA is shown in Figure 9.1. The calculations were conducted at Vp = Vbh, Vtemp = Vcl = 0 and k = 0, since the experimental data were obtained at 135 °C, i.e., at T > Tg (Tg ≈ 105 °C for PMMA [24]). This figure reveals sufficiently good mutual agreement of both data. A fractal conception of rubber-like elasticity has been put forward by Balankin [27]. The stress F depends on it from the modulus of elasticity stress E as: F=

(

E 2 λ − λ−2.5 4.5

)

(9.6)

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Polymer Yearbook Since F and E are proportional to Δn and the network density, respectively [8], the following formula can be used to estimate |Δn| at T ≥ Tg:

(

Δn = CVα λ2 − λ−2.5

)

(9.7)

This formula has been shown to coincide with the experiment at λ < 3 (Figure 9.1) even better than Equation (9.3). At λ ≥ 3, both equations give somewhat overestimated results, indicating that using the rate k ≠ 0 at high strains is necessary due to possible breakdown of binary hooking junctions especially for chains with low molecular mass [28]. In order to facilitate comparison of data Figure 9.2 depicts both experimental values of |Δn| versus λ [8] and those calculated from Equation (9.3) for the samples stretched at 30, 90 and 100 °C. The calculation was conducted at Vp = Vbh, Vtemp = Vcl and k = 2.0,

Figure 9.2 Dependence of birefringence |Δn| on the macroscopic draw ratio λ at T = 30 °C (1, 4), 90 °C (2, 5) and 100 °C (3, 6, 7) for PMMA. 1, 2, 3: experimental data [6]; 4, 5, 6: calculation by equation (9.3) by using K = 2.0; 7: calculation by equation (9.3) by using K = 1.3 for T = 100 °C.

256

Description of PMMA Molecular Orientation due to Clustering: Theoretical Model since PMMA orientation was accomplished at T < T g. There is again a good correspondence between theory and experiment, whereas some lowering of calculated |Δn| values relative to experimental ones, as temperature of stretching increases, can be easily eliminated by decreasing k. It was shown for the |Δn| versus λ curve at T = 100 °C by adopting K = 1.3.

9.4 Conclusions The results of the present investigation have shown that independently determined parameters of cluster entanglement network enable rather accurate description of the experimental data on molecular PMMA orientation. The cluster model of structure is postulated in [1, 2] and this is the one that is used in this chapter.

References 1.

V.N. Belousov, G.V. Kozlov, A.K. Mikitaev and Yu.S. Lipatov, Doklady Akademii Nauk SSSR, 1990, 313, 3, 630.

2.

D.S. Sanditov, G.V. Kozlov, V.N. Belousov, Yu.S. Lipatov, Ukrainian Polymer Journal, 1991, 1, 3-4, 241.

3.

Ultra-High Modulus Polymers, Ed., A. Ciferri and I.M. Ward, Applied Science Publishers, London, UK, 1984.

4.

G.V. Kozlov, D.S. Sanditov and V.D. Serdyuk, Vysokomolekulyarnye Soedineniya, Seriya B, 1993, 35, 2, 2067.

5.

D.Y. Brown, Polymer Communications, 1985, 26, 2, 42.

6.

P.A. Botto, R.A. Duckett and I.M. Ward, Polymer, 1987, 28, 2, 257.

7.

S. Raha and P.B. Bowden, Polymer, 1972, 13, 4, 174.

8.

N. Kahar, R.A. Duckett and I.M. Ward, Polymer, 1978, 19, 2, 136.

9.

M.F. Milagin and N.I. Shichkin, Vysokomolekulyarnye Soedineniya, Seriya A, 1988, 30, 11, 2249.

10. S. Wu, Journal of Polymer Science: Part B - Polymer Physics, 1989, 27, 4, 723. 11. A. Charlesby and E.M. Jaroszkiewicz, European Polymer Journal, 1985, 21, 1, 55.

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Polymer Yearbook 12. D. Richter, B. Farago, L.Y. Fetters, J.S. Huang, B. Ewen and C. Lartigue, Physical Review Letters, 1990, 64, 12, 1389. 13. B. Qian, Z. Wu, P. Hu, J. Qin, C. Wu and J. Zhao, Journal of Applied Polymer Science, 1993, 47, 9, 1881. 14. M.F. Milagin and N.I. Shishkin, Vysokomolekulyarnye Soedineniya, Seriya A, 1972, 14, 2, 357. 15. N.V. Lomonosova, Vysokomolekulyarnye Soedineniya, Seriya A, 1978, 20, 10, 2270. 16. V.N. Shogenov, V.N. Belousov, V.V. Potapov, G.V. Kozlov and E.V. Prut, Vysokomdekulyarnye Soedineniya, Seriya A, 1991, 33, 1, 155. 17. V.N. Belousov, G.V. Kozlov, N.I. Mashukov and Yu.S. Lipatov, Doklady Russian Akademii Nauk, 1993, 328, 6, 706. 18. V.A. Beloshenko and G.V. Kozlov, Mekhanika Kompozitnykh Materialov, 1994, 30, 4, 451. 19. V.A. Beloshenko, G.V. Kozlov and V.N. Varyukhin, Fisika i Tekhnika Vysokykh Davlenyi, 1994, 4, 2, 70. 20. V.A. Beloshenko, G.V. Kozlov and Yu.S. Lipatov, Fizika Tverdogo Tela, 1994, 36, 10, 2903. 21. D.S. Sanditov and G.V. Kozlov, Fisika i Khimia Stekla, 1993, 19, 4, 593. 22. S-D. Hong, S.Y. Chung, R.F. Fedors and J. Moacanin, Journal of Polymer Science: Polymer Physics Edition, 1983, 21, 9, 1647. 23. Y-H. Lin, Macromolecules, 1987, 20, 12, 3080. 24. E.L. Kalinchev and M.B. Sakovtseva, Properties and Processing of Thermoplastics, Khimia, Leningrad, Russia, 1983, [In Russian]. 25. D.C. Prevorsek and B.T. De Bona, Journal of Macromolecular Science – Physics, 1981, B19, 4, 605. 26. W.W. Graessley and S.F. Edwards, Polymer, 1981, 22, 10, 1329. 27. A.S. Balankin, Doklady Akademii Nauk SSSR, 1991, 319, 5, 1098. 28. N.I. Shishkin, M.F. Milagin and A.D. Gabaraeva, Fizika Tverdogo Tela, 1963, 5, 12, 3453.

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10

The Fractal Analysis of Curing Processes of Epoxy Resins G.V. Kozlov, A.A. Bejev and Yu.S. Lipatov

10.1 Introduction This chapter considers possible models for the irreversible aggregation and fractal analysis for the curing kinetics of halogen containing epoxy polymers. There are two different modes of curing (homogeneous and nonhomogeneous), responding to the conditions, D a constant and D a variant as a function of the reaction time, where D is a fractal dimension of the microgel. The first condition corresponds to the microgels having identical dimensions and the second one, to the microgels having a distribution of dimensions. The mode of curing was determined by the level of the fluctuations of the density in reaction medium. It is also shown that the fractal reactions on curing of crosslinked polymers can be of two classes: reactions of fractal objects and reactions in fractal space. The basic difference between two classes of reaction is the dependence of their rate on the fractal dimension of reaction products. The application of the method of fractal analysis and theory of percolation makes it possible to show that the first gelation point of crosslinked polymers is a structural transition that occurs when the microgels fill the reaction space. The physical nature of auto-acceleration (auto-stopping) effect in curing reactions is determined. The models of irreversible aggregation have come into use in physics recently. These models were developed for the description of such practically important processes as flocculation, coagulation, polymerisation, etc., [1]. Many examples of the successful application of these models for the description of a number of the real processes have been obtained [2-8]. Therefore the use of the same models for the description of the polymerisation processes, in particular, curing of crosslinked polymers is of undoubted interest. It should be noted that the application of the percolation and some other models for the decision of this problem has not given the expected result [9]. In the models of the irreversible aggregation, general concepts for the physical processes such as scaling and classes of the universality are widely used [10]. The sense of scaling (scale invariance) consists in abstracting from the details of structure and allocation of simple universal features that are the characteristic for a wide class of systems. Frequently used scaling parameters (indices) are the fractal dimensions. The hypothesis of the universality is closely connected to the hypothesis of scaling whose essence comprises

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Polymer Yearbook the following: if the same limiting conditions (interaction of parts of system) are characteristic for the mechanism of formation of different systems, these systems get to one class of the universality of the physical phenomena. The two most widespread classes of the universality (types of aggregates) during the irreversible aggregation are the systems formed by the particle-cluster [11] and cluster-cluster [12, 13] mechanisms whose distinction follows from their name. Earlier the methods of the fractal analysis, of the scaling approach, and models of the irreversible aggregation were successfully applied for the description of various aspects of physics of polymers. Such aspects are the behaviour of macromolecular coils in solution [14-17], the description of polymerisation kinetics and its basic final parameters [18-21] and the interrelation of polymer structures in a solution and in a condensed state [22-24]. Especially, it is necessary to note the successful attempts of application of the methods of the fractal analysis for the description of features of curing reaction [25-27]. The purpose of the present review is the application of the previously mentioned models for the description of a specific type of polymerisation – formation of crosslinked networks of epoxy polymers. It will be made using as example two series of halogen containing epoxy polymers [28].

10.2 Experimental Kinetics of curing of a haloid containing diepoxide based on hexachlorobenzene has been studied. This oligomer (EPS-1) was cured by 4,4´-diaminodiphenylmethane (DDM) in the stochiometric ratio DDM:EPS-1. Haloid containing epoxy polymer with conditional designation EPS-1/DDM has the chemical structure shown in Figure 10.1. The curing kinetics of system EPS-1/DDM was studied by a method of reverse gas chromatography (RGC) [29]. The basic parameter received from processing of the experimental data, was the constant of reaction rate kr determined for an interval of conversion degrees α = 0.1-0.7 of the kinetical curve degree of conversion-time (α-t). For the determination of kr the standard procedure was used: the dependences, α, on the reaction time t, as lg[α/(1-α)]=f(t) which have appeared linear were made. Then the value kr (see Equation (10.4)) was determined from a slope of these linear diagrams. Ketones (metyl ethyl ketone, 1,4-dioxane, cyclohexanone) were chosen as the standard substances for the determination of retention time with argon as the gas-carrier. Also, the kinetics of curing a haloid containing diepoxide on a basis of diphenylolpropane and hexachloroethane (HCE) were studied.

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The Fractal Analysis of Curing Processes of Epoxy Resins Cl

Cl

CH3 H2C

CH

CH2

O

C

CH3 O

O

CH3

O

C

O

CH2

CH

CH3 Cl

CH2

O

Cl

R

Figure 10.1 The chemical structure of the epoxy polymer EPS-1/DDM

This diepoxide (code designation 2DPP+HCE) was also cured with DDM at the stochiometric ratio DDM:2DPP+HCE (see Figure 10.2). The study of curing kinetics of system 2DPP+HCE/DDM was carried out using a method of IR spectroscopy using a Perkin-Elmer spectrometer. To avoid the dependence on the thickness of a diepoxide layer put on a substrate, an internal standard was applied. To measure the contents of epoxy groups we used not the optical density of an analytical band of 920 cm-1, but its ratio to the optical density of a standard as which the IR-band of skeletal vibrations for an aromatic ring 1510 cm-1 are used, as this concentration is constant during the process of curing. The optical densities of an analytical band and the bands of the standard were determined using a baseline method. In curing of diepoxides by 4,4´diaminodiphenylmethane, polymers with a crosslinked structure are formed.

CH3 H2C

CH O

CH2

O

C CH3

Cl O

CH3

Cl C

O

C

Cl

Cl

C

O

CH2

CH

CH3

CH2

O

R

Figure 10.2 The chemical structure of the epoxy polymer 2DPP + HCE/DDM

One can see, the hydroxyl groups (-OH) are formed, which according to accepted models help to open the epoxy groups in the schematic as shown in Figure 10.3. The following temperatures of curing Tcur were used: for system EPS-1/DDM – 383, 393 and 403 K, for system 2DPP+HCE/DDM – 295, 333, 353, 373, 393 and 513 K.

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Polymer Yearbook OH CH2

OH …R

CH2

CH

CH2

CH

OH CH2

R

CH2

CH

CH2 OH

N

CH2

C

N

CH2

…R

CH2

CH

CH2

OH

R…

CH2

R…

CH2

N

CH2

C

CH2

CH

CH2 OH

N CH2

CH2

CH

CH2

R

OH

OH

Figure 10.3 Schematic of crosslinked structure formation of an epoxy resin

δ+

H2C

CH2 Oδ

–

OH H

N

H

Figure 10.4 Schematic of epoxy group formation

10.3 Results and Discussion In Figures 10.5 and 10.6 are the kinetic curves α(t) for the 2DPP+HCE/DDM and EPS1/DDM systems. Two basic distinctions of curves α(t) for the studied systems attract our attention. First, for the system 2DPP+HCE/DDM, the smooth decrease of a slope of curves α(t) is observed

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The Fractal Analysis of Curing Processes of Epoxy Resins

Figure 10.5 Kinetic curves α(t) for system 2DPP+HCE/DDM at curing temperatures: 353 (1), 373 (2), 393 (3) and 513 K (4)

Figure 10.6 Kinetic curves α(t) for system EPS-1/DDM at curing temperatures: 383 (1), 393 (2) and 403 K (3). The arrows point to the first gelation point

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Polymer Yearbook during increase of t, whereas for system EPS-1/DDM the linear dependence α(t) up to the large (about 0.8) values of α is observed. Secondly, if the limiting degree of conversion of the curing reaction for the system 2DPP+HCE/DDM as a the function of Tcur (the larger Tcur, the greater this degree), then for system EPS-1/DDM such a dependence is not present and at all the Tcur used the maximum values α ≈1 are observed. Let us consider the reasons of the distinctions mentioned, involving the representations of models of the irreversible aggregation and of the fractal analysis. In terms of the fractal analysis, kinetics of polymerisation is described by a general relationship [18]: α ~ t( 3− D) / 2

(10.1)

where D is a fractal dimension formed at the curing of cluster, of so-called microgels [27, 30, 31]. The formal kinetics of curing within the framework of the traditional approaches is formulated in such a way: dα = k r (1 − α) dt

(10.2)

Differentiating relationship (10.1) by t, we obtain: dα (1− D) / 2 ~t dt

(10.3)

The combination of relationship (10.2) and (10.3) allows one to obtain the equation connecting values of D and the kinetic parameters of curing process: t(D −1) / 2 =

c1 k r (1 − α)

(10.4)

where c1 is constant found from the boundary conditions. Now it is possible to calculate value D, using the reaction rate constant kr for the studied systems given in [28], as a function t or α. The calculation has shown the basic distinction of behaviour D that is the characteristic of the microgels structure, for system 2DPP + HCE/DDM and EPS-1/DDM. For the first system the value D does not depend on α at initial part (approximately up to α ≈ 0.7) of curve α(t), but is the function of Tcur. So, in the interval Tcur = 295-513 K the value D changes within the limits of 1.22-1.95. Let us note that the values of D calculated in this way correspond well to the value determined by a method of small angle neutron scattering in [26]. This means that the increase of curing temperature determines the formation of more compact microgels at small interval t. For the system EPS-1/DDM, the similar (but weaker) dependence on Tcur was observed, but simultaneously there appears clearly expressed dependence D on t. Therefore in the interval of curing time 300-3600 s,

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The Fractal Analysis of Curing Processes of Epoxy Resins the value of D varies according to: at Tcur = 383 K, D = 1.65-2.24, at Tcur = 393 K, D = 1.60-2.38 and Tcur = 403 K, D = 1.51-2.42. In Figure 10.7 the modelling calculations of a curve α(t) are given at Tcur = 383 K for different situations. So, curve 1 is an experimental curve α(t). The calculation according to relationship (10.1) under condition of D = constant = 1.76 gives curve 2 which does not agree with the experimental curve, but it is qualitatively very similar to curves α(t) for the system 2DPP + HCE/DDM (Figure 10.5). The latter effect, proceeding from the condition of D = constant = 2.24 gives curve 3 which again does not correspond to the experimental curve α(t), but it is very similar to the curve α(t) for the same system at Tcur = 403 K (Figure 10.6). This fact proves to be true by the comparison of curve 3 with the experimental points 4 for the pointed experimental curve α(t). This comparison shows that the form of the curve α(t) in the initial stages of microgel formation is characterised by its fractal dimension D. The calculation by relationship (10.1), but with the variable value D, determined according to Equation (10.4), gives the excellent correspondence with the experiment (points 5). Modelling the curves for α(t) and their comparison with the appropriate experimental curve given in Figure 10.7 confirms the

Figure 10.7 Comparison of experimental (1, 4) and theoretical (2, 3, 5) kinetic curves for system EPS-1/DDM. 1: experimental curve for Tcur = 383 K; 2: calculation of a relationship (Equation 10.1) under condition of D = Constant = 1.76; 3: calculation of a relationship (Equation 10.1) under condition of D = constant = 2.24; 4: experimental data for Tcur = 403 K; 5: calculation of a relationship (Equation 10.1) with D, calculated from Equation (10.4).

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Polymer Yearbook assumption made previously about the reason for the different forms of the kinetic curves for systems 2DPP + HCE/DDM and EPS-1/DDM. Let us consider the reasons for the different dependences D(t) for the systems studied. As mentioned above, the common variation D for both systems as a function of t and Tcur gives a D of 1.22-2.42. This interval D corresponds to the aggregation mechanism of a cluster-cluster type [10]. It was shown [32] that the dimension D of the cluster formed by the joining of two clusters with dimensions D1 and D2 (D1≥D2) in the case of the mentioned aggregation mechanism is determined in such a way: D=

d(2D1 − D2 ) d + 2(D1 − D2 )

(10.5)

where d is the dimension of Euclidean space in which the process of clustering is considered. Obviously, in our case d = 3. If the condition (10.6) is broken, the value D will not be constant (it will be increased or decreased): D1 = D2 = D = cons tan t

(10.6)

For the realisation of increase of D with increase t it is required that at the previous stage of curing there should be clusters (microgels) in the system corresponding to the condition D1 ≠ D2, or else the distribution of clusters’ dimensions is required. So, the average dimension D = 1.64 at the previous stage needs an interval D1-D2 = 1.70-1.58, i.e., ΔD = D1-D2 = 0.12. The average dimension D = 2.24 already needs an interval D1-D2 = 2.352.12, i.e., ΔD = 0.23, for the systems which have similar processes to EPS-1/DDM. Increasing t, the average value of microgels’ dimension D and the width of their distribution increase. Following from these results, we have defined the kinetics of cure, similar to those observed for the system 2DPP + HCE/DDM (Figure 10.5). Corresponding to the condition D = constant, as homogeneous, and similar to that observed for the system EPS-1/DDM (Figure 10.6) and corresponding to the condition D = variant as nonhomogeneous. The probable reason for the distinction in the curing kinetics is the different level of fluctuation density in these systems [33]. For the confirmation of this assumption we have made an attempt to describe curves α(t), shown in Figure 10.5 and 10.6, in frameworks of the scaling approaches for the reactions of low-molecular substance [33]. Let us consider the reaction in which particles P, of a chemical substance diffuse in the medium containing the random located static nonsaturated traps T. By the contact of a particle P with a trap T the particle disappears. Nonsaturation of a trap means that the reaction P + T→T can repeat itself an infinite number of times. It is usually considered that the concentration of particles and traps is large or the reaction occurs at intensive stirring, the process can be considered as the classical reaction of the

266

The Fractal Analysis of Curing Processes of Epoxy Resins first order. It also means the presence of large-scale fluctuations of density (heterogeneity) in the reaction medium. Samples for studies by IGC were prepared by the dissolution of oligomer and a curing agent in acetone, putting a mixture of their solutions on a substrate and subsequent drying. Thus, the heterogeneity of a mixture existing in a solution, was fixed during the evaporation of the solvent and was kept in a solid-state reaction of curing. The traps (T) in the reactions studied are thought to be the forming microgels and the particles – molecules of oligomer. In this case it is possible to consider that the concentration decrease of particles decreases with time as [33]: c(t) ≈ exp(− At)

(10.7)

where A is constant and t is the reaction time. However, if the concentration of randomly located traps is small, then in the spaces are areas that are practically free from traps. The particles getting into these areas, can reach the traps only during rather a long time and, hence, the decrease of their number in the course of reaction will be slower. The formal analysis of this problem shows that the concentration of particles falls down under the law [33]: c(t) ≈ exp(−Btd /(d +2) )

(10.8)

being dependent on the dimension of space d (B is constant). If the traps can move, their mobility averages the influence of spatial heterogeneity, so the assumptions resulting from (10.7) will be carried out better. In this case concentration of particles falls down under the combined law [33]: c(t) ~ exp(− At) exp(−Btd /(d +2) )

(10.9)

In Figure 10.8 the dependences ln(1 – α) on t, corresponding to Equation (10.7), for systems 2DPP + HCE/DDM and EPS-1/DDM cured at Tcur = 393 K are given. As it follows from the graphs shown, kinetics of curing of system 2DPP + HCE/DDM is well described by the linear dependence in coordinates of Figure 10.8, whereas dependence [ln(1–α)](t) for system EPS-1/DDM deviates from linearity. It means that the homogeneous reaction of curing of system 2DPP + HCE/DDM, described by Equation (10.7) under the previously mentioned conditions, is a classic reaction of the first order proceeding in reaction medium with small fluctuations of density. The attempts to linearise the dependence (1 – α) on t for system EPS-1/DDM with the use of Equations (10.8) and (10.9) have not resulted in success. It means that the pointed nonhomogeneous reaction proceeds in the reaction medium with large fluctuations of density, but it is not described by the Equations (10.8) and (10.9) for low-molecular substances. Thus, the assumption about the connection of curing reaction type with a level of fluctuation of density of reaction medium is confirmed.

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Polymer Yearbook

Figure 10.8 Dependences (1-α) of reaction time (t) in logarithmic coordinates corresponded to Equation (10.7) for systems 2DPP + HCE/DDM (1) and EPS-1/DDM (2).

For the theoretical description of nonhomogeneous reaction of curing the following assumption was made. Equation (10.8) describes kinetics of low-molecular substance reaction at large fluctuations of density in Euclidean space with dimension d (equal to 3 in the considered case). If we assume that the formation of fractal clusters (microgels) with dimension D defines a course of curing reaction in a fractal space with dimension D, the dimension d in Equation (10.8) should be replaced by D. The dependence ln (1 – α) on tD/(D+2), corresponding to Equation (10.8) with the mentioned replacement, is given in Figure 10.9. In such a treatment the scaling relationship (10.8) gives the linear correlation and this circumstance points out that the nonhomogeneous curing reaction of system EPS-1/DDM proceeds in the conditions of large fluctuations of density in a fractal space with dimension D. Hence, the fractal reactions of polymerisation can be divided, as a minimum, into two classes: reactions of fractal objects (homogeneous) whose kinetics are described similarly to the curves shown in Figure 10.5, and reactions in a fractal space (nonhomogeneous) whose kinetics are described similarly to the curves shown in Figure 10.6. The reactions of the second class correspond to the formation of structures on fractal lattices [34]. The basic distinction of the pointed classes of reactions is the

268


Figure 10.9 Dependence (1-α) of parameter tD/(D+2) on logarithmic coordinates corresponding to the Equation (10.8) for system EPS-1/DDM.

dependence of their rate on fractal dimension D of products forming during the reaction (macromolecular coils, microgels). The first class of reaction is well described by Equation (10.1). The example of such description is given in Figure 10.10 for system 2DPP + HCE/DDM, cured at 393 K, under the following conditions: D = constant = 1.78 and constant equals 8.06 x 10-3. Experimental and theoretical curves correspond well up to t = 2400 s where there is a change of the class of universality of the system owing to the gelation and the appropriate change of value D from 1.78 up to ~ 2.5 [35, 36]. The relationship (10.1) is deduced on the basis of the theoretical conclusions [37] where it is supposed that the less D is the less compact is the structure of a fractal cluster and there more are tree sites on the cluster surface which are accessible to reaction. In Figure 10.11 three modelling curves α(t), appropriate to Equation (10.1) with an identical constant for D = 1.5, 1.8 and 2.1 are shown. As it follows from the given curves, the increase D really sharply reduces the rate of reaction and decreases α at the comparable values of t. As to reactions in fractal spaces, here the situation is quite opposite. As is known [38], if we consider a trajectory of diffusive movement of oligomer and curing agent molecules

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Polymer Yearbook

Figure 10.10 Comparison of experimental (1) and calculated values of a relationship (10.1). (2) kinetic curves α(t) for system 2DPP + HCE/DDM.

Figure 10.11 Theroretical curves α(t) for reactions of fractal objects calculated from relationship where D = 1.5 (1), 1.8 (2) and 2.1 (3)

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The Fractal Analysis of Curing Processes of Epoxy Resins as a trajectory of random walks, the number of sites 〈S〉, visited by means of such walks, is proportional to: S ~ td s / 2

(10.10)

where ds is a spectral dimension of space describing its connectivity [39]. For Euclidean space, ds = 3 [39], for cured microgels ds = 1.33 [39]. From relationship (10.10) it follows that the value 〈S〉 which can be treated as a number of contacts of reacting molecules, is proportional to t1,5 in Euclidean and t0,655 in fractal spaces. At the identical t the greater number of the pointed contacts in Euclidean space determines the faster curing reaction in comparison with a fractal space [21]. In this connection we shall note an interesting detail. As is shown in [27], for an ideal phantom network the relationship is correct: D d = s D+2 2

(10.11)

It is easy to see the obvious analogy between the parameters of Equation (10.8) (at replacement d on D) and relationship (10.10). In Figure 10.12 the curves α(t), calculated according to Equation (10.8) under the condition B = constant for D = 1.5, 1.8 and 2.1 and also for d = 3 are given. It is easy to see that in accordance with the previously-stated treatment the rate of reaction increases in process of increase D and reaches the greatest value in Euclidean space at d = 3. It should be noted that in reactions of fractal objects according to relationship (10.1), at D = d = 3, α = constant, and in view of a boundary condition α = 0 at t = 0, it means that such reactions for three-dimensional Euclidean objects do not proceed at all. Further we shall consider the conditions of formation of microgels in curing reactions of haloid containing epoxy polymers. The first theory of crosslinked polymers gelation developed by Carothers and Flory, considers a gelation point as a formation of an infinite network of chemical links [30, 31]. As this theory does not always correspond to the experimental data, the concept of ‘the gelation period’ was suggested. According to the pointed concept, there are two gelation points. The first of them corresponds to the moment of appearance of branched crosslinked clusters (microgels) particles, characterised by infusibility and indissolubility in the reaction medium. The second point of gelation responds to considerably later stage of reaction – crosslinking the microgel particles and transformation of liquid fluid system with crosslinked clusters in elastic polymer [40]. This reaction is determined by the total area of microgels particles and is described as a particles reaction of the first order by Avrami-Erofeev equation. The theoretical conditions

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Figure 10.12 Theoretical curves α(t) for reactions of fractal space, calculated from Equation (10.1) at D = 1.5 (1), 1.8 (2), 2.1 (3) and d = 3 (4).

of achievement of the first gelation point including methods of fractal analysis and theory percolation will be considered later in this section [40, 41]. In Figure 10.13 the kinetic curves α(t) for system 2DPP+HCE/DDM at five temperatures of curing are given. It follows from relationship (10.1), if we put the dependence α(t) on the graph in double logarithmic coordinates, in case of their linearity from a slope of these diagrams it is possible to estimate values D. In Figure 10.14 such dependencies for system 2DPP + HCE/DDM are given at three temperatures of curing. It follows from these graphs, the increase of Tcur is accompanied by a decrease of the slope of the linear graphs of α(t) in double logarithmic coordinates or increase of D. In interval Tcur = 295513 K the increase D from 1.22 up to 1.95 is observed, as was mentioned previously. For the highest Tcur = 513 K the discrete change of a slope of the graph corresponding to the increase of D from 1.95 up to ~2.68 is observed. Such a transition in terms of the fractal analysis corresponds to the second gelation point [35, 36], i.e., a formation of a network that is spreading over the sample. From Figure 10.11 it also follows that the second gelation point for Tcur = 353 and 373 K in scale t of Figure 10.13 is not reached. In the Table 10.1 the experimental values of gelation time t1e for the first gelation point, determined by IR spectroscopy are given. The values in Figure 10.13 are marked by

272


Figure 10.13 Kinetic curves α(t) for system 2DPP + HCE/DDM at Tcur = 333 (1), 353 (2), 373 (3), 393 (4) and 513 K (5). The arrows point to the first gelation point.

vertical arrows. It is interesting to note that the gelation point for all Tcur is reached approximately at an identical value of α, equal to ~0.19. In order to explain this observation, we use percolation theory [42] and model irreversible aggregation [43], appropriate to the simultaneous growth of many clusters, that will correspond to the real situation at curing of epoxy polymers. According to model [43], the growth of such clusters stops when contact with other clusters occurs. Therefore we can consider the first gelation point, characterised by time t1e , as a point in which the contact of many spherical microgels is realised. According to the percolation theory [42], the volume fraction of such spheres f can be determined from the relationship: fx c ≈ 0.15

(10.12)

where xc is a percolation threshold. If we assume that the time t1e corresponds to a threshold of percolation of spherical microgels densely filling the reactionary space, xc = 0.19 and f = 0.79. Such value f really corresponds to dense packing of spheres of about an equal diameter [44]. This implies that the first gelation point is characterised by the termination of microgels densely filling the reactionary space, at their contact.

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Figure 10.14 Dependence of a degree of conversion α, on time of reaction t, in double logarithmic coordinates corresponding to Equation (10.1) for system 2DPP + HCE/DDM at Tcur= 353 (1), 373 (2) and 513 K (3).

Table 10.1 The dependence of time of achievement of the first gelation point from curing temperature Tcur for system 2DPP+HCE/DDM

274

Tcur, κ

t1e × 10-3, s

295

5.04

333

1.44

353

0.36

373

0.30

393

0.18

513

0.12

The Fractal Analysis of Curing Processes of Epoxy Resins From relationship (10.1) it is possible to obtain:

t1T

⎛α ⎞ ~ ⎜ 1⎟ ⎝ η0 ⎠

2 /( 3− D)

(10.13)

where t1T is a theoretical value of the time of the first gelation point, α1 is value α, corresponding to t1e and equal to ~0.19, η0 is viscosity of reaction medium, which is substituted into the complex proportionality factor of relationship (10.1), representing the product: K1η0c0, where K1 is a constant, c0 is initial concentration of reagents. From relationship (10.13) it follows that the value t1T is defined by two parameters: η0 and D. Therefore it is possible to assume that there is a correlation between the parameters η0 and D. Such correlation is given in Figure 10.15, and a very strong increase in η0 follows in process of increase D, expressed analytically in this way: 1

(10.14)

η08 = 0.585D

The extrapolation of dependence η08 (D) to η0 = 0 gives D = 0, i.e., the zero viscosity is reached in a limit of low-molecular substances (points or zero-dimensional objects). 1

Figure 10.15 A correlation between viscosity of reaction medium η0 and fractal dimension of microgels D for system 2DPP + HCE/DDM.

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Figure 10.16 Comparison of experimental (1) and theoretical (2, 3) dependences of gelation time t1 on fractal dimension of microgels D in logarithmic coordinates systems 2DPP + HCE/DDM (2) and EPS-1/DDM (3).

The combination of Equations (10.13) and (10.14) allows the estimation of the value t1T . The comparison of experimental and theoretical dependencies of the gelation time for its first point of appearance from the fractal dimension of microgels D for system 2DPP + HCE/DDM is given in Figure 10.16. It follows from this comparison, that good agreement between the theory and experiment results is obtained (the use of logarithmic scale for t1 was used for reasons of convenience). In Figure 10.6, the kinetic curves α(t) at three values Tcur for system EPS-1/DDM are shown, in Figure 10.17, the comparison of dependences of peak height of IGC h(t) and curve α(t) for Tcur = 403 K. The minimum of dependence h(t) corresponds to time t1e on a scale t. In Figure 10.2 these values are marked by arrows. Again value t1e is reached under condition α1 = const, but the absolute values, in this case, are equal to 0.47. If we use Equation (10.12) for estimating the value f, then for system EPS-1/DDM we shall receive f ≈ 0.32. Such a value of f will correspond excellently to a volume fraction of spheres for chain structures consisting of overlapping spherical microgels [44]. Thus, in homogeneous and nonhomogeneous reactions of curing the different types of percolation structures of

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Figure 10.17 Kinetic curve α(t) (1) and dependence of height h of IGC on reaction time (t). (2) for system EPS-1/DDM, curing at Tcur = 403 K.

microgels are formed, subsequently at the transition of epoxy polymers in the condensed state forming globules [30, 31]. Again such a distinction should be connected to the different level of fluctuation of density in reaction medium [33]. As a conclusion of this chapter the fractal treatment of the effect of crosslinked polymers will be considered. There are two modified variants of Equation (10.2), which take into account the course of curing reactions with auto-acceleration or autoslowing-down [45]: dα = k r (1 − α)(1 + cα) dt

(10.15)

dα = k r (1 − α)(1 − ξα) dt

(10.16)

where c and ξ are characteristics of effects of auto-acceleration and auto-stopping, respectively. Using the same procedure, as well as the deduction of Equation (10.4), we obtain: t(D −1) / 2 =

cr k r (1 − α)(1 + cα)

(10.17)

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Polymer Yearbook t(D −1) / 2 =

cr k r (1 − α)(1 + ξα)

(10.18)

where cr is a constant. From the comparison of Equations (10.4), (10.17) and (10.18) it is easy to see that in case D = constant (homogeneous reaction of curing) the members in a numerator of Equations (10.17) and (10.18) ((1+cα) and (1-ξα), respectively) are equal to one. In the case D = D(t) (nonhomogeneous reaction of curing) two ways of describing the kinetic curves α(t) (see Figure 10.1 and 10.2) are possible. The first way provides the application of function D(t), determined by some independent way, and then c = 0 and ξ = 0. The second way assumes D = constant and the value D can be arbitrary chosen from the interval D(t) for the concrete curing reaction. The comparison of the kinetic curves given in Figure 10.18 for the systems 2DPP + HCE/DDM and EPS-1/DDM shows that at t 1200 s it is the reverse.

Figure 10.18 Kinetic curves α(t) of the process of curing for systems EPS-1/DDM (1) and 2DPP + HCE/DDM (2).

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The Fractal Analysis of Curing Processes of Epoxy Resins This means that during the curing of system EPS-1/DDM at t < 1200 s, the effect of autostopping is observed, and at t > 1200 s, the effect of auto-acceleration. Having calculated the value of D at t = 1200 s, for known values kr and α from Equation (10.4) and believing it to be a constant, it is possible to estimate parameters c and ξ in Equations (10.17) and (10.18), accordingly. In practice such an approach involving the use of the two mentioned equations is not required anymore: if in Equation (10.17) c < 0, it means the presence of auto-stopping effect, and c > 0 – auto-acceleration. In Figure 10.19 the dependence D(t) for system EPS-1/DDM calculated from Equation (10.4) is given, and the broken line shows constant value D for the system 2DPP + HCE/DDM. The data show that when t = 1200 s the value of D for both of the systems are equal, when t < 1200 s the value of D for the system EPS-1/DDM is lower than the corresponding value for the system 2DPP + HCE/DDM, and when t > 1200 s, vice versa. The comparison of the graphs in Figure 10.5 and Figure 10.6 enables us to draw the next two conclusions. Firstly, the effect of auto-acceleration (auto-stopping) can be

Figure 10.19 Dependence of the fractal dimension of microgels, D, on the reaction time, t, for system EPS-1/DDM. The broken line shows the condition D = constant for system 2DPP + HCE/DDM.

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Polymer Yearbook realised only in reactions of nonhomogeneous curing. In reactions of homogeneous curing (D = constant) c = 0 and ξ = 0. The value c (or ξ) is defined by the relation of the values D in homogeneous (Dhom) and nonhomogeneous (Dnon) reactions of curing. In the case when Dhom > Dnon c < 0 the effect of auto-stopping is observed, in the case when Dnon>Dhom c>0 the effect of auto-acceleration is seen. Thus, in the suggested treatment both the absolute value and the sign c are defined by the given difference Dhom-Dnon = ΔD. In Figure 10.20 the correlation c (ΔD) for the system EPS-1/DDM is given, where the value c is calculated from Equation (10.17) on the condition D = constant = 1.75. As it was supposed, the negative values ΔD correspond to the negative magnitudes c (auto-stopping) and the positive values D to the positive magnitudes c (auto-acceleration). The correlation of absolute values ΔD and c is well approximated by a linear dependence (Figure 10.20).

Figure 10.20 Correlation between the characteristic of auto-acceleration (autostopping) c (or ξ) and difference ΔD for system EPS-1/DDM

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10.4 Summary Thus, the results given in the present chapter have shown the possibility of application of models of the irreversible aggregation and the fractal analysis to the description of curing kinetics of haloidcontaining epoxy polymers. There are two different modes of curing (homogeneous and nonhomogeneous), corresponding to conditions D = constant and D = variant as a function of reaction time t. The first condition corresponds to the identical dimension of formed microgels, and the second one, to the distribution of these dimensions. The mode of curing is determined by a level of fluctuation of density in the reaction medium. Besides it was shown that the fractal reactions at curing of crosslinked polymers can be of two classes: reactions of fractal objects and reactions in fractal space. The basic difference of two mentioned classes of reactions is the dependence of their rate on the fractal dimension of reaction products. The application of the methods of the fractal analysis and percolation theory show that the first gelation point of crosslinked polymers is a structural transition which is realised by the filling of the reaction space by microgels. The gelation time in the mentioned point is defined by fractal dimension D of microgels. Between values D and the viscosity of reaction medium η0 there is a correlation: the increase of D causes a strong increase in η0. The physical nature of auto-acceleration (autoslowingdown) effect in curing reactions has been determined. This effect is realised only for nonhomogeneous reactions of curing and its sign and intensivity are defined by the relation of the values D when D = constant and D=D(t). Otherwise, the factors mentioned are defined by the character of changing of the microgels structure in the process of curing together as the function of time.

References 1.

Fractals in Physics, Proceedings of the Sixth Trieste International Symposium on Fractals in Physics, Trieste, Italy, 1985, Eds., L. Pietronero and E. Tosatti, NorthHolland Publishing, Amsterdam, The Netherlands, 1986.

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R.M. Brady and R.S. Ball, Nature, 1984, 309, 5965, 225.

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D.A. Weitz, J.S. Huang, M.Y. Lin and J. Sung, Physical Review Letters, 1984, 53, 17, 1657.

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J.H. Kaufman, C.K. Baker, A.I. Nazzal, M. Flickner, O.R. Melroy and A. Kapitulnik, Physical Review Letters, 1984, 53, 18, 1932.

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J.H. Kaufman, O.R. Melroy, F.F. Abraham and A.I. Nazzal, Solid State Communications, 1986, 60, 9, 757.

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A.T. Skjeltorp, Physica D, 1989, 38, 1-3, 315.

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C. Camoin and R. Blank, Journal de Physique Lettres, 1985, 46, 2, L67.

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P. Richetti, J. Prost and P. Barois, Journal de Physique Lettres, 1984, 45, 23, L1137.

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M. Adam, M. Delsanti, D. Durand, G. Hilg and J.P. Munch, Pure and Applied Chemistry, 1981, 53, 6, 1489.

10. A.G. Kokorevich, Ya. A. Gravitis and V.G. Ozol-Kalnin, Khimiia Drevesiny, 1989, 1, 3. 11. T.A. Witten and L.M. Sander, Physical Review Letters, 1981, 47, 19, 1400. 12. P. Meakin, Physical Review Letters, 1983, 51, 13, 1119. 13. M. Kolb, R. Botet and R. Jullien, Physical Review Letters, 1983, 51, 13, 1123. 14. G.V. Kozlov, K.B. Temiraev and N.I. Kaloev, Doklady Russian Academiia Nauk, 1998, 362, 4, 489. 15. G.V. Kozlov and I.V. Dolbin, Vysokomolekulyarnye Soedineniya, Serya B, 2002, 44, 1, 115. 16. G.V. Kozlov, K.B. Temiraev, E.N. Ovcharenko and Yu.S. Lipatov, Reports of the National Academy of Sciences of the Ukraine, 1999, 12, 136. 17. G.V. Kozlov, K.B. Temiraev and V.A. Sozaev, Zhurnal Fizicheskoi Khimii, 1999, 73, 4, 727. 18. G.V. Kozlov, K.B. Temiraev and A.H. Malamatov, Khimicheskaia Promyshlennost, 1998, 4, 230. 19. G.V. Kozlov, G.B. Shustov and K.B. Temiraev in Fractals and Local Order in Polymeric Materials, Ed., G. Kozlov and G. Zaikov, Nova Science Publishers, New York, NY, USA, 2001, p.29-35. 20. K.B. Temiraev, G.B. Shustov, G.V. Kozlov and A.K. Mikitaev, Plasticheskie Massy, 1999, 2, 30. 21. G.V. Kozlov, K.B. Temiraev and V.V. Afaunov, Plasticheskie Massy, 2000, 2, 23-24.

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22. G.V. Kozlov, K.B. Temiraev, G.B. Shustov and N.I. Mashukov, Journal of Applied Polymer Science, 2002, 85, 6, 1137. 23. N.I. Mashukov, K.B. Temiraev, G.B. Shustov and G.V. Kozlov, Proceedings of the 6th International Workshop of Polymer Reaction Engineering, Berlin, Germany, 1998, 134, 429. 24. G.V. Kozlov, K.B. Temiraev, R.A. Shetov and A.K. Mikitaev, Materialovedenie, 1999, 2, 34. 25. B. Chu, C. Wu, D. Wu and J.C. Phillips, Macromolecules, 1987, 20, 10, 2642. 26. W. Wu, J. Bauer and W. Su, Polymer, 1989, 30, 8, 1384. 27. W. Hess, T.A. Vilgis and H.H. Winter, Macromolecules, 1988, 21, 8, 2536. 28. A.A. Bejev, Epoxide Oligomers, Polymers and Composite Materials on their Basis with Improved Working Characteristics, Tashkent Technological Institute, 1991. [PhD Thesis] 29. B.N. Stepanov, The Study of Epoxide ResinsCured by Azomatic Diamines by Reversed Gas Chromatography, Chemical Technological Institute, Moscow, Russia, 1976. [PhD Thesis] 30. W.H. Carothers, Collected Papers by Wallace Hume Carothers on High Polymeric Substances, Interscience Publishers, New York, NY, USA, 1940. 31. P.J. Flory, Journal of the American Chemical Society, 1970, 62, 8, 2261. 32. H.G.E. Hentschel and J.M. Deutch, Physics Review A, 1984, 29, 3, 1609. 33. Z.B. Djordjevic in Fractals in Physics, Proceedings of the Sixth Trieste International Symposium on Fractals in Physics, Trieste, Italy, 1985, Ed.. L. Pietronero and E. Tosatti, North-Holland Publishers, Amsterdam, The Netherlands, 1986, p.413. 34. J. Vannimenus, Physica D, 1989, 38, 1-3, 351. 35. R. Botet, R. Jullien and M. Kolb, Physics Review A, 1984, 30, 4, 2150. 36. M. Kobayashi, T. Yoshioka, M. Imai and Y. Itoh, Macromolecules, 1995, 28, 22, 7376. 37. P. Pfeifer, D. Avnir and D. Farin, Journal of Statistical Physics, 1984, 36, 5/6, 699.

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Polymer Yearbook 38. M. Sahimi, M. McKartnin, T. Nordahl and M. Tirrell, Physics Review A, 1985, 32, 1, 590. 39. S. Alexander and R. Orbach, Journal de Physique Lettres, 1982, 43, 17, L625. 40. T.E. Lipatova, Catalytic Polymerisation of Oligomers and Formation of Polymeric Networks, Naukova Dumka, Kiev, 1974. 41. J. Feder, Fractals, Plenum Press, New York, NY, USA, 1989. 42. B.I. Shklovsky and A.L. Efros, Uspekhi Fizicheskikh Nauk, 1975, 117, 3, 401. 43. T.A. Witten and P. Meakin, Physical Review B, 1983, 28, 10, 5632. 44. A.N. Bobryshev, V.N. Kozomasov, L.O. Babin and V.I. Solomatov, Synergetics of Composite Materials, NPO-ORIUS, Lipetsk, 1994. 45. P.U. Morgan, Condensation Polymers: by Interfacial and Solution Methods, Interscience Publishers, New York, NY, USA, 1965.

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11

Fractal Analysis of Macromolecules V.U. Novikov and G.V. Kozlov

Abstract Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequilibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept and of the possibility of modelling in terms of the percolation theory and diffusionlimited irreversible aggregation are discussed. It is noted that not only macromolecular coils but also the segments of macromolecules between topological fixing points (crosslinks, entanglements) are stochastic fractals; this is confirmed by the model of structure formation in a network polymer.

11.1 Introduction The theory of fractals and its application to physical and chemical processes has been developing vigorously in recent years [1-8]. To facilitate the understanding of the results presented in this chapter, we shall introduce some notions and definitions and consider briefly the grounds for applying the principles of synergetics and fractal analysis to the description of structures and properties of polymers. Fractals are self-similar objects invariant with respect to local dilatations, i.e., objects that reproduce the same shape during observation at various magnifications. The concept of fractals as self-similar ensembles was introduced by Mandelbrot [1], who defined a fractal as a set for which the Hausdorff-Besicovitch dimension always exceeds the topological dimension. The fractal dimension D of an object inserted in a d-dimensional Euclidean space varies from 1 to d. Fractal objects are the natural filling of the gap between known Euclidean objects with integer dimensions 0, 1, 2, 3 ... The majority of naturally existing objects proved to be fractal, which is the main reason for the vigorous development of the methods of fractal analysis. According to the Family classification [9], fractal objects can be divided into two main types, namely, deterministic and statistical objects. Deterministic fractals are self-similar objects that can be precisely constructed on the basis of several fundamental laws.

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Polymer Yearbook Typical examples of these fractals are the Cantor set (‘dust’), the Koch curve, the Sierpinski gasket, the Vicsek snowflake, etc. Two properties of deterministic fractals are most important, namely, the possibility of exact calculation of the fractal dimension and the infinite range of self-similarity (-∞ ; +∞). Since a line, a plane, or a volume can be divided into an infinite number of fragments in different ways, it is possible to construct an infinite number of deterministic fractals with different fractal dimensions. Therefore, deterministic fractals cannot be classified without introducing other parameters, apart from the fractal dimension. Statistical fractals are generated by disordered (random) processes. An element of disorder is typical of most real physical phenomena and objects. The fact that disorder, i.e., the absence of any spatial correlation, is a sufficient condition for the formation of fractals was first noted by Mandelbrot [1]. A typical example of this type of fractal is the randomwalk path. However, real physical systems are often inadequately described by purely statistical models. Among other reasons, this is due to the effect of excluded volume. The essence of this effect lies in the geometric restriction that forbids two different elements of a system to occupy the same volume in space. This restriction is to be taken into account in the corresponding modelling [10, 11]. The best-known examples of this type of models are self-avoiding random walk, ‘lattice animals’ and statistical percolation. In a definite range of scales, fractals have different topological structures depending on the maximum number of elements connected with the given element of the system. If each element can be connected to not more than two other elements, the resulting structure has no branching. By analogy with linear polymers, Family [9] has called these types of fractals: linear fractals. If branching does occur, the resulting fractal has a framework structure; these types of fractals are referred to as branched fractals. The microstructure of polymers can possess a high degree of self-ordering of either natural or artificial origin [12]; this represents one extreme case. The other extreme case is represented by chaos, which is the antithesis of order. Fractal analysis considers intermediate situations, i.e., those located between full order and full chaos. As a rule, these systems are obtained under conditions far from thermodynamic equilibrium; they fill the gap between periodic structures and fully disordered systems [13]. In other words, fractal structures should possess a certain level of intermediate order. Therefore, when studying thermodynamically nonequilibrium solids (the class to which polymers normally belong [14]) possessing a local order [15], it is important to consider the relationship between the level of local order and the degree of fractality. At present, it is beyond doubt that the approximation of a real polymer by a continuous medium is inadequate [16]. Even during the synthesis of polymers, numerous micro, meso- and macro-defects arise; during use, these could develop further. Moreover, it has

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Fractal Analysis of Macromolecules been found empirically that even those media that are initially homogeneous acquire upon deformation a hierarchical block structure, the characteristic dimensions of which Li obey, with rather high accuracy, the relationship: Λi =

L i +1 = cons tan t Li

where Λi is the automodelling coefficient, i = 0, 1, 2, ... [3, 17, 18]. An important characteristic of structural elements of a solid is the Euclidean dimension d, which can take on the following values: d = 0 implies point defects, d = 1 corresponds to linear defects (dislocations), d = 1 means planar defects (grain boundaries, twins, etc.), and d = 3 describes three-dimensional structures. The Euclidean dimension can characterise highly ordered symmetrical microstructures that do not often arise even in materials produced under quasi-equilibrium conditions. Non-equilibrium systems produced under essentially non-equilibrium conditions, which represents dynamic dissipative structures, cannot at all be adequately described in terms of classical methods of metallography or radiography [17-21]. This is even more so for solid (vitreous) polymers, which are, by definition, thermodynamically nonequilibrium systems. Indeed, the atomic structure of nonequilibrium materials can possess a quasi-crystalline order, characterised by five-, seven-, thirteen- or higher-fold elements of symmetry [21] forbidden by the Brouwer theorem, which underlies the classical techniques of X-ray diffraction analysis. Moreover, numerous fractographical [4, 17, 21] and geophysical [18] studies have revealed fractality of the structures of many materials and essentially non-Euclidean geometry of the deformation and the fracture of solids. Therefore, the traditional methods of the mechanics of continua, which are based on the assumption of homeomorphism of deformations, regarded as imaging of the body being deformed to the Euclidean space, are unable to describe adequately the rheological behaviour and fracture of real materials, in particular, polymers. A significant breakthrough in tackling this problem is associated with the introduction into physicochemical analysis practice of the ideas and methods of synergetics and fractal analysis [3, 5, 6, 8, 20, 21]. (Synergetics is an interdisciplinary field of knowledge dealing with identification of the general features of the processes of formation, stability and destruction of ordered time and space patterns in complex nonequilibrium systems of diverse natures.) In particular, it was shown that chaotic systems (amorphous phases, fractured surfaces, etc.) formed under nonequilibrium conditions which are totally disordered at first glance, actually display unusual elements of order [2, 20]. Whereas crystals possess a certain symmetry and translational invariance, nonequilibrium systems can possess chirality even if they have no semi-crystalline structure [3] and, what is the most important, these systems are scale invariant in a definite range of self-similarity [2, 3]. Self-similarity is

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Polymer Yearbook characterised quantitatively by the so-called Renyi dimension dq. Unlike the topological dimension, it can be both an integer and a fraction [1] and is defined by the relationship:

⎧ ⎤ ⎡ M ⎪ ⎢ ln Piq (ε ) ⎥ ⎪ ⎥ ⎢ lim ⎢ i =1 ⎪ ⎥, q ≠ 1 ε →∞ (1 − q ) ln ε ⎪ ⎥ ⎢ ⎪ ⎥ ⎢ ⎪ ⎦ ⎣ dq = ⎨ M ⎤ ⎡ ⎪ ⎢ ln Piq (ε ) ln Pi (ε ) ⎥ ⎪ ⎥ ⎪ lim ⎢ i =1 ⎥, q = 1 ⎪ε →∞ ⎢ ln ε ⎥ ⎢ ⎪ ⎥ ⎢ ⎪⎩ ⎦ ⎣

∑

∑

where M is the minimum number of d-dimensional boxes with side ε needed to cover all the elements of a structure, Pi(ε) is the probability that a point of the structure belongs to an i-th element of the bulk coverage εd, and q is the parameter of transformation of the measure (‘magnification parameter’). For Euclidean objects (smooth curves or regular lattices in a plane or in a bulk, etc), the following identity holds [16]: dq ≡ d, where − ∞ < q < ∞

In the case of regular mathematical fractals such as the Cantor set, the Koch curves and Sierpinski gaskets constructed by recurrent procedures, the Renyi dimension dq does not depend on q but [16]: dq = dH = const. < d, − ∞ < q < ∞

where dH is the Hausdorff-Besicovitch dimension (Hausdorff dimension). According to the mathematical definition [4], the Hausdorff dimension dH is a local characteristic of a set in the range of scales chosen, which can be covered by ‘spheres’ not necessarily having identical diameters, provided that the diameter of each sphere is smaller than a chosen diameter. The fractal dimension of the structure of a macromolecule df can be determined physically in the range of scales in which the structure elements are self-similar, i.e., when they are fractals. Since the ranges of df and dH coincide, the df = dH is referred to as the fractal (Hausdorff) dimension of a macromolecule.

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Fractal Analysis of Macromolecules Natural fractals such as clouds, polymers, aerogels, porous media, dendrites, colloidal aggregates, cracks, fractured surfaces of solids, etc., possess only statistical self-similarity, which, furthermore, takes place only in a restricted range of sizes in space [1, 4, 16]. It has been shown experimentally for solid polymers [22] that this range is from several angstroms to several tens of angstroms. The relationship between the level of local order and the degree of fractality of disordered solids can be described using general mathematical terms [3]. In particular, as regards the structure of solid polymers, it is noteworthy that the majority of researchers take for granted that segment-size structural associates are formed in polymers, although the particular type of packing in these associates is still debated [15, 23]. It should be emphasised that the view on the amorphous state as being totally disordered is incorrect. According to the Ramsay theorem [3], any rather great number i > R(i,j) of points or objects (in this particular case, structural elements) necessarily contain a highly ordered subsystem of Nj ≤ R(i,j) elements. Thus, no totally disordered systems (structures) exist. It can be shown in a similar way that any structure consisting of N elements, where Nj > BN{j), is a set comprising a finite number k≤ j of self-similar structures embedded into one another and having, in the general case, different Hausdorff dimensions. This means that, irrespective of its physical nature, any system consisting of a relatively great number of elements is a multifractal (in a special case, monofractal) characterised by a spectrum of Renyi dimensions dq, q == — ∞ to ∞ [3]. The tendency of condensed systems to self-organisation into scale invariant multifractal forms is a consequence of fundamental principles of thermodynamics of open systems and dq values are determined by the competition between short- and long-range interatomic interactions, which stipulate the volume compressibility and the shear rigidity of solids, respectively [24]. Since the physicochemical properties of polymers depend appreciably on the topology of the structure, the real polymer structures can be studied using the results of physical and mechanical measurements [25, 26]. Yet another important property of fractals which distinguishes them from traditional Euclidean objects is that at least three dimensions have to be determined, namely, d, the dimension of the enveloping Euclidean space, df, the fractal (Hausdorff) dimension, and ds, the spectral (fraction) dimension, which characterises the object connectivity. [For Euclidean spaces, d = df = ds; this allows Euclidean objects to be regarded as a specific (‘degenerate’) case of fractal objects. Below we shall repeatedly encounter this statement] [27]. This means that two fractal dimensions, df and ds, are needed to describe the structure of a fractal object (for example, a polymer) even when the d value is fixed. This situation corresponds to the statement of non-equilibrium thermodynamics according to which at least two parameters of order are required to describe thermodynamically nonequilibrium solids (polymers), for which the Prigogine-Defay criterion is not met [28, 29]. In conclusion, we consider the relationship between the characteristics of percolation and fractal clusters. First of all, note that a percolation cluster near the percolation

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Polymer Yearbook threshold is a fractal with a dimension of ~2.5 (for d = 3) [7, 30, 31]. This value can be easily derived from the known relationship between d and the critical percolation indices β and v [9, 30]. The relationships between the critical percolation indices β, v and t and fractal dimension of a percolation cluster df have been reported [7]: β=

1 2 4 , ν= , t= df df df

The critical indices estimated from these relations fall into the admissible ranges of variation: β = 0.39-0.40, ν = 0.8-0.9, and t = 1.6-1.8, determined in terms of the percolation model for three-dimensional systems. The researchers [7] noted that not only numerical values but also the meanings of these values coincide. Thus the index β characterises the chain structure of a percolation cluster. The l/β value, which serves as the index of the first subset of the fractal percolation cluster in the model considered [7], also determines the chain structure of the cluster. The index ν is related to the cellular texture of the percolation cluster. The 2/df index of the second subset of the fractal percolation cluster is also associated with the cellular structure. By analogy, the index t defines the large-cellular skeleton of the fractal percolation cluster. The relationship between the critical percolation indices and the fractal dimension of the percolation cluster for three-dimensional systems and examples of determination of these values for filled polymers are considered in more detail in the book cited [7]. Thus, these critical indices are universal and significant for analysis of complex systems, the behaviour of which can be interpreted in terms of the percolation theory. It has been noted previously that the structures and properties of polymers are studied using the principles of synergetics and methods of fractal analysis. This is based on several prerequisites. Firstly, amorphous glassy polymers have thermodynamically nonequilibrium structure [32]. Schaefer and Keefer [33] showed that fractal structures are formed in nonequilibrium processes. Therefore, there is good reason to believe that there are fractal structures in glassy polymers and that they can be described using the methods of synergetics. These assumptions have been repeatedly confirmed by experiments [32, 34-40]. For example, the low-frequency region of the spectra of inelastic light scattering of amorphous polymers is a broad structureless plateau [22]. This is due to the fractal structure of polymers on small linear scales [22, 36]. Fractal objects are characterised by the following relationship between the mass M (or density p) and the linear scale of measurement L [3]: M(L ) ~ Ld m

where dm is the mass scaling index.

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(11.1)

Fractal Analysis of Macromolecules Unlike mathematical fractals, real fractals (including polymers) have two natural scale lengths, Lmin and Lmax (Figure 11.1); for lengths outside this range, the object is not a fractal [3]. The lower limit Lmin is related to the finite size of structural elements, while the upper limit Lmax is associated with the tending to the limit of df. It has been found experimentally for polymers [22, 36, 41] that Lmim has an order of several angstroms and Lmax is about several tens of angstroms. It is noteworthy that the same range of existence of a local order is typical of the cluster model in which the size (length) of a statistic segment/st is the lower limit and the distance between the clusters Rcl is the upper limit. It often turns out in studies of polymers that strictly derived relationships describe adequately the behaviour of rubbers (i.e., polymers at temperatures above the glass transition temperature, Tg) but do not hold for the vitreous state. This is explained, first of all, by the sharp decrease in the mobility of chains below the Tg or by ‘freezing’ of the structure [42]. Strictly speaking, there is no fundamental difference between the molecular structure above and below the Tg; in both cases, the structure is formed by long-chain macromolecules. They differ in the fact that the thermodynamically unstable state of the polymer existing below Tg is replaced by a quasi-equilibrium state above Tg. Within the framework of fractal analysis, this means that the polymer structure ceases to be a fractal at T ≥ Tg and becomes a Euclidean body (or, at least, a fairly close approximation). As noted by Flory [43], the ability to withstand severe deformations and restore entirely the initial characteristics when

Figure 11.1 Density (ρ) versus the length scale (L) of the real fractal. The range Lmin to Lmax is the region of existence of the fractal.

291

Polymer Yearbook the stress has been relieved is a property exhibited, under appropriate conditions, by almost any polymer consisting of long-chain macromolecules. This feature is also manifested to some degree beyond the temperature range in which the ‘rubber elasticity’ phenomenon is observed. In other words, the macromolecular ‘essence’ of the polymer is more significant than the state in which the polymer occurs. Therefore, the use of the real (fractal) dimension of the object in the relations derived for rubbers [43] is expected to provide fairly accurate results when applied to vitreous polymers. Secondly, polymers are known to possess multilevel structures (molecular, topological, supermolecular, and floccular or block levels), the elements of which are interconnected [43, 44]. In addition, an external action on a polymer can induce the formation of new (secondary) structural elements — cracks, fractured surfaces, plastic flow regions, etc. These primary and secondary structural elements as well as the processes forming them are characterised by miscellaneous parameters; therefore, only empirical correlations have been obtained, at best, between these parameters. If each of the above-mentioned elements (processes) is described by a standard parameter, for example, fractal dimension, one can derive analytical equations relating them to one another and containing no adjustable parameters. This is very significant for the computer synthesis of structure and for the prediction of properties and behaviour of polymeric materials during performance. Note that fractal analysis has been used successfully to describe the phenomena of rubber elasticity [16, 45, 46] and fluidity [25, 47-49]. Thirdly, legitimate application of these methods requires the use of a physically justified number of parameters describing the polymer structure. In this sense, the Euclidean and fractal objects are fundamentally different: the former require only one space dimension (Euclidean), whereas fractal objects (spaces) require not less than three dimensions. Yet another important aspect is the change in the fractal dimension of polymers when they are simulated on fractal rather than Euclidean lattices. This fact is also important from the practical standpoint for multicomponent polymer systems. The introduction of a dispersed filler into a polymer matrix results in structure ‘perturbation’; in terms of fractal analysis, this is expressed as an increase in the fractal dimension of this structure. As shown by Novikov and co-workers [25], the particles of a dispersed filler form in the polymer matrix a skeleton which possesses fractal (in the general case, multifractal) properties and has a fractal dimension. Thus, the formation of the structure of the polymer matrix in a filled polymer takes place in a fractal rather than Euclidean space; this accounts for the structure modifications of the polymer matrix in composites. Proceeding from general statements, note that the term ‘multi-fractal’ can be understood in two ways as applied to polymers. It is shown in Section 12.2, that the fractal dimension of a chain section between points of chemical crosslinking (or between physical entanglements) D is determined by the molecular mass of this section Ms, (Men) or by the

292

Fractal Analysis of Macromolecules crosslinking density vs (or density of the entanglement network ven). The Ms (Men) value has a definite distribution [27]; hence, the dimension D would be characterised by a similar distribution [50]. Since the parameter D is uniquely related to the fractal dimension df of the supermolecular structure, df would be also characterised by a certain distribution. In other words, we are dealing with the distribution of fractal dimensions or multifractals. In addition, all the primary and secondary structural elements mentioned above are also multifractals; therefore, a polymer can be represented as a combination of elements having different weights, i.e., again as a multifractal. Below we shall use averaged values of only the fractal dimensions of particular elements, at least as long as this approximation is useful for the understanding of the physical essence of the problem in question but does not decrease substantially the accuracy of estimates. Thus, the purpose of this review is to describe systematically the results obtained within the framework of fractal formalism and concerned with the studies of structure and properties of polymer macromolecules (linear, crosslinked, amorphous, etc).

11.2 Modelling of Macromolecules 11.2.1 Fractal Dimension The complexity of the polymer structure is reflected in the large number of dimensions needed to describe it. Alexander and Orbach [28] proposed the use of spectral or fracton dimension ds for the description of the density of states on a fractal. The necessity of introducing ds is due to the fact that the fractal dimension defined by Equation (11.1) does not reflect this parameter. The investigators made use of the fact that anomalous diffusion of particles is expected on a fractal and, hence:

(r (t)) ~ t 2

2 /(2 + δ)

(11.2)

where r(t) is the distance covered by a diffusing particle in time (and δ is a scaling index for the diffusion constant). Having omitted the intermediate calculations, we present the final result obtained by Song and Roe [14] ds =

2df 2+δ

(11.3)

The spectral dimension ds is a true property of a fractal and is determined only by its connectivity. It differs from the mass scaling index [see Equation (11.1)] or fractal dimension df and from the scaling index of the diffusion constant δ by the fact that it does not depend on the way in which a fractal has been inserted into the Euclidean space with dimension d. The dependence of ds and δ on df is described by Equation (11.3). 293

Polymer Yearbook

Table 11.1 Values of d, ds, df and δ for percolation clusters [28] d

ds

df

δ

2

1.36

1.9

0.80

3

1.42

2.5

1.55

4

1.39

3.3

2.71

5

1.44

3.8

3.30

∞

4/3

4.0

4.00

Alexander and Orbach [28] found that for a separate linear polymer chain, ds = 1. In the case of a critical percolation cluster, the ds value does not depend on d and amounts to ~ 4/3 (Table 11.1). The dimensions of a linear macromolecule in different states have been considered [51]. The following states are known [51, 52] to be the most typical: 1 – compact globule, 2 – coil at the θ-point, 3 – impermeable coil in a good solvent, 4 – permeable coil (the state typical of rigid-chain macromolecules), 5 – completely uncoiled rod-like macromolecule. The radius of gyration (Rg) of a macromolecule depends on the molecular mass (M) and on the geometry of distribution of the molecule in space and is characterised by the scaling index v [32, 51]. R g ~ Mν

(11.4)

From Equations (11.1) and (11.4), it follows that [25]: df =

1 ν

(11.5)

Baranov and co-workers [51] introduced the dimension dF, determined from the Flory formula [53] for good solvents: dF =

3 − 2νF νF

(11.6)

The dF value reflects the dimension of the sub-lattice in which the macromolecule is arranged, i.e., it is a fractal dimension of the medium in which the molecule is located rather than of the molecule itself; dF does not always coincide with the Euclidean

294

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Table 11.2 Values of ν, df, dF (for d = 3) for various states of a macromolecule [51] No.

State of macromolecule

ν

df

dF

Poor solvent 1

Globule

1/3

3

-

2

Coil at the θ-point

1/ 2

2

-

Good solvent 3

Coil

3/5

5/ 3

3

4

Permeable coil

2/3

3/2

2.5

5

Uncoiled chain

1

1

1

dimension. The v, df and dF values of the three-dimensional space and the states of the macromolecule considered previously are listed in Table 11.2 [54]. State 1 is encountered in globular proteins or on precipitation (below the θ-point) of linear macromolecules from highly dilute solutions [52, 55]. Conformation 5 is typical of some proteins or linear chains exposed to particular types of external action; conformations 2-4 are more trivial and fairly well studied [53]. Analysis of the data of Table 11.2 leads to the conclusion that, for example, a macromolecular coil in the most frequently encountered states 2-4 is always a fractal (at d = 3).

11.3 Polymer Fractal Cates [56] introduced the notion ‘polymer fractal’ by replacing the rigid bonds in a percolation cluster by flexible (phantom) links. This model can be used to describe the gelation process (Figure 11.2) [57]. Within the framework of this approach, Cates [56] described variations of the structure and the dynamics of dilute solutions of polymers. This approach is based on the following main ideas. The replacement of rigid bonds in a percolation cluster by long phantom chains does not change the connectivity of a fractal (therefore, additional contacts between chains are regarded as imaginary) but does influence the dimension and the dynamic properties of the object. To describe the changes, at least three fractal dimensions are required [28]. The dimension of the initial fractal (in the percolation lattice) is determined by the fractal dimension dfo using a mass scaling relation similar to (11.1) [58]. The subscript 0 corresponds to the initial fractal with

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Figure 11.2 Scheme of the percolation of bonds during gelation: (a) pre-gel state, (b) gelation point, (c) post-gel state; ξ is the characteristic linear scale.

rigid bonds [56]. The dynamic properties can be studied using the spectral dimension ds or using random walkers (the dimension dw,) arranged on a fractal (whichever is equivalent). The latter version implies a scaling law for the root-mean-square displacement r [see Equation (11.2)] of a random walker on a fractal at time t [57]: rdw 0 ~ t

(11.7)

where dw0 is the random-walk dimension at d = 2. The case where dwo = 2 corresponds to the classical Einstein diffusion. The r value is expressed in Euclidean distances; the process with dw0>2 is usually referred to as slow anomalous diffusion. The density of states is determined by the dimension ds: ds =

2df 0 d w0

(11.8)

It has been noted previously that ds is a true parameter of a fractal determined completely by the object connectivity. The replacement of rigid bonds by flexible links in a percolation

296

Fractal Analysis of Macromolecules cluster does not change ds, i.e., in the Cates procedure [56], ds is an invariant value. However, the fractal dimension (df) and the walk dimension (dw), change upon execution of this procedure. By using the ‘Einstein correlation’ relating the scaling indices of a fractal (in this case, df is used as the index) to the resistivity (a component of viscosity) ξ, it can be shown [56, 59] that for polymers with phantom bonds (i.e., for polymers with no excluded volume, for which, ξ = 2) the dw value can be represented by the sum: d w = df + 2

(11.9)

Cates showed [56] that relationship (11.9) is also valid for structures containing loops. In the case of an ideal polymer fractal with Gaussian chains and the connectivity parameter (d1), the fractal dimension (df) of a percolation cluster with phantom bonds can be expressed as follows: df =

2d1 2 − d1

(11.9a)

For d1 = 1 (linear chains), Equation (11.9a) provides the correct value, df = 2, corresponding to a macromolecular coil at the θ-point (see Table 11.2). As noted previously, ds = 4/3 for a percolation cluster, irrespective of the dimension of the Euclidean space (see Table 11.1); therefore, from Equation (11.9a), we obtain df= 4, which is consistent with the FloryStockmayer theory [60] for phantom chains. For three-dimensional space, df > 3 has no physical meaning because the object cannot be packed more densely than an object having a Euclidean dimension. It is evident that this discrepancy is due to the phantom nature of the polymer chains postulated by Cates [56]; it is therefore, necessary to take into account self-interactions of chains due to which the dimension of a polymer fractal assumes a value that has a physical meaning. In Equation (11.9a), df has the same meaning as the fractal dimension of phantom Gaussian chains; therefore, the standard mean-field theory, taking account of the factor of excluded volume, can be applied to a polymer fractal [57]. The Flory approach can be used as the first approximation for this purpose [60]. In this case, the free energy F of an object with self-interactions can be represented by the sum [54]: 2

⎛ R⎞ M2 F = ⎜ ⎟ + νu d ⎝ R0 ⎠ R

(11.10)

where R is the size of a real fractal, R0 is the size of an ideal phantom fractal without allowance for the interactions of excluded volume, Vu is an excluded volume parameter,

297

Polymer Yearbook M is the total mass of the fractal (R0D ~ M), and d is the dimension of the Euclidean space in which the fractal has been inserted. The first term in Equation (11.10) is the elastic (or entropic) component of the free energy and the second term takes into account the volume interactions in terms of the mean-field theory [54, 60]. By minimising the free energy with respect to R, one can find the fractal dimension D of a swollen fractal, which is determined by the equation:

D=

ds (d + 2) ds + 2

(11.10a)

In the case of percolation clusters, Equation (11.10a) gives D = 2 for ds = 4/3 and d=3 [57], while for linear polymers, D = 5/3 for ds = 1 and d = 3 [61], which corresponds to an impermeable coil in a good solvent (see Table 11.2, state 3). The resulting dimensions are typical of macromolecular coils in monomeric solvents. Using the concept of polymer fractals, one can answer the question of what would happen if the monomeric solvent is replaced by a polymeric one, i.e., whether the polymer clusters and the clusters of a highmolecular-mass ‘solvent’ would be separated from one another or ‘entangled’. This question can be answered by the equation [61]: N = RDg 1 + D 2 − d

(11.10b)

where N is the number of intersections of two arbitrary fractals with dimensions D1 and D2. The final relationships for the dimensions of systems involving mixtures of polymer fractals (fractals in low- and high-molecular-mass solvents, melts of identical and arbitrary fractals) are given in Table 11.3 [61]. The problems of penetration of polymers with arbitrary connectivity into confined spaces (for examples, pores or slits) have been discussed [62]. It has been noted that the Flory theory, the blob model [62] and the scaling concept provide identical results for linear chains; however, in the case of branched polymers, the Flory theory and scaling can lead to contradictory results when applied without invoking additional information. For branched (and, hence, for crosslinked) polymers, the equation for the index v in relation (11.4) has the form [62]: ν=

298

ds + 2 d+s

(11.11)

Fractal Analysis of Macromolecules

Table 11.3 Final relations for the dimensions of systems comprising mixtures of polymer fractals [61] Monomeric solvent δs = df = 0

Parameter

Polymeric solvent δs = 1, df = 2

Melt of identical Melt of fractals δs = ds, arbitrary fractals δ f = df

Fractal dimension in terms of ds

in terms of df Saturation condition a

ds (d + 2)

ds (d + 1)(2 − δ s )

ds + 2

d+2 2

ds (d + 2) 2

2(2 + ds − 2)

d+2 2(1 + 1/ df )

d+2 2

d+2 2 + 1/ df

d+2 2 − (δ f − 2) / df

–

d≤2

ds ≥

2d d+2

δf ≥ 2 +

df (d − 1) d

Note. The ds and df values are the spectral and fractal dimensions of the interglobular space in a solvent. a Transition from fractal to non-fractal behaviour.

and the fractal dimension (D) is determined by the ratio: D=

ds ν

(11.12)

Equation (11.5) is a special case of Equation (11.12) for linear chains (ds = 1). In order to avoid the use of values such as the connectivity parameter (or chemical dimension) d1 or spectral dimension ds, Lhuillier [63] proposed a d-independent universal index r in the dependence: r R g max ~ N m

(11.13)

where Rg max is the maximum radius of gyration of a macromolecular coil and Nm is the number of base units (monomers) in the chain. The r value is supposed to vary in the range 1/d ≤ r ≤ 1. It is believed that the r-fractals thus introduced provide a simple description for real polymers: r = 1 for linear chains

299

Polymer Yearbook and r = 3/4 for branched chains. However, Vilgis [64] has found that, in essence, the following relationship holds: r −1 = ds

(11.14)

this, in turn, implies that r-fractals can be reduced to polymer fractals, as postulated by Cates [56]. A study by Stapleton and co-workers [65] was among the first which confirmed experimentally the fractal nature of a polymer chain taking a protein as an example. In a study of a frozen aqueous solution of a haemoprotein by electron spin relaxation, its fractal dimension was estimated to be 1.65 ± 0.004. In the opinion of the researchers, this value is in good agreement with the fractal dimension of a self-avoiding random walk, which is equal to 5/3 [58]. This conclusion was drawn using the equation for the density of the phonon states ρ(ω): ρ(ω ) ~ ω ds −1

where ω is frequency. It has been suggested [65, 66] that the exponent in the equation for ρ(ω) is determined by the fractal dimension. However, Alexander and Orbach [28] showed that in this case, the spectral dimension ds is involved, which is not equal to df [see Equation (11.8) and Table 11.1]. Note that the publication by Stapleton and co-workers [65], appeared earlier than the study by Alexander and Orbach [28]. In the case of self-avoiding random walk, ds = 1; substitution of this value into the equation for ρ(ω) gives a result which, as shown by Young [67], is at variance with experimental results. Attempts to resolve this contradiction have been undertaken [68]. Maritan and Stella [69] calculated the fractal dimensions for 50 proteins using two methods. In one method, fractal dimension is a scaling index for the contour length of a macromolecule with respect to the distance between its ends (it is equal to 1.19-1.82), while in the other method, the fractal dimension is a scaling index for the total mass with respect to the length, which is equal to 1.62-2.24. The calculations were performed using X-ray diffraction crystallographic parameters of proteins. In our opinion, the results obtained for proteins [65, 66] do not appear contradictory. Undoubtedly, the fractal dimension presented in the study [65] is the spectral dimension ds. Its value (ds = 1.65) does not seem too great either, if one takes into account that the values ds = 1.65-1.80 were obtained for block poly(methyl methacrylate) (PMMA) [36]. These large values of spectral dimension can be due to several reasons, first of all, to the high connectivity of the polymer chain [28].

300

Fractal Analysis of Macromolecules In addition, the polymer chain cannot be modelled by self-avoiding random-walk, as has been done by Young. Finally, Kopelman [70] demonstrated that the effective ds value can be influenced by the non-homogeneity of block specimens, for example, porosity or inter-grain boundaries. The difference between the d1 and df values found by Colvin and Stapleton [66] can also be easily explained. Indeed, d1 is a chemical dimension, as follows from the way of its determination [27], df is the Hausdorff dimension. These values do not necessarily coincide. By using Equation (11.10a) for a fractal swollen in a monomeric solvent, we obtain D ≈ 2.26 for ds = 1.65 and d = 3, which is in good agreement with both experimental data and the limiting D value for branched polymers [9]. The following relationship has been proposed [63]: d1 =

df z

(11.15)

where: z=

4 + 3D , for 4 / 3 < D < 4 8

(11.16)

When D ≈ 2.26, the parameters z and d1 are 1.348 and 1.68, respectively, which is consistent with the estimate made by Colvin and Stapleton [66]. Calculation by an equation similar to (11.8) gives dw ≈ 2.74, i.e., slow anomalous diffusion of the fractal takes place [28, 57]. The following expression relating dw, to dl has been proposed [31]: ⎛ 1⎞ d w = df ⎜1 + ⎟ d1 ⎠ ⎝

(11.17)

Assuming that dw = 3.37 (‘lattice animals’ [31]), we obtain dl = 0.93-1.98. This interval agrees with the range of dl found experimentally [66]. Thus, there are no contradictions suggested by Young between the estimates made in the two studies cited above [65, 676] but the large number of fractal dimensions used to describe the polymer structure creates certain difficulties. This is not a matter of principle because the dimensions considered above are interrelated [28, 56, 57, 6164, 71-74].

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Polymer Yearbook

11.4 Statistical Fractal Family [9] considered the conformations of statistical branched fractals (which simulate branched polymers) formed in equilibrium processes in terms of the Flory theory. Using this approach, he found only three different states of statistical fractals, which were called uncoiled, compensated, and collapsed states. In particular, it was found that in thermally induced phase transitions, clusters occur in the compensated state and have nearly equal fractal dimensions (~ 2.5). Recall that the value df = 2.5 in polymers corresponds to the gelation point; this allows gelation to be classified as a critical phenomenon. The fractal dimension of purely statistical models, i.e., models without the effect of excluded volume, can be determined accurately [see Equation (11.9a)]. For linear polymers, this model corresponds to phantom random-walk. In the case of branched statistical fractals, the corresponding model is a statistical branched cluster, whose branching obeys the random-walk statistics. Since the root-mean-square distance between the random-walk ends is proportional to the number of walk steps N, then D = 2 irrespective of the space dimension. These types of structures have been studied [61, 7577]. The value D = 4 irrespective of d was obtained for a branched fractal. Unlike ‘ideal’ statistical models, models with excluded volume, i.e., those involving correlations, cannot be accurately solved in the general case. The Df values for these systems are usually found either using numerical methods such as the Monte Carlo method or taking into account the spatial position of a renormalisation group. What are the physical conditions under which a statistical fractal has the most branched structure? It is clear that, when a large number of clusters are present in the system, they all occupy the available volume. The presence of other clusters restricts the degree of branching of each cluster; a cluster is more branched in the isolated state than in a concentrated solution. For polymer coils, this is expressed as an increase in D from its value in a dilute solution in a good solvent to the value at the θ-point in concentrated solutions [73]. Yet another factor which also influences the shape of the cluster is whether or not attractive interactions are present. As the temperature increases, the attractive interactions diminish. For example, no interactions of this sort are found in isolated macromolecular coils in good solvents at high temperature [77]. Family [9] defined this state of a statistical fractal as an uncoiled state because in this case, it is characterised by the smallest fractal dimension. Then Family used the version of the Flory theory proposed by Isaacson and Lubensky [78] for determination of the fractal dimension of an isolated statistical cluster. The method is based on the determination of the most probable cluster conformation using the free energy of repulsion. Under the influence of elastic free energy, the radius of the real cluster ‘tends’ to the radius of the ideal cluster that involves no repulsive interaction.

302

Fractal Analysis of Macromolecules After minimisation of the total free energy, the Df value for an uncoiled cluster can be found from the expression: D=

2(d + 2) 5

(11.18)

which was first obtained by Isaacson and Lubensky [78] for branched polymers in dilute solutions. Equation (11.18) has two peculiar features: firstly, D depends appreciably on d and, secondly, there exists a critical dimension of Euclidean space dc = 8 for which D = 4 in accordance with the ideal statistical model, i.e., the model without correlations. At dc > 8, the correlations caused by the effect of excluded volume are no longer significant and Df does not change. The value dc = 8 was found in studies of branched polymers and ‘lattice animals’ [79]. Calculations using formula (11.18) are in good agreement with the known results for ‘lattice animals.’ To elucidate the effects that increase D, Family considered conformations of one big cluster comprising N particles in the presence of other clusters with a size distribution. The large cluster does not ‘feel’ the presence of other clusters as long as their average diameter is small compared to its diameter. On the scale of lengths much greater than the radius of an average cluster, the big cluster interacts only with clusters similar to itself. It was found for polymers that, as the sizes of other clusters increase, they start to screen the effect of excluded volume that is effective in the big cluster. The screening can change the fractal dimension of this cluster. The best examples of processes with a cluster distribution are percolation and thermal critical phenomena, which are reflected, for example, by the Ising, Potts, and other models. Under equilibrium conditions in a system consisting of clusters with a size distribution, the average cluster size deviates in the vicinity of the critical point. The state of a statistical fractal in which the excluded volume effect is compensated by the screening effect is referred to as the compensated state. For this state, Family has found that: D=

d+2 2

(11.19)

This expression is expected to be valid for any statistical critical cluster in the presence of clusters having a size distribution. The upper critical dimension for critical clusters can be determined assuming that in Equation (11.19), D=4. The result thus obtained, dc=6, is in good agreement with the data for percolation [78].

303

Polymer Yearbook The previous results confirm that the presence of numerous clusters and the deviation of the mean cluster size near the critical point results in the screening of the critical volume effect and in an increase in D. Another way of decreasing the repulsive interactions is to enhance the attractive interactions between the elements of an isolated cluster. In the general form, the free repulsive energy can be represented as a power series with respect to density with virial coefficients w2, w3, ..., which describe the effects of interaction between pairs, triplets, etc [80]. The first term (with w2) in this power series predominates. However, in the presence of attractive interactions, the second virial coefficient w2 tends to zero and the term with w3 should be taken into account. When w2 → 0, the polymer occurs in the vicinity of the θ-point [77]. In this case, with minimisation of the total free energy with respect to R: D=

4(d + 1) 7

(11.20)

This relation was first obtained by Bantle [81] for the conformation of an isolated branched polymer at the θ-point. Calculation in terms of Equation (11.20) for D = 4 gives dc = 6, as for the compensated state. Thus, the fractal dimension D increases near the compensation point; this is due either to the geometric screening of the excluded volume effect or to the enhancement of the attractive interaction. Big clusters near the critical point in thermally induced phase transitions and polymers at the θ-point are examples of statistical fractals in the compensated state [9]. Study of the conformation of a statistical fractal in a system occurring below the critical point and in the isolated state at w2dt should hold [16]. In the case where a macromolecular section between chemical crosslinking points is represented by the freely jointed Kuhn chain, the following equality should hold [104]: 2

(11.30)

Rs = L s A

where Rs is the smallest (straight-line) distance between chemical crosslinks. A fractal broken line can be described by the relationship [91]: L ⎛ R⎞ =⎜ ⎟ a ⎝ a⎠

D

(11.31)

where L is the length of the line, R is the straight-line distance between its ends, a is the scale of measurements in the macromolecule. By dividing both parts of Equation (11.30) by A2, we find that: L s ⎛ Rs ⎞ =⎜ ⎟ A ⎝ a⎠

2

(11.32)

i.e., a freely jointed Kuhn chain is a broken line with dimension 2 provided that condition (11.30) is fulfilled. Note that in this case, the chain is a fractal because D>dt. Since the random-walk dimension dw, for this model of a macromolecule is also equal to 2 [68], the spectral dimension ds of the chain can be estimated [see Equation (11.8)]. For a freely jointed Kuhn chain, it is also equal to 2. Let us consider conditions under which ds = 2. For a real polymer, with allowance for the effect of excluded volume, one can write that [57]: D=

2ds α − ds

(11.33)

where α = ds +

2(ds + 2) d+2

(11.34)

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Polymer Yearbook When D = ds = 2, Equations (11.32) and (11.34) are correct only when d = 2. This means that the ranges of variation of the fractal dimension of a macromolecule section between crosslinking points are dtBN(j) which represents a finite number set K≤j enclosed one into another self-similar structures. The fractal (Hausdorff) dimensions of these structures are generally different. Thus any structure, irrespective of its physical nature, consisting of a rather large number of elements, is multifractal (in individual case – a fractal), and is characterised by a spectrum of Renyi dimensions dq, q = 0, 1, 2,… [2]. It is well known [3, 4], that polymers have fractal structure. This situation assumes that the structures used for the description of polymers also have a real fractality identical to that expressed by the theory. In this chapter the multifractal concept of polymers is considered on different levels: molecular, supermolecular and macroscopic.

14.2 Results and Discussion Fractals are macromolecular coils in good solvents and in Euclidean space with dimension d = 3 their fractal dimension is df = 1.65 [5]. To demonstrate this situation or the fractality of a polymer at a molecular level the following will be considered as an example. In the review [6], the data for the variation of radius of a macromolecule’s gyration Rg and molecular weight (M w) are presented for polymethyl methacrylate (PMMA) and polyethylene (PE). It is known [3] that the fractal relationship between size Rg and the length of the macromolecule Lw can be expressed as: L w ~ Rdg f

(14.1)

379

Polymer Yearbook The length of a macromolecule as a function of Mw can be defined using the parameters m and b for a polymer chain and the simple relationship: L w = M wb / m

(14.2)

Where M is the molecular weight [7] and b is the length of real band [8] of the polymer main chain. On Figure 14.1 double logarithmic dependencies are shown and Lw (Rg) is linear and passes through an origin of coordinates. It means that it corresponds to the Equation (14.1) and the dimension df determined by the slope of a plot that is equal to ~ 1.60 and close to the analogous dimension for the macromolecular coil (in good solvent (df=1.66 [5]). In the insert of Figure 14.1 is shown the variant of elements of Koch figures with a dimension df = 1.62. The Koch figures are mathematical (regular) fractals, which are constructed by iteration methods [2, 3]. This is considered to be good evidence for fractality of polymers at a molecular level. It has also been proposed [9] that the cluster’s model for the structure of an amorphous polymer in the solid state allows the

Figure 14.1 Double logarithmic dependence of length (Lw) on the radius of gyration (Rg) of a macromolecular coil for 1: polystyrene, 2: PMMA and 3: PE. Insert: variation of elements of a Koch figure having a dimension of df = 1.61 [3].

380

Levels of Fractality in Polymers

Figure 14.2 Schematic diagram of the structure of a cluster of polymers in the amorphous state.

quantitative description of the supermolecular organisation in the solid state. According to this model, the amorphous polymeric phase consists of clusters, representing the set of collinear segments of different macromolecules which have length equal to length of a statistical segment and are surrounded by a loosely packed matrix. The schematic diagram for such a cluster is presented on Figure 14.2. It is possible to see that the appearance of this cluster with chains leaving it – ‘tie’ molecules - is similar in appearance to the well known cluster model of Witten-Sander (WS-model) [10]. If such a cluster isolates the structure of a polymer by a spherical radius section (Rsp) as shown in Figure 14.2, it is obvious, that it has, at least, two properties, typical of the WS-cluster model. First, self-similarity of the system is provided by the presence of nonstable clusters, consisting of a small number of segments that form thermodynamic stable clusters. They are shown in Figure 14.2 as consisting of two segments. Secondly, it is obvious that the density of the particles forming the cluster – statistical segments – will be reduced in accordance with the distance from the centre of the cluster. As we already know [3], between the size of a cluster (Rsp) and the number of particles there is the following fractal correlation: N ~ Rdspf

(14.3)

We shall consider the methods of an estimation of size N and Rsp from the cluster’s model [9]. In the model, a cluster is strictly considered as a multifunctional junction of a fluctuating

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Polymer Yearbook network of macromolecular entanglements and by virtue of the common molecular weight of chains in one cluster, Mcl is estimated according to Flory [11] as follows: M cl = Mefcl F / 2

(14.4)

where Mefcl is the effective molecular weight of a fragment between clusters, F is the functionality of a cluster, that is the number of chains leaving from it. The size of Mefcl is determined from the Moony-Rivelin equation and F from the Graessley equation [12]. By dividing the value of molecular weight of a statistical segment (Mcl), we obtain the number of particles (statistical segments) (Nst) in one cluster. As the size (Rsp) is half of the edge of a cube of length L, which equals that of the cluster. It is possible to calculate size L as follows: L = (2Vcl / F )

−1 / 3

(14.5)

where Vcl is the density in the cluster network for macromolecular entanglement, determined by methods which are described in references [9, 12].

Figure 14.3 Double logarithmic dependence of number statistical segments (Nst) in a cluster on its radius (Rst) for 1: amorphous and 2: semicrystalline polymers.

382

Levels of Fractality in Polymers In Figure 14.3, the double logarithmic dependence is presented by Nst = f (Rsp) for five amorphous and five semicrystalline polymers, where Rsp = 0.5. From this correlation it can be seen that Equation (14.3) is obeyed and from its slope it is possible to determine the value, df which appears to be equal to ~ 2.75. It is known [3] that the fractal dimension of a cluster in WS-model lies within the limits 2.25-2.75, which is in excellent agreement with the estimation obtained from Figure 14.3. The dimension, df for the structure of an amorphous polymer in the solid state is possible by using the following relationship [4]: df = 2(1 − μ )

(14.6)

where μ is Poisson’s ratio. It follows from values quoted previously for df for the cluster in the WS-model, the value, μ will vary in the limits 0.123-0.375, which is well within the range of the variation for these polymers [13]. As an example of a polymer which displays fractality at a macroscopic level we shall consider the growth of cracks in a film sample of an amorphous polymer – polyarylate sulfone [14]. According to the present considerations the crack shown in the inserts to Figure 14.4 of the microphotograph, it is possible to make at least two conclusions. Firstly, the surface of the cracks in these samples are characterised by the presence of roughnesses, with a minimum size between ~ 2 μm and ~ 20 nm, and this provides the basis for the fractal models [15]. Secondly, the triangular form of the crack on the whole external of its growth, allowed the Mosolov [15] relationship for fractal cracks to be applied: δ ≈ rD / 2

(14.7)

where δ – opening of a crack, r – distance up to tip of a crack, D – fractal dimension of a crack. In Figure 14.4 double logarithmic dependences 2 ln δ = f(ln r) are presented for two amorphous polymers which have appeared to be linear and by virtue of it, correspond to Equation (14.7). Otherwise, the stable crack in film polymeric samples is a stochastic fractal with dimension ~ 1.48. Linearity of the diagrams presented on Figure 14.4 reflects the self-similarity of a crack at different stages of its growth. Thus, at the macroscopic level polymers the fractal properties are also displayed. The examples considered do not reflect all the variety of fractalities in polymers. So, it is possible to show that stochastic fractals are not only macromolecular coils, but also sections of chains between clusters, crazes etc. These are all examples of the term ‘multifractality’ with the reference to polymers.

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Polymer Yearbook

Figure 14.4 Double logarithmic dependence of an opening crack, distance up to the tip of the crack or the length of a stable crack for a 1: polycarbonate and 2: polyarylate. Inserts – microphotograph boundary of a crack (a) and common appearance of a stable crack (b).

References 1.

A.S. Balankin, Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 1991, 17, 6, 84.

2.

A.S. Balankin, Synergetics of a Deformable Body, Ministry of Defence (MO SSSR), Moscow, Russia, 1991, [in Russian].

3.

B.M. Smirnov, Uspekhi Fizicheskikh Nauk, 1986, 149, 2, 177.

4.

A.S. Balankin, Doklady Akademii Nauk SSSR, 1991, 319, 5, 1098.

5.

G.M. Bartenev and S.J. Frenkel, Physics of Polymers, Khimiya, Leningrad, Russia, 1990.

6.

V.P. Lebedev, Uspekhi Khimii, 1978, 47, 1, 127.

7.

A.G. Mikos and N.A. Peppas, Journal of Chemical Physics, 1988, 88, 2, 1337.

8.

S.M. Aharoni, Macromolecules, 1983, 16, 9, 1722.

384

Levels of Fractality in Polymers 9.

V.N. Belousov, G.V. Kozlov, A.K. Mikitaev and Y.S. Lipatov, Doklady Akademii Nauk SSSR, 1990, 313, 3, 630.

10. T.A. Witten and L.M. Sander, Physical Reviews B, 1983, 27, 9, 5686. 11. P.J. Flory, Polymer Journal, 1985, 17, 1, 1. 12. D.S. Sanditov, G.V. Kozlov, V.N. Belousov and Y.S. Lipatov, Ukrainian Polymer Journal, 1992, 1, 3-4, 241. 13. A.S. Balankin, A.L. Bugrimov, G.V. Kozlov, A.K. Mikitaev and D.S. Sanditov, Doklady Russian Akademii Nauk, 1992, 326, 3, 463. 14. G.V. Kozlov, V.N. Shogenov and A.K. Mikitaev, Vysokomolekulyarnye Soedineniya, Seria B, 1987, 29, 3, 218. 15. A.B. Mosolov, Zhurnal Technicheskoyi Fiziki, 1991, 61, 7, 57.

385

Polymer Yearbook

386

15

The Fractality of the Fluctuation Free Volume of Glassy Polymers G.V. Kozlov, B.D. Sanditov, D.S. Sanditov and A.B. Bainova

15.1 Introduction The fluctuation free volume in crosslinking epoxy polymers has a fractal structure and the microvoids formed in the matrix are simulated by Df dimensional spheres. The size of a microvoid is considered as the volume that is necessary for its formation and is a consequence of the accumulation of thermal fluctuations. It has been established that the structure of an amorphous polymer is fractal with a fractal dimension (df) (2 ≤ df < 3). Therefore we ought to expect, that the fluctuation free volume should also have fractal properties. The purpose of this chapter is to investigate the fractality of the fluctuation free volume in glassy polymers and epoxy polymers are selected as an example. For the proof of fractality of free volume, it is firstly necessary to show that the general relationship [1] is correct: N h ~ rhD f

(15.1)

where Nh is the number of fluctuation microvoids, rh is their characteristic size, Df is the fractal dimension of fluctuation free volume.

15.2 Experimental Epoxy polymers (EP) based on diglycidyl ether of bisphenol A were used. The curing was performed using 3,3´-dichloro-4,4´-diaminodiphenylmethane (EP-1) and methyltetrahydrophthalic anhydride in the presence of a catalyst tri(dimethylaminomethyl)-2,4,5 phenol (EP-2). The ratio of the curing agent to epoxy oligomer with reactive groups (Kst) was varied at 0.50-1.50. Thus, it was possible to produce a number of EP specimens with different topologies of polymer networks. They were tested once they had been prepared (EP-1) and after being aged in air at a temperature of 293 K for two years (EP-3).

387

Polymer Yearbook

15.3 Results and Discussion The value of rh has been evaluated as being the linear size of a microvoid of free volume rh = νh1/3, and the values νh and Nh have been calculated using the formulae [2]:

νh = Nh =

3(1 − 2μ )kTg fg E

(15.2)

fg νh

where E is the elastic modulus, μ is the Poisson’s ratio, Tg is the glass transition temperature and fg is the fraction of fluctuation free volume (Vf/V), frozen at the glass transition temperature. In Figure 15.1, are shown the dependence of Nh on rh in double log-log coordinates corresponding to the relationship (15.1). As can be seen, this dependence for all three series are linear, which is characteristic of fractal behaviour. From the slope of this straight line, we define the fractal dimension: for EP-1 and EP2, Df = 3.75 and for EP-3, Df = 2.7. In order to be able to establish the fractality of the object it is necessary to demonstrate that a common ratio exists (15.1), it is necessary to prove self-similarity, and to indicate an interval of the scales of this self-similarity (15.3). For self-similar fractal objects while using a technique based on a ratio (15.1), condition [3] should be carried out:

(N

hi

)

− N h i − 1 ~ rh−D f i

(15.3)

where Nh and Nh-1 are a number of microvoids in adjacent structural levels, rh i is the size of microvoids in i-th level. As can be seen in Figure 15.2, the dependence (15.3) is correct for the epoxy polymers investigated and confirms the self-similarity of a cluster of microvoids of fluctuation free volume. The interval of the scale of the self-similarity, with allowance for correlations between Df and fractal dimension of the structure of the polymer df may be assumed. This interval coincides with a similar interval for the structure of an amorphous polymer which is distributed from several units up to several tens of Ångström (5-50 Å) [1, 4]. Let us consider the physical sense of the parameter Df. It is obvious that the value of Df obtained from the slope of a straight line, ln Nh-ln ηf (Figure 15.1), is the average of the values. Nevertheless the microvoids of the fluctuation free volume form a DF dimensional fractal cluster.

388

The Fractality of the Fluctuation Free Volume of Glassy Polymers

Figure 15.1 The dependence of a number of microvoids on their size rh in logarithmic coordinates for epoxy polymers 1: EP-1, 2: EP-2 and 3: EP-3.

−D Figure 15.2 The dependence of a value (Ni-Ni-1) on a parameter rh i f for epoxy polymers 1: EP-1, 2: EP-2 and 3: EP-3.

389

Polymer Yearbook Therefore there are grounds to suppose that Df coincides with the dimension of area of a localisation of the extra energy D′f, defined by the relationship [1, 5]: Df′ =

1(1 − η) 1 − 2η

(15.4)

The dimension df is characterised by a real geometric object. Df (or D′f) is an energetic characteristic. The energetic state of structure is interdependent with a geometric polymer structure (see Equation 15.5). Df′ = 1 +

1 3 − df

(15.5)

In reality, it is possible to show the numerical values, Df and D′f actually coincide for epoxy polymers. The value Df can be evaluated using the following formula [1]: Df =

4πT

( )

Tg ln l / fg

(15.6)

which is obtained on the basis of concepts of free fracture of rigid bodies [6] and representation of a microvoid of free volume by Df dimensional sphere. According to current ideas [7-9], the formation of a fluctuation void in a liquid or glass is caused by a limiting fluctuation deviation of a kinetic unit (atom, group of atoms) from a position of a equilibrium. Otherwise, by limiting the strain of interatomic bond which is appropriate to a maxima of the interaction force. The microvoids of the fluctuation free volume represent the sources of the internal stress, local areas consisting of stretched or compressed elements [8], where the extra energy is located. Therefore the dimensions, Df and D′f in a physical sense should be close.

15.4 Summary Thus, the fluctuation free volume in a crosslinking epoxy polymer has a fractal structure and the microvoids, forming are simulated by Df dimensional sphere. The volume that is necessary for accumulation of the thermal fluctuation energy, sufficient for its formation controls the size of a microvoid.

390

The Fractality of the Fluctuation Free Volume of Glassy Polymers

References 1.

G.V. Kozlov and V.U. Novikov, Synergetics and Fractal Analysis of Crosslinked Polymers, Klassika, Moscow, Russia, 1998.

2.

D.S. Sanditov and G.M. Bartenev, Physical Properties of Disordered Structures, Nauka, Novosibirsk, Russia, 1982.

3.

D. Farin, S. Peleg, D. Yavin and D. Avnir, Langmuir, 1985, 1, 4, 339.

4.

M.G. Zemlanov, V.K. Malinovsky, V.N. Novicov, P.P. Parshin and A.P. Sokolov, Journal of Experimental and Theoretical Physics, 1992, 101, 1, 284, [in Russian].

5.

A.S. Balankin, Synergetics of a Deformable Body, Ministry of Defence (MO SSSR), Moscow, Russia, 1991, [in Russian].

6.

E.I. Shemyakin, Doklady Akademii Nauk SSSR, 1988, 300, 5, 1090.

7.

D.S. Sanditov and S.S. Sangadiev, Khimia i Fizika Stekla (Chemistry and Physics of Glass), 1998, 24, 4, 417, [in Russian].

7.

A.M. Gleser and B.V. Molotilov, Structure and Mechanical Properties of Amorphous Alloys, Metallurgiya, Moscow, Russia, 1992. [In Russian]

9.

V.I. Betextin, A.M. Gleser, A.G. Kadomzev and A.Y. Kipatkova, Fizika Tverdogo Tela (St. Petersburg), 1998, 40, 1, 85.

391

Polymer Yearbook

392

16

Rapid Method of Estimating the Fractal Dimension of Macromolecular Coils of Biopolymers in Solution G.V. Kozlov, I.V. Dolbin and G.E. Zaikov

16.1 Introduction In this chapter a method is proposed for finding the fractal dimension (D) of a macromolecular coil in solution, which uses only the characteristic viscosity of the polymer in an arbitrary solvent and a θ solvent. Several examples are given to illustrate the applicability of the proposed method to biopolymers of different classes. From D, one can determine a number of other important parameters characterising the behaviour of polymers in dilute solutions. Linear polymer macromolecules are known to occur in various conformational and/or phase states, depending on their molecular weight, the quality of the solvent, temperature, concentration, and other factors [1]. The most trivial of these states are a random coil in an ideal (θ) solvent, an impermeable coil in a good solvent, and a permeable coil. In each of these states, a macromolecular coil in solution is a fractal, i.e., a self-similar object described by the so-called fractal (Hausdorff) dimension D, which is generally unequal to its topological dimension dt. The fractal dimension D of a macromolecular coil characterises the spatial distribution of its constituent elements [2].

16.2 Theoretical Basis Determination of D is the first step in studying macromolecular coils by fractal analysis. D is usually estimated by finding the exponents in the Mark-Kuhn-Houwink type equation, which relate the characteristic viscosity [η], the translational diffusion coefficient D0, or the rate sedimentation coefficient (S0) with the molecular weight (M) of polymers [3]:

[η]

M

D0

M− b D

(16.2)

S0

Mbs

(16.3)

bη

(16.1)

393

Polymer Yearbook Then D can be calculated from the expressions [3]: Dη =

3 bη + 1

(16.4)

DD =

1 bD

(16.5)

Ds =

1 1 − bs

(16.6)

All these methods require quite complex and laborious measurements [3-5]. The simplest of these methods, which requires no sophisticated instrumentation, is measurement of [η], which can be performed in virtually any laboratory. Therefore, in this work, we propose a simple rapid method of estimating the fractal dimension (D) of macromolecular coils in solutions, which is based on the same principles as applied in deriving Equations (16.4)-(16.6). The coefficient of swelling of a macromolecular coil is known to be defined as [6]: ⎛ h −2 ⎞ α = ⎜ −2 ⎟ ⎝ hθ ⎠

1

2

(16.7)

where h –2 and h θ–2 are the root-mean-square distances between the ends of the macromolecule in an arbitrary solvent and an ideal (θ) solvent, respectively. In its turn, α is related to the characteristic viscositys [η] and [η]θ of the polymer in arbitrary and θ solvents, respectively, by the expression [6]: α3 =

[η] [η]θ

(16.8)

The parameter of the bulk interactions (ε), which causes a deviation of the coil shape from the ideal, Gaussian shape are found using [6]: ε=

d ln α 2 α2 − 1 = d ln M 5α 2 − 3

(16.9)

Both ε and the fractal dimension D of the coil depends on the exponent bη in MarkKuhn-Houwink Equation (16.1) [5]: ε depends on bη as: 394

ε=

2b η − 1

(16.10)

3

and the dependence of D on bη is given by Equation (16.4). Combining Equations (16.4) and (16.7)-(16.10), one can obtain the following relationship, which enables one to determine D only from the characteristic viscosities [η] and [η]θ:

([ ] [ ] ) D= 3([ η] /[ η] ) 5 η / ηθ θ

2

2

3

−3

3

−2

(16.11)

The characteristic viscosity [η]θ can be estimated either directly from experiment, or from Equation (16.1) under the condition that b = 0.5, which is valid at the point, if the constant in this equation is known. To test the relationship (16.11), we used the data of Pavlov and co-workers [4] for the polysaccharide rhodexman, for which the Mark-KuhnHouwink equation has the form:

[η] = 2.33 × 10−2 ⋅ M0.75

(16.12)

16.3 A Comparison of Calculated and Experimental Results The fractal dimension (D) calculated by Equation (16.4) is ~1.71. Estimates of D by Equation (16.11) are listed in Table 16.1 for eight fractions of rhodexman with the molecular weights in the range (27-103) x 103 g/mol. Table 16.1 also presents the [η] values [4] and the [η]θ values calculated from Equation (16.12) at bη = 0.5. As Table 16.1 shows, D varies within a very narrow range 1.68-1.70, which agrees well with the estimate made by Equation (16.4). There is a certain increase in D with decreasing M, which is also consistent with the known data [5]. If, for a polymer, the constants in Equations (16.2) and (16.3) are known, then the proposed rapid method allows estimation of D0 and S0 from the known D values by Equations (16.2), (16.5) and (16.3), (16.6), respectively. Table 16.2 presents the comparison of the experimental values [4] of D0 and S0 with their estimates made by the described method. There is a satisfactory agreement between both sets of the experimental and estimated values, although the experimental values systematically exceed the estimates made. This discrepancy is due to the strong dependence of D0 and S0 on bD and bs, respectively, which is inherent in power laws, to which the Mark-Kuhn-Houwink equations belong.

395

Polymer Yearbook

Table 16.1 Comparison between the fractal dimensions (D) calculated by two methods for a macromolecular coil of rhodexman in aqueous solution M × 103 [4], g/mol

[η η] × 103 [4], m3/kg

[η η]θ × 103 [4], m3/kg

103

135

7.48

-

1.68

93

115

7.11

-

1.69

90

104

6.99

-

1.69

72

98

6.25

1.71

1.69

67

82

6.03

-

1.69

45

62

4.94

-

1.69

32

51

4.17

-

1.69

27

37

3.83

-

1.70

D, D, Equation (16.4) Equation (16.11)

Table 16.2 Comparison of the experimental translational diffusion coefficient (D0exp) and the experimental rate sedimentation coefficient (S0exp) with the respective calculated values D0calc and S0calc of these parameters for rhodexman in aqueous solution M × 10 [4], g/mol

D0exp × 1011 [4], m2/s

D0calc × 1011, Equation (17.2), m2/s

S0exp × 1013, [4] s

S0calc × 1013, Equation (17.3), s

103

2.35

1.78

3.4

2.49

93

2.20

1.89

2.9

2.38

90

-

-

3.0

2.35

72

2.50

2.20

2.55

2.15

67

2.70

2.29

2.55

2.09

45

3.50

2.90

2.2

1.77

32

4.25

3.55

1.9

1.54

27

4.80

3.93

1.8

1.44

3

396

Obviously, the proposed method based on no specific assumptions is applicable to not only bio-polymers but also other types of polymer chains in solution. Askadskii [7] gave the b-n values for a number of polyarylates in various solvents. From these values, one can calculate D for these polymers by Equation (16.4). In addition, Askadskii [7] presented the coefficients Kη in the Mark-Kuhn-Houwink equation (16.1) for the same polymers and also provided the approximate equation:

(

κ η = 0.268 ⋅ 6.03 × 10 −5

)

bη

(16.13)

which gives Kη for a θ solvent at bη = 0.5. Using these data, one can calculate [η] and [η]θ at the same molecular weight for the given polyarylates in different solvents and then compute D from Equation (16.11). Table 16.3 presents the comparison between the fractal dimensions D calculated by Equations (16.4) and (16.11) for seven polyarylates (for these, we retained Askadskii’s notation [7]). As Table 16.3 shows, the fractal dimensions D calculated by both methods agree satisfactorily with each other, and the discrepancy between them does not exceed 10%.

Table 16.3 Comparison between the fractal dimensions (D) calculated by two methods for macromolecular coils of polyarylates D Polymer

Solvent

PP-1I

Discrepancy (%)

Equation (17.4)

Equation (17.11)

Tetrachloroethane

1.80

1.93

7.2

PP-2I

Dioxane

1.67

1.70

1.8

PP-2I

Tetrahydrofuran

1.64

1.69

3.0

PP-2E

Tetrachloroethane

1.77

1.95

10.0

PP-7E

Tetrachloroethane

1.78

1.87

5.1

PD-10I

Tetrachloroethane

1.83

1.95

6.6

PD-10E

Tetrachloroethane

2.00

1.94

3.0

Note: PP – polyarylates of phenolphthalein and phenolphthalein anilide; PD – polyarylates of di(4-oxyphenyl)methane, 2,2-di(4-oxyphenyl)propane, and 2,2-di(4´-oxyphenyl)fluorene; I – synthesised by interface polycondensation; E – synthesised by equilibrium polycondensation.

397

Polymer Yearbook Equation (16.13) is a special case of the more general expression obtained by Pavlova and Rafikov [8]:

κη =

⎞ 21 ⎛ 1 ⎜ ⎟ m 0 ⎝ 2500m 0 ⎠

bη

(16.14)

where m0 is the average molecular weight of a monomeric unit of a polymer without side chains. Thus, knowing the chemical structure of a polymer chain for determining m0 and also knowing D for estimating bη by Equation (16.4), one can find the parameters of the Mark-Kuhn-Houwink Equation (16.1) and evaluate the molecular weight of the polymer by the simple method using only the characteristic viscosities [η] and [η]θ. Table 16.4 offers a comparison between these parameters (κη and bη) found experimentally [7] and estimated by the above method for the polyarylates listed in Table 16.3. As one can see, the calculated and experimental values again agree satisfactorily. If the six arbitrary values of [Η] in the range 0.1-1.2 dl/g are used to evaluate the viscosityaverage molecular weight M η by the Mark-Kuhn-Houwink equation using both experimentally [7] and calculated values obtained the above method the constants κη and bη can be obtained, Table 16.4 for the polyarylate PP-2I in tetrahydrofuran. Comparison between the values of Mη obtained are presented in Table 16.5, demonstrating a satisfactory agreement between the different approaches.

Table 16.4 Parameters of the Mark-Kuhn-Houwink equation κη × 104, [7]

bη, [7]

κη × 104, Equation (17.13)

bη, Equation (17.4)

Polymer

Solvent

PP-1I

Tetrachloroethane

3.350

0.670

12.3

0.554

PP-2I

Dioxane

0.883

0.800

1.59

0.765

PP-2I

Tetrahydrofuran

0.724

0.828

1.44

0.775

PP-2E

Tetrachloroethane

2.421

0.696

1.44

0.538

PP-7E

Tetrachloroethane

4.095

0.684

7.58

0.604

PD-10I

Tetrachloroethane

23.05

0.640

14.4

0.538

PD-10E

Tetrachloroethane

5.220

0.495

13.3

0.546

398

Table 16.5 Comparison between the viscosity-average molecular weights Mη of the polyarylate PP-2I in tetrahydrofuran [η η], dl/g

Mηexp, g/mol

Mηcalc, g/mol

0.1

6300

4600

0.3

14600

19100

0.5

44200

36900

0.7

66400

57000

1.0

102300

90300

1.2

127500

114200

Note: Mηexp and Mηcalc are estimated by the Mark-Kuhn-Houwink equation; Mηexp are found using Kη and bη determined experimentally [7]; and Mηcalc are obtained with the use of Kη and bη calculated by equations (17.13) and (17.4), respectively.

The proposed method of estimating the fractal dimensions D of macromolecular coils in solutions allows simple and comparatively accurate estimation of D and also a number of parameters that depend on D. This method is likely to be the most useful in comparative assessment of D for several polymers (or a single polymer in several solvents), since the estimates made by this method can disagree quite considerably with data obtained by other methods: such a disagreement is inherent in power laws. Note that this limitation holds for all similar methods (see Table 2 in [3]). Knowing the chemical structure of a polymer and its fractal dimension D, one can estimate the parameters κη,and bη in the Mark-Kuhn-Houwink equation and calculate the viscosity-average molecular weight of the polymer without resorting to more laborious methods.

References 1.

V.G. Baranov, S.Y. Frenkel and Y.V. Brestkin, Doklady Akademii Nauk SSSR, 1986, 290, 2, 369.

2.

A.G. Kokorevich, Y.A. Gravitis and V.G. Ozol’-Kal-nin, Khimiia Drevesiny, 1989, 1, 3.

3.

A.P. Karmanov and Y.B. Monakov, Vysokomolekulyarnye Soedineniya, Seriya B, 1995, 37, 2, 328.

399

Polymer Yearbook 4.

G.M. Pavlov, E.B. Komeeva, N.A. Mikhailova and E.P. Anan’eva, Biofizika, 1992, 37, 6, 1035.

5.

G.M. Pavlov and E.B. Komeeva, Biofizika, 1995, 40, 6, 1227.

6.

O.B. Ptitsyn and Y.E. Eizner, Zhurnal Tekhnicheskoi Fiziki, 1959, 29, 9, 1117.

7.

A.A. Askadskii, Physical Chemistry of Polyarylates, Khimiya, Moscow, Russia, 1968, [in Russian].

8.

S.A. Pavlova and S.R. Rafikov, Vysokomolekulyarnye Soedineniya, 1959, 1, 4, 624.

400

Abbreviations and Acronyms

3FMA

2,2,2-Trifluoroethyl methacrylate

AC

Acryl acid

AIBN

Azo-bis(isobutyronitrile)

AlR

Al(i-C4H9)3

AMA

Alkyl-(meth)acrylates (s)

AO

Alexander - Orbach hypothesis

AS

Aharoni - Stauffer hypothesis

BPO

Benzoyl peroxide

CHCl3

Chloroform

DCR

Diffusion controlled reaction

DDM

4,4´-Diaminodiphenylmethane

DGEBA

Diglycidyl ester of bisphenol

DHP

Dehydropolymer

DL

Dioxane lignin

DLA-Cl-Cl

Cluster-cluster types

DLA-P-Cl

Diffusion-limited aggregation of particle-cluster

DMA

N,N-dimethylacetamide

DMF

N,N-dimethylformamide

DMFA

Dimethylformamide

DMSO

Dimethylsulfoxide

DNTA

8-Tetracarboxylic acid dianhydride

DPP

Diphenylolpropane

DPTA

Perylene-3,4,9,10-tetracarboxylic acid dianhydride

DSC

Differential scanning calorimetry

DTA

Dynamic thermal analysis

401

Polymer Yearbook EDA

Ethylenediamine

EP

Epoxy polymers

EPS-1

Hexachlorobenzene

ET

Ethylene

FA

Fluorine acrylate

FMA

Fluoroalkyl(meth)-acrylate(s)

FMC

Fluoromethacrylic copolymers

FOAα-FA

1, 1-Dihydrodioxaperfluorogeptyl -α- fluorine acrylate

FOAA

Fluorine-oxygen-containing (meth)acrylates

GC

Gas chromatography

GLC

Gas liquid chromatography

GMA

Glycidyl methacrylate

GPC

Gel permeation chromatography

Hal3

Halogen

HCE

Hexachloroethane

HELC

Highly efficient liquid chromatography

HFP

Hexafluoropropylene

IGC

Inverse gas chromatography

IPA

Isophthalic acids

IR

Infra red

L

Ligand

LC

Liquid crystalline

LCP

Liquid-crystal aromatic polyester(s)

LCV

Lignocarbohydrate valence bonds

Ln

Lanthanide

LP

Lauryl peroxide

MALDI-TOF MS Matrix assisted laser desorption ionisation – time of flight mass spectrometry MB

Bohr magneton

MMA

Methyl methacrylate

402

Abbreviations and Acronyms MMD

Molecular mass distribution

MMP

N-methyl-2-pyrrolidone

Mn

Number average molecular weight

MPPh

Monomer - polymeric phase

MS

Mass spectrometry

Mw

Molecular weight

Mw

Molecular weight

MWL

Milled wood lignin

NMP

N-methylpyrrolidone

NMR

Nuclear magnetic resonance

PαFMA

Poly α-fluoroalkyl(meth)-acrylate(s)

PA

Polyamide

PAI

Poly(alkane imide)

PAIM

Polyamidoimide

PBO

Polybenzoxazole

PC

Polycarbonate(s)

PCA

Phosphorus-containing additives

PD

Polyarylates of di(4-oxyphenyl)methane, 2,2-di(4-oxyphenyl)propane, and 2,2-di(4´-oxyphenyl)fluorene

PDI

Pyromellite diimide

PDMS

Polydimethylsiloxane(s)

PE

Polyethylene

PEC

Polyethercarbonate(s)

PEI

Polyesterimide

PEK

Polyether ketone

PENI

Poly(ether naphthalene carboximides)

PES

Polyether sulfone

PFMA

Perfluoroalkyl methacrylates

PHE

Polyhydroxy ether

403

Polymer Yearbook PHE-Gr I

PHE with a non-activated graphite filler

PHE-Gr II

PHE with an activated graphite filler

PI

Polyimide (s)

PMMA

Polymethylmethacrylate

PMPh

Polymer-monomer phase

PNI

Poly(naphthalene carboximides)

PNIB

Poly(naphthylimidebenzimidazole)

POF

Polymer optical fibre(s)

PP

Polyarylates of phenolphthalein and phenolphthalein anilide

PPA

Polyphthalamides

PPTI

N-phenylphthalimide

PPI

Poly(perylenecarboxyimides)

ppm

Parts per million

PPP

2,2´-(1,4-Phenylene)-bis-(3-phenylpyrazine)

PPQ

Poly(phenylquinoxaline)

PS

Polystyrene

PSF

Dichlordiphenylsulfone

PSP

Polyphenyl sulfide

PTFE

Poly(tetrafluoroethylene)

Rg

Radius of gyration

RGC

Reverse gas chromatography

RSA

X-ray structural analysis

RWCO

Random walk without crossover

SPPQ-1

Copolyimidophenylquinoxaline

St

Styrene

TBP

Tributyl phosphate

TFE

Tetrafluoroethylene

Tg

Glass transition temperature(s)

TGA

Thermogravimetric analysis

404

Abbreviations and Acronyms THF

Tetrahydrofuran

TMPO

2,2,6,6-Tetramethylpiperydine-1-oxide

TPA

Terephthalic acid

UV

Ultraviolet

VA

Vinyl acetate

VDF

Vinylidene fluoride

VF

Vinyl fluoride

WS

Witten-Sander model

405

Polymer Yearbook

406

Author Index

A

E

Aharoni, A 324 Alexander, S. 293, 294, 300, 305, 324 Aloev, V.Z. 251 Askadskii, A.A. 397

Elshina, L.B. 7 Erins, P.P. 50 Evstigneev, E.I. 51

F B Bainova, A.B. 387 Balankin, A.S. 255 Bantle, S. 304 Baranov, V.G. 294 Bejev, A.A. 373 Beloshenko, V.A. 328, 335 Bobalek, E.G. 52 Bolker, H.J. 53 Botto, P.A. 253 Bratus, A. 101 Brenner, H.S. 53 Bulycheva, E.G. 7, 9

C Carothers, W.H. 271 Cates, M.E. 295, 297, 300, 307, 323 Colvin, J.T. 301

Family, F. 285, 286, 302, 303, 304 Flat, A.Y. 329 Flory, P.J. 51, 271, 291, 297, 309, 382

G Gardon, J.L. 57 Ghassemi, H. 13, 15 Goring, D.A. 50, 53, 57, 64 Gravitis, Y.A. 52, 62 Gumargalieva, K.Z. 185

H Hafiychuk, G. 101 Hay, A.S. 31, 32 Helman, J.S. 323

I

D

Isaacson, J. 302, 303 Iwata, S. 240

De Gennes, P.G. 50 Dolbin, I.V. 373, 393

J Jean, Y.C. 329, 331

407

Polymer Yearbook

K

O

Kalugina, E.V. 185, 200 Karayannidis, G. 11 Karmanov, A.P. 49, 65 Kausch, H.H. 322 Keefer, K.D. 290 Khananashvili, L. 141 Kiseleva, O.F. 131 Kogan, S.I. 64 Kopelman, R. 301, 306 Kozlov, G.V. 251, 333, 335, 349, 373, 379, 387, 393 Kytsya, A. 101

Olemskoi, O.I. 329 Orbach, R. 293, 294, 300, 305, 324 Ozol-Kalnin, V.G. 52, 53, 54

L

P Panov, A.A. 131 Panov, A.K. 131 Pavlov, G.M. 395 Pavlova, S.A. 398 Pla, F. 60, 64

R

Lachinov, M.B. 209, 216 Lebedev, V.P. 307 Lekishvili, N.G. 209 Lhuillier, D. 299 Lipatov, Y.S. 349, 368 Lubensky, T.C. 302, 303

Rafikov, S.R. 398 Robert, A. 60 Roe, R-J. 293 Rostovskii, E.N. 213 Rubinovich, L.D. 213 Rusanov, A.L. 7, 39

M

S

Mandelbrot, B.B. 285, 286 Maritan, A. 300 Mason, S.G. 57 Medvedevskikh, Y. 101 Meladze, S. 141 Mills, N.J. 354 Minsker, K.S. 131 Monakov, Y.B. 49, 75 Mosolov, A.B. 311, 383 Mukbaniani, O. 141 Müllen, K. 7

Sabirov, Z.M. 75 Sandakov, G.I. 322 Sanditov, B.D. 387 Sanditov, D.S. 387 Sarkanen, K.V. 63 Schaefer, D.W. 290 Sek, D. 33, 34 Shcherbakova, T.S. 196 Song, H-H. 293 Stapleton, H.J. 300, 301 Stauffer, D 324 Stella, A.L. 300 Stoldore, I.A. 62 Szabo, A. 53

N Novikov, V.U. 292 Novotortseva, T.N. 185

408

Author Index

T Tsvetkov, V.N. 63 Turovski, A. 101

U Urazbaev, V.N. 75

V Vilgis, T.A. 300, 307, 322

Y Yan, J.F. 53 Young, E. 300, 301

Z Zaichenko, A. 101 Zaikov, G.E. 75, 101, 131, 141, 185, 209, 379, 393

409

Polymer Yearbook

410

Index

1

H NMR spectra 146, 150, 156, 157, 178 2,2´-(1,4-phenylene)-bis-(phenylpyrazine) structure of 201 29 Si NMR spectra 158, 161 2DPP+HCE 261 2DPP+HCE/DDM 262-267, 269, 271, 272, 275, 278 curing 279 fractal dimension 274 fractal dimension of microgels 276 gelation point 275 gelation time 276 kinetic curves 272 viscosity 274 3FMA copolymerisation constants 241 4FMA polymerisation of 217, 218 8FMA polymerisation of 217, 218, 219 12FMA polymerisation of 217, 218

A Additives phosphorus containing 185 Adhesion 351, 353, 359 surface structure of the filler 356 Adhesion joints fracture of 353 Adhesion parameters fractal dimension 361

Aggregate surface fractal dimension 355, 356 Aggregation of particles 352 Aliphatic-aromatic polyamides thermo-oxidative degradation 198 Amorphous polymers 382, 383, 387 cluster model 308 fractal dimension 310 Aromatic heterochain polymers 185 Asahi Garasu Co. 212 Avrami-Erofeev equation 271

B Binary hooking 251, 252 Biopolymers macromolecular coils of 393 Biosynthetic lignin scaling characteristics 66 Bis(N-aminoimides) 13 Bis(organocyclosiloxane) oxides physical-chemical properties 155 Blob model 298 Brillouin light scattering 252 Brouwer theorem 287 Brown equation 366 Butadiene 86, 88 active centres 81 mechanism of stereoregulation 81 polymerisation 81-83, 85, 92, 93

C 13

C NMR spectra 146, 149, 156 Cantor set 286, 288

411

Polymer Yearbook Catalysts lanthanide 75 Ziegler-Natta 75 Catalytic dehydrocondensation 168 Catalytic poison 79 Chain termination 189 Chemical crosslinking points 331, 334 cis-regulation 94 Cluster entanglement network 251 Cluster structure 381 Composites dielectric characteristics 351 mechanical characteristics 364 (co)polymerisation total heat effect 229 (co)polymerisation rate transformation degree 231 (co)polymerisation time transformation degree 230 Copoly(ether imides) 31 Copoly(imidophenylquinoxalines) thermo-oxidative degradation of 186 Copolyethersulfone formals dielectric loss 336 Copolyimides 20 block 20 statistical 20 Copolymerisation kinetics 228 Copolymers comparative physical properties 163 fractionation of 143 properties of 14 viscosities of 234 Copolymers with carbophenylcyclosiloxane fragments elementary analysis 154 physical-chemical properties 154 Copolymers with methylcyclosiloxane fragments elementary analysis 155

412

physical-chemical properties 155 Copolymers with phenylcyclosiloxane fragments elementary analysis 153 physical-chemical properties 153 Curing processes 326 fractal analysis 259 Cyclolinear copolymers synthesis of 175 CYTOP 212

D DDM:EPS-1 260, 373 Decamethyl-cyclotetrasiloxane IR spectra of 158 Dehydrocondensation 169, 170 reaction 168, 172 Delignification 51 Dewar parameters 213 Dienes polymerisation 78, 79, 80, 81 Differential scanning calorimetry 12, 15, 178 patterns 180 Diffusion-controlled reaction 102 DNTA 19, 21, 22, 23, 29, 31, 35 DPTA 7, 11, 13, 15, 35 Draw ratio 251, 337 Dynamic thermal analysis 191 Dynamic thermogravimetric analysis 187

E Einstein correlation 297 Elastic fracture linear mechanics 365 Electron bond populations 85 Electron microscopy transmitting 350 Endoperoxides 188

Index Epoxy group formation schematic of 262 Epoxy polymer: 2DPP + HCE/DDM chemical structure of 261 Epoxy polymer: EPS-1/DDM chemical structure of 260 Epoxy polymers curing 373 fractal analysis for the curing kinetics 259 microvoids 389 molecular characteristics 330 Epoxy resins crosslinked structure formation 263 curing processes of 259 kinetic curves 263, 264 EPS-1/DDM 264, 266-269, 278, 374-376 auto-acceleration 281 curing 279 fractal dimension of microgels 276, 278 gelation time 276 kinetic curves 263, 277 Ethylsiloxane oligomers physical-chemical properties 171 yields 171 Euclidean dimension 287 Euclidean lattices 292 Euclidean objects 289 Euclidean space 271, 285, 293, 297, 324, 373, 375, 379 Extrusion channel polymer melting 134 Extrusion head 133 construction of 131, 132 hydrodynamic performances 134 many stream 132, 133 Extrusion processes ultrasound 131

F 19

F NMR 244 Filler fraction of 356 Filler particles 359 radius of aggregates 356 Filler surface 360 Flory swelling coefficient 60 Flory theory 52, 298, 302 Flory-Stockmayer gelation 53 Fluctuation free volume 388, 390 Fluorine containing copolymers covers of optical fibres 243 Fluorine-containing alcohols methacrylates of 227 Fluorine-containing methacrylates block polymerisation 234 nitroxyl radicals 234 Fluorine-oxygen containing monomers general characteristics of 239 Fluorine-containing (meth)acrylate copolymers properties of 240 Fluoroalkylmethacrylates block radical polymerisation 209, 213 copolymerisation 224 kinetics of 215 polymerisation of monomers 220 relative activity of 213 FOAA copolymers thermal degradation parameters 241 FOAMA-1 copolymer molecular-mass characteristics 240 Fourier - IR spectroscopy 190 Fractal analysis 264, 292, 349 macromolecules 285 Fractal clusters 289, 322 Fractal concepts 50

413

Polymer Yearbook Fractal dimension 67, 293, 297, 299, 322, 325, 335, 388, 395-397 determination of 305 method of estimating 393 Fractal objects 290 Fractal properties 383 Fractal space 373, 376, 377 Fractal structure 387, 390 Fractals 379, 380 annihilation kinetics 306 scaling properties 54

Heterodyads 224 Homodyads 223, 224 Homological reactions polar effects in 193 Homopolycondensation reactions 198 Homopolymerisation kinetics 226, 232 Huckel method 87 Hydrogen conversion 172, 176, 178 Hydrosilylation reaction 175

I G Gel chromatography 159 Gel permeation chromatography 160, 198 Gel-effect 220, 221, 232, 233 intensity 234 Gelation 297 Gelation point 272 Glassy epoxy polymers deformability 332 Glassy polymers fluctuation free volume 387 fractality 387 Glycidyl methacrylates 101, 103 bulk photopolymerisation 101 homogeneous system 109 kinetic model 103, 104, 120 linear polymerisation 121 microheterogeneous system 111, 121 Graessley equation 382 Graphite 350

Impact strength 364 Inductively coupled plasma 197 Initiator decomposition 117 Interfacial adhesion 360, 364 Interfacial layer adhesion parameter 363 strength 362 strength of 360 Intermolecular crosslinking 188 Internal light-reflection 209 Interphase layer 111 Inverse gas chromatography 267, 373 IR spectroscopy 84, 186, 261 Irreversible aggregation 259, 260 cluster theory 349 models of 352 Isomerisation anti-syn 91, 92, 93 Isophthalic acid 202 Isoprene 86, 88 polymerisation 80 steric hindrances 90

H Hausdorff dimension 301 Hausdorff-Besicovitch dimension 285, 288 Heat of crossed propagation 229

414

K Kerner equation 352, 360 Kinetic curves 120 Kinetic model

Index GMA 109 homogeneous system 110 microheterogeneous system 112, 114, 115 Koch curves 286, 288 Koch figures 308, 381 Kogan-Gandelsman-Budtov model 64, 65 Kuhn chain 312, 313, 314

L Lanthanide catalysts 75, 77, 81, 82, 84 activity 76 diene polymerisation 75 organometallic component 78 principal groups of 75 regioselectivity 89 stereospecificity 76 Laser interferometry 103 Lattice animals 301, 303, 333 Laury-Mayer method 226 LCP degradation products composition 198 kinetics 198 thermoresistance 196 Leidner-Woodham equation 351, 361, 362 Levels of fractality 307 Ligand nature of 77 Lignin 49 alkali 64 biosynthetic 49, 57 Braun’s 51 cyclisation 52 degree of condensation 54 degree of intramolecular cyclisation 57 dioxane 57, 60, 63 dissipative structure 54 distribution of the rings 54

formation 53 fractal dimensionality 57 gelation of 51 heterogeneity 52 hydrodynamic properties 57, 59 industrial 57 macromolecular properties 49 microgel particles 57 microgelation 52 milled wood 57, 58, 64 native 57 natural 49, 51, 67 network structure 53 network topology 51 NMR spectra of 52 structure of 50 topological structure 49, 50 Lignin chains topology of 54 Lignocarbohydrate valence bonds 50 Liquid-crystal aromatic polyesters 195 Liquid-crystal copolyesters thermo-oxidative degradation of 192

M Macromolecular coils fractal dimension 394 Macromolecular entanglements cluster network 252 Macromolecular skeletons 325 Macromolecules fractal analysis 285 fractal characteristics of 312 fractal dimension of 314, 319, 320 modelling of 293 scaling representation of 328 MALDI-TOF MS 244 Mark-Kuhn-Houwink equation 57, 60, 62-63, 67, 394-395, 397-399 parameters of 61

415

Polymer Yearbook Mark-Kuhn-Houwink type equation 393 Mark-Kuhn-Howinck-Sakurada equation 160 Mass spectroscopy 190, 197 Methacrylates fluorine containing 221 fluorine-oxygen containing 225 Methyl methacrylate copolymerisation constants 241 quantum-chemical parameters 215 thermal degradation parameters 241 Methylcyclosiloxane copolymers comb-type 166, 171 Methyldichlorosiloxymethylcyclosiloxanes 13 C NMR spectra 148 Methylsiloxane copolymers comb-type 169 Methylsiloxane oligomers comb-type 177 Microgels 259, 264, 266, 267, 271, 374 fractal dimensions 374, 375 structure 373 Microheterogeneous model 102 Microvoids 388, 390 Milled wood lignin hydrodynamic properties 58 MMA-8FMA 1 H-NMR spectrum 223 Molecular entanglement networks 253 Molecular mobility fractal characteristics 335 Molecular orientation draw ratio 252 Monolignols 49 coniferyl 49 p-coumaryl 49 sinapyl 49 Monomer-polymeric phase 105 Monte Carlo method 54, 302 Moony-Rivelin equation 382

416

N N-methylpyrrolidone 19 Naphthalene-1,4,5,8-tetracarboxylic acid dianhydride 19 National Bureau of Standards, USA 186 Native lignin hydrodynamic properties 62 Network polymer model of 325 morphology of 334 Non-condensed bis(naphthalic anhydrides) polyimides based on 32 Nuclear magnetic resonance 82

O Octamethylcyclotetrasiloxane IR spectra of 159 Oligoethylhydride-siloxanes 174 catalytic dehydrocondensation 173 dehydro-condensation 172 dehydro-condensation of 172 thermogravimetric curves 174 Optical fibre coating 210 Organocyclosiloxane monomers dichloro containing 143 Organocyclosiloxanes physical-chemical properties 145 Organodichlorosiloxymethylcyclosiloxanes 13 C NMR chemical shifts 148 1 H NMR chemical shifts 146, 147 Organometallic compounds 84 Organosilicon copolymers cyclosiloxane fragments 141 Organosiloxane copolymers synthesis of 151 Organosiloxane oligomers synthesis of 168 Oxygen absorption kinetics 197 Ozonolysis 77

Index

P Paramagnetism 188 PAI 191 Pariser-Parr-Pople method 188 Particle aggregation 351 fractal dimension 354 Particle-cluster 260 Particulate-filled polymer composites adhesion 349 PENI 31, 32, 39 Percolation cluster 289, 290, 294, 295 Percolation of bonds 297 Perfluoroalkyl methacrylates copolymerisation of 223 geometry of molecules 214 heats of polymerisation 216 quantum-chemical parameters 215 radical polymerisation of 220 PFA mechanical properties 242 optical properties 242 physico-chemical properties 242 PGE-Gr-I 354 PGE-Gr-II 354 PHE-Gr-I 353, 356, 359-361, 363-364, 366-367 PHE-Gr-II 353, 356, 359-361, 363-364, 366-367 Phenylsiloxane copolymers comb-type 168 Phonon states 300 Photopolymerisation GMA 107 Pinus silvestris 59 Piperylene 77, 84, 86, 88, 91 regioselectivity 91 polymerisation steric hindrances 90 Plastic deformation 366 Plasticised cable

explosive effort of extrudate 138 swelling on stress 138 PNIB 23, 26 POF components 211 Poly(alkane imide) structure of 189 thermo-oxidative degradation 189 Poly(ethyleneterephthalate) orientation 252 Poly(hydroxyether) 350 Poly(naphthalenecarboximides) 7, 19, 21-23, 29, 31, 33-36, 39, 41 properties 24, 25, 37, 38 synthesis 7 Poly(perylenecarboximides 7 synthesis 7 Poly(phenylquinoxaline) 186 thermo-oxidative degradation of 186 Poly-α-fluoroacrylate 238 Polyalkyl(meth)acrylates fluorine-containing 236 Polyamidoimide thermo-oxidative degradation 198 thermo-oxidative resistance 199 Polyani-Semenov rule 216 Polyarylates 385 macromolecular coils 397 Polycarbonate 385 Polydimethylsiloxanes 157, 166 Polyesterimides thermo-oxidative degradation 198 Polyesterketones thermo-oxidative degradation of 192 Polyethylene 379, 381 Polymer fractals 295, 299 Polymer melt flow characteristics 135 performance of 136 spray 136 ultrasonic oscillations 131

417

Polymer Yearbook Polymer structure 349 Polymer-monomeric phase 107, 108 Polymerisation diene 87 glycidyl methacrylate block 101 GMA 104 kinetics of GMA 104 Polymerisation system microheterogeneity 126 Polymers boat form 29 chair form 29 effective spectral dimensions 306 fluorine-containing 209 graphite-filled 350 levels of fractality 379 microstructure of 286 stabilisation of 185 thermoresistance of 196 Polymethyl methacrylate 379, 381 birefringence 256 density of entanglement 255 macroscopic draw ratio 255, 256 mechanical properties 242 molecular orientation 251 optical properties 242 physico-chemical properties 242 structural parameters 255 Polyphthalamides stucture of 199 thermo-oxidation 199 Polypyromellitimide thermo-oxidative degradation of 186 Polystyrene 381 flow state of melt 135 melt cost of 137 Polysulfones thermo-oxidative degradation of 192 Populus trichcarpa 62

418

PPI 8, 11, 15 molecular parameters 16, 17 properties of 10 rigid-chain 9 solubility 16, 17 Prigogine - Defay criterion 289 Process thermooxidation initiation of 202 PSF chemical shifts of carbon 194 PTFE mechanical properties 242 optical properties 242 physico-chemical properties 242 Pyromellite diimide 188, 190 stucture of 201

Q Quantum-chemical calculations 84

R Raman light scattering 305, 306 Ramsay theorem 289 Real fractal 291 Regioselectivity 86 Renyi dimension 288, 289 Reverse gas chromatography 260 Rheological measurements capillary viscometer 135 Rhodexman 395 macromolecular coil 396 rate sedimentation coefficient 396 translational diffusion coefficient 396 Rouse-Zimm dynamics 307

S Scaling concept 298 Scaling index 293

Index Semicrystalline polymers 382 Sierpinski gasket 286, 288 Small-angle neutron scattering 305 Solid properties polymeric items 137 Solvent nature of 80 Statistical fractal 302 Stereoselectivity 86 Stockmayer-Fixman equation 64 Structural parameters estimation of 332 Synergetics 287

T Thermal-oxidative stability 165 Thermo-oxidative degradation 203 Thermogravimetric analysis 22, 162, 165, 174, 179 data 39, 199 method 197 Thermoresistant heterochain polymers thermo-oxidation of 185 Topological fixing points 321 Tsvetkov-Klenin hydrodynamic invariant 57, 62 Tudos-Kelen method 221

U ULTEM 32

V Vicsek snowflake 286 Vilgis models 323 Viscosity 354

W Walk dimension 297 Wall and Medvedev formulae 225 Weiberg index 214, 215 Wide angle x-ray investigation 173 Witten-Sander model 66, 308, 381

X X-ray analysis 167, 242 X-ray diffraction analysis 15, 287 crystallographic 300 X-ray investigation 178 X-ray structure analysis 196

Z Ziegler-Natta catalysts 81, 82 Zimm-Kilb model 64, 65

419

Polymer Yearbook

420

ISBN: 1-85957-383-5

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