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
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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
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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
Results and Discussion .................................................................... 374
13.4
Summary ......................................................................................... 377
References ................................................................................................... 378 14 Levels of Fractality in Polymers ................................................................... 379 14.1
Introduction .................................................................................... 379
14.2
Results and Discussion .................................................................... 379
References ................................................................................................... 384 15 The Fractality of the Fluctuation Free Volume of Glassy Polymers ............. 387 15.1
Introduction .................................................................................... 387
15.2
Experimental ................................................................................... 387
15.3
Results and Discussion .................................................................... 388
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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)
+
+
+
Tetrachloroethane:phenol mixture
---
-- -
-- -
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
+
Tetrachloroethane:phenol mixture
+
NMII
+
DMA
Solubility
Table 1.4 Some properties of PNI of the general formula [14] continued
+
DMF
+
CHCl3
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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).
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Polymer Yearbook
Scheme 1.17
40
Advances in the Synthesis of the Poly(perylenecarboximides) and Poly(naphthalenecarboximides)
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.
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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.
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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
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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
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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
Macromolecular Properties and Topological Structure of Lignin
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
Macromolecular Properties and Topological Structure of Lignin
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
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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.
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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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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
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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: La
Gd>Tb>Dy>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
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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
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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
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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 (<0.5% mol/l) and the polymerisation temperature increases (from 25 to 80 °C) the dependence of the number of cis-1,4-units in the polymer on the structure of AlR3 becomes more pronounced [10]. When an organomagnesium compound i-C 8H17MgC4H9 was used instead of the organoaluminum compound (triisobutylaluminum), all other conditions being the same, the activity of the catalyst markedly decreases [51]. To achieve reasonable conversions, the polymerisation with the catalyst NdCl3•3TBP-iC8H17MgC4H9 was conducted for several days (compound i-C8H17MgC4H9 is catalytically inactive under these conditions). For this catalyst, the yield of the polymer depends on the ratio between the starting components with a sharply pronounced maximum at Mg/Nd = 12/13, which is not characteristic of the lanthanide systems.
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Polymer Yearbook The fact that the replacement of trialkylaluminum by dialkylmagnesium in the cisregulating halide-containing catalyst NdCl3⋅3TBP-AlR3 leads to the inversion of the stereospecificity was also unexpected. At Mg/Nd =12/13, a highly stereoregular transpolybutadiene is formed. This polymer contains 95% of trans-1,4-units and 5% of 1,2units at a maximum activity of the catalyst NdCl3⋅3TBP-i-C8H17MgC4H9. As the Mg/Nd ratio increases and goes beyond this range, not only does the yield of polydiene drop but its microstructure also changes: the share of 1,2-units increases and, when toluene is used as a solvent, cis-1,4-units appear in the polymer. Therefore, polybutadiene of mixed structure is formed at Mg/Nd = 60 in this solvent (the amounts of cis-1,4-, trans-1,4-, and 1,2-units are 47, 44 and 9%, respectively). Although the inversion of stereospecificity of the ion-coordination system under the action of the organometallic compound is not quite common, nevertheless, in our opinion, it is consistent with the regularities conventional for the lanthanide systems. The trans-regulating effect of the halide-containing system is apparently associated with the formation of a catalytically active halide-free alkyl derivative of neodymium of LnR3 type. The reaction is between the starting components of the catalyst and it is known that RLnCl2 initiates the cis-polymerisation of dienes, whereas R2LnCl is catalytically inactive [28]. Complete replacement of chloride ions by hydrocarbon radicals in the reaction of f-metal chloride with organomagnesium compound was reported [52, 53]. This assumption is also supported by the fact that the microstructures of polybutadienes formed with the LnR3 [30, 33, 36] and NdCl3⋅3TBP-i-C8H17MgC4H9 catalysts are similar.
3.3.4 The Nature of the Solvent In all cases, the rate of process is higher in aliphatic than in aromatic hydrocarbons. The data for n-heptane and toluene show that in these solvents, propagation rates are different, Table 3.1. A similar effect was observed earlier [28] for polymerisation of isoprene in nhexane [Kp = 730 l/(mol min)] and in toluene [Kp = 240 l/(mol min)] at 25 °C on the catalytic system (C6H5)3CNdCl2•THF-Al(i-C4H9)3. The reduction in the propagation rate constant under the effect of aromatic hydrocarbon is due to hydrocarbon and diene monomer competing for coordination at the active centre. The effect of slowing down the polymerisation reaction is due to the fact that aromatic hydrocarbon forms an arene complex with the lanthanide atom. The higher the π-electron-donating ability of the aromatic hydrocarbon, the lower the rate constant for polydiene chain propagation. Thus, the rate of polymerisation of dienes decreases in the series benzene > 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
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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.
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Diene Polymerisation Mechanism with Lanthanide Catalytic Systems
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
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Diene Polymerisation Mechanism with Lanthanide Catalytic Systems
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.
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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 βR´C αHR-antiCH2CγHCβR´CαHR-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: CH2HCγHCβR´CαHR-CH2CγHCβR´CαHR-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
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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.
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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
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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
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Diene Polymerisation Mechanism with Lanthanide Catalytic Systems
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.
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Diene Polymerisation Mechanism with Lanthanide Catalytic Systems
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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
102
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
103
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
104
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
105
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:
106
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 << ϕs in the stage of micrograin propagation. At the end of the monolithisation stage, when ϕv << ϕs, the condition will be the other way round, ϕvs ∼ ϕv. Suppose that the micrograin of PMPh is the mass fractal for which the fractal dimensions of surface and volume are coincident [32, 33]. Then using the probability of contact in the model of the black and white balls (the value of the interface layer should be proportional to the product of black and white concentration) in accordance with [23], we approximate the relationship between ϕvs, ϕv and ϕs, with the use of an approximate function: ϕ vs ≅ Fvs ϕ v ϕ s
(4.2)
where the coefficient of proportionality Fvs depends upon fractal characteristics of micrograins of PMPh in MPPh and microdrops of MPPh in PMPh, their number and thickness of interphase layer. In the approximation where the volume of the interphase layer is small and the relationships ϕvs << ϕv + ϕs, ϕv + ϕs ≅ 1 are fulfilled, Equation (4.3) is obtained instead of Equation (4.2): ϕ vs ≅ Fvs ϕ s (1 − ϕ s )
(4.3)
7. Polymerisation in the polymer-monomeric phase is characterised by two main factors. First, the rate at which it proceeds as a consequence of the gel-effect, where by virtue of the sizeable loss of transmitting and segmental mobility of macroradicals, control changes from the rate of chain termination to the rate of it’s propagation. Thus the process of chain propagation and chain termination take place as two different results
108
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion of the interaction of the active radical Rs with the functional groups of the monomer. This leads to the formation of active radicals which are able to propagate the chain or frozen radicals, in accordance with the terminology [24, 25] of the so-called selfburial radicals, i.e., inactive radical Rz (linear chain termination). This can be represented by the scheme: (4.4) From the stationary state condition applied to the active radicals Rs it follows that the specific rate of polymerisation in PMPh is equal to:
(
)
w s = kps / kts vis
(4.5)
where vis is a specific rate of initiation in PMPh, and kps/kts s is the length of chain. The second condition that the polymerisation proceeding in PMPh the new polymeric phase, i.e., polymer with the limited conversion near 1, cannot be allocated an independent phase, since a great viscosity enhancement of PMPh takes place. That is why polymerisation inside of the micrograins of PMPh can be considered to lead to the glass transition process, where reduction of reactive volume of PMPh occurs. The glass transition process of micrograins develops non-uniformly with the radius of the micrograin and this is why the summarised rate of polymerisation in PMPh will be characterised by an integral character.
4.3.2 The Kinetic Model 4.3.2.1 Homogeneous System Polymerisation proceeds in a homophase system in accordance with the classic kinetic Scheme (4.1) up to a monomer concentration [M] ≥ [Mv0] or conversion P ≤ Pv0 with a specific rate: 12
−d[ M ] / dt = kpv [ M ]viv
12
/ ktv
(4.6)
where viv is initiation rate. The conversion P in the polymerisation rate is described by the expression: 12
−dP / dt = kpv (1 − P )viv
12
/ ktv
(4.7)
109
Polymer Yearbook The weak gel-effect, which is exhibited in the linear section of the kinetic curve up to the stage of auto acceleration caused by partial diffusion control upon rate of quadratic chain termination. The constant rate ktv of chain termination is represented in following form: ktv = 1 / kc + 1 / kd
(4.8)
where kc and kd are constant rates of termination, controlled by radical interaction and diffusion delivering them to the point of interaction accordingly. Viscosity, ηv, of MPPh is described by the linear function in the interval 0 ≤ P ≤ Pv0: ⎛ η0 − η ηv = η0 ⎜1 + v 0 0 η0Pv ⎝
⎞ P⎟ ⎠
(4.9)
where η0 and ηv0 are viscosities of pure monomer in the block- and monomer-polymeric solution, respectively, at P = Pv0. Accepting kd as the inversely proportional viscosity of solution (kdη = const), the equation can be rewritten as: 1 ⎛ η0 − η = ⎜1 + v 0 0 kd ⎝ η0Pv
⎞ P⎟ / kd0 ⎠
(4.10)
where kd0 is a constant rate of radical diffusion in the monomer. By combining Equations (4.8) and (4.10), we obtain: 0 1 / ktv = (1 + aP ) / ktv
(4.11)
0 1 / ktv = 1 / kc + 1 / kd0
(4.12)
where:
(
)
0 a = ktv η0v − η0 / kd0 η0Pv0
(4.13)
Thus, ktv0 is a rate constant of chain termination in pure monomer (P = 0). On substitution of (4.11) into (4.7), the rate of polymerisation in MPPh at P ≤ Pv0 will be described by the equation: ⎛ 0 1 2⎞ dP / dt = kpv / ktv (1 − P)(1 + aP)1 2 viv1 2 ⎝ ⎠
110
(4.14)
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion
4.3.2.2 Microheterogeneous System As the P ≥ Pv0 polymerisation proceeds in the three reactionary zones, it’s rate is described by the sum: −d[ M ] / dt = w v ϕ v + w vs ϕ vs + w s ϕ s
(4.15)
where wv and wvs are specific rates of the process in a saturated monomer-polymeric solution and interphase layer on the boundary of MPPh and PMPh, respectively, and <ws> is average specific rate of polymerisation in PMPh per volume of micrograins. Instead of Equation (4.15) we can write: dP / dt = w v ϕ v /[ M0 ] + w vs ϕ vs /[ M0 ] + w s ϕ s /[ M0 ]
(4.16)
The contribution (dP/dt)v = wvϕv / [M0] of the polymerisation process proceeding in MPPh into total rate is described by the same Equation (4.14), but at the constant value P = Pv0 and variable ϕv = 1 – ϕs:
(dP / dt )v = ⎛⎝ kpv / ktv0
1 − P )(1 + aP ) ⎠(
1 2⎞
0 v
0 v
12
(1 − ϕ s )viv1 2
(4.17)
Specific rate of polymerisation in the interphase layer is described by the classic Equation (4.6), but with the constant rate of termination ktvs, in which the contribution of diffusion control has been considerably increased, Equation (4.18) is obtained:
(
12
w vs = −d[ M ] / dt = kpv / ktvs
)[ M
12 vs ]vivs
(4.18)
The ktvs = constant until the moment that the phases coexist. Accepting the fact that the concentration of monomer [Mvs] is proportional to [Mv0]([Mvs] = km[Mv0]), at an interface and taking that into account and that the initiation rate vivs is proportional to viv (vivs = kvviv), we can describe the contribution of polymerisation rates at an interface (dP/dt)vs = wvsϕvs/ [M0] by total kinetics which takes into account Equation (4.3), giving the next expression:
(dP / dt )vs = k2 (1 − Pv0 )ϕ s (1 − ϕ s )viv1 2
(4.19)
where:
(
12
k2 = kp / ktvs
)F k k
vs m v
(4.20)
k2 is an effective constant rate of polymerisation in the interphase layer.
111
Polymer Yearbook Summarising Equations (4.17) and (4.19), namely (dP/dt)v + (dP/dt)vs = (dP/dt)v+vs is obtained: (dP/dt)v+vs = k1(1 – Pv0)[(1 + aPv0)1/2 + k2js/k1](1 – js)viv1/2
(4.21)
where: 12
0 k1 = kp / ktv
(4.22)
The magnitude (dP/dt)v+vs determines the rate of new PMPh selection from MPPh. Let us determine the connection between them. In the moments of time t and t + dt, the monomer quantity in MPPh is equal to [Mv0](1–ϕs) and [Mv0](1–ϕs–dϕs), respectively. Monomer quantity passed into PMPh for time dt equal to [M s0]dϕs . At the expense of copolymerisation into the MPPh and interface layer, d[M]v+vs has been reacted. From the balance follows:
([ ] [ ])
−d[ M ]v + vs = Mv0 − Ms0 dϕ s
Thus, we have:
(dP / dt )v + vs = (Ps0 − Pv0 )dϕ s / dt
(4.23)
Comparing Equations (4.21) and (4.23), let us rewrite the latter to dϕs / dt:
(
⎡ dϕ s 1 − P0 = 0 v 0 k1 ⎢ 1 + aPv0 dt Ps − Pv ⎣
)
12
+
k2 ⎤ ϕ s ⎥(1 − ϕ s )v1iv2 k1 ⎦
(4.24)
In turn, the summarised rate of the process in a microheterogeneous system can be described as:
(
)
[ ]
dP / dt = Ps0 − Pv0 dϕ s / dt + w s ϕ s / M0
(4.25)
Returning to <ws>, which is the average specific rate of polymerisation in volume of micrograins of PMPh. Even though tv0 is the time needed for the achievement of conversion Pv0 in MPPh and for the appearance of PMPh nucleus. Let us take this time as an emanating point, assuming that tv0 = 0 is beginning of new phase separation. Let us consider the element dϕs, which was allocated from MPPh in the moment of time t ≥ 0. In this moment the concentration of monomer is equal to [Ms0], and the part 1 – β of glass transition, the 112
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion so-called inactive part of polymer with limited conversion, is equal to zero. At τ ≥ t a part of non-glass transitioned matter is equal to β ≥ 0, at the expense of polymerisation. So, the specific rate of polymerisation in element volume dϕs, separating in a moment of time t, is equal to: −d[ M ]s / dτ = w sβ
(4.26)
where β is a function τ – t and a specific rate ws of the process. In this case, in a moment of time t removing the unit volume of PMPh – β = 1, and the amount of a monomer is equal to its concentration [Ms0]. In a moment of time τ > 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
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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, –<(dc/dt) 1/2> = (γεc0J0)1/2, – = γεc0J0, and at the large optical density: εc0l >> 1, –<(dc/dt)1/2> = (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 << 1 in our experiments is not rigorous enough. That is why, by taking into account, that l is small and varies in a narrow range accordingly to the previous analysis, let us use the average approximations instead of the strict Equations (4.54) and (4.55): − (dc / dt )
12
= ( γJ0 )
12
− dc / dt = γJ0 (εc0 )
2m
(εc0 )m
(4.56) (4.57)
where 0 < m < 1/2. Introducing the further factors of fv and fs, we will obtain the next equation for the homogeneous polymerising system at P ≤ Pv0: v1iv2 = ( γ v J0 )
12
118
(εc0 )m
(4.58)
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion For the microheterogeneous polymerising system at P >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<< k2 , when the polymerisation rate at an interface takes the main share into (dϕs/dτ)max. The maximum of this polymerisation rate is determined by the function ϕs(1–ϕs). 121
Polymer Yearbook (a)
(b)
Figure 4.3 The dependence calculated via Equation (4.62) and at various concentrations of the photoinitiator (% by mass) in microheterogeneous system: 1: 0.5%, 2: 1.5%, 3: 3%, E0 = 37.4 W/m2, T = 283 K
Under the same condition, k1<< k2 , but at the non-equilibrium photoinitiator distribution (L < 1), the maximum rate of polymerisation in the interphase layer according to the function ϕs(1–ϕs)β, where β = 1 – mα, is achieved at the value ϕs(max) = 1 / (1 + β), i.e., at ϕs(max) = 0.555. The lower value ϕs(max) = 0.525 in numerical calculations indicates, that the condition k1<< k2 (where k1 is 25 times lower than k2 ) is not completely fulfilled and takes a small share into a value (dϕs/dτ)max. But at the same time this share is noticeable in the process of polymerisation in liquid MPPh.
122
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion In Figure 4.4 are compared: the calculated summarised rate dP/dτ (4.63) and its constituents, namely: (dP/dτ)v+vs = (Ps0–Pv0)dϕs/dτ which is the summarised rate of polymerisation in MPPh and the interphase layer on the boundary of MPPh and PMPh, and also (dP / dτ)s = k3 J 0 (c0 L)2m U(τ) which is the polymerisation rate in PMPh.
(a)
(b)
(c) Figure 4.4 Calculated dependence via Equations (4.62) and (4.63) and also the summary polymerisation rate, dP/dt in the microheterogeneous system (curve 3) and it components, namely: (dP/dt)s is polymerisation rate in volume of PMPh (curve 1), (dP/dt)v+vs is polymerisation rate in volume of MPPh and interphase layer on the boundary of a MPPh and PMPh (curve 2). Variants a), b) and c) correspond to variants presented in the Table in Figure 4.2.
123
Polymer Yearbook The maximum values (dP/dτ)v+vs are observed at the same times as dϕs/dτ; the maximum values (dP/dτ)s are observed at later times. The summarised rate of the process dP/dτ at small t from the PMPh extraction at the beginning is completely determined by (dP/dτ)v+vs, and at the great τ, i.e., on the finished stage of polymerisation process, by rate (dP/dτ)s of polymerisation in PMPh. An extreme of the summarised rate dP/dτ of polymerisation via time is located between extremes (dP/dτ)v+vs and (dP/dτ)s, but is considerably near to an extreme (dP/dτ)v+vs. In another case, the main share (up to 70%) into the maximum value dP/dτ brings the (dP/dτ)v+vs. However, by increasing the photoinitiator concentration this share decreased slowly, and the share (dP/dτ)s is increased. When the extreme dP/dτ slightly shifted relative to the extreme dϕs/dτ, the values ϕs0>ϕs(max) correspond to maximum values of dP/dτ. The calculated data give a value ϕs0 = 0.625. Thus, the conversion P0, corresponding to the maximal rate of polymerisation is determined in our case by the equation P0 ≈ Pv0(1– 0.625) + P 0s 0.625, where P 0s is the average value of conversion into PMPh in the moment of time corresponding to the maximum dP/dτ. Dependence of calculated values P s accordingly to Equation (4.68) upon time at various photoinitiator concentrations are represented in Figure 4.5. The values P 0s corresponding to the maximal rates of the summarised process, are very slightly increased (from 0.85 up to 0.87) with the photoinitiator concentration increasing. From this follows, that the magnitudes P0 should be also increased with the photoinitiator concentration increasing from ≈ 0.72 at c0 = 0.5% (by mass) up to 0.74 at c0 = 3% (by mass). The experimental data don’t allow observation of this weak effect. Nevertheless, the first order upon the photoinitiator takes into account the gradient of illumination reducing until 2m = 0.8, the rate (dP/dτ)s is increased 2.7 times when the photoinitiator concentration is increased 6 times (see Figure 4.4). It is connected to the fact, that the comultiplicant before the integral U(τ) is increased with the photoinitiator concentration increasing in the rate expression (dP/dτ) s for polymerisation in PMPh, but the integral U(τ) is decreased. Behaviour of the integral V(τ) is the similar. Their behaviour via time at the different photoinitiator’s concentrations is shown in the Figure 4.6. Two extreme cases are possible depending upon the ratio of the rates in PMPh and MPPh and the interphase layer. If the PMPh separation rate is considerably faster than the polymerisation rates in PMPh, we would obtain the average conversion into PMPh equal to (Ps ≅ Ps0 ) practically up to the value ϕs ≅ 1. This conversion is equal to the PMPh separation rate. The kinetic curve of the process should be characterised by a long slow ‘tail’ at the polymerisation in PMPh at ϕs ≅ 1. Conversely, if the rate of polymerisation into PMPh is considerable higher, than the rate of PMPh separation, then the average conversion into PMPh will be equal to Ps ≅ 1. In this case the polymerisation process is simultaneously finished in all reactionary zones in accordance
124
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion
Figure 4.5 Average conversion into PMPh, calculated dependence from Equation (4.68) at the different concentration of the photoinitiator c0 (% mass): 1:0.5%, 2:1.5%, 3:3.0% (E0 = 37.4 W/m2, T = 283 K).
(a)
(b)
Figure 4.6 Calculated in accordance with the Equations (4.64) and (4.70), behaviour of integrals U(τ) and V(τ) via time at the different concentration of the photoinitiator c0 (% mass): 1:0.5%, 2:1.5%, 3:3.0% (E0 = 37.4 W/m2, T = 283 K).
with the condition ϕs ≅ 1 and P ≅ 1, and the kinetic curve did not have the long slow tail. This variant approximates the kinetics of linear polymerisation up to three-dimensional ones, at which polymer with limiting conversion Ps0 ≅ 1 is selected in solid phase at once.
125
Polymer Yearbook
4.5 Conclusions The main feature of the linear polymerisation is that this chemical process proceeds in a medium, whose properties sharply varied until the transition into a new phase state. We cannot obtain the quantitative kinetic model without using the formalism of diffusion control with a quadratic chain termination rate. The microheterogeneity of the polymerisation system in a case of three-dimensional polymerisation is observed at very low conversions and is not an experimentally proven fact. Theoretically, this fact can be explained both thermodynamically (as a poor coexistence of the network polymer with monomer) and kinetically (by small viscosity of the monomer block, the solubility of polymer in which is small). The observed generality (for example, order increasing upon initiator) are the kinetic features for block polymerisation up to the high degrees of conversions of matrix photopolymerisation [35]. Also for polymerisation in the presence of porous fillers [36] or at adsorption immobilisation on the carrier surface of the polymeric initiator [37], and these indicate that the solid phase creates the special ordered structure of the reaction space, in which the transmitting and segmental mobility of macroradicals are sharply reduced. That is why polymerisation in the ordered reaction space can proceed in accordance with other kinetic regularities, rather than in liquid monomer space. Such idealised conception of two reactionary zones (liquid monomer phase and interphase layer on the boundary ‘liquid monomer-solid polymer’) allowed us to obtain the quantitative kinetic model of stationary and non-stationary processes for threedimensional polymerisation and to explain their special peculiarities [23-25]. The same approach for the three reaction regions, are used in this work for the construction of a kinetic model for stationary linear polymerisation. However, at the linear polymerisation even at conversion Pv0, corresponding to limited solubility of polymer in monomer, the microphase separation of system can not be characterised with so unambiguous character, as in a three-dimensional polymerisation one. Two factors hinder this process, namely: first a large thermodynamic compatibility of linear polymer with monomer and secondly a high viscosity of monomer-polymer solution at conversion Pv0. Therefore, instead of the strict microphaseous distribution we have the glass transition process of polymerising system, i.e., the process of initiation, propagation and confluence of fluctuations both of density and structure, which is conditional on the microvolumes of the polymer-monomer phase. Since the fluctuation microvolumes associated with higher structural ordering than the ‘liquid monomer-polymeric phase’, they and their diffusion part (so-called interphase layer) are reaction spaces with other kinetics of polymerisation, than in a liquid monomer-polymer solution. Despite of the formality and idealism of this concept, it allows one to obtain the kinetic model of the linear polymerisation process quantitatively corresponding to all the sets of experimental data.
126
Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion
References 1.
A.A. Berlin, G.V. Korolev and T. Ya. Kefeli, Acrylic Oligomers and Materials, Chimiya, Moscow, Russia, 1983. [In Russian]
2.
D.L. Kurdikar and N.A. Pepas, Polymer, 1994, 35, 1004.
3.
I. Shen, Y. Tian and G. Wang, Macromolecular Chemistry, 1991, 192, 2669.
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A.L. Efimov, A.I. Dyachkov and S.I. Kuchanov, Vysokomolekulyarnye Soedineniya Seriya B, 1982, 24, 83.
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A.I. Dyachkov, A.L. Efimov and L.I. Efimov, Vysokomolekulyarnye Soedineniya Seriya A, 1983, 25, 2176.
6.
S. Zhu, Y. Tian and A. Hamilies, Macromolecules, 1990, 23, 1144.
7.
A.L. Efimov, T.A. Bugrova and A.I. Dyachkov, Vysokomolekulyarnye Soedineniya Seriya A, 1990, 32, 2296.
8.
D. Doetschman and R. Mechlenbacher, Macromolecules, 1996, 1807.
9.
E.B. Broon, V.A. Ivanov and V.A. Kaminskyj, The Reports of the USSR Academy of Sciences, 1986, 291, 618.
10. E.B. Broon, V.A. Ivanov and V.A. Kaminskyj, Vysokomolekulyarnye Soedineniya Seriya A, 1992, 34, 40. 11. S.I. Kuchanov and E.S. Povolotskaya, The Reports of the USSR Academy of Sciences, 1976, 227, 1147. 12. G.I. Litvinenko, M.B. Lachinov and E.B. Sarkisova, Vysokomolekulyarnye Soedineniya Seriya A, 1994, 36, 327. 13. T.J. Tulig and M. Tirrell, Macromolecules. 1981, 14, 5, 1501. 14. H. Boots, Journal of Polymer Science, 1982, 20, 1695. 15. D. Kurdikar and N. Peppas Macromolecules, 1994, 27, 4084. 16. C. Bowman and N. Peppas, Macromolecules, 1991, 24, 1914. 17. K. Anseth, C. Bowman and N. Peppas Journal of Polymer Science A: Polymer Chemistry Edition, 1994, 32, 139.
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Polymer Yearbook 18. V. Budtov and B.V. Revnov, Vysokomolekulyarnye Soedineniya Seriya A, 1994, 36, 1061. 19. D.K. Vasylev and I.M. Belgovskyj, Vysokomolekulyarnye Soedineniya Seriya B, 1990, 32, 678. 20. D.K. Vasylev and I.M. Belgovskyj, Vysokomolekulyarnye Soedineniya Seriya A, 1989, 31, 1233. 21. G. Korolev, I. Mogylevich and I. Golikov, Microheterogenous Structures, Physical Networks, Deformation Processes, Chimiya, Moscow, Russia, 1995, 48. [In Russian] 22. M. Volkova, I. Belgovsky and I. Golikov, Vysokomolekulyarnye Soedineniya Seriya A, 1987, 28, 435. 23. Yu. Medvedevskikh, O. Zahladko, A. Turovski and G. Zaikov, International Journal of Polymeric Materials, 1999, 43, 157. 24. O. Zahladko, Yu. Medvedevskikh, A. Turovski and G. Zaikov, International Journal of Polymeric Materials, 1998, 39, 227. 25. Yu. Medvedevskikh, O. Zahladko, A. Turovski and G. Zaikov, Russian Polymer News, 1999, 4, 33. 26. A. Bratus, A. Turovski, Yu. Medvedevskikh, I. Semenyuk and G. Zaikov, International Journal of Polymeric Materials, 2001, 48, 371. 27. L. Pietronero, Physics Review, 1983, B27, 5887. 28. J. Liklema, Kinetically Propagating Self-Avoiding Random Walls: Fractals in Physics, Myr, Moscow, Russia, 1988, 131-137. [In Russian] 29. Yu. Medvedevskikh, O. Zahladko, A. Bratus and A. Turovski, Reports of National Academy of Sciences of the Ukraine, 2000, 10, 148. 30. V. Kolegov, Vysokomolekulyarnye Soedineniya Seriya A, 1995, 37, 16. 31. V. Treushnikov, N. Zelentsova and A. Olejnik, Journal of Scientific & Applied Photography and Cinema, 1988, 33, 146. 32. B. Smirnov, Successes of the Physical Sciences, 1986, 149, 178. 33. D. Shefer and K. Kefer, Structure of Random Silicates: Polymers, Colloids and Solids, Myr, Moscow, Russia, 1988, 62-71.
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Kinetic Model of the Bulk Photopolymerisation of Glycidyl Methacrylate for High Degrees of Conversion 34. B. Borovych, V. Zuev and O. Krohin, Journal of Experimental and Theoretic Physics, 1973, 64, 1184. 35. V. Ivanov, A. Romavyuk and V. Shybanov Vysokomolekulyarnye Soedineniya Seriya A, 1994, 35, 119. 36. S. Minko, I. Luzinov and B. Smirnov, Vysokomolekulyarnye Soedineniya Seriya A, 1990, 32, 750. 37. S. Minko, A. Sydorenko and S. Voronov, Vysokomolekulyarnye Soedineniya Seriya A, 1995, 3, 1403.
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130
5
Influence of Ultrasound on the Channels of the Forming Head in Extrusion Processes A.K. Panov, O.F. Kiseleva, A.A. Panov, K.S. Minsker and G.E. Zaikov
Introduction The increasing volume of polymer production in the chemical industry and the wide range of items being manufactured require an increase in the capability for the production and quality of the products produced. It has been established that an underlying problem is the distortions introduced as the melted polymer flows through the extrusion channels. Analysis of the extrusion heads, has allowed identification of certain parameters which can positively be controlled to improved performance; reduction of the pressure required leading to a decrease in cost, increase of output of the flow, increase in the hardness of extrudate and decrease the post-extrusion swelling. The percussive effect of high intensity vibrations generated in an extruded polymer melt can be influenced by ultrasonic oscillations. The periodic shift in the pressure generated by the action of the screw affects the processed material and the energy transferred to the material is dissipated as elastic vibrations. By analysing the construction of the extrusion head and exploring the effects of the addition of ultrasound, it is possible to make the following recommendations: • Enhancement of the efficiency and quality of production of the extrudate can be achieved by application of ultrasound. • For selected irradiation, using magnetostriction transducers, which are preferable to piezo-ceramics, is effective in changing processing parameters. • Among the magnetostrictive transducers it is more expedient to use those, which in their construction allows them to be used inside the extrusion head. The installation of transducers in the body of the forming tool, reduces the impact of the ultrasonic oscillations on the polymer. • The ability to cool the ultrasonic transducer is necessary to maintain its operation at high temperatures.
131
Polymer Yearbook • The number of industrial acoustic heads is now rather limited in comparison with the availability of forming tools working without the ultrasonic affect, despite the significant enhancement of performance. The existing construction allows application of the ultrasonic effect to the production of film, sheets and tube structures, whereas the demand for high-quality profile items is increasing for other sections. It is possible to draw the conclusion that the development of forming tools for the production of polymeric items in which application of ultrasound is possible is an important new direction for research.
5.1 Construction of an Extrusion Head for Producing Polymers A survey of extrusion heads for fabrication of profiled plastic items and a study of the rheological performance of melts of polymers in channels when ultrasound was used, was carried out [1]. The construction of a many stream extrusion head for the fabrication of continuous extrusion using ultrasonic oscillations has been produced [2]. The design improved the continuous extrusion profile process and increased the output of the extrusion head. This improvement is achieved by using an ultrasonic horn within a many stream extrusion head. The magnetostrictive transducer horn is located in the extrusion channel and is cooled. The channels of the profile section are formed between the profile section and the horn (Figure 5.1). The profile section and the components of the horn are produced separately for supply of high fidelity and control of the inner surfaces. The extrusion heads for fabrication profile – per unit length of polymeric items with the application of ultrasonic oscillation are as follows: The polymer melt created by the auger of the extruder, passes through a homogenisation grating (8) and then goes into a channel. On entering the channel for equalisation of the flow rates, the equalisation of the speed is promoted by a gentle heel tooth notch of the end of the horn of the cross-edged form (5). The melt is injected into the profiling channel (7), formed by the surfaces of the horn (5) and half-cylindrical section (3) and (4). The melt passes on to the forming channels, the melt of polymer is chilled and formed into a continuous profile. To produce a high quality surface (10-12), it is necessary to avoid a discontinuous flow of the melt through the profiling channel. A high quality profile with a polished surface is produced with degradation of the polymer surface as a consequence of the effect of the magnetostrictive transducer. The ultrasonic oscillations reduce the toughness of the polymer and the resistance of the wall affect the melt flow at the channel boundary.
132
Influence of Ultrasound on the Extrusion Processes in Channels of the Forming Head The economic efficiency achieved by the use of the many stream extrusion head for fabrication of a profile of unit length from polymeric materials is that it allows: • An increase in the quality of an item at the expense of the effect of ultrasonic oscillations on the mass of polymer in the forming zone. • To exclude unevenness of an output of the extrudate at the expense of a uncambered location of channels. • To increase extrusion output.
(a)
(b)
1 - body; 2 - socket sleeve; 3, 4 - profile section; 5 - horn; 6 - washer; 7 - profiling channel; 8 - a homogenisation grating; 9 - flange; 10 - indoor (interior) cylindrical channels; 11 - choke; 12 - choke; 13 - magnetostrictive transducer; 14 - source of ultrasonic oscillations; 15 - channels for chilling; 16 - choke
Figure 5.1 The many stream extrusion head for the production of a profile of unit length with use of ultrasound (longitudinal (a) and cross-cut (b) cutaway)
133
Polymer Yearbook
5.2 Investigation of the Hydrodynamic Performances of the Extrusion Head Mathematical description of the process of polymer melting in the extrusion channel is complex when ultrasound is used. The description requires firstly, consideration of the mass flow of the polymer, knowledge of the flow characteristics of the melt, the temperature and pressure of extrusion, sizes of the channel and frequency of ultrasonic oscillations. Secondly, coefficient of swelling of the extrudate, effective viscosity of polymer, pressure of melt, and frequency of oscillations. In order to establish the way in which these various factors influence the performance of the extrusion head, studies were conducted on the flow characteristics of the polymer melts. The effects of the extrusion temperature and pressure were also studied together with the influence of the frequency of the ultrasound and construction of the channel; the effectiveness of producing a high elasticity of the spray in the melt and the final properties of the solid produced. The experiments used an industrial extruder ATL-45. The extrusion installation included a forming unit composed of a forming head to produce a square section 45 x 45 mm. Ultrasonic oscillations were produced in the forming head by two standard magnetostrictive transducers: PMC-6-2 ultrasonic USF-1-4 oscillations. For each of four kinds of profile, channels of three lengths 70, 90 and 110 mm were used (see Figure 5.2). The following polymers were studied: cable plastic GOST 5660 and polystyrene GOST 20282. The pressure of the extrusion was increased from 1 to 6 MPa, frequency of ultrasonic oscillations from 18.5 up to 23.5 GHz. The experiments were conducted in a range of temperatures from 413 up to 453 K.
Figure 5.2 Cross sections of polymeric items investigated
134
Influence of Ultrasound on the Extrusion Processes in Channels of the Forming Head
5.2.1 Investigation of Flow Characteristics of Polymer Melts Rheological measurements were carried out using a capillary viscometer and the studies were conducted with and without application of ultrasonic oscillation. The results obtained are shown in Figure 5.3 and indicate the dependence of the effective flow state ϕef on the stress shear. The definition of the toughness depends on the arguments about the influence of the ultrasonic oscillations using the expression:
(
ηω = ηef / 1 + ω 2 Τ 2
)
where ηef = τist / γ is the effective viscosity, γ is the gradient of the rate of shear, ω is the circumferential frequency of the ultrasonic oscillations and T = η/E the delay time (time lag) and E is the modulus of elasticity. It was established, that for all the extrusion modes investigated and for all the polymers studied, the tendency to magnify the flow state of the melt by the ultrasonic oscillation was observed.
Figure 5.3 Effective flow state of melt of polystyrene from shear stress (a) 438 K; 1: without USF; 2: 22.1 GHz; 3: 21.6 GHz (b) 453 K; 1: without USF; 2: 22.1 GHz; 3: 23.5 GHz; 4: 21.6 GHz
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Polymer Yearbook
5.2.2 Account of the Performance of Polymer Melts The ultrasound leads to anomalous hydrodynamic behaviour in the prismatic channels and was explored mathematically using the following structures: a channel with a slothole and a round section. The analysis produced equations describing the motion in the channels and indicated the polymer melt was forming two layers in the channel. An exterior stratum with a reduced viscosity ηw, and the central part of the melt, where the ultrasound does not penetrate, is characterised by effective viscosity, ηef [2]. An expression was obtained indicating the effect of ultrasound on a thick liquid channel of compound formation on the cost: τ0 b ⎫ ⎧τ 1 δ τb ⎪ a ρ S ⎪ (R Ζ − δ ) τ Q= b ⎨ dτ + dτ⎬ , ηef ηω τ0 ⎪ 0 ⎪⎭ τ1 ⎩
∫
∫
where a and b are coefficients of the form of the extrusion channel; ρ is the density of the polymer; τ0 is the mean stress of shear; Rz is the hydraulic radius; S is the floor space of the section of the channel; δ is the depth of penetration of the ultrasound in polymer; τ is the stress of shear; ηef is the effective viscosity; and ηw is the toughness of the melt as a result of the ultrasound. The idealised studies of the hydrodynamic performance on the cost is demonstrated in Figure 5.4.
5.3 Results of a Study on High-Elastic Rating of a Polymer Melt Spray On exiting from the channel in which it is formed, the fluid is constrained in the transverse direction and changes its dimensions and inflates. The swelling depends on the flow characteristics of the polymer, size of the forming channel and modes of deformation of the melt. If ultrasound is used in the formation zone, it is possible to change the flow characteristics and this has the effect of dropping the coefficient of swelling. To confirm this prediction, studies were carried out to establish the significance of the coefficient of clay swelling for these polymers. The outflow through the channels of a compound section were investigated:
Κ = Β⋅ a
136
m1
⋅b
m2
⋅ ( γ˙ ⋅ θ)
n1
⎛η ⎞ ⋅⎜ ω ⎟ ⎝ ρ θ⎠
n2
⎛ L ⎞ ⋅⎜ ⎟ ⎝ Sκ ⎠
n3
,
Influence of Ultrasound on the Extrusion Processes in Channels of the Forming Head
Figure 5.4 Dependence of the cost of polystyrene melt from pressure drop at the temperature of 438 K (a) section of an item (b) section of an item -
;
; 1: without USF; 2: 22.1 GHz; 3: 21.6 GHz
where the coefficient Κ depends on the kind of material and m1, m2, n1, n2, n3 are the indicies of the exponents; θ is the argument describing highly elastic properties of the polymer; ρ is the pressure of the melt; ηω is the toughness of the melt affecting by the ultrasound; L, Sκ are the length and section of the channel. From the equation it is seen, that the ultrasonic oscillations have the effect on the extrudate through the ηω coefficient. To check the calculations, experiments were performedusing the conditions indicated in Figure 5.5.
5.4 Rating of Solid Properties of the Polymeric Items As far as the service properties are concerned the data obtained by measuring the expansive effects of extrudates, the melt in the channels, both with and without the influence of ultrasound and without noise (Figure 5.6).
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Polymer Yearbook
Figure 5.5 Dependence of coefficient of swelling on stress for plasticised cable. Section of an item -
. Sκ = 110 mm
(a) At the temperature of 403 K; (b) at the temperature of 423 K; 1: without USF; 2: 18.5 GHz; 3: 20.55 GHz; 4: 22.1 GHz; 5: 21.6 GHz
Figure 5.6 Dependence of explosive effort of extrudate from pressure for plasticised cable. Section of an item . Sκ = 70 mm (a) temperature - 413 K; (b) temperature – 433 K, 1: without USF; 2: 21.6 GHz; 3: 22.1 GHz; 4: 23.5 GHz
138
Influence of Ultrasound on the Extrusion Processes in Channels of the Forming Head
5.5 Conclusions The studies indicated that: 1. For all the polymers investigated the increase in the flow state of the melt is observed by the use of ultrasonic oscillations. 2. The percussive affect allows an increase in the throughput capacity of the channel and reduces the temperature in the formation zone. The mass flow is increased by 20-30%. 3. The ultrasonic oscillation causes a drop of the coefficient of a swelling of 5-7%. 4. Use of the extrusion head with application of ultrasound allows the hardness of an item to be increased and expand the opportunities to use new kinds of polymeric items with complex configurations.
References 1.
A.H. Panov, O.F. Kiseleva and N.S. Shulaev, inventors; N.S. Shulaev, assignee; RU 2147989C1, 2000.
2.
A.H. Panov and A.R. Anasov, Hydrodynamics of Anomalous Streams - Tenacity of Polymeric Systems in Forming Channels, UGNTU, Bashkortostan, Russia, 1994, 260.
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Polymer Yearbook
140
6
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain O. Mukbaniani, S. Meladze, G. Zaikov and L. Khananashvili
6.1 Introduction Organodichlorosiloxyorgano-cyclotri(tetra-penta)siloxanes have been prepared by heterofunctional condensation of hydroxyorganocyclotri(tetra-penta)-siloxanes with organotrichlorosilanes in the presence of amines. The hydrosilylation of methylvinyltetraphenyltrisiloxane with methyldichlorosilane in the presence of platinum chlorohydric acid leads to dichloroorganosilacarbocyclotrisiloxane. The composition and structure of difunctional organocyclosiloxanes was determined by elementary and functional analysis, molecular mass determination, IR, NMR (1H, 13C) and mass spectral data. The heterofunctional condensation of dichlororganosiloxycyclotri(tetra-penta)siloxanes and dichlororganosililcarbocyclotrisiloxane with dihydroxydimethylsiloxanes in the presence of pyridine has been investigated. It was shown that for short lengths of the linear dimethylsiloxane link (n ≤ 4), the reaction of heterofunctional condensation proceeds both intermolecularly with formation of copolymers and intramolecularly with formation of bicycloorganosiloxanes. The catalysed reaction of the dehydrocondensation of α,ω-bis(trimethylsiloxy) ethylhydridsiloxanes with hydroxyorganocyclosiloxanes in the presence of an alkaline metal catalyst has been investigated and organosiloxane copolymers with various amounts of cyclic fragments in the side chain has been obtained. Dehydrocondensation reaction order, rate constants and activation energy were measured. Organosiloxane copolymers with cyclic fragments in the side chain have been obtained by hydride addition of α,ω-bis(trimethylsiloxy)methylhydridsiloxane to vinylorganocyclosiloxanes in the presence of platinum chlorohydric acid. Hydrosilylation reaction order, rate constants and activation energy were determined. It was established, that the insertion of cyclic fragments in the side chain hinders the chain transfer reactions that proceed with release of the Dn-type cycles during thermal depolymerisation. The conformational and hydrodynamic properties of some polymethylsiloxanes with organocyclosiloxane fragment as pendant groups have been studied.
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Polymer Yearbook Before our investigations [1, 2] there was no information in the literature about branched dimethylsiloxane copolymers containing diorganocyclosiloxane fragments, instead of the linear dimethylsiloxane links [3]. From the literature [4] it is known that the main difference between oligo(dimethyl)methylsiloxanes with branched structure and the equal viscosity linear oligodimethylsiloxanes, is the absence of a tendency to crystallise above a definite branching content of methylsilsesquioxane links. The main reason for the suppression of the crystallisation in oligo(dimethyl)methylsiloxanes is the break of regular structure of the linear siloxane chain by the insertion of methylsilsesquioxane links. The most effective method of modification of linear organosilicon polymers is the insertion of various elements or groups with a different chemical nature into the structure of the macromolecular chain. As a result of the insertion in the dimethylsiloxane chain of different fragments there are changes in the physical chemical properties [5]. The insertion of the cyclic fragments in the main linear dimethylsiloxane chain hinder the chain transfer reactions, which proceed with the release of Dn-type (where D = Me2SiO) cycles during the thermal depolymerisation, that raises the thermal-oxidative stability of the polymers [6]. The main reason for the investigation was to create convenient methods for the synthesis of organosiloxane copolymers with monocyclosiloxane fragments in the side chain. To establish the influence of the cyclic fragment on the properties of copolymers the initial difunctional organodichlorosiloxyorganocyclosiloxanes and a new class of cyclolinear copolymers, with monocyclic fragments in the side chain were synthesised.
6.2 Experimental The organic solvents were purified by drying and distillation. The initial organodichlorosiloxyorganocyclosiloxanes and organodichlorosililcarbosiloxanes were synthesised using well-known methods [7]. The α,ω-dihydroxydimethylsiloxanes were synthesised by hydrolysis of corresponding α,ω-dichlorodimethylsiloxanes. Hydroxyorganocyclosiloxanes were obtained by known methods [7]. The IR spectra of all the samples were taken on an IR-20 spectrophotometer, while the NMR spectra on a Perkin-Elmer R-32 instrument at an operating frequency of 90 MHz in a solution of CCl4 and dioxane with an internal standard of hexamethydisiloxane or tetramethylsilane and on a JNOL-FX-100 spectrometer in a solution of deuterium chloroform, the line of which was used as a reference. 29Si NMR spectra were taken on an WP-200 SY (Bruker) instrument at an operating frequency of 29Si –39.77 MHz. Molecular masses of monomer type organocyclosiloxanes were determined by ebulliometric (determination of molecular masses) and mass spectrometry methods. Molecular weight distribution analysis was carried by gel permeation chromatography (GPC) on a KhZh - 1302 instrument (USSR). The determination of the average molecular weights was carried out on an Wescan osmometer (USA) in toluene solution at the 320 K.
142
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain The fractionation of copolymers was carried out by two methods: (1) by raising the temperature, and (2) by dropping the temperature. The viscosities of copolymers were investigated in toluene solutions at the 25 °C. The purity of the obtained organodichlorosiloxycyclosiloxanes and bicycloorganosiloxanes was verified by gas-liquid chromatography (GLC), using a Chromatron NAW, with a Chromasorb column (2 m), coated with LKh - 8 MD phase SKTF - 100 (10%) and helium as carrier gas. The X-ray curves were obtained on a DRON-2 instrument (USSR), A-CuKα, were measured without a filter the angular velocity of the motor w ≈ 2 °C/min. Thermomechanical curves were obtained on a custom made installation at a heating rate of V ≈ 5 °C/min and stress δ ≈ 0.1 kg/cm2. Thermogravimetric investigations were carried out on a Paulic-Paulic-Erdey derivatograph, model MOM-102. The test conditions were: temperature rise rate v ≈ 5 °C/min, in the open area.
6.2.1 Results and Discussion 6.2.1.1 Dichloro Containing Organocyclosiloxane Monomers Synthesis of organocyclosiloxanes with a known arrangement of functional groups at the silicon atoms may be realised by two ways: (1) by construction of a cyclosiloxane skeleton, and (2) modification of functional groups containing organocyclosiloxanes. The construction of an organocyclosiloxane skeleton with a known arrangement of functional groups may be easily achieved by heterofunctional condensation (HFC) of dihydroxydiorganosilanes and dihydroxydiorganosiloxanes with organochlorosilanes and organochlorosiloxanes in the presence of acceptor-amines [8, 9]. The hydrolytic cocondensation of dichlorocontaining organosilanes proceeds with the formation of organocyclosiloxanes, with statistical arrangement of functional groups; the yield of organocyclosiloxanes is lower. For the purpose of synthesis of organocyclosiloxanes with dichloroorganosiloxy functional groups at silicon the reaction of HFC of hydroxyorganocyclotri(tetra, penta)siloxanes with organotrichlorosilanes in the presence of amines was investigated. During HFC of hydroxyorganocyclosiloxanes with trimethylchlorosilane in the presence of amines it was proved that the reaction also proceeds by homofunctional condensation with formation of a bicyclic structure [10].
143
Polymer Yearbook For increase of the yield of chloroorganosiloxyorganocyclosiloxanes and to decrease the byproducts the HFC was carried out (with an excess of organochlorosilanes) at 1:2 ratio of the initial compounds, in a 10% anhydrous solution of toluene (in case of 1-hydroxy-1-organotetraphenylcyclotrisiloxanes and 1-hydroxy-1-organohexaphenylcyclotetrasiloxanes) or anhydrous ether (in case of hydroxymethylcyclosiloxanes), in the presence of pyridine in the temperature range –5 to –10 °C. However under these conditions of the reaction, HFC proceeds with formation of by-products, according to the following scheme [2, 7]:
Scheme 6.1 Where for the structure I and III: m=2, R=Ph, R′=Me(I, II); R=R′=Ph (III, IV); m=3, R=Ph, R′=Me (V, VI); m=3, R=R′=Me (VII, VIII); m=4, R=R´=Me (IX, X), R=Me, R´=Ph (XI, XII).
The reaction using Scheme 6.1 proceeds in several directions and in addition to the organochlorosiloxycyclosiloxanes with the structure I, the bis(cyclosiloxy) organochlorosilane with the structure III are obtained. By GLC it was established that in addition to compounds with structure III there were present about 3-5% of bis(organocyclosila)oxides with structure II. The synthesised siliconorganic compounds were investigated using by functional and elementary analysis, molecular mass determination, IR and NMR spectra data [7]. Yields and some physical-chemical properties of synthesised organocyclosiloxanes are presented in Table 6.1.
144
Yield, %
Tboil, °C (P; Pa) Tmel, °C nD25
d425 Formula C H Cl Si
Elementary composition, %* M RD M
I
66
230-232 626 57.92 3.76 10.15 16.82 95-96 _ _ C31H28Cl2Si4O4 _ (535) 647 57.50 10.97 17.31 4.32 315-317 1100 63.47 4.13 3.10 17.13 182-183 _ _ C61H53ClSi7O8 II 23 _ (535) 1144 63.98 4.63 16.91 2.73 268-270 60.93 4.23 15. 82 9.25 690 120-121 _ _ C36H30Cl2Si4O4 III 77 _ (345) 60.41 10.01 15.79 3.85 709 1250 64.32 4.02 15.95 2.14 338-340 IV 17 _ 190-191 _ _ C66H55ClSi7O8 1206 65.64 4.56 2.94 16.25 (345) 252-254 820 60.84 4.65 7.51 16.07 141-142 _ _ C43H38Cl2Si5O5 V 79 _ (175) 845 61.06 4.50 16.56 8.40 315-317 1510 65.45 4.92 1.98 16.88 145-147 _ _ C85H73ClSi9O10 VI 7 _ (175) 1540 66.21 4.74 2.30 15.36 54-55 22.98 5.88 16.94 34.06 93.2 410 VII 85 _ 1.4061 1.0826 C8H24Cl2Si5O5 (175) 23.36 17.27 33.83 5.84 93.4 411 26.43 6.51 5.02 93-95 37.28 157.6 671 VIII 6 _ 1.4079 1.0516 C15H45ClSi9O10 26.76 6.69 37.47 157.4 5.28 (175) 672 70-71 24.61 6.03 14.28 34.13 111.8 484 _ 1.4058 1.0643 C10H30Cl2Si6O6 IX 86 (345) 24.74 6.18 14.64 34.64 112.3 485 115-118 27.62 6.83 37.40 3.60 X 8 _ 1.4128 _ _ _ C19H57ClSi11O12 (345) 27.78 6.95 4.32 37.53 104-106 32.74 5.63 12.60 30.48 132.3 546 XI 82 _ 1.4444 1.0990 C15H32Cl2Si6O6 (345) 32.91 5.83 12.98 30.71 132.1 547 113-114 32.63 6.31 3.80 34.62 _ 1.4594 _ C24H59ClSi11O12 XII 10 _ _ (345) 32.40 6.68 34.90 4.02 85 224-228 148-149 _ _ C28H3OCl2Si4O3 57.09 4.91 11.16 18.98 1194 XIII _ (345) 56.28 11.89 18.76 5.03 1217 *In numerator: experimental values, in denominator: calculated values Molecular masses were found by ebuliometric and mass spectrometric methods. d425: specific density (g/cm3 at 25 °C); Tmel: melting temperature; nD25: refraction index of individual compounds for sodium D-line at 25 °C; M: molecular mass; P: pressure; MRD: molecular refraction from Lorentz-Lorentz formula
N
Table 6.1 Physical-chemical properties of organocyclosiloxanes
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
145
Polymer Yearbook In the 1H NMR spectra of compound I (Figure 6.1) and V one can observe a singlet signal with chemical shift δ ≈ 0.57 ppm and δ ≈ 0.58 ppm, respectively, and a multiplicity of signals in the range δ ≈ 7.1–7.7 ppm. In the 1H NMR spectra of compound II one can see the singlet signal of the methyl groups with chemical shift δ ≈ 0.54 ppm and a multiplicity of signals for the phenyl groups in the range δ ≈ 7.0–7.7 ppm. 1H NMR spectra of compound VII contain a singlet signal for the methyl groups of the silsesquioxane atom of silicon with chemical shift δ ≈ 0.20 ppm and a singlet signal for the protons of methyl groups in a linear fragment with a chemical shift δ ≈ 0.80 ppm (3H). One can also see the broadened signals for two pairs of enantiotopic methyl groups, distinguished from each other in space disposition with reference to the cyclosiloxane fragment with a chemical shift δ ≈ 0.11∼0.13 ppm and for methyl groups (this group does not exchange) at δ ≈ 0.16 ppm (Figure 6.2). The 1H and 13C NMR spectra of organodichlorosiloxymethylcyclotetra(penta)siloxanes were studied at room temperature. The NMR spectra of cyclic part in methylcyclosiloxanes have been studied previously [11]. In 1H NMR spectra of compound VII (see Table 6.2) it was observed that there are two pairs of enantiotopic methyl groups Me4a, Me8a and Me4b, Me8b distinguished from each other in spatial disposition by the substitution of methylsiloxy groups. For Me6a and Me6b group (this group does not exchange in symmetric operations), which leads to appearance of spin-spin interaction between protons of heminal methyl groups (4JHCSiCH
Figure 6.1 1H NMR spectra of compound I
146
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.2 1H NMR spectra of compound VII
Structure of compounds VII and XI
Table 6.2 1H NMR chemical shifts of methyl groups in organodichlorosiloxymethylcyclosiloxanes (δ ppm) M e2
Me4a,8a
Me4b,8b
6a
6b
R
0.20
0.13
0.16
0.11
0.13
0.80
M e2
4a,10a
4b,10b
6a,8a
6b,8b
IX
0.21
0.11
0.16
0.11
0.13
0.79
XI
0.40
0.25
0.29
0.25
0.27
-
No.
Position of groups
VII Position of groups
R: methyl or phenyl group substituted in VII, IX or XI
147
Polymer Yearbook ≈ 0.4 Hz) [12]. So that in the 1H NMR spectra of a cyclic part of the compound it is necessary to expect the appearance of a singlet signal corresponding to protons Me2 and four quartet signals of protons Me4a,8a, Me4b,8b, Me6a and Me6b. But it should be noted that the appearance of quartet signals for the methyl protons is only possible on a spectrometer operating at more than 200 MHz. During measurement of the spectra on a spectrometer of comparatively lower resonance frequency, there is an overlap of the resonance lines. This results in splitting of a spin-spin interaction of protons of heminal methyl groups which can only be judged by the observed broadening of the absorption lines, however it is possible to reliably pick out the signal of protons of Me2 groups in which the broadening is not exhibited. The resonance signals of other methyl groups are characterised by integral intensities of 2:3:1. In the 13C NMR spectra of methyldichlorosiloxymethylcyclosiloxanes (Table 6.3 and Figure 6.3 and 6.4) it is easy to identify the absorption lines of Me2 carbon nucleus. The resonance signals of other methyl groups of a cyclic part of the compound VII are represented as two groups of lines with a ratio of integral intensity of 2:4. For the synthesised chloroorganosiloxymethylcyclosiloxane materials mass spectrometry investigation have been carried out. Mass spectra of the compounds points to the presence in the molecules of fragments, correspondingly determined to distinctive structural elements and does not contradict the suggested structures. By reaction of hydride addition of methyldichlorosilane to 1-vinyl-1methyltetraphenylcyclo-trisiloxane in a 1:1 ratio of the initial compounds, in the presence of a catalyst, 0.1 M solution of platinum chlorohydric acid in tetrahydrofuran, in the temperature range 50-60 °C and also in the presence of the catalyst octacarbonyldicobalt
Table 6.3 13C NMR chemical shifts of methyl groups in organodichlorosiloxymethylcyclosiloxanes (δ ppm) Position of groups
M e2
Me4a,8a
Me4b,8b
6a
6b
R
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
No.
VII
-0.09 Position of groups
Me
2
0.60 a
a
0.60 b
0.71 b
a
a
0.71 b
5.98
b
4 ,10
4 ,10
6 ,8
6 ,8
IX
-2.80
0.77
0.68
0.89
0.89
6.00
XI
-2.65
0.77
0.77
0.92
0.92
-
148
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.3 13C NMR spectra of compound VII
Figure 6.4 13C NMR spectra of compound IX
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Polymer Yearbook [CO2(CO)8], in both cases the dichloromethylsililcarbocyclotrisiloxane XIII has been obtained [13, 14]. The reaction proceeds according to Scheme (6.2):
Scheme 6.2
The yields and some physical-chemical properties of synthesised compounds are presented in Table 6.1. In the 1H NMR spectra of compound XIII one can observe a broadened singlet signal (4H) with a chemical shift of δ ≈ 0.77 ppm for the fragment –CH2-CH2-, a singlet signal (3H) with a chemical shift of δ ≈ 0.49 ppm for the –O-SiMe-O- fragment, a singlet signal (3H) of δ ≈ 0.28 ppm for the –SiMeCl2 fragment and a complicated multiplet in the range δ ≈ 6.90-7.60 ppm for phenyl protons (See Figure 6.5).
Figure 6.5 1H NMR spectra of compound XIII
150
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain Consequently it is possible to conclude that hydride addition of methyldichlorosilane to 1-vinyl-1-methyltetraphenyl-cyclotrisiloxane proceeds with formation of a β-adduct. The synthesised difunctional compounds are interesting products for the production of cyclolinear copolymers with cyclic fragments in the side chain.
6.2.1.2 Synthesis of Organosiloxane Copolymers with Monocyclic Fragments in the Side Chain Using HFC there are two possibilities of synthesising organosiloxane copolymers with monocyclic fragments in the side chain. The first one is the reaction of heterofunctional condensation of dichloroorganosiloxyorganocyclosiloxanes with dihydroxydiorganosiloxanes and the second the modification reaction of functional group containing linear organosiloxanes by the insertion of cyclic fragments. From the literature this modification reaction is known for the modification of α,ω− bis(trimethylsiloxy) ethylhydridesiloxane by the reaction of catalytic dehydrocondensation with hydroxyorganocyclosiloxanes, and hydride addition converting α,ω−bis-(trimethylsiloxy) methylhydride-siloxane to vinylorganocyclosiloxanes [12]. In this chapter both methods will be examined.
6.2.1.3 Synthesis of Organosiloxane Copolymers with Monocyclic Fragments in the Side Chain by Heterofunctional Condensation The synthesis of the linear organosiloxane copolymers with the regular arrangement of the cyclosiloxane fragments in the side chain using the reaction of HFC of organodichlorosiloxyorganocyclosiloxanes with α,ω-dihydroxydimethylsiloxanes and dihydroxydimethylsilane in the presence of pyridine as an acceptor of hydrogen chloride was carried out. It is known that the use of such an acceptor leads to an increase of depth of HFC [15, 16]. The reaction was carried out at room temperature, at the completing stage the reaction mixture was heated up to the boiling point of solvent being used. With a small length of linear dimethylsiloxane, the copolymers yield was low. During heterofunctional polycondensation of dichloroorganosiloxydiorganocyclosiloxanes with 1,5-dihydroxyhexamethyltrisiloxane low-molecular weight products were isolated, after polymer reprecipitation from the mother solution. The structure of these products corresponds to a bicyclic compound. Consequently this reaction of HFC proceeds according to Scheme (6.3) [17-23]. The copolymers depending on surrounding groups of the silicon atom are transparent or slightly opalescent substances, soluble in ordinary organic solvents with ηsp ≈ 0.04-0.4. The yield obtained of the copolymers is 72-95%. Some physical-chemical properties,
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Polymer Yearbook
Scheme 6.3 Where: m = 2, R = R´ = R´´ = Ph, A = O: :n = 2(XIV), 3(XV), 4(XVI), 8(XVII), 34(XVIII), 51(XIX); m = 2, R = R´ = Ph, R´´ = Me, A = O: :n = 2(XX), 3(XXI), 4(XXII),8(XXIII), 34(XXIV), 51(XXV); m = 2, R = Ph, R´ = R´´ = Me, A = C2H4: n = 2(XXVI), 4(XXVII), 8(XXVIII), 34(XXIX), 51(XXX); m = 3, R = R´ = Ph, R´´ = Me, A = O: n = 2(XXXI), 4(XXXII), 8(XXXIII), 34(XXXIV), 51(XXXV); m = 3, R = R´ = R´´ = Me, A = O: n = 1(XXXVI), 2(XXVII), 3(XXXVIII); m = 4, R = R´ = R´´ = Me, A = O: n = 1(XXXIX), 2(XL), 3(XLI); m = 4, R = R´ = Me, R ´´ = Ph, A = O: n = 1(XLII), 2(XLIII), 3(XLIV).
elementary analysis and yields of copolymers are listed in Tables 6.4-6.6. The data shown in Tables 6.4-6.6 are for small lengths of the dimethylsiloxane links (n = 2-4), the yield of synthesised copolymers is slightly lower, which may be explained by the fact, that besides the reaction of intermolecular condensation, intramolecular cyclisation with formation of bicyclic compounds about ∼8% also takes place. After reprecipitation of synthesised copolymers (XXI, XXXVIII and XLI) from the mother solution of toluene and after removal of solvent, products were obtained with structure 2 in reactions (6.1) and (6.3). For these products molecular masses, IR and NMR spectra were determined. On the basis of these results the bicyclic structure of these products were established. Such bicyclic structures were obtained directly by the HFC of dichloroorganosiloxyorganocyclosiloxanes with 1,5-dihydroxyhexamethyltrisiloxane with a 1:1 ratio of the initial components in the presence of aniline in a 5% solution of ether at –5 to 10 °C according to Scheme (6.4) [7]. 152
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Table 6.4 Elementary analysis, some physical-chemical properties and yields of copolymers with phenylcyclosiloxane fragments in the side chain Copolymer No.
Yield, %
Tg, °C
d 1, Å
ηsp*
XIV
73
18 - 20
10.05
XV
73
8 - 10
XVI
78
XVII
Elementary analysis, %** C
H
Si
0.08
59.98 59.85
5.84 5.24
20.34 20.95
-
0.09
56.38 56.01
5.59 5.12
21.92 21.45
0-5
-
0.11
54.92 55.58
6.12 5.68
23.27 23.58
85
-38
-
0.14
50.41 50.08
5.71 6.26
26.33 26.97
XVIII
94
-115
-
0.20
39.02 39.37
7.68 7.38
33.25 33.56
XIX
95
-123
7.54
0.24
37.16 37.40
7.82 7.59
33.95 34.28
XX
76
5 - 10
8.64
0.06
57.00 56.46
5.12 5.35
22.18 22.46
XXI
77
0
-
0.08
54.81 54.56
5.25 5.65
24.67 24.28
XXII
80
-12
-
0.12
52.97 53.42
5.95 6.39
25.63 25.57
XXIII
85
-50
7.59
0.19
47.26 47.63
6.21 6.42
28.35 28.37
XXIV
94
-108
-
0.28
38.75 38.22
7.31 7.46
33.86 34.23
XXV
94
-123
7.31
0.37
36.41 36.55
7.39 7.65
35.51 35.27
*In 1% solution of toluene, at 25°C. **In numerator: calculated values, in denominator: experimental values.
The composition and structure of the compounds XLV - XLVII were determined by means of elementary analyses, molecular mass measurements, IR and NMR spectral data (see Table 6.7).
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Scheme 6.4 Where: R = R´ = Ph, R´´ = Me, m = 2, n = 3 (XLV); R = R´´ = R´´ = Me, m = n = 3 (XLVI); R = R´ = R´´ = Me, m = 3, n = 4 (XLVII).
Table 6.5 Elementary analysis, some physical-chemical properties and yields of copolymers with carbophenylcyclosiloxane fragments in the side chain Elementary analysis, % Copolymer Yield, ηsp Tg, °C d 1, Å No. % C H Si 56.21 5.87 23.84 XXVI 72 0–7 10.05 0.07 55.65 6.09 24.35 50.62 7.04 25.91 XXVII 74 -20 0.10 51.55 6.44 26.73 7.12 29.85 46.83 XXVIII 89 -65 0.13 47.23 6.97 30.05 38.04 7.32 34.32 XXIX 94 -123 7.42 0.20 37.63 7.74 34.76 7.43 35.27 35.82 XXX 95 -123 0.26 36.16 7.74 35.69 59.76 5.62 20.95 XXXI 73 16 10.40 0.06 60.13 5.33 20.89 57.11 5.32 22.81 XXXII 80 -2 0.08 56.35 5.71 23.20 5.81 27.02 51.05 XXXIII 88 -40 0.10 51.23 6.22 26.34 40.01 6.62 32.95 XXXIV 92 7.50 0.15 40.29 7.32 33.03 34.65 37.63 6.88 XXXV 95 -123 0.21 7.54 34.36 38.12
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Table 6.6 Elementary analysis, some physical-chemical properties and yields of copolymers with methylcyclosiloxane fragments in the side chain Copolymer No.
Yield, %
Tg, °C
d 1, Å
ηsp
XXXVI
82
-90
7.83
XXXVII
76
-95
XXXVIII
76
XXXIX
Elementary analysis, % C
H
Si
0.032
27.81 27.90
6.34 6.97
39.01 39.07
-
0.10
28.11 28.57
6.94 7.14
38.51 38.88
-100
-
0.06
28.31 28.57
7.02 7.14
37.92 38.09
82
-105
8.19
0.03
28.31 28.57
7.16 7.14
38.33 38.88
XL
78
-110
-
0.06
26.12 27.27
6.42 6.60
40.44 40.87
XLI
76
-118
-
0.08
29.13 29.44
7.16 7.36
38.16 38.65
XLII
82
-83
8.76
0.05
35.93 36.04
6.37 6.71
34.41 34.63
XLIII
75
-88
-
0.08
34.81 35.07
6.32 6.77
34.27 34.46
XLIV
81
-96
-
0.10
35.11 35.29
6.70 7.00
34.12 35.29
Table 6.7 Some physical-chemical properties of bis(organocyclosiloxane)oxides No.
Yield, %
Tboil, °C (P; Pa)
Tmel, °C
nD25
d425
MRD
M
XLV
57
120-123 (25)
62-63
-
-
-
817 814
XLVI
62
87-89 (25)
-
1.4031
1.0216
138.1 138.9
580 578
XLVII
67
93-95 (25)
-
1.4045
1.0135
157.5 157.7
651 652
155
Polymer Yearbook In the IR spectra of all the synthesised compounds XLV - XLVII, one can see the absorption band of asymmetric valence oscillation of the ≡Si-O-Si≡ bonds in the region 1020, 1075 and 1080 cm-1. One can see also the absorption bands of ≡Si-Ph, Si-Me bonds at 1000, 1445 and 1275 cm-1. In the 1H NMR spectra [12] of the compound XLV one can observe a singlet signal for methyl group (3H), with a chemical shift of δ ≈ 0.11 ppm, and two pairs of enantiotropic methyl groups distinguished in space disposition with reference to methylcyclotetrasiloxane fragments Me4a, Me8a and Me4b, Me4b with chemical shifts δ ≈ 0.12 and δ ≈ 0.13 ppm and methyl groups Me6a and Me6b (this group does not exchange) at δ ≈ 0.14 ppm. Also a complicated multiplet is observed in the region 6.8-7.4 ppm for phenyl groups. Figure 6.6 shows 1H and 13C NMR spectra of compound XLVII (Scheme 6.5).
Scheme 6.5
Figure 6.6 1H and 13C NMR spectra of compound XLVII
156
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain Analysis of the 1H NMR spectrum of compound XLVII is a sufficiently difficult problem, since the whole of the range of absorbing the protons does not exceed 0.04 ppm. Whereas, substituted groups at Si2 and Si2′ in this instance are organocyclosiloxanes, resonance line of protons of groups Me2 and Me2′ must be observed within the range of chemical shifts δ ≈ 0.097-0.111 ppm. It is possible to attribute a low field band (δ ≈ 0.14 ppm) include resonance signals of the protons of groups Me4,8b and Me4,10b, and to attribute a band with the highest intensity (δ ≈ 0.10 ppm) to Me2, Me2′, Me6′,8′a and Me6a. Resonance signals of other methyl groups are characterised by intermediate values of chemical shifts. In the 13C spectrum of compound XLVII in the strong-field area, are two signals, which possibly refer to the absorbing core of carbon groups C2 and C2′ (strong-field shift is stipulated by the bridge of the oxygen atom). Comparative strong-field signal with the chemical shift δ ≈ 2.71 ppm possibly refers to the core of C2, but signal δ ≈ 2.51 ppm refers to the core C2′. Integral intensity of the absorbing signals of the rest of the carbon core of methyl groups is approximately seven times greater than the total integral intensity of the strong field signals, that correspond to the structure of compound XLVII. Absorption of the carbon core of these methyl groups is observed in the spectrum as three bands with centres δ ≈ 0.92, 0.77 and 0.65 ppm, moreover the average band has the most intensity. Using the given NMR spectra for compounds VII and IX and considering the above as a reference, it is possible to consider that the signal under δ ≈ 0.92 ppm, corresponds to the carbon core of the methyl groups C6,8 (both types), band under δ ≈ 0.77 ppm - C6 (both types), and one enantiotipic type C4′,8′ or C4′,10′, but signals under δ ≈ 0.65 ppm - other type C4,8 or C4,10. In the IR spectra of copolymers in the region 1000-1100 cm-1, the characteristic asymmetric valence oscillations of the ≡Si-O-Si≡ bonds are found, beside the absorption bands at 1020 cm-1, where the absorption bands of the linear siloxane overlap the absorption bands of ≡Si-O-Si≡ bonds in cyclotrisiloxane ring. From the literature it’s known that the absorption bands at 1075-1080 cm-1 are characteristic for ≡Si-O-Si≡ bonds in cyclotetraand - pentasiloxane rings. The transition from dimethylsiloxane links with n = 2 to n ≈ 51 increases the signals of asymmetric valence oscillation for ≡Si-Me bonds, as compared with ≡Si-Ph at 1410 -1412 and 1435 cm-1. The structure of some synthesised copolymers was determined by IR and 29Si spectra [23]. The molecular weights, molecular weight distribution, characteristic viscosities, hydrodynamic and conformational characteristics of copolymers were determined. In Figure 6.7a one can observe the absorption bands for ≡Si-O-Si≡ bonds in an eightmembered ring (D4) at 1075-1080 cm-1 and in Figure 6.8a the absorption bands of a tenmember ring at 1080 cm-1 (D5). It is necessary to note that in the IR spectra of copolymers XXXVI and XXXIX additional absorption bands appear at 1020 cm-1 which are characteristic for linear polydimethylsiloxanes (PDMS), however in PDMS these bands are narrow, but in our case these bands are rather wide (Figure 6.7b and 6.8b).
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Figure 6.7 IR spectra of octamethylcyclotetrasiloxane (a), and copolymer XXXVI (b)
29
Si NMR spectra of copolymer XXXVI (Figure 6.9, in chloroform) possesses signals in the region – 19.0 to –22.0 ppm (for D links) and –65.0 to –68.0 ppm (for silsesquioxane T links). Each of mentioned ranges contains two groups of signals. Weak signals in this range (–19.00 to –19.22 ppm and –65.0 to –68.5 ppm) are attributed to the cyclic fragment of the copolymer structure. Correlation of integral intensity corresponds to the suggested structure. The main signals of 29Si NMR spectra of copolymer XXXIX (Figure 6.10) is in the range –21.0 to –21.6
158
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.8 IR spectra of decamethyl-cyclotetrasiloxane (a) and copolymer XXXIX (b)
ppm (D links) and –66.5 to –68.5 ppm (T links). Within this range it is very difficult to distinguish between the signals. Figure 6.11 shows the gel chromatography of copolymer XXXVI. As the copolymer XXXVI was not reprecipitated, it has a wide molecular weight distribution (MWD). Copolymer XXXIX was also made by gel chromatography (Figure 6.12), its coefficient of polydispersity equals Mw/Mn = 1.23. The fractionation of copolymers XXXVI and XXXIX was carried out and the results are shown in the Tables 6.8 and 6.9. On the basis of fractionation data and determination,
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Figure 6.9 29Si NMR spectra of copolymer XXXVI
Figure 6.10
29
Si NMR spectra of copolymer XXXIX
Mn of fractions and characteristic viscosity (η) the integral curves of distribution were constructed according to MW and (η) for copolymer XXXIX (Figure 6.13). For the same copolymer, the value of constant K in the Mark-Kuhn-Howinck-Sakurada equation was calculated as K ≈ (2.38 ± 0.01) x 10-4 as well as the value of the parameter α ≈ (0.5579 ± 0.004).
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.11 GPC of copolymer XXXVI
Figure 6.12 GPC of copolymer XXXIX
Table 6.8 Viscosity and molecular weight characteristics of copolymer XXXVI [η η] in toluene at 25 °C, dl/g
Mn in Acetone at 25 °C
lg[η]
lgMn
1
0.322
9585
-1.4921
3.9815
2
0.0248
3520
-1.6055
3.5465
3
0.021
2500
1.6778
3.3979
4
0.043
6270
-1.3665
3.7978
5
0.05
-
-1.3011
-
6
0.0295
1080
-
-
Unfractionated
0.032
4157 - 5460
-1.4979
3.6187 - 3.732
Fraction No.
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Table 6.9 Viscosity and molecular weight characteristics of copolymer XXXIX Fraction No.
[η η] in Weight of Mn in toluene at Acetone fraction 25 °C, at 25 °C (Pi, g) dl/g
Mass of fraction (Wi)
Mass of fraction (Σ Σ Wi)
lg[η]
1
0.02
3080
0.6129
0.1127
0.0564
-1.6989
2
0.0204
1916
2.7165
0.4994
0.5558
-1.6989
3
0.027
4207
0.3047
0.0560
0.6118
-1.5686
4
0.021
3450
0.7522
0.1383
0.7501
-1.6778
5
0.031
5227
0.2956
0.0543
0.8044
-1.5086
6
0.026
5073
0.2248
0.0413
0.8457
-1.5850
7
0.036
6634
0.2398
0.0441
0.8898
-1.4559
8
0.0275
-
0.1565
0.0288
0.9186
-1.5607
9
0.0358
9375
0.1365
0.0251
0.9437
-1.4461
Unfractionated
0.021
2116
5.4395
1.0000
-
-1.6778
Figure 6.13 Integral curves of distribution according to MW and [η] for copolymer XXXIX
Comparison of the equilibrium rigidity parameter of the copolymer XXXVI with the volume of the cyclic substituent in the copolymer XXXIX results in an increase in equilibrium rigidity of macromolecules of copolymer A ≈ 27 Å, compared to that of PDMS A ≈ 10 Å and polydimethyldiphenylsiloxanes A ≈ 16 Å. Table 6.10 shows some comparative physical data.
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Table 6.10 Some comparative physical properties of copolymers Copolymer 1. Polymethylcyclosiloxane
Polymer Unit
M1=Mo/λo
Kuhn Segment Å
Free Rotation
Factor Break of Rotation
XXXIX
100Å
27.0
-
2.12
~(Me2SiO)n~
-
10.0
0.362
1.35
~(MePhSiO)n~
-
22.3
0.362
1.56
4. cis-PMPS
~(MePhSiO)n~
-
21.2
0.365
1.97
5. trans-PMPS
~(MePhSiO)n~
-
22.1
0.365
2.0
~(Me2SiO)5(Ph2SiO)5~
-
16.0
0.365
1.71
2. Polydimethylsiloxane 3.
6.
Polymethylphenylsiloxane (PMPS)
Polydimethyldiphenylsiloxane
The thermogravimetric investigation of synthesised copolymers was carried out. Figures 6.14-6.17 show thermogravimetric curves for the copolymers. From Figure 6.14 it can be seen that the replacement of part of the methyl groups by the phenyl ones at a silsesquioxane atom of silicon and in a cyclic fragment, results in an increase of decomposition of starting temperature up to 280-300 °C. This is
Figure 6.14 The thermogravimetric curves for copolymers: curve 1: copolymer XIV, curve 2: XIX, curve 3: XXIV
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Polymer Yearbook
Figure 6.15 The thermogravimetric curves for copolymers: curve 1: copolymer XXVI, curve 2: XXVII
Figure 6.16 The thermogravimetric curves for copolymers: curve 1: copolymer XXXI, curve 2: XXXII, and curve 3: XXXIV
associated with a high resistance of phenyl groups to oxidation as well as with their inhibiting effect on oxidation of methyl groups [24]. The replacement of an oxygen bridge by an ethylene group results in a slight decrease of thermal-oxidative stability of the copolymer (Figure 6.15) [21].
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.17 The thermogravimetric curves for copolymers: curve 1: to copolymer XXXVI, curve 2: XXXIX
With an increase in the volume of cyclic fragments, that is to say, by replacement of pentaphenylcyclotrisiloxane fragment by a heptaphenylcyclotetrasiloxane, a slight decrease of a thermal-oxidative stability takes place (Figure 6.16). A similar phenomenon is observed when a heptamethylcyclotetrasiloxane fragment is replaced by a nonamethylcyclopentasiloxane. For phenyl containing copolymers, 5% mass losses are observed in the temperature region 300-350 °C; and with an increasing temperature the loss of mass keeps on increasing. The main destruction process proceeds over the range 300-600 °C, above 700 °C the curves of mass losses do not change. For copolymers with methylcyclosiloxane fragments as a pendant groups 5% mass losses can be observed in the temperature region 230-250 °C (Figure 6.17). With an increase of the length of dimethylsiloxane chain the thermal-oxidative stability of copolymers decreases. Comparison of thermal-oxidative stability of copolymers with phenylcyclosiloxane fragments in the side chain and copolymers containing cyclotetra-, penta-, and hexa-siloxane fragments along the main chain [25-28], showed approximately the same thermal-oxidative stability, because the insertion of cyclic fragments in the side chain hinders the chain transfer reactions that proceed with release of the Dn-type cycles. Therefore, the authors claim that cyclic fragments in the side chain in the case of destruction behave like copolymers with cyclic fragments along the dimethylsiloxane chain. The thermomechanical investigation of the synthesised copolymers was performed. From Figure 6.18, one can observe the dependence of the glass transition temperature (Tg) on the mole% of phenylcyclosiloxane fragments in the side chain. As is evident 165
Polymer Yearbook
Figure 6.18 Dependence of the Tg on the mole% of phenylcyclosiloxane fragments. Curve 1: copolymers XX - XXV; curve 2: XIV - XIX; curve 3: XXXI - XXXV
from Tables 6.4-6.6, the Tg of copolymers rises with an increase of amount of surrounding cyclosiloxane fragments. The replacement of one methyl group by a phenyl one in the silsesquioxane link leads to a rise in Tg by ~10 °C, which is in agreement with early published data [25-28]. With all synthesised copolymers an increase of the length of the linear dimethylsiloxane chain (n) leads to a decrease of the Tg of the copolymers right to the Tg of linear PDMS. With the insertion in the cyclic fragment diphenylsiloxy links leads to a rise of Tg of copolymers of about at ~15 °C. This is explained by the influence of the phenyl groups, whose presence in the PDMS chain involves a rise in the Tg [29]. With the replacement of an oxygen bridge by an ethylene group in copolymers XXVIXXX, the flexibility of copolymers increases, which leads to a decrease of Tg as compared with copolymers XX-XXIV. As is evident from Table 6.6 the insertion of methylcyclotetrasiloxane fragments in the dimethyl-siloxane chain does not lead to a considerable rise of Tg. The Tg of copolymers with methylcyclopentasiloxane fragments in the side chain decreases due to increasing flexibility of methylcyclopentasiloxane fragments. At the same length (n) of the linear dimethylsiloxane links, the difference between glass temperatures of copolymers with monocyclic fragments (methylcyclotetra-, cyclopentasiloxane) in the side chain is about 10 °C (see Figure 6.19). With an increase
166
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.19 Thermomechanical curves of comb-type methylcyclosiloxane copolymers. Where curve 1: copolymer XXXIX, curve 2: XXXVIII, curve 3: XXXVII and curve 4: XXXVI.
of the length of the linear dimethylsiloxane link with one dimethylsiloxane unit the Tg decreases by 5 °C (copolymers XXV-XLIV). X-ray analysis of the synthesised copolymers showed that all copolymers are amorphous systems with two diffraction maximums. The first diffraction maximum d1, which characterises interchain distance, falls in the region 7.54-10.05 Å (see Figure 6.20), while the second one d2 is of more complicated nature and corresponds both to intrachain and interchain atomic distances [30]. The value of d1 in all copolymers changes inconsiderably. In the case of small values of n the interchain distance reached its maximum value (Tables 6.4-6.6). The replacement of the methyl group by a phenyl one in the silsesquioxane link, the value of d1 increases from 8.64 Å to 10.05 Å (Tables 6.4 and 6.5). With the replacement of heptamethylcyclotetrasiloxane fragments by nonamethylcyclopentasiloxane fragments the value d1 increases from 8.19 Å to 8.76 Å (Table 6.6, Figure 6.22). Analogous increases of the value of interchain distance d1 is noted when pentaphenylcyclotrisiloxane fragments are replaced by heptaphenylcyclotetrasiloxane fragments, Figure 6.21. The value of d1 in all copolymers changes inconsiderably. In the case of small values of n the interchain distance reached its maximum value (Tables 6.4-6.6). The replacement of a
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Polymer Yearbook
Figure 6.20 Diffraction patterns of comb-type methylsiloxane copolymers with phenylcyclo-trisiloxane fragments in the side chain. Where curve 1: copolymer XIX, curve 2: XX, curve 3: XIV
methyl group by a phenyl one in the silsesquioxane link, the value of d1 increases from 8.64 Å to 10.05 Å (Tables 6.4 and 6.5). With the replacement of heptamethylcyclotetrasiloxane fragments by nonamethylcyclopentasiloxane fragments the value d1 increases from 8.19 Å to 8.76 Å (Table 6.6, Figure 6.22). Analogous increases the value of interchain distance d1 is noted when pentaphenylcyclotrisiloxane fragments are replaced by heptaphenylcyclotetrasiloxane fragments, Figure 6.21.
6.2.1.4 Synthesis of Organosiloxane Oligomers with Cyclic Fragments in the Side Chain by the Reaction of Catalytic Dehydrocondensation One of the light methods of synthesis of organosiloxane copolymers with cyclic fragments in the side chain is the modification of functional group containing methyl- and ethylhydridesiloxanes. From this modification reaction it must be noted that the dehydrocondensation reaction of ≡Si-H and ≡Si-OH containing organosiloxanes in the presence alkaline catalysts proceeds with elimination of hydrogen without cleavage of ≡Si-O-Si≡ bonds. 168
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.21 Diffraction patterns of comb-type phenylsiloxane copolymers with phenylcyclotetrasiloxane fragments in the side chain. Where curve 1: copolymer XXXI, curve 2: XXXIV
For the purpose of synthesising organosiloxane copolymers containing cyclosiloxane fragments in the side chain, a commercially available oligoethylhydridesiloxane with end trimethylsiloxy groups (GkZh-94, Russian product) with degree of polymerisation n ≈ 15, was used as the starting compound. The reaction of catalytic dehydrocondensation of methylhydridesiloxane with hydroxyorganocyclosiloxanes was carried out in the presence of platinum chlorohydric acid or an anhydrous powder like potassium hydroxide as a catalyst, at various proportions of the starting compounds, at 40-60 °C. It was shown that in this condition polymerisation or polycondensation starting products do not occur. It was shown that at a starting ratio of 1:15 of the initial compounds, the dehydrocondensation reaction does not proceed completely and dehydrocondensation of all the active ≡Si-H centres is impeded, which might be explained by steric difficulties due to organocyclosiloxane fragments at macromolecular chain formation. A detailed analysis of the reaction mixture by GLC showed the presence of unreacted hydroxyheptamethylcyclotetrasiloxane (D4OH). At the ratio of 1:7.5 the conversion of hydrogen is about 96%. It was shown that the
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Polymer Yearbook
Figure 6.22 Diffraction patterns of comb-type methylsiloxane copolymers with methylcyclosiloxane fragments in the side chain. Where curve 1: copolymer XXXIX, curve 2: XLII and curve 3: XXXVI
reaction of dehydrocondensation has a great influence on a used catalyst. In the presence of platinum chlorohydric acid the reaction proceeds slowly at 60 °C and over six hours the hydrogen conversion does not exceed 50%, while in the presence of potassium hydroxide dehydrocondensation proceeds more vigorously. The dehydrocondensation reaction proceeds according to Scheme 6.6 [31, 32]. Table 6.11 shows the results of elementary analysis, physical chemical properties and the yield of ethylsiloxane oligomers containing cyclic fragments in the side chain. In the IR spectra of oligomers with cyclic fragments in the side chain one can observe the absorption bands characteristic of asymmetric valence oscillations of the ≡Si-O-Si≡ bonds in the region 1020 and 1080 cm-1 characteristic of both linear siloxane links and cyclosiloxane rings. In the IR spectra one can also observe absorption bands for unreacted ≡Si-H bonds at 2160 cm-1. As can be seen from Figure 6.23 with the increase of temperature from 40 to 60 °C, the hydrogen conversion increases from 65 to 80%. The dehydrocondensation reaction
170
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Scheme 6.6 Where: m ≈ 15; (a+b)c ≈ m; R = Me, n = 3 (XLVIII1 –40 °C), (XLVIII2 –50 °C), (XLVIII3 –60 °C) (all ratio 1:15); XLVIII4 –60 °C (ratio 1:7.5). R = Ph, n = 2 (XLIX –60 °C) (Ratio 1:15).
Table 6.11 Some physical-chemical properties and the yields of ethylsiloxane oligomers with organocyclosiloxane fragments in the side chain Oligomer No.
Yield, %
ηsp*
XLVIII1
87
0.04
-
-
XLVIII2
90
0.04
8.27
XLVIII3
90
0.04
XLVIII4
91
XLIX
88
d1, Å
Tg, °C
H2 conversion, %
Elementary composition, % C
H
Si
65
30.06 30.24
7.28 7.19
37.71 37.59
-8 0
72
29.95 29.84
7.24 7.15
37.72 37.67
8.27
-7 6
80
29.85 29.78
7.21 7.11
37.72 37.67
0.03
7.97
-9 5
98
29.93 29.80
7.27 7.20
37.09 37.16
0.03
8.73
-
66
57.46 57.29
5.49 5.30
22.03 22.26
*In 1% solution of toluene, at 25 °C.
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Polymer Yearbook
Figure 6.23 Hydrogen conversion in dehydro-condensation of oligoethylhydridesiloxane with hydroxyheptamethylcyclotetrasiloxane. Where curve 1 corresponds to a reaction temperature of 40 °C, curve 2 is at 50 °C, curve 3 is at 60 °C, all with a 1:15 ratio of initial compounds.
proceeds vigorously during the first 1.5-2 hours and 5 hours later the conversion changes only slightly. In addition, these data are evidence that at an initial compound ratio of 1:15, the reaction does not proceed completely and dehydro-condensation of all the active centres is impeded, which may be explained by steric effects created by organocyclosiloxane fragments in course of the formation of macromolecular chain. At a 1:7.5 ratio of the initial compounds the reaction proceeds further and faster, Figure 6.24. The reaction in the presence of anhydrous KOH (0.1% of the total amount of the initial components, C ≈ 0.2271 mole/l) was studied at 40, 50 and 60 °C. Figure 6.25 shows the time dependence on the reverse concentration. One can see that the dehydrocondensation reaction is of the second order. The reaction rate constants at various temperatures were calculated: K40 °C ≈ 0.923 x 10-1, K50 °C ≈ 1.6 x 10-1, K 60 °C ≈ 2.85 x 10-1. From the dependence of the logarithm of the reaction rate constants on the reverse temperature (Figure 6.26), the activation energy of dehydrocondensation reaction was calculated as E ≈ 51.5 KJ/mole. It was found that for each increase in temperature of about 10 °C, the reaction rate constant increases approximately ∼1.7 times. The thermomechanical investigation of the oligomers was performed. As is shown in Table 6.11, the Tg for oligomer XLVIII1 is –80 °C, for oligomer XLVIII4 is –95 °C, which indicates that for an increase in the amount of methylcyclotetrasiloxane fragments, the Tg of copolymers also increases. This may be explained by the increase in the rigidity of the oligomeric segments.
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.24 Hydrogen conversion in dehydrocondensation of oligoethylhydridesiloxane with hydroxyheptamethylcyclotetrasiloxane. Where curve 1 corresponds to a reaction temperature of 40 °C, curve 2 is at 60 °C, with a 1:7.5 ratio of initial compounds.
Figure 6.25 Dependence of inverse concentration on the time, in the reaction of catalytic dehydrocondensation of oligoethylhydridesiloxane with hydroxyheptamethylcyclotetrasiloxane at a 1:15 ratio. Where curve 1 is at 40 °C, curve 2 is at 50 °C and curve 3 is at 60 °C.
By wide angle x-ray investigation it was shown that the interchain distance of oligomers XLVIII3 and XLIX is different. Since the interchain distance increases from 7.97 Å (for oligomer XLVIII4) to 8.27 Å (for oligomer XLVIII3), this may be explained by an increase in the number of cyclic fragments in the side chain (Figure 6.27).
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Polymer Yearbook
Figure 6.26 Dependence of the logarithm of the reaction rate constants on the reverse temperature.
Figure 6.27 Diffraction patterns of oligoethylhydride-siloxanes with methylcyclosiloxane fragments in the side chain. Where curve 1 corresponds to oligomer XLVIII3 and curve 2 corresponds to oligomer XLVIII4.
Thermogravimetric investigations of the synthesised oligomers were performed. According to Figure 6.28 mass losses for oligomers at 240-250 °C do not exceed 5%. The main destruction process proceeds in the temperature range 300-550 °C and above 600 °C the curves of mass losses do not change. The thermal-oxidative stability of oligomers also increases with an increase in the number of cyclic fragments in the side chain, because
174
Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.28 Thermogravimetric curves of oligoethylhydridesiloxanes with methylcyclosiloxane fragments in the side chain. Where curve 1 corresponds to oligomer XLVIII3 and curve 2 corresponds to oligomer XLVIII4.
this increase of cyclic side chain fragments prevents the chain transfer in the case of depolymerisation [6].
6.2.1.5 Synthesis of Cyclolinear Copolymers by the Hydrosilylation Reaction From the literature [33-37] it is known, that the hydrosilylation reactions are widely used for synthesis of cyclolinear copolymers. In this section the synthesis of organosilicon copolymers with carbocyclosiloxane fragments in the side chain by the reaction of hydride addition of vinyl containing organocyclosiloxanes to methylhydridesiloxanes and methylhydridesiloxanedimethylsiloxane copolymers is discussed. It was shown [33-37] that in the reaction of hydride addition of dihydrideorganocyclosiloxanes to divinyl containing organocyclosiloxanes in the presence of platinum chlorohydric acid breaking of the cyclosiloxane ring does not take place. In the modification reaction using the reaction of hydrosilylation, the authors successfully used trimethylsiloxy end blocked methylhydridesiloxanes [38, 39]. By hydride addition of unsaturated organic compounds, allyl glycidyl ether [40, 41], allyl alcohol [42, 43] or dicyclopentadiene [39, 44] to methylhydridesiloxanes in the presence of a catalyst, combtype methylsiloxane copolymers has been obtained. For the purpose of synthesis of carbosiloxane copolymers with cyclic fragments in the side chain, the reaction of hydrosilylation of methylhydridesiloxanes to
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Polymer Yearbook vinylorganocyclosiloxanes in the presence of catalysts have been investigated [45]. Preliminary heating of 1-vinyl-1-methyltetra-phenylcyclotrisiloxane (concentration, C ≈ 0.02628 mole/l) during 8 hours in the presence of platinum chlorohydric acid (9 × 10-5 g per 1 g of substances) in the temperature range 80-100 °C showed that polymerisation of vinylorganocyclosiloxane under the experimental conditions does not take place and no changes in 1H NMR spectra for methyl protons are observed. The reaction of hydrosilylation methyl-hydridesiloxane (n ≈ 35) with 1-vinyl-1methyltetraphenyl-cyclotrisiloxane at a 1:35 ratio of initial compounds was studied at 80, 90 and 100 °C. As it is seen from Figure 6.29 with the increase of temperature from 80 to 100 °C the hydrogen conversion increases from 85% up to 95%. The hydrosilylation reaction proceeds vigorously during first 50-60 minutes and after 80 minutes the hydrosilylation proceeds slightly. It is necessary to denote that the hydrosilylation reaction does not proceed completely and replacement all active ≡ Si–H groups with cyclo-trisiloxane fragments does not take place. Which may be explained by steric effects created by organocyclosiloxane fragments during the formation of macromolecular chain. At the ratio of initial compounds 1:17.5 the hydrosilylation proceeds completely. The hydride addition proceeds according to the general scheme (Scheme 6.6).
Figure 6.29 Hydrogen conversion in the reaction of hydride addition of α,ω-bis(trimethylsiloxy)methyl-hydridesiloxane to 1-vinyl-1-methyltetraphenylcyclotrisiloxane, where curve 1 corresponds to a reaction temperature at 100 °C, curve 2: 90 °C and curve 3: 80 °C.
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Scheme 6.7 where: n ≈ 35, (a+b)c = n, p = 2: R = Ph (L1: –80 °C, L2: –90 °C, L3: –100 °C, ratio 1:35); (LI ratio 1:17.5; 100 °C); p = 2, R = Me (LII: –90 °C); p = 3, R = Me (LIII: –90 °C).
The synthesised copolymers are light-yellow liquid or solid systems, depending on the length of dimethylsiloxane chain, dissolve well in ordinary organic solvents, with ηsp of 0.05-0.07. The structure and composition of synthesised copolymers was determined by means of elementary analysis, by IR and NMR spectra data. Some physical-chemical properties of comb-type methylsiloxane copolymers with carbocyclosiloxane fragments in the side chain are presented in Table 6.12.
Table 6.12 Some physical-chemical properties and the yields of comb-type methylsiloxane oligomers with organocarbocyclosiloxane fragments in the side chain Oligomer Yield, No. %
p
R
Treac, °C
Ratio of initial composition
ηsp
d1, Å
L1
93
2
Ph
80
1:35
0.05
10.30
-
85
2
94
2
Ph
90
1:35
0.06
-
-
90
3
94
2
Ph
100
1:35
0.07
10.30 12 - 15
95
LI
96
2
Ph
100
1:17.5
0.05
9.80
0-3
100
LII
96
2
Me
90
1:35
0.05
8.45
-94
92
LIII
95
3
Me
90
1:35
0.05
8.76
-110
90
L L
H2 Tg, °C conversion, %
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Polymer Yearbook In the IR spectra of copolymers one can see that the absorption bands characteristic of the Si-H bond in the range 2160-2170 cm-1 do not vanish completely. In the IR spectra one can see new absorption bands at 1150 cm-1, typical for fanshaped oscillations of the CH2 groups. One can also observe the absorption bands characteristic of asymmetric valence oscillation of Si-O-Si bonds in the region 1020 and 1075 cm-1 are characteristic of both linear siloxane links and siloxane bonds in cyclotri- and cyclo-tetrasiloxane ring. In copolymers with cyclotrisiloxane fragments in the side chain the absorption bands characteristic of asymmetric valence oscillation of Si-O-Si bonds in linear dimethylsiloxane chain is superimposed with absorption bands of Si-O-Si bonds in the cyclotrisiloxane ring. In 1H NMR spectra of copolymer L3 one can see broadened signal for methyl protons (3H) in the fragment -O-SiMe-O- with a chemical shift of 0.27 ppm, for methyl protons in main chain with a chemical shift of 0.10 ppm. In 1H NMR spectra of copolymer LII and LIII one can observe a broadened singlet signal (4H) with a chemical shift of 0.72 ppm, for the fragment –CH2-CH2-, singlet signals for methyl groups with chemical shift of 0.30 ppm for –O-SiMe-O- fragment, one can also observe singlet signals for methyl groups with chemical shifts of 0.10, 0.13 and 0.15 ppm. As is seen in Figure 6.29, with the increase in temperature from 80 °C to 100 °C the hydrogen conversion increases from 85% up to 95%. The hydrosilylation reaction proceeds vigorously during the first 2 hours. Figure 6.30 shows the reverse concentration dependence on the time. Proceeding from the data of Figure 6.30, it is evident that in the beginning stages the hydrosilylation is a second order reaction. The hydrosilylation rate constants were calculated: K: 80 °C, 5.5431 × 10-1, K: 90 °C, 7.5355 × 10-1, K: 100 °C, 1.0. From the dependence of logarithmic reaction rate constants lgK on reverse temperature (Figure 6.31) the activation energy was calculated, which is equal to an E of 31.6 KJ/mole. By x-ray investigation it was shown that the synthesised oligomers are one phase amorphous systems and the maximum value of interchain distances for oligomer L3 is equal to d1 ≈ 10.30 Å. With the decrease of amount of cyclotrisiloxane fragments and volume of the cyclic fragments in the side chain the value of interchain distance decreases. In Figure 6.32 the differential scanning calorimetry (DSC) curves of synthesised oligomers are represented. As is visible from the figures indicated and also from the Table 6.12, the oligomer L3 is characterised by a higher softening temperature compared with copolymer XIX and XXVI, which may be explained by the higher rigidity of the oligomeric chain, which is induced by the presence of phenyl groups in cyclosiloxane fragments. With the decrease of amount of cyclic fragments the value of Tg decreases (see Table 6.12). With the replacement of methylcycloterasiloxane fragment by methylcyclopentasiloxane the Tg decreases by about 10-12 °C, which is in agreement with data published earlier [8].
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain
Figure 6.30 Dependence of inverse concentration on the time, in the reaction of hydride addition of methylhydridesiloxane with 1-vinyl-1-methyltetraphenylcyclotrisiloxane at a ratio of 1:35. Where curve 1 is at 80 °C, curve 2 is at 90 °C and curve 3 is at 100 °C.
Figure 6.31 Dependence of logarithm of the reaction rate constants on the inverse temperature.
By thermogravimetric investigation it was shown that oligomers are characterised with higher thermal-oxidative stability compared with copolymer XIX and XXVI. Thus, for the first time methylsiloxane oligomers and copolymers with various cyclic fragments in the side chain were synthesised by us and it was shown that cyclic fragments in the side chain behave in thermal destruction processes as cyclic fragment in the main chain.
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Polymer Yearbook
Figure 6.32 DSC patterns of oligomers with cyclic fragments in the side chain. Where curve 1 corresponds to oligomer L3 and curve 2 corresponds to oligomer LI.
References 1.
S.M. Meladze, I.G. Esartia, L.M. Khananashvili, O.A. Ckhakaia and O.V. Mukbaniani, Proceedings of the Georgian Academy of Sciences, 1982, 8, 238.
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O.V. Mukbaniani, S.M. Meladze, I.G. Esartia and L.M. Khananashvili, Proceedings of the Georgian Academy of Sciences, 1982, 8, 75.
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O.V. Mukbaniani and L.M. Khananashvili, International Journal of Polymeric Materials, 1994, 27, 31.
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M.V. Sobolovski, Oligoorganosiloxanes, Properties, Synthesis and Applications, Khimia, Moscow, Russia, 1985, 71.
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V.P. Mileshkevich, Kauchuk i Rezina, 1978, 6, 4.
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T.H. Thomas and T.C. Kendrick, Journal of Polymer Science, Part A2: Polymer Physics, 1969, 7, 537.
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I.G. Esartia, Linear Polyorganosiloxanes with Cyclic Fragments in the Side Chain, Izvestia Djavakhishvili Tbilisi State University, Georgia, 1993, 1-217, [Candidate Dissertation].
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S.M. Meladze, O.V. Mukbaniani and L.M. Khananashvili, Zhurnal Obshchei Khimii, 1981, 51, 1624.
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N.N. Sokolov, Zhurnal Obshchei Khimii, 1959, 29, 248.
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain 10. I.G. Esartia, O.V. Mukbaniani, L.M. Khananashvili and N.N. Nizharadze, Proceedings of the Georgian Academy of Sciences, 1991, 142, 537. 11. N.N. Makarova and B.D. Lavrukhin, Izvestia Academy of Sciences USSR, Seria Khimicheskaia, 1986, 3, 652. [In Russian] 12. I.G. Esartia, V.G. Tsitsishvili, O.V. Mukbaniani and L.M. Khananashvili, Zhurnal Obshchei Khimii, 1992, 62, 1120. 13. V.A. Achelashvili, Cyclic Organosiloxanes, Organocarbosiloxanes and Copolymers in their Bases, Izvestia Djavakhishvili Tbilisi State University, Georgia, 1989, 1-237, [Candidate Dissertation]. 14.
O.V. Mukbaniani, V.A. Achelashvili, S.M. Meladze and L.M. Khananashvili, Proceedings of the 7th International Symposium in Organosilicon Chemistry, Japan, Kyoto, 1984, 216.
15. Y.A. Yuzhelevski, T.V. Kurlova, B.G. Kogan and M.V. Suvorova, Zhurnal Obshchei Khimii, 1972, 42, 2006. 16. K.A. Andrianov, A.I. Nogaideli, N.N. Makarova and O.V. Mukbaniani, Izvestia Academy of Sciences USSR, Seria Khimicheskaia, 1977, 6, 1388. [In Russian] 17. I. Nagy, R. Farkas, O.V. Mukbaniani, I.G. Esartia and L.M. Khananashvili, Proceedings of the 7th International Symposium in Organosilicon Chemistry, Kyoto, Japan, 1984, 162. 18. O.V. Mukbaniani, I.G. Esartia, L.M. Khananashvili, I. Nagy and R. Farkas, Proceedings of the 31st IUPAC Macromolecular Symposium, Merseburg, Germany, 1987, 93. 19. I.G. Esartia, O.V. Mukbaniani, L.M. Khananashvili and S.M. Meladze, Proceedings of the Georgian Academy of Sciences, 1986, 12, 234. 20. O.V. Mukbaniani, I.G. Esartia and L.M. Khananashvili, Bulletin of the Georgian Academy of Sciences, 1991, 144, 277. 21. O.V. Mukbaniani, I.G. Esartia and L.M. Khananashvili, Bulletin of the Georgian Academy of Sciences, 1991, 144, 381. 22. I.G. Esartia, O.V. Mukbaniani and L.M. Khananashvili, Proceedings of the Georgian Academy of Sciences, 1993, 19, 212. 23. O.V. Mukbaniani, S.M. Meladze, I.G. Esartia, I.I.Tverdokhlebova and L.M. Khananashvili, Journal of Applied Polymer Science, 1999, 74, 583.
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Polymer Yearbook 24. A.F. Bulkina, V.S. Papkov, A.A. Zhdanov and K.A. Andrianov, Vysokomolekulyarnye Soedineniya, 1972, 20A, 70. 25. K.A. Andrianov, A.I. Nogaideli, G.L. Slonimsky, V.Yu. Levin, N.N. Makarova, Yu.P. Kvachev and O.V. Mukbaniani, 1976, Vysokomolekulyarnye Soedineniya, 18B, 359. 26. S.M. Meladze, O.V. Mukbaniani and L.M. Khananashvili, 1984, Vysokomolekulyarnye Soedineniya, 26B, 250. 27. N.A. Koiava, O.V. Mukbaniani and L.M. Khananashvili, 1985, Vysokomolekulyarnye Soedineniya, 27A, 2261. 28. V.A. Achelashvili, O.V. Mukbaniani, L.M. Khananashvili and G.I. Sturua, Proceedings of the Georgian Academy of Sciences, 1988, 53. 29. K.A. Andrianov, G.L. Slonimsky, V.Y. Levin, A.A. Zhdanov, Yu.K. Godovsky, N.K. Kuznetsova, D.Ya. Tsvankin, V.A. Moskalenko and I.I. Kuteinikova, 1970, Vysokomolekulyarnye Soedineniya, 12A, 1268. 30. K.A. Andrianov, L.M. Kononov and D.Y. Tsvankin, 1968, Vysokomolekulyarnye Soedineniya, 10B, 320. 31. O.V. Mukbaniani, L.M. Khananashvili, I.G. Esartia and S.D. Khaduri, International Journal of Polymeric Materials, 1994, 24, 131. 32. O.V. Mukbaniani, Organosilicon Copolymers and Block-Copolymers with Various Structures of Macromolecules, Tbilisi State University, Tbilisi, Georgia, 1993. [DSc thesis] 33. O.V. Mukbaniani, L.V. Khananashvili, N.A. Koyava, G.V. Porchkhidze and Y.I. Tolchinsky, International Journal of Polymeric Materials, 1992, 17, 113. 34. M.G. Karchkhadze, N.O. Mukbaniani, L.M. Khananashvili, S.M. Meladze, N.G. Kvelashvili and T.P. Doksopulo, International Journal of Polymeric Materials, 1998, 41, 89. 35. N.O. Mukbaniani, M.G. Karchkhadze, A.Sh. Samsonia, R.Sh. Tkeshelashvili and L.M. Khananashvili, Bulletin of the Georgian Academy of Science, 1999, 160, 1, 84. 36. A.A. Zhdanou, T.A. Priakhina, T.V. Strelkova, R.I. Afonina and V.M. Kotov, Izvestia Academy of Sciences USSR, Seria Khimicheskaia, 1993, 35, 5, 475.
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Organosilicon Copolymers with Cyclosiloxane Fragments in the Side Chain 37. O.V. Mukbaniani, L.M. Khananashvili, M.G. Karchkhadze, R.Sh. Tkeshelashvili and N.O. Mukbaniani in Synthesis and Properties of Polymers, Ed., G.E. Zaikov, Nova Science Publishers, Inc., Commack, NY, USA, 1996, p.89. 38. O.V. Mukbaniani, M.G. Karchkhadze and L.M. Khananashvili, Proceedings of the XIth International Symposium on Organosilicon Chemistry, Montpellier, France, 1996, PB-61. 39. O.V. Mukbaniani and Kh.E. Kobendze, Proceedings of a Conference Dedicated to the 95th Birthday of K.A. Andrianov, Moscow, Russia, 2000, p.37. 40. O.V. Mukbaniani, U. Scherf, G.N. Gurgenidze, M.G. Karchkhadze, S.M. Meladze and L.M. Khananashvili, International Journal of Polymeric Materials, 2001, 48, 3, 267. 41. G.N. Gurgenidze, S.M. Meladze, O.V. Mukbaniani and L.M. Khananashvili, Proceedings of the Georgian Academy of Sciences, 2000, 26, 1-2, 78. 42. O.V. Mukbaniani, G.N. Gurgenidze, S.M. Meladze and L.M. Khananashvili, Russian Polymer News, 2001, 6, 4, 18. 43. O.V. Mukbaniani, G.N. Gurgenidze, S.M. Meladze and L.M. Khananashvili in Radical and Ion Reactions, Problems and Ways of their Solution, Ed., G.E. Zaikov, Nova Science Publishers, Inc, Huntington, NY, USA, 2001, p.79. 44. O.V. Mukbaniani, U. Scherf, M.G. Karchkhadze, Kh.E. Koberidze and M.O. Labartkava, International Journal of Polymeric Materials, 2000, 48, 2, 177. 45. N.O. Mukbaniani, S.M. Meladze and V.A. Achelashvili, Proceedings of the Annual Scientific Conference in Chemistry, Tbilisi, Georgia, 1998, p.45.
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7
Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers E.V. Kalugina, T.N. Novotortseva, K.Z. Gumargalieva and G.E. Zaikov
7.1 Introduction The main progress in the science of ageing and stabilisation of polymers has generally been related to large tonnage carbochain polymers: polyolefins, poly(vinyl chloride), rubbers, acrylic polymers. This is a consequence of not only their interest to industry, but also of the existence of fundamental investigations of cracking and oxidation of individual aliphatic compounds. No such investigations have been performed for aromatic heterochain polymers (AHP). Thus there are many unclear and doubtful aspects in understanding the degradation mechanism. Studies performed at G. Petrov Research Institute for Plastics (Moscow) and Research and Production Company ‘Polyplastic’ (Moscow) over the last 15 years concerning APH ageing and stabilisation, have been analysed. Specific features of hightemperature oxidation (300-400 °C) in melt and solid-phase oxidation (150-200 °C) of APH have been investigated. The general features in the thermo-oxidation of aromatic and aliphatic-aromatic polyimides (PI), polyesterimides, poly(phenylquinoxalines), polysulfones, etc., have been considered. It has been shown that APH degrades according to the radial-chain mechanism, but the process differs from that of aliphatic polymers by the presence of initiation acts. Thermally realised electron-excited states of polymers and molecular complexes with oxygen are shown up as the most probable structures. Possible directions of APH stabilisation with the help of fluorine-containing additives and/or compounds of variable valence metals are discussed. At high temperatures, degradation changes in polyimides, based on dianhydrides of diphenyltetracarboxylic and benzophenontetracarboxylic acids, m- and p-phenylene diamines, aniline fluorene, poly(alkane imides), etc., are reduced by 1.5-2 times. For example, a glass-plastic composite based on stabilised polyimide linkage reatains its strength at 150 MPa at 350 °C over 1000 hours, whereas an unstabilised material degrades completely during this time. Beside inhibiting thermooxidative ageing, phosphorus containing additives increase radiation resistance of polyimides and poly(alkyl terephthalates): the rate of evolution of the aromatic ring radiation degradation product - CH4 reduces two-fold.
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Polymer Yearbook
7.2 Thermo-oxidative Degradation of Polypyromellitimide, Poly(phenyl-quinoxaline) and Copoly(imidophenylquinoxalines) [1-11] Judging from the temperature index value, determined by the methodology of the research organisation, the National Bureau of Standards, USA, temperature limits of the aromatic polyimide (PI) Capton (Russian version is PM film), within which the material retains 30% of exploitation properties for 30 thousand hours, is 200-220 °C. PM absorbs 0.5 mole of O2/base-mole at 200 °C during 2000 hours of oxidation and 0.2 mol/base-mole CO2 is released. At 250 °C, the kinetics of O2 absorption displays all specific features. The film absorbs 3.5 mole of O2/base-mole during 5000 hours. The kinetic curve has three stages: •
The first, σ-ideal stage lasts for about 1000 hours with absorption of 1.5 mol/basemole O2 and is described by a first order equation.
•
The second stage with exposure during up to 4000 hours displays almost constant rate of O2 absorption and exhibits zero order kinetics.
•
The third stage displays acceleration of the reaction and the kinetics are described by the equation χ = A × exp(γ−τ), where γ−τ is the autoacceleration factor, s-1, χ is the concentration of O2 and A is a constant.
The main gas products are H2, CO, CO2, and H2O, with release kinetics that are similar to O2 absorption. Balance reduction by O2, absorbed by PM and released with oxidation products, shows that in the initial stages, the polymer links 50% of O2. According to IRspectroscopy data, new oxygen-containing structures of the quinoid type (absorption at 1640 cm-1) occur in the oxidised film. Higher expanse of aromatic rings compared with heterocycle (comparison of absorption bands of 1500 cm-1 for C=Car, 1090, 1120 and 820 cm-1 for C-Har, 1244 cm-1 for Car-O-Car with 1380 and 720 cm-1 for imide cycles) is also displayed. Moreover, a solid individual product, identified as pyromellite diimide (PDI) by NMR and MS, was also observed for PM thermo-oxidation. As the result of degradation at 300 °C, the outputs of PDI and H2 are 0.015 and 1.1 × 10-3 mol/basemole, respectively. Formation of H2 explains PM crosslinking, in which the gel-fraction increases at solid-phase ageing: ~3 crosslinks per macromolecule are formed at 300 °C over 20 hours. In the study of the model compound, N-phenylphthalimide (PPTI), oxidised under the same conditions, the typical composition of PM oxidation products was proved with the presence of PDI and H2. Thereafter, no PDI and H2 are formed during thermolysis of PPTI and PM. Thermo-oxidation kinetics and composition of degradation products of poly(phenylquinoxaline) (PPQ) at 200-300 °C are analogous to PM. The following compounds were identified: H2, CO, CO2, H2O, and 2,2′-(1,4-phenylene)-bis-(3-phenylpyrazine).
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Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers Depending on exposure conditions, PPQ heating in air causes partial or complete loss of polymer solubility. Heating at 300 °C for 20 hours formed about 4 crosslinks per macromolecule. Gel-fraction accumulation correlates with H2 release. New oxygen-containing structures of the quinoid type (IR-absorption at 1640-1670 cm-1) are formed in PPQ. The authors [8] have confirmed PPQ affinity to crosslinking in experiments on model compounds. For example, under the thermo-oxidation conditions mentioned, beside carbon oxides and water, a dimer with molecular weight of 652 (2MDPQ-2: marking of the dimer) and H2, not formed under the same conditions in vacuum, were identified. According to dynamic thermogravimetric analysis (TGA) data, thermostability of aromatic structure copolymers (PPQ-1) in tests in vacuum does not depend on the concentration of ether-aromatic units. For PPQ-1, temperature corresponding to 10% of mass loss (T10) falls within the range of 570-580 °C. Thermal degradation of fatty aromatic copolymers (PPQ-2) starts at a lower temperature and falls within the range of 520-450 °C decreasing with increase of CH2-groups. Substitution of ether-aromatic fragments by aliphatic ones not only decreases the PPQ thermal stability, but also changes the decomposition type. Degradation transforms from practically a one-stage process into multistage one: intensive decomposition at 420-500 °C is changed by abrupt deceleration, which is probably associated with using less thermostable aliphatic parts and formation of a more thermostable structure. Above 650 °C the process is accelerated again. In the presence of O2, degradation reactions are sharply intensified, copolyimidophenylquinoxaline (SPPQ-1) begins degrading at 490-500 °C, SPPQ-2; at 500-400 °C, Tdecomp.start decreases with growth of aliphatic parts. Increase of methylene groups in SPPQ-2 leads to intensifying absorption of O2 and formation of CO and CO2. For SPPQ-2 with CH2 contents of 5.9 and 0.8, effective activation energies, calculated from kinetic absorption curves for O2, are 72 and 116 kJ/mol, respectively. Comparison of SPPQ and homopolymer: poly-2,2′-(1,4-phenylene)-6,6′-oxybis-(3-phenylquinoxaline), shows that copolymers containing ether-aromatic and aliphatic groupings in 5.2 and 0.8 wt.% concentrations, respectively, differ insignificantly from the homopolymer. For SPPQ, PPQ and PI, the kinetic curves of O2 absorption and carbon oxides and water extraction are identical. The molecules of SPPQ-2 absorbed 65% of O2 during first stage oxidation whereas the PI film absorbed 50% of O2 during the same stage. According to DTA data, reactions of the aliphatic part (300-420 °C) and aromatic rings (above 420 °C) oxidation were successfully extracted during dynamic thermo-oxidation of SPPQ-2. Use of CH2 for oxidation is confirmed by IR-spectroscopy data – by narrowing the absorption band at 2900 cm-1 (νCH2). There is an oxidation decrease in absorption at 2900 cm-1. The absorption at 1700, 1670, 1740, 1330, 1220 cm-1 remains unchanged. The presence of aliphatic fragments in the structure as if activates thermo-oxidation of heterocycles reducing the decomposition onset temperature by 20-60 °C. Oxidation of SPPQ, as well as homopolymers, is accompanied by formation of intermolecular bonds, the presence of methylene chains accelerating crosslinking. Gel-fraction concentration in SPPQ-2 is 2-fold higher, than in PPQ at 300 °C during 20 hours of thermo-oxidation.
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Polymer Yearbook Thus, let us denote the general features of PI, PPQ and SPPQ thermo-oxidation. The first important likeness of the degradation behaviour is O2 absorption at rather low temperatures (200 °C). At temperatures 250 °C or higher, when it becomes possible to search O2 absorption kinetics in real time, polymers display equal oxidation types independently of temperature – the three-stage kinetics, sequentially described by laws of the first and the zero orders with future autoacceleration. Only about 10% of absorbed O2 is removed from polymers with carbon oxides and water in the first stage of oxidation. This effect failed to be explained by the difference in chains (structure defectiveness) of macromolecules, because PPQ possessing a practically defectless structure, absorbs almost twice as much more O2, than PM film. For example, there is practically no alternative to the statement that the first stage of PM, PPQ and SPPQ thermo-oxidation is associated with the features of their chemical structure. The second important likeness in the degradation behaviour of the polymers mentioned (which accounts for the structure of the elementary unit) is formation of a similar type of degradation products, namely, pyromellite diimide (PMD) and 2,2′-(1,4-phenylene)-bis(3-phenylpyrazine) (PPP). The ratio of PMD and CO2 outputs (in moles) during PM thermo-oxidation at 300 °C is close to 1:24, i.e., to separate PMD, aromatic structures of amine components must be oxidised to CO2. A random O2 attack along the macrochain would cause formation of a selection of oligomeric products with end PDI-groups, but this does not happen. Intermolecular crosslinking (Mc), is relatively less frequent (Mc = 1000) but induces practically complete loss of polymer solubility, is general for PI and PPQ. Oxygen participates indirectly in crosslinking and is absent in the crosslinking unit (bridge). However, crosslinking in the absence O2 does not practically proceed at these temperatures. Interaction of O2 with an aromatic structure probably activates the C-Hbond break in the aromatic ring, which thereafter enters intermolecular interaction. Based on the results of isotopic O2 composition analysis under PM and PPQ thermo-oxidation using 30-50% O2 conversion (high-temperature oxidation at 350-400 °C) it was concluded that a direct interaction between PM and PPQ with O2 exists, and oxygen in the O-O form is present, i.e., so-called endoperoxides with aromatic rings are formed. Oxygen is easily attached to the triplet aromatic system (long wave limit of the fluorescence for PM is 520-530 nm, which corresponds to energy of 217-226 kJ/mol). Bond energies in model compounds were calculated with the help of quantum chemistry method (the PariserParr-Pople method) and indicated the possibility of the described reaction proceeding for both PI and PPQ. As the endoperoxide is formed, π-electron conjugation system on the aromatic ring changes. Decomposition of endoperoxides leads to the occurrence of oxygen-containing structures in the phenylene fragment. Deeper oxidation causes splitting of the benzene ring and CO2 and CO release. Electron excitation and formation of endoperoxides are just initial initiation stages. Paramagnetism increases in the polymer with degradation as hexadiene oxidised structures, radicals and biradicals are accumulated, and the conjugation system increases. This is the third oxidation stage. This stage of the
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Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers process is of theoretical interest only, because deterioration of exploitation characteristics of the materials ends at the second stage. The classical inhibition of oxidative processes is based on termination of oxidation kinetic chains and deactivation of branching intermediate products. In the case of APH, the chain nature of the process does not seem obvious. Chain termination by additives suggests inertness of the remaining inhibitor. These radicals are active at temperatures above 200 °C. That is why, classical antioxidants are ineffective at high temperatures. For example, APH should be thermostabilised in the direction of reducing structure transition into the electron-excited state by quenching these states, interaction or complex formation with amine residues in macromolecules to reduce their reactivity. The highest effect in increasing thermostability was displayed by additives of phosphorus containing additives (PCA). For example, at the optimal stabiliser content, PDI output from PM reduces by 2.5-3 times, and output of carbon oxides by 1.5-2 times. Fiberglass plastic based on stabilised PI linkage preserves strength at 150 MPa during 1000 hours at 350 °C, and unstabilised material degrades completely during this time.
7.3 Thermo-oxidative Degradation of Poly(alkane imide) [12-29]
Figure 7.1 Structure of poly(alkane imide) (PAI)
Poly(alkane imide) (PAI) (Figure 7.1) absorbs O2 in the melt with release of CO2, CH2O, CO and H2O. Kinetics of O2 absorption at 300-350 °C is the two-stage process: the first is the fast stage with C-shaped kinetic curve, high initial rates and formally first kinetic order, and the second is the slow stage with a constant rate. Depending on temperature, the first stage lasts 2-5 hours with absorption of O2 of about 8 mol/basemol; the second stage lasts tens of hours with additional absorption of up to 2 moles of O2. Ea of PAI oxidation in melt, determined by initial rates of O2 absorption, equals 57 kJ/mol, whereas the Ea of CO2 and CO release (identical two-stage kinetics) equal 135 and 163 kJ/mol, respectively. CO2 and CH2O are the main volatile products of PAI high-temperature oxidation, e.g., their output in PAI oxidation at 350 °C during 1 hour equals 0.5 and 0.53 mol/base-mol, respectively. The output of CO and H2O is much smaller. The balance by oxygen indicates that the main part of O2 is linked by the polymer and is contained in non-volatile products.
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Polymer Yearbook Spectral data [NMR, Fourier - IR spectroscopy, mass spectrometry (MS)] point to the destruction of methylene chains, at the expense of CH2-groups and accumulation of aliphatic C=O-groups, destruction of imide cycles and occurrence of heavy products representing macrochain fractures at degradation of a fatty chain or heterocycle. For example, pyromellite diimide (PDI), dodecamethylene diphthalimide, products of the RPI-C(O)R′ type, where R and R′ are linear aliphatic radicals of H, and PI is the pyromellitimide residue. The part of products with destroyed imide cycles (phthalimides, nitrile phthalimides) increases at temperatures above 350 °C. However, judging by output ratios of products with whole and partly degraded pyromellitimide cycles, hightemperature PAI oxidation is generally directed on fatty chains and oxidative degradation of cycloarylene structure is insignificant. Judging by the shape of O2 absorption and CO2 and CO release kinetic curves, solidphase PAI oxidation at 200-250 °C is similar to the initial stage of high-temperature oxidation, but it lasts hundreds of hours and is characterised by noticeably lower values of Ea = 21 kJ/mol. Although the balance by oxygen, absorbed and released with volatile products, points to its accumulation in the polymer, and IR-spectroscopy data confirms expense of CH2-groups, accumulation of aliphatic C=O-groups and future low expense of imide cycles. Heavy oligomeric products are not extracted during solid-phase oxidation, excluding PDI, which itself does not contain atmospheric oxygen and is just a fragment of the structure. Formally, ageing kinetics is presented as complete oxidation of fatty chains to carbon oxides and extraction of pyromellitimide fragment, resistant to oxidation, as the product. Oxidation at 200 °C causes formation of hydroperoxides in PAI, accumulation kinetics of which is characterised by a maximum (~0.015 mmol/base-mol) at ~400 hour exposure. ROOH decay in vacuum at 200 °C proceeds due to the first kinetic order law with the rate constant of 0.017 min-1. Judging by the value of α (10-2) characterising ROOH output per absorbed oxygen, solid-phase oxidation in PAI develops mostly in the hydroperoxide direction. PAI thermo-oxidation is accompanied by H2 release, which output after 800 hours of ageing at 200 °C is 0.63 mmol/base-mol. Kinetics of H2 release correlates with accumulation of gel-fraction at PAI ageing. At the first glance, phenomenology of high-temperature and solid-phase PAI oxidation is determined by fatty chain oxidation and must be described by the known radical-chain oxidation scheme of hydrocarbonic polymers with its modification accounting for a possibility of process development beside hydroperoxides, for example, via decay of peroxy radicals. The known attack reactions of O2 on α-CH2-bonds are weakened due to the proximity of the π-conjugated system of the pyromellitimide fragment. The following experimental data exist, which do not allow exclusion of a cycloaromatic fragment from consideration of the PAI thermo-oxidation mechanism or reducing its role to activation of the neighbouring methylene chain only, and at high temperature – participation in the conjugated oxidation:
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Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers •
The methylene PAI chain is much more stable than aliphatic chains in polyethylene (PE) and aliphatic ones in polyamide (PA);
•
PDI is the only heavy product of the solid-phase PAI oxidation;
•
Correlation between PAI crosslinking and H2 release at oxidation;
•
PAI thermo-oxidation inhibition by additives of transition metals compounds and phosphorus-containing additives (PCA).
The first of these facts is explained by the dependence of polymer oxidation kinetics on molecular mobility of macrochain. Combination of pyromellitimide fragment and aliphatic chain with even number of methylene groups provides for forming rigid high-crystalline PAI-12 structure [(CH2)12 methylene chain length]. The physical structure of the closest ‘uneven’ homologues [(CH2)11 and (CH2)13 in PAI-11 and PAI-13, respectively], is less organised (wide bands NMR data), and consequently, these polymers are oxidised faster in the solid phase. The rest of the facts should be explained: •
PDI extraction requires synchronisation of the oxidative process in neighbouring methylene chains, separated by a polymellitimide fragment. Random chain initiation and transmission would cause the occurrence of a series of oligomers in products of solid-phase oxidation.
•
H2 release and crosslinking macrochains during oxidation at relatively low temperature is untypical for methylene chains of aliphatic polymers, but this phenomenon accompanies oxidative ageing of fully aromatic PI and PPQ.
•
Transition metals compounds stabilise PAI at both low and high temperatures, but sharply accelerate thermo-oxidation of methylene chains, for example, PE.
Search for an alternative or an addition to the radical-chain scheme indicated new properties of PAI. Judging by shear in electron spectra of the model compound, didodecylpyromellitidiimide, at solution blowing through by argon first and then by oxygen, polymellitimide structure forms a molecular complex with O2. Preliminary PAI treatment by I2 possessing a strong complex forming effect leads to a significant decrease of the first exothermal dynamic thermal analysis (DTA) peak characterising the initial oxidation phase at dynamic heating. Moreover, study of magnetic properties indicated PAI paramagnetic properties. The polymer displays an electron spin resonance signal – the singlet with q av = 2.183. Measurements of magnetic susceptibility by the separate Faraday method shows that PAI possesses the magnetic
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Polymer Yearbook moment μeff = 0.77-0.94 MB (24 ºC). Temperature dependence of μeff in the range of negative temperatures is typical of cluster compounds. The value of exchange parameter ζ i,j = 226 cm-1 points to high conjugation degree along the polymeric chain or between chains. As the chemical structure of PAI with a long chain of σ-bonds does not provide for the conjugation system along the chain, the unique possibility of its realisation is formation of intra- and intermolecular complexes between pyromellitimide fragments. Copper sulfate, the effective PAI thermostabiliser, possesses μ eff = 1.86 MB. The additivity rule of total molar magnetic susceptibilities for mechanical mixtures of PAI and CuSO4 is not obeyed both at room temperature and after thermal treatment of the mixture at 320 °C. Thermal treatment in vacuum, in the air or in the inert gas medium leads to a significant increase of magnetic susceptibility and efficient magnetic moment of PAI and PAI mixture with CuSO 4, but the effect is much higher at thermal treatment in the air. Studies of magnetic properties point to the interaction of macromolecule and additive, this interaction being obviously realised by pyromellitimide fragment. To ‘include’ pyromellitimide fragments into oxidation independently of methylene chains, the initiation act of thermo-oxidation is suggested via formation of O2 molecular complexes with π-system and/or thermal transmission of PAI conjugated system (cluster) into electron-excited state, from which radical reactions and transmission of H atoms are initiated, in particular, crosslinking of aromatic rings with H2 release. Adding initiation of thermo-oxidation radical chain scheme by these acts gives a possibility to explain regularities of PAI thermo-oxidation. For example, efficiency of transition metals compounds as thermostabilisers can be associated with formation of the additive-πsystem complex considering this act as the one competitive to occurrence of a molecular complex with O2.
7.4 Thermo-oxidative Degradation of Polysulfones, Polyesterketones, Liquid-Crystal Copolyesters [21, 30-39] Mass losses at dynamic heating of polysulfone based on bisphenol A and dichlordiphenylsulfone (PSF) in the absence or in the presence of O2 is characterised on the initial stage by rate constants equal to: 2.4 × 1013⋅exp(-190/RT) and 4.3 × 107 exp(-92/RT) min-1, respectively, i.e., in the absence of O2, decomposition is sharply accelerated. Oxygen absorption and release of CO2, H2O and CH2O accompany PSF heating at 300-350 °C. By the shape of kinetic curves, PSF oxidation is similar to other APH described previously: two-stage kinetics with the fast initial stage lasting 2-4 hours and the second slow stage with total O2 absorption depending on the temperature of, for example, 1-2 mol/base-mol during the next 10 hours and with effective activation energies of 72 and 11 kJ/mol for both stages, respectively. As oxygen partial pressure
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Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers reduces from 400 to 30 kPa, the oxidation kinetics (by O2 absorption and extraction of appropriate products) changes from σ- to s-shape. Thermo-oxidation in the melt leads to gel formation and PSF yellowing. These changes are identical to O2 absorption and depend on its pressure. At 300-350 °C the gel formation point corresponds to 1.5-3 hour exposure. However, the increase of all molecular mass distribution moments, especially Mz, is observed from the very beginning of thermo-oxidation. These changes are realised by branching PSF macromolecules, the branching frequency (λ) increasing linearly with exposure, finally reaching the limit value of λ = 0.250.36 per base-mole near the gel formation point. The calculation was performed for the long chain model that allowed determination of the intercross link point distance as ≅ 4-5000. In the absence of O2 at 320 °C, an insignificant branching (λ = 0.0055) is observed only 10 hours after, whereas the analogous process in the air gives λ = 0.008-0.015. The effect of shear loads on branching under the conditions of PSF thermo-oxidation is rather low. For example, in the test on rheoviscometer device, λ increases by 20% only with a 10-fold load. 13C NMR-spectra of PSF, oxidised in melt, display new signals of substitutes and non-substituted aromatic carbon atoms with chemical shears at 140-150 and 110-120 ppm. IR-spectroscopy data also confirm new substitutions of aromatic rings and expense of the main p-phenylene structure. It has been suggested that branchings occur from aromatic carbon atoms with branching points of the following types (Figure 7.2).
Figure 7.2
This enables us to introduce a concept of polar effects in homological reactions, seen in the kinetics of radical polymerisation and homolytic arylation of p-substituted benzenes. Combination of heterogroups with different electronegativity in the PSF structure – strong electron-acceptor sulfonyl (the Hammet constant σn = + 0.7) and electron-donor ether (σn = –0.32) groups, as well as weak electron-donor isopropylydene group (σn = –0.197), causes alternation of electron density on aromatic carbon atoms, which is naturally displayed in values of chemical shears of 13C NMR (see Figure 7.3). As chemical shifts of neighbouring ring atoms C differ by ~10 ppm, the difference in πelectron density reaches 0.055 e at the average proportionality coefficient of 180 ppm per electron. Aromatic radicals also display polar effects of p-substituents. PSF structure, as well as the one of polyestersulfones (PSF purely aromatic homologues, the ones based
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Figure 7.3 Sizes of chemical shifts of the nucleus of carbon in a molecule of PSF
on dioxydiphenylsulfone and dichlordiphenylsulfone and/or bis(4-chlorphenylsulfonyl)biphenol), is conductive to radical attachment decreasing activation barrier of the reaction at the sacrifice of the Coulomb interaction. The possibility of this qualitative approach is confirmed by weak crosslinking, compared to PSF and PES, structuring of polycarbonate (PC) under equal conditions – the polyester, produced similarly to PSF on the base of bisphenol A. Judging by 13C NMR, aromatic p-substitution in PC induces weaker alternation of π-electron density by ring C atoms. Homolytic arylation substitutes active radicals by hexadienyl or arylhexadienyl ones, are relatively stable due to polar effects of substituents. Calculation of the bond energy shows that C-CH3 in the isopropylidene fragment is a relatively weak bond in PSF and equals ≅ 220 kJ/mol. By all fragments of the structure, the previously-mentioned aromatic PSF homologues are characterised by bond strengths, levelled as ≅ 330-450 kJ/mol, and possess higher thermoresistance in the absence of oxygen. At thermo-oxidation, O2 greatly contributes to degradation. In the case of classical thermo-oxidation mechanism, O2 attack is aimed at aliphatic C-H-bonds under the condition of interlocking phenolic end groups. In response to PSF oxidation, only about 20% of absorbed O2 transits into volatile products: CO2, H2O and CH2O. The main part of O2 remains in PSF in the form of polymeric oxidation products. Aliphatic, C=O-, and aromatic, –OH- and C=O-, groups, accumulated simultaneously with expending CH3, are found in the oxidised polymer. Accumulation of aromatic oxygen containing groups in PSF and PES is already noted on the initial stage of the process, corresponding to the sigmoidal part of the kinetic curve of O2 absorption. For example, about 60-80% of CH3-groups remain after thermo-oxidation at 320 °C during 15-20 hours. Hence, the universally accepted model of separate oxidation of aliphatic fragments first, and then aromatic ones, is excluded. High-temperature oxidation touches upon and develops in aromatic and isopropylidene fragments of the PSF macrochain simultaneously. Similarity of oxidation gross-kinetics of PSF and polyethersilfone (PES), as well as of polyesterketones (PEK) indicates participation of aromatic rings in oxidation already on initial stages. Difference in thermoresistance is determined by microchain rigidity. Thermoresistance decreases (according to dynamic
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Specific Features of the Thermo-oxidation of Thermoresistant Heterochain Polymers TGA data in the air) in the sequence PEK > polydiphenylesterketone > 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
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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.
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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
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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
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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
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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,
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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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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(perfluoroalkyl- methacrylates) 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)
Poly(fluoromethacrylate)
Core Core
PMMA
Poly(fluoromethacrylate)
Poly-(MMA-S-azeotropic mixture), PC
PS
VA-ethylene copolymer
Poly(tetrafluoroethylene (plasma application)
Poly(organosiloxanes)
Poly(fluoromethacrylate)
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
Fluorine-containing polymers for materials with the complete internal light-reflection
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
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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
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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
Fluorine-containing polymers for materials with the complete internal light-reflection
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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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
Fluorine-containing polymers for materials with the complete internal light-reflection
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
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Fluorine-containing polymers for materials with the complete internal light-reflection
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
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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
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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; <ΔH12 + ΔH21>/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 <ΔHeff> 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 <ΔHeff> 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.
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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
Fluorine-containing polymers for materials with the complete internal light-reflection
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
Fluorine-containing polymers for materials with the complete internal light-reflection
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
Fluorine-containing polymers for materials with the complete internal light-reflection
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
Fluorine-containing polymers for materials with the complete internal light-reflection
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
Fluorine-containing polymers for materials with the complete internal light-reflection
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.
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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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A. Tanaka, H. Sawada and W. Noboru, Fujitsu, Science and Technology (Japan), 1987, 23, 3, 166.
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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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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.
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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
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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.
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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.
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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.
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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
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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
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The Fractal Analysis of Curing Processes of Epoxy Resins
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
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The Fractal Analysis of Curing Processes of Epoxy Resins
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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The Fractal Analysis of Curing Processes of Epoxy Resins
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 the curing reaction for the first system proceeds faster than for the second one and for 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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The Fractal Analysis of Curing Processes of Epoxy Resins
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.
290
(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.
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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
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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
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Fractal Analysis of Macromolecules
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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Polymer Yearbook
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,
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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
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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.
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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].
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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 w2<0 showed that the fractal is very compact and has a globular conformation in both cases. This state of a fractal was called collapsed, by analogy with the collapsed state of polymers. The conformation of clusters under these conditions was determined using the approach proposed [80] for studying the conformation of a branched polymer in a monodisperse melt, i.e., in a solution of coils with identical sizes. In the case of minimisation of the free energy with respect to R: D=d
(11.21)
For a purely statistical fractal for which D = 4, we obtain dst = 4. This means that this type of statistical cluster is compact up to d = 4. Therefore, Family [9] called this state of statistical fractals the collapsed state. In the case of an isolated fractal, attractive interactions predominate below the compensation point; the second virial coefficient w2 is negative and cannot be neglected in the power
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Fractal Analysis of Macromolecules series mentioned previously. The conformation of a fractal is determined by the balance between the first two terms in this series. The results are identical to Equation (11.21) for dst = 4. Thus, the conformation of an isolated statistical fractal below the compensation point is the same as the conformation of a big cluster below the critical point.
11.5 Experimental Determination of Fractal Dimensions Let us consider several experimental estimates of various fractal dimensions for polymers with allowance for the above theoretical statements. The index v in Equation (11.4) has been determined by small-angle neutron scattering for epoxy polymers [81]; it was found that v = 0.6. It has been suggested [82] that so great a v value is due to the enhanced chain rigidity of epoxy polymers. However, the use of Equation (11.11) with ds = 4/3 and d = 3 gives v = 0.666, which is close to the experimental v value (see Table 11.2, the permeable coil model). Calculation using Equation (11.12) for ds = 4/ 3 and v = 0.6 gives D ≈ 2.22, which is close to the fractal dimension for the compensated state of branched polymers in accordance with Equation (11.20). Silicate gels and epoxy polymers have been studied by Raman light scattering [35, 82]. The spectral dimension 4, of silicate gels falls within the range from 1.11 to 1.43, depending on the method of calculation, which is consistent with the conclusion drawn by Alexander and Orbach [28]. The results of estimates of ds from the data of Raman scattering and small-angle neutron scattering for two epoxy polymers with crosslinking densities differing by a factor of two and for the monomer used to prepare these epoxy polymers are presented in Table 11.4. Attention is drawn to the fact that the ds values for all the three specimens are virtually equal (if the inaccuracy of determination of ds is taken to be ±0.05 [36]), the slight difference being due to the determination method used.
Table 11.4 Value of ds for the DGEBA monomera and for epoxy polymers based on it determined by Raman light scattering (I) and small-angle neutron scattering (II) methods [82] Example
I
II
b
1.37
1.44
b
1.33
1.44
1.32
1.52
DGEBA EDA 1X DGEBA EDA 2X DGEBA a
b
Diglycidyl ester of bisphenol A. Ethylene diamine.
305
Polymer Yearbook The results of investigation of the transfer of energy between molecules acting as electron density donors and acceptors have been reported [83, 84]. The Raman scattering method gives actually the fractal dimension of the surface on which the energy transfer takes place [84]. The fractal dimensions found for silicates are in the range of 2.23-2.82 [84]; that for a polystyrene film is 2.2 [83]. Kopelman and co-workers [70] have studied the annihilation of the triplet excitons in naphthalene aggregates located in the pores of various materials including polymers. A common feature of these systems is non-classical annihilation kinetics, which resemble the annihilation kinetics of fractals. The coefficient of the annihilation rate ka varies with time t: ka ~ t − h
(11.22)
where h is the non-homogeneity index (0 < h < 1), which is equal to zero only for homogeneous specimens. The effective spectral dimension of the medium d′s is given by the relation [73]: ds′ = 2(1 − h)
(11.23)
The d′s values for several polymers are listed in Table 11.5. Kopelman and co-workers [10] also measured h as a function of temperature. At low temperatures, all the polymers studied exhibit properties similar to the properties of fractals. As the temperature increases, h decreases, i.e., the d′s value increases. In some specimens, h → 0 as the temperature is raised. This implies that all the effects described by fractional dimensions are associated with disorder [85]. A number of specimens also behave as fractals at room temperature. It is noteworthy that the d′s values for the polymers studied vary over wide limits, from 0.8 to 1.8. In the case of PMMA, d′s exactly corresponds to the spectral dimension determined by Raman scattering measurements [22, 35]; it is ~ 1.8 in both cases.
Table 11.5 Effective spectral dimensions d′s for some polymers [10] Pore size, mm
T/κ
H
d′s
Acetate A8
0.2
4
0.16
1.2-1.7
Acetate A1
0.1
4
0.47
0.8-1.1
Acetate A3
1.2
4
0.44
0.9-1.1
Nylon B214
0.2
4
0.21
1.2-1.6
Poly(methyl methacrylate)
—
77
0.1
1.8
Polymer
306
Fractal Analysis of Macromolecules The theoretical concepts outlined previously are confirmed rather accurately by experimental data. Nevertheless, it is worth noting that the concept of polymeric (macromolecular) fractal [56] has been developed for polymer solutions, while the Vilgis theory [61, 62] is applicable only to rubbers and polymer melts, although it has been developed for condensed media. Therefore, it can be expected that extension of these concepts to the vitreous state of polymers would require some corrections taking into account the specific features of this state. Some possible approximations have been considered by Cates [56], who concentrated attention on macromolecular entanglements, which play an important role in the description of the behaviour of block polymers [86-89]. Cates believes that the fact that the concept of polymer fractal neglects the effects of macromolecular entanglements is the main drawback of this theory. Nevertheless, Cates [56] introduced several simplifications that make it possible to ignore these effects for dilute solutions and relatively low molecular masses. However, in the opinion of Cates, even in the case of predominant influence of entanglements, theoretical interpretation of this phenomenon is impossible without preliminary investigation of the properties of the system in terms of Rouse-Zimm dynamics, which can serve as the basis for a more complex theory. It was assumed [56] that the effects of entanglement can be due to the substantially enhanced local friction of macromolecules.
11.6 Levels of Fractality Polymers exhibit the fractality inherent in them at different structural levels; both primary and secondary structural elements can be fractals. For example, macromolecular coils in θ or in good solvents with df ≈ 1.66 (with the Euclidean dimension d = 3) are fractals [1, 29]. The fractality of a polymer at the molecular level can be demonstrated as follows. Lebedev [90] reported data on the change in the radius of gyration (Rg) of the macromolecules of block polystyrene, PMMA and polyethylene with the molecular mass Mw. The Rg value is related to the length of a macromolecule Lw in the following way [91]: L w ~ Rdg f
(11.24)
The length of a macromolecule can be determined from the known Mw, the molecular mass of one unit m0, and the projection of the bond length l0 on the macromolecular axis using the simple dependence: Lw =
M wl 0 m0
(11.25)
The m0 and l0 values for the polymers mentioned above were taken from [92] and [93], respectively.
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Polymer Yearbook
Figure 11.3 (a) Chain length Lw versus the radius of gyration (Rg) for (1): a macromolecular coil of polysterene (2): PMMA and (3): polyethylene and (b) a variant of the elements of the Koch curves having df = 1.61.
Figure 11.3a shows the variation of Lw versus Rg. Taking account of this dependence, it was found that df ≈ 1.60, which is close to the corresponding value for a macromolecular coil in a θ-solvent (df ≈ 1.66, see Table 11.2). The elements of Koch figures (Figure 11.3b) resemble most closely the freely jointed chain model, which is normally used to simulate macromolecules [94]. For this version, df = 1.61. Thus, the fractality of a block polymer at a molecular level can be regarded as proven. The cluster model of the structure of amorphous polymers (Figure 11.4) provides a quantitative description of supermolecular (supersegmental) structures in this type of polymer. The cluster with chains protruding from it (‘interpenetrating’ molecules) assumed in this model resembles the well-known cluster used in the Witten-Sander (WS) model [80, 81]. Such a cluster distinguished in a polymer bulk restricted by the radius Rw would possess at least two features typical of fractal clusters. One feature is self-similarity, caused by the presence of unstable clusters consisting of fewer segments than thermodynamically stable clusters (Figure 11.4 shows them consisting of two segments). The other feature is that the density of particles (statistical segments) comprising the cluster would decrease on moving away from the cluster center and thus stipulate the ρ(L) dependence typical of fractals (see Figure 11.1). In conformity with this dependence, it is assumed that the
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Fractal Analysis of Macromolecules
Figure 11.4 Cluster model of the structure of an amorphous polymer.
structure of an amorphous polymer contains sorts of ‘thickened’ and ‘rarefied’ sections. This ‘thickening’ of the material can be explained by assuming the existence of a local order (as opposed to the model of interpenetrating macromolecular coils, i.e., the ‘felt’ model, proposed by Flory) [95, 96]. Thus, the fractality of the structure of amorphous polymers in the ~ 0.3-5.0 nm range, shown experimentally in a number of studies [22, 36], is confirmed indirectly by the presence of local order. The size of a fractal cluster Rw and the number of particles in it (Nr) are related to each other by the following expression [92]: N r ~ Rdwf
(11.26)
Let us consider the procedure for estimation of the Nr and Rw values in terms of the cluster model [15, 89]. A cluster is regarded as a multifunctional unit in a fluctuation net-work of macromolecular entanglements; therefore, according to Flory [43], the reduced molecular mass M per cluster is estimated from Equation (11.4). By dividing M into the molecular mass of a statistical segment, we obtain the number of particles (statistical segments) (Nst) per cluster. The distance between the clusters Rcl should be taken as Rw: ⎛ 2V ⎞ R cl = 18⎜ cl ⎟ ⎝ F ⎠
− 13
(11.26a)
where Vcl is the density of the cluster network and F is the cluster functionality.
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Polymer Yearbook
Figure 11.5 Number of statistical segments (Nst) in a cluster versus its radius Rw for (1): amorphous and (2): amorphous-crystalline polymers under the assumption that the size of fractal and percolation cluster are equal.
Figure 11.5 presents the dependence of Nst on Rw, for five amorphous vitreous and five amorphous-crystalline polymers [8]. It can be seen that this correlation is fully consistent with relationship (11.26). The df value of the cluster structure determined from the slope of the straight line is ~ 2.75. The fractal dimension of the cluster in the WS model lies in the range of 2.25-2.75 [91], which is in agreement with the above estimate. The fractal dimension for the structure of the amorphous polymer can be found from the relationship [97]: df = (d − 1)(1 + μ )
(11.27)
where μ is the Poisson ratio. For a cluster structure with df ≈ 2.75, the μ value is equal to ~ 0.375, which is consistent with the known μ values for amorphous glassy polymers [98, 99]. As an example of fractality displayed in polymers at a macroscopic level (a secondary structural element), we shall consider the growth of a crack in a film of amorphous vitreous polyarylate-sulfone [100] (see Figure 11.6).
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Fractal Analysis of Macromolecules
Figure 11.6 Crack coast-line versus the distance to its tip rsk for 1: polycarbonate and 2: polyarylate.
This provides grounds for describing them in terms of fractal models [101-103]. The triangular profile throughout the whole period of growth of the crack allows the use of the relationship proposed by Mosolov [101]: D sk / 2 dsk ~ rsk
(11.28)
where dsk is the crack opening, rsk is the distance from the crack tip and Dsk is the fractal dimension of the crack. Figure 11.6 shows the plots for the variation of δsk versus rsk for two amorphous polymers; the plots correspond to relationship (11.28). In other words, a stable crack in polymer film samples is a stochastic fractal with the dimension Dsk ≈ 1.48. The linearity of plots shown in The examples considered previously do not reflect the whole diversity of manifestation of fractality in polymers. Nevertheless, they help to understand the meaning of the term ‘multifractality’ as applied to polymers.
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Polymer Yearbook
11.7 Fractal Characteristics of Macromolecules Condensed systems start to behave as polymers after a certain molecular mass has been attained and a network of macromolecular entanglements or chemical nodes has been formed [57]. In consideration of condensed polymers, it is especially important to describe the sections of the macromolecule between the points of chemical crosslinking or entanglements [56]. The deformability and mobility of these sections largely determine the macroscopic properties of polymers [57, 104]. The general physical grounds that account for the fractality of these chain sections are considered next in relation to epoxy polymers. To determine the fractality of an object, three aspects are usually considered [12]. First, as noted previously, a real physical object possesses fractal properties only in a definite scale range (see Figure 11.1). The boundary sizes for a macromolecular section can be determined using the data of several publications [22, 36, 105]. The lower boundary is related to the finite size of a structural element; in terms of the cluster model, this is the length of the statistical segment lst. lst = l0C ∞
(11.29)
where lo is the length of a chemical bond and C∞ is the characteristic ratio. For most polymers, l0 = 0.125 nm [93], the minimum C∞ = 2 [94]; therefore, the minimum possible lst is 0.25 nm. This value is in good agreement with the experimental estimate of the lower limit of fractality in polymers (~ 0.3 nm [22]) and should be accepted as the Lmin for the chain section between chemical crosslinks. The length of this section Ls can be taken as the upper limit. For most of the epoxy polymers considered, this value is in the range from ~ 1.6 to 7.4 nm, which is also consistent with the data of [22, 36]. The second aspect is associated with the self-similarity of the object considered. A section of the macromolecule between chemical crosslinking points represented by a freely jointed Kuhn chain or by a chain with free or hindered rotation about the bond [94] is simulated by a broken line having the topological dimension dt = 1 [3]. In the case of simulation by the freely jointed Kuhn chain, the broken line consists of Ns statistical segments of length A, each of them being simulated by a straight-line segment. These straight-line segments are standard self-similar objects but the chain sections consisting of them are self-similar only when their lengths Ls and the A values vary proportionally. For the epoxy polymers in question, this condition is fulfilled [106]; therefore, these sections are self-similar objects [107].
312
Fractal Analysis of Macromolecules Finally, the third aspect concerns determination of the fractal dimension D of an object [12]. For fractals, the condition: D>dt 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 dt
R2s = L s A −
(
A 1 − e −2L s A 2
)
(11.35)
Equation (11.35) points to a decrease in Ls at a constant Rs and, hence, to a decrease in D, in conformity with Equation (11.31). Note that the condition Ls/A<10 holds for nine of the ten specimens of epoxy polymers; this automatically means that D < 2 [8]. The hindrance of rotation of the macro-chain around bonds, which necessarily occurs in a vitreous polymer, accounts for the decrease in the real A value to Arot according to the relationship [94]: σ2 =
A A rot
(11.36)
The hindrance parameter σ can be determined from the empirical equation [104]: Tg = C(σ − 1)
(11.37)
where Tg is the experimental glass transition temperature and C is a constant (for carbonchain polymers, C = 270 K). Now we can calculate non-fractal values Rs and Ls as functions of the crosslinking density (νs) using Equation (11.29) and the relationship [107]: Ls =
Fch 2Sνs
(11.38)
where Fch is the functionality of a chemical crosslinking point (hereinafter, we assume that Fch = 4) and S is the cross-section area of the macromolecule.
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Fractal Analysis of Macromolecules
Figure 11.7 Fractal dimension (D) of a macromolecule section between chemical crosslinking points versus crosslinking density (vs) for epoxy polymers based on epoxy oligomers and amino-containing curing agents. The D values were found from Equation (11.31) for a=Arot (1), A (2) and 0.25 nm (3).
The results of calculation of D as a function of vs for the epoxy polymers considered here using Equation (11.31) with a = Arot, L = Ls and R = Rs are shown in Figure 11.7, curve 1. It can be seen that the allowance for the hindered character of rotation has resulted in a monotonic decrease in D following an increase in As [104], this implies a decrease in the mobility (deformability) of the macromolecule section between the points of chemical crosslinking. The calculation of D from Equation (11.31) for a = A gives D ≈ 2 irrespective of vs; (Figure 11.7, curve 2). Finally, when persistence of the chain section is taken into account, i.e., the chain parameters vary according to Equation (11.35), a somewhat higher D value is obtained, although the difference does not exceed ~3%. The change in the scale of measurements also changes the fractal dimension of the chain. Curve 3 in Figure 11.7 reflects the dependence of D on vs for a = 0.25 nm, i.e., for the minimum size. This curve runs parallel to curve 1 but is characterised by somewhat lower D (by ~ 3%-13%). Our choice of the scale of measurement of Arot (or lst) is due to the fact that it reflects the real state of the chain under particular conditions (‘natural’ scale of measurements). Let us discuss in more detail the physical meaning of the fractal dimension (D) of a chain section between chemical crosslinking points (or between entanglement points). Substitution of L = Ls, R = Rs, and a = lst in Equation (11.31) gives the relationship [104, 109]:
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Polymer Yearbook L s ⎛ Rs ⎞ =⎜ ⎟ lst ⎝ lst ⎠
D
(11.39)
which implies that when D=1, Ls=Rs, i.e., the chain between the crosslinks is completely stretched and loses the capacity for deformation (mobility). This is consistent with the data of a paper [53] according to which D = 1 corresponds to a completely uncoiled chain (see Table 11.2). Recall that the condition D = 1 means that the given section of the macromolecule has completely lost fractal properties. When D = 2, we obtain the maximum possible length of the chain section Ls for a fixed Rs and the greatest Lst, i.e., the chain deformability (mobility) is the most pronounced in this case. Note that the highest stretching ratio Amax for a given chain section is equal to Ls/Rs [110, 111]. It is clear that D = 2 is attained for rubbers, and intermediate values, 1
1 − cos θ ν cos θ ν
(11.40)
Figure 11.8a shows schematically two consecutive bonds with the length l0. The total length of such a section l projected onto the axis of one of the bonds is equal to: l = l0 + l0 cos θ ν
(11.41)
It is clear that the smaller θv, the greater the second term in Equation (11.41) and the greater Ls. The maximum Ls value is attained for tetrahedral angles (θv = 70.5°) [94]. The distance between the crosslinks determined in this way (we shall call it conformational length Lconf) is obviously equal to: L conf =
L sl 2l0
(11.42)
Another physical representation of the effect in question is the use of the reptation model [42], in which a macromolecule is assumed to be encapsulated in a ‘tube’ of a finite
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Fractal Analysis of Macromolecules
Figure 11.8 Schemes of two adjacent bonds of (a) macromolecule and (b) the enveloping tube
thickness (Figure 11.8b). In this case, the topological skeleton of the chain consists of Npr units of length Npr, which form a primitive path with the length: L pr = N prl pr
It is also assumed that the ends of fragments of the primitive path with the length lpr are fixed in a definite manner; therefore, the Npr and Lpr values can be found fairly easily using lpr. The Lpr value can be expressed as follows [42]: L pr = L s
A rot l pr
(11.43)
where lpr is assumed to be equal to the distance between clusters Rcl, which can be calculated from Equation (11.26a). The length of the fractal broken line Lf is expressed in the following way [3]: L f = L ′a1− D
(11.44)
where L′ > 1 is the length of the non-fractal line.
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Polymer Yearbook Since the L s value determined using Equation (11.38) is calculated, in the first approximation, as the length of a cylinder with the cross-section area S, i.e., of a nonfractal object, it can be assumed that L′ ≈ Ls. If the two examples above point to the presence of fractal properties of a section between chemical crosslinks (entanglements), the following relation should be obeyed: L f ≈ L conf ≈ L pr
(11.45)
Relationship (11.45) actually holds (with a deviation of ± 20%) for epoxy polymers based on bisphenol A and cured by diamine (EP-1) or anhydride (EP-2) (Figure 11.9) [48]. This indicates that the fractality of the macromolecule section between chemical crosslinking points (entanglements) in a vitreous polymer is due to known mechanisms of the change in the statistical rigidity. It follows from Equation (11.39) that the loss of fractality by a chain section, irrespective of the scale of measurements, takes place in the case of full stretching of this section between crosslinking points (entanglements), i.e., when Ls = Rs. In addition, for a → 0, the L(a) value would tend to a final limit equal to the length of the straight line. Figure 11.10 shows the D(a) plots for EP-1. It can be seen that, when a → 0, the fractality of the
Figure 11.9 Relationships between the conformational length Lconf (1, 3) and primitive path Lpr (2, 4) of the chain section between chemical crosslinking points and its fractal length Lf for EP-1 (1, 2) and EP-2 (3, 4).
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Fractal Analysis of Macromolecules
Figure 11.10 Fractal dimension of the macromolecule section between chemical crosslinking point (D) versus scale of measurement a for EP-1 with vs of 1: 0.2 × 10-27m-3, 2: 0.6 × 10-27m-3, 3: 1.7 × 10-27m-3.
chain section between crosslinking points is retained. Therefore, the behaviour of this section of a macromolecule is more intricate than that of a fractal broken line; this can be due to a more complex structure of the macromolecule. Indeed, transition to a nonfractal behaviour requires not only that condition Ls = Rs be fulfilled, as for an ordinary broken line, for example, for a coast-line, but also that a conformation condition — Equation (11.30) — be fulfilled. In this case, it is necessary that the bond angle θv reach a value which complies with the equality (for lst = A): C∞ =
θ A cos ν 2 l0
(11.46)
A chain for which D ≠ 1 can be referred to as ‘true fractal’. Examination of Equations (11.26a) and (11.38) leads to yet another, at least formal, reason for the fractal properties of the section of a macromolecule between the crosslinks. For a given crosslinking density, the Ls value (unlike Rs) depends on the cross-sectional area S of the macromolecule, which should also result in the variation of D. Figure 11.11 shows the dependences of D on S for two arbitrary vs values, namely, 1 × 1027 and 2 × 1027 m-3. It can be seen that D rapidly decreases as S increases; when S ≈ 0.80 and 0.55 nm2, respectively, D reaches the lower limit (D = 1). This implies full ‘freezing’ of the molecular mobility of the chain [104], which should result in a high
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Polymer Yearbook
Figure 11.11 Fractal dimension of a section of macromolecule between chemical crosslinking points (D) versus cross-sectional area of the macromolecule S with vs of 1: 1 × 10-27m-3, 2: 21 × 10-27m-3.
fragility of the polymer. This assumption is confirmed in practice. It is known that polystyrene and PMMA are fragile polymers (S = 0.698 and 0.638 nm2, respectively), and poly(n-dodecyl methacrylate) and poly(n-octyl methacrylate) are highly fragile polymers (S = 1.766 and 1.351 nm2, respectively) [112]. Thus, the section of the macromolecule between chemical crosslinks and physical entanglements possesses fractal properties. This is due to the fact that the length of this section is shorter than the size of the macromolecule. This factor is due to various steric restrictions, which induce deviations from the behaviour predicted by Equation (11.30). In the general case, Equation (11.30) is valid for a non-perturbed (quasi-equilibrium) coil [32]; therefore, the fractality of the chain section considered can be interpreted as being due to the deviation from the quasi-equilibrium state [12]. The deviation changes the degree of the ‘sinuosity’ of the macromolecular section (i.e., the length of the statistical segment); therefore, the lst (or A, or Arot) value can be considered to be a ‘natural’ scale of measurement. Since the structure of a macromolecule is more complex than the geometric image represented by a broken line, its behaviour would also be more complicated; this is confirmed by the change in D when a → 0. In other words, the section of a macromolecule between crosslinks has configurational fractal properties, stipulated by the mutual arrangement of the rigidity sections of the macromolecule, and conformational fractal properties, caused by the state of the bonds within this rigidity section (statistical segment).
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Fractal Analysis of Macromolecules
11.8 The Dimension of the Sections of a Macromolecule Between Topological Fixing Points A crosslinked polymer is formally one giant macromolecule (fractal cluster); therefore, the models considered above provide the dimension df of exactly this cluster. The Vilgis concept [61, 62] assumes the existence of several clusters of this type and linear macromolecules between them. In practice, parameters used more widely are the density of the network of nodes (chemical crosslinks) νs or the molecular mass of the macromolecular section between the crosslinks Ms, which are related to each other in the following way: νs =
ρN A Ms
(11.46a)
where NA is the Avogadro number and ρ is the polymer density. In a study by Sandakov and co-workers [50], the term ‘molecule’ for crosslinked polymers was used to denote only a section of the macromolecule with the molecular mass Ms, because it is known [44] that it is the parameters vs and Ms that determine the properties of network polymers. In addition, the difference between the scales of fractality of a big macromolecular cluster and the polymer structure in the vitreous state should be taken into account, i.e., one should have in view lengths of the order of ~ 0.3-5.0 nm where a macromolecule is a fractal [22]. Below we consider practical aspects of the estimation of the fractal dimension D of a macromolecule section between chemical crosslinking points with allowance for these statements as well as for those considered in the preceding Sections. This approach differs fundamentally from that of the Cates [56] and Vilgis models [61, 62]. All the foregoing is valid not only for a network of chemical bonds but also for a network of macromolecular entanglements in linear polymers. Several methods for the estimation of the D value exist. One method makes use of the relationship [113]: D=
ln nst ln lst
(11.47)
where nst is the number of statistical segments of length lst in a chain fragment between entanglements (chemical crosslinks).
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Polymer Yearbook Yet another variant of calculation of D is given by Equation (11.39). The following relationship has been obtained [114]: 2 = CD ∞ ϕ cl
(11.48)
where (ϕcl is the relative part of local order (clusters) in the polymer. The relationship between D and df [see Equation (11.27)] is reflected by the expression [115, 116]: D=
ln nst ln( 4 − df ) − ln(3 − df )
(11.49)
The D values estimated using Equations (11.39) and (11.47)-(11.49) vary from 1 to 2. The use of fractal analysis makes it possible to relate molecular parameters to characteristics of supermolecular structure of polymers. Figure 11.12 illustrates the linear correlation between D and df [df was estimated from Equation (11.27)] for epoxy polymers. When the molecular mobility is suppressed (D = 1), the structure of the polymer has the fractal dimension df = 2.5, which corresponds to μ = 0.25. The given value of the Poisson coefficient corresponds to the boundary of ideally brittle structure; at μ< 0.25, the polymer is collapsed without viscoelastic or plastic dissipation of energy [3]. This is fully consistent with the Kausch conclusion [117] stating that any increase in the molecular mobility enhances dissipation of the mechanical energy supplied from the outside and, as a consequence, increases plasticity of the polymer. When D = 2 the df value is equal to 3, which corresponds to μ = 0.5, typical of the rubbery state. Figure 11.12b shows the variation of D versus Vs for the epoxy polymers considered here. The dependence is non-linear, the D value decreases with an increase in vs; even for small vs values, a substantial decay in D is observed. It is of interest that the end of this decay and transition to a much slower decrease in D takes place at vs ≈ 8 x 1026 m-3, which corresponds to ~ 10 monomer units between the crosslinks. Actually, this can be interpreted as transition to densely crosslinked epoxy polymers in which an increase in vs influences the suppression of the molecular mobility to a substantially lower degree than in the region where vs = 0.8 x 1027 m-3 [8]. If the conformational and/or physical state of the section between crosslinks are assumed to coincide with that of the whole macromolecule (see Table 11.2), the plot shown in Figure 11.12b allows one to judge the nature and the ranges of variation of these states. The first characteristic dimension D = 2 corresponds to the state of a statistical coil in an 322
Fractal Analysis of Macromolecules
Figure 11.12 Correlation between fractal dimensions of the structure df and the chain section between chemical crosslinking points D(df) dependence (a)and the D(vs) dependence (b) for EP-1 (1) and EP-2 (2) [109]. The straight line was drawn through the points: D = 1.1, df = 2.5 and D = 2.0, df = 3.0.
ideal solvent, the second one D ≈ 1.67 corresponds to an impermeable coil in a good solvent, the third one D = 1.50 is matched by a permeable coil (the state typical of rigidchain polymers), and the fourth value, D = 1, describes a completely uncoiled macromolecule [51]. It can be assumed that the increase in the crosslinking density between the above D values is accompanied by gradual transition from a state with greater D to a state with smaller D. Thus, depending on vs, a network polymer can be both a rubber and a rigid-chain polymer [118]. Therefore, it is evident that the knowledge of these regularities is important for controlling the properties of network polymers. Now we attempt to estimate D within the framework of the theoretical views on polymer fractals [22, 36, 56, 61-64]. It is assumed [68] that the fractal dimensions ds, dw, and D are related to one another via an expression similar to Equation (11.8). The relationship between the parameters ds and D has been considered [6]. It is believed that d´s is a dynamic value which responds to a change in the conditions of the interaction of a macromolecule with its surrounding and D is a static parameter. However, in our opinion, the opposite situation occurs in reality; this is indicated by the following facts, some of which have been noted previously. It has been shown experimentally [72] that a two-fold increase in the crosslinking density does not change ds, while, according to the plot shown in Figure 11.12b, vs has an appreciable influence on D. Moreover, the monomer and the crosslinked epoxy polymer have nearly identical ds values (see Table 11.4). Helman
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Polymer Yearbook and co-workers [68] proposed a fractal model in which they use the notion of weightless bridges. In accordance with this model, ds is equal to D when the concentration of these bridges is relatively high. However, theoretical analysis and computer simulation [10] show that the inclusion into consideration of bridges of a finite length does not change the spectral dimension of the system. With allowance for this fact, it was assumed that the ds value would be equal to that determined experimentally for an epoxy polymer in a three-dimensional space, ds = 1.44 [72]. Two hypotheses can be used to estimate dw: the Alexander - Orbach (AO) and the Aharoni - Stauffer (AS) hypotheses [10]. The AO hypothesis is based on the following relationship: dw =
3 df 2
while the AS hypothesis assumes the relationship: d w = 1 + df
It is considered that dw is determined by the properties of the supermolecular structure of epoxy polymers, namely, by the degree of local order in them. This assumption arises due to the well-known succession of relationships between the diffusion process and dw [28], between the diffusion process and the fluctuation free volume ffv [119], and between ffv and the cluster structure [120]. Therefore, the fractal dimension of the cluster structure of crosslinked polymers [105, 110], estimated from Equation (11.27), is taken to be ds. Since the D value is determined for an Euclidean space with d = 2, it was also assumed in Equation (11.27) that d = 2. The ds value was found for a three-dimensional space; therefore, a graph [121] for converting ds from three- to two-dimensional space was used in subsequent calculations. The D values were further calculated from Equation (11.8) in terms of the AO and AS hypotheses. Figure 11.13 shows the dependences of D on vs calculated from Equations (11.8) and (11.39). The dependences of D on vs and the absolute magnitudes of D are in good agreement, especially when the AO hypothesis is used. When vs is low, the D values calculated from Equation (11.39) deviate toward the curve estimated using the AO hypothesis. Nevertheless, the discrepancy between the calculations by two methods does not exceed 10%. Thus, the fractal dimension of a section of the macromolecule between chemical crosslinking points in network polymers varies over limits close to those predicted for a fractal broken line, i.e., 1≤D≤2. The dimension D can serve as a measure of the molecular mobility and is related to the fractal dimension of the cluster structure of epoxy polymers
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Fractal Analysis of Macromolecules
Figure 11.13 Fractal dimension of the chain section between chemical crosslinking points (D) versus crosslinking density versus calculation using Equation (11.39) for EP-1 (1) and EP-2 (2); calculation using Equation (11.8) for EP-1 and EP-2 in terms of the AS (3) and AO (4) hypotheses.
df. The dependence of D on df can also be derived theoretically. The calculation procedures proposed take into account the influence on D of characteristics of the molecular and topological structural levels of crosslinked polymers.
11.9 The Concept of Macromolecular Skeletons 11.9.1 The Model of a Network Polymer The model of network polymers considered next describes quantitatively the formation of structure (and, hence, properties) and is based on fundamental principles of physics. The initial parameters used for crosslinked systems are the v s value (topological characteristics) and some generally accepted molecular parameters. Since the chemical crosslinking processes are complex, the model makes use of the simplest scheme of structure formation, which does not take into account, for example, the decrease in the rate of structure formation with time when one structure element starts to influence the conditions of formation of an adjacent element. An example of taking account of effects of this type has been reported [117]. Although this scheme is simple, it provides a quantitative description of the processes considered and the structures formed. One point of the model under discussion is estimation of the relationship between vs and the level of local order in the structure of epoxy polymers, which is characterised by the
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Polymer Yearbook density Vcl of the cluster network of macromolecular entanglements [104-106]. A parameter characterising the level of local order more rigorously is the fraction of clusters ϕcl in the polymer. Curing is supposed to be a turbulent process because it requires mobility of structural elements and takes place in a viscous medium. In addition, transition to a turbulent mode implies an increase in the degree of ordering, i.e., self-organisation of dissipative structures such as clusters [122]. A fundamental property of turbulent flows is fractality of turbulent structures [3, 10]. It is generally believed that dissipation of energy in threedimensional turbulent flows is concentrated on a set with a non-integral fractal dimension. However, experimental data on the beginning of fluctuations indicate that the smallscale properties of a turbulent flow cannot be described by virtue of fractals [3]. Therefore, turbulent dissipative structures are described using ‘non-homogeneous fractals’, the rules of formation of which are chosen at random at each step of scale hierarchy in accordance with some probability distribution [123, 124]. In this case, the transfer of energy is described by virtue of a random fragmentation model with the assumption that no correlations exist between stages of the process. Nevertheless, it is possible to calculate the fractal dimension of turbulent structures (Df), which is defined by the relationship: N n ~ L−nD f
(11.50)
where Nn is the number of active vortices at an n-th fragmentation step, Ln is the scale of the n-th vortex, and D is estimated using the following Equation [10]: Df = 3 + log 2β
(11.51)
in which β is the fraction of the volume occupied by vortices of the scale Ln. As a first approximation, it can be assumed that Df = dft, where dft is the fractal dimension of the topological structure of the polymer, which can be found from Equation (11.27). It is clear that the chain fragments with the molecular mass Ms are considered in a plane (d = 2) and the formation of clusters is discussed in a volume (d = 3). The D value calculated from Equation (11.39) for a two-dimensional fractal can be used to find the value for a three-dimensional fractal by applying Equation (11.27) to the dimension dft. This method is not highly accurate but simple. Equation (11.51) makes it possible to determine the fraction of volume β occupied by vortices of the Ln scale. Assuming that the β and ϕcl values are equal, the Vcl value can be calculated from the relationship: Vcl =
326
ϕ cl Sl0C ∞
Fractal Analysis of Macromolecules Comparison of the Vcl values found in this way with those obtained experimentally [48] for systems EP-1 and EP-2 showed that the two methods provide the same order of magnitude. Nevertheless, to attain better agreement between the results, it can be assumed that not all the active turbulent vortices are converted into local order regions; in general, this is obvious due to the fluctuational nature of these regions [92]. This means that ϕcl = Cβ, where C is a proportionality coefficient. Assuming that for EP-1 and EP-2, C = 0.6, we obtain a much better quantitative agreement between experimental and calculated data. It is clear that the coefficient C reflects the influence of variable characteristics of curing such as temperature, time, viscosity of the medium, etc. The fact that the dimension of non-homogeneous fractal Df is always greater than the dimension of the corresponding homogeneous fractal dft might serve as yet another reason for the inconsistency between the ϕcl and β values, mentioned above [125]. The condition Df > dft implies a decrease in β in the calculations using Equation (11.51). Fractality of the structures of polymers influences their properties. According to modern concepts [126-128], the T g of amorphous polymers is regarded as the formation of ‘frozen’ local order (dissipative structures). Generally, for amorphous systems, this is considered to be a complex and hierarchically multistage process. The first stage involves the formation of seeds of microcrystals, which are unable to grow and serve as a sort of substrate for deposition of amorphous clusters. The second stage is characterised by self-organisation of mesoclusters [129]. As applied to the T g of polymers, these processes can be specified in the following way. The first stage starts at the temperature of so-called liquid-liquid transition Tll, in which regions of dynamic short-lived local order are formed [23]. At the T g , avalanche-like accumulation of clusters takes place, which characterises the formation of ‘frozen’ local order (the second stage). For this process: τ* ~ (R *)
df
(11.51a)
where τ* is the time before the onset of this process and R* is the critical cluster size [101]. Since the temperature-time superposition is correct for polymers, we assume that R* ~ lst and write relationship (11.51a) in the following form: Tg ~ lst−a
The dependence of the experimental Tg values [115] on lst for epoxy polymers can be represented by a correlation function. In addition, α = 0.28, which complies with the necessary condition α = d — df [91]. Hence, the change in Tg upon the variation of vs is also an indication of the fractal structure of network polymers.
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Polymer Yearbook Note that the behaviour of network polymers is in agreement with several other fundamental physical principles. Let us illustrate this by two examples. An integral stoichiometry implies stability and ordering of the structure of a compound [3]. This is confirmed by the data of Beloshenko and co-workers [105], according to which the maximum degree of local ordering in epoxy polymers is attained when an oligomer and a curing agent are taken in stoichiometric amounts, i.e., when K = 1.0 (or is close to 1). Structure parameters and characteristics of properties of epoxy polymers are not random values either. Thus the length of statistical segment lst obeys the automodelling relationship: lst , i lst ,( i +1)
=Δ
1
m
(11.52)
where Δ = 10 and m varies according to a geometric progression law: m = 1, 4, 8,16, 32,… , 2 n ,… , ∞
(11.53)
Hence, formation of the structure and properties of epoxy polymers during curing is determined by fundamental physical principles. This is accompanied by the change in the characteristic ratio C∞ (molecular characteristics), although the structure of the macromolecule remains invariant. The use of the above physical principles even in the simplest version provides a correct description of the structure and properties of network polymers.
11.9.2 Scaling Representation of a Macromolecule A number of methods exist for the modelling of polymers at a molecular level. One of the most widely used methods is scaling presentation [54], according to which the diameter ø of the ‘tube’ in which the macromolecule is enclosed (it is equal to the distance between the entanglement points) can be estimated from the ratio [75]: Ø2 = C ∞
Msl20 m0
(11.54)
The main difference between physical entanglements (loops) and chemical crosslinks is that the former allow creeping of chains. The density of both types of link are determined using the same rubber elasticity equation, a factor of 0.8 being frequently added to take creeping into account [75].
328
Fractal Analysis of Macromolecules Yet another representation of a macromolecular chain as a fractal is considered next. Olemskoi and Flat [130] have noted that the concept of fractals rather than the description of an observed geometric image is usually applied to condensed media. As regards a macromolecule, modelled by a freely jointed chain consisting of statistical segments, one can hardly find a geometrical image more vivid than a fractal broken line. In addition, it should be noted that representation of a macromolecule by either one-dimensional (as a curve) or a three-dimensional (as a cylinder) object appears to be a fairly rough approximation in view of the real structure of a macromolecule, i.e., the presence of side chains, flexible bonds, rigid segments, etc. As noted above, a change in the density of chemical crosslinking (vs) in epoxy polymers results in an extremal variation of the characteristic ratio (C∞) with the minimum K ≈ 1.0 [118]. If the section of a macromolecule between chemical crosslinks is modelled by a freely jointed chain, the use of known Ls and lst values results in a typical fractal dependence [122]: N st (ξlst ) = ξ −DN st (lst ), ξ < 1
(11.55)
where Nst is the number of statistical segments per fragment of a macromolecule with the molecular mass Ms, and ξ is a similarity parameter. With the assumption that Ls = const and Κ = 1.0, ξ = 0.85 was obtained; with Ls = const and Κ > 1.0, the calculations gave ξ = (0.85)1/2 = 0.926. The calculation of the dimension D from Equation (11.55) gave 1.17. Thus, when the condition mentioned above is fulfilled, the section of a macromolecule between chemical crosslinking points can be represented as a fractal. Variation of K changes the crosslinking density vs and, hence, Ls. As a consequence, the chain ceases to be a self-similar fractal. Nevertheless, it can still be modelled by a non-homogeneous fractal with the same fragmentation step but with a variable D value, determined from relationship (11.39). The D values calculated in this way are listed in Table 11.6. The results of calculation of the characteristic ratio C∞ from Equation (11.54) are inconsistent with the data obtained by Jean and co-workers [131]. Indeed, the maximum rather than the minimum C∞ is attained at K = 1.0. Since: Ø2 ~ νs−2 / 3 , Ms ~ νs−1
then, according to Equation (11.54), the C∞ value should be proportional to vs1/2. In other words, an increase in the density of crosslinks should increase the chain flexibility, which is inconsistent with the extremal increase in the glass transition temperature of epoxy polymers [118, 132].
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Polymer Yearbook
Table 11.6 Calculated molecular characteristics of epoxy polymers [8] κ
D
0.50
Polymer EP-1
EP-2
C∞ I
II
III
2.06
5.23
4.83
5.28
0.75
1.60
4.32
6.91
3.50
1.00
1.25
3.38
9.94
3.68
1.25
1.35
3.75
8.89
3.19
1.50
1.50
4.05
7.68
3.34
0.50
1.85
5.27
6.54
5.35
0.75
1.43
3.98
8.89
4.69
1.00
1.32
3.40
9.24
3.37
1.25
1.35
3.70
9.24
3.90
1.50
1.55
4.10
7.96
4.29
Note. The following designations are used: I – data of Reference [121], II – equation (12.54), III – equation (12.57).
Let us consider the reasons for this inconsistency. Since: C ∞ l0 = lst ,
Ml0 = L0 m
multiplication and division of Equation (11.54) by lst2 gives the relationship [8]: L 0 ⎛ Rs ⎞ =⎜ ⎟ lst ⎝ lst ⎠
2
(11.56)
which is similar to Equation (11.39). Comparison of Equations (11.39) and (11.56) shows that the scaling relationship (11.54) is a specific case of the fractal formula (11.39) for D = 1. For the epoxy polymers considered, the condition D = 2 does not hold (see Table 11.6); this may account for the discrepancy found. Using relationships (11.39) and (11.56), the scaling Equation (11.54) can be written in a more general form: −1 aD = CD ∞
330
MslD 0 m
(11.57)
Fractal Analysis of Macromolecules The calculation of C∞ using Equation (11.57) gives values that are in good agreement with the results obtained by Jean and co-workers [131]. It has been shown [93] that in the case of linear polymers, the following empirical correlation is obeyed for physical entanglements: Rs ≈ 10 C ∞
(11.58)
Taking into account the data presented above, the same (or similar) correlation should be expected for chemical crosslinks in network polymers. The relationship between the C∞ values found using Equation (11.57) and Rs calculated using Equation (11.26a) is linear: Rs ≈ 5 C ∞
(11.59)
which is illustrated by Figure 11.14. Equations (11.58) and (11.59) are qualitatively similar and the discrepancy of numerical coefficients can be due to the approximate character of these relations and to the difference between the methods used to calculate Rs [133]. Recall that the parameter D characterises the degree of deformability (mobility) of a macromolecule fragment between chemical crosslinking points. Indeed, an increase in the chain flexibility brings about an increase in C∞, i.e., an increase in D. It should be
Figure 11.14 Distance between chemical crosslinking points (Rs) versus characteristic ratio (C∞) for 1: EP-1 and 2: EP-2.
331
Polymer Yearbook noted that extrapolation of straight line D(C∞) to D = 1 gives C∞ ≈ 2.55; evidently, this is the limiting value for the epoxy polymers considered. It is also noteworthy that it is close to C∞ for a linear polymer with a similar structure, for example, for polycarbonate, which has C∞ = 2.4 [93]. Apparently, the deformability of a macromolecule in glassy epoxy polymers is determined not only by their molecular characteristics but also by supermolecular (supersegmental) ‘frozen’ structure, which can be characterised quantitatively in terms of the cluster model. It should be borne in mind that an amorphous polymer contains regions of local order (clusters) and that fixing of one or several statistical chain segments in a cluster should change the D value. The most probable reason for the change in D is that the fixed segment becomes expelled from the freely jointed chain, as it has lost its mobility in the junction points. Evidently, this decreases the L, value in Equation (11.39) by lst and, finally, induces a decrease in D. Thus for epoxy polymer EP-1, elimination of one statistical segment induces a decrease in D from 2.06 to 1.73; when two segments are eliminated, D decreases to 1.65; for three segments, it decreases to 1.56, etc. In the absence of ‘frozen’ local order, i.e., for rubbers (ϕcl = 0), D = 2 and the loss of chain mobility (deformability) is attained at (ϕcl ≈ 0.65. The opposite effect is also possible; an increase in vs induces a decrease in D, i.e., the chain becomes more taut, which should increase the level of local order [134]. For linear polymers, the network of macromolecular entanglements is the analogue of the network of chemical bonds; their density Ven is determined at T > Tg. Thus, relationship (11.54) is a specific case of a more general fractal relation (11.57) and is applicable only to rubbers, for which it has actually been derived.
11.9.3 Estimation of Structural Parameters The cited examples demonstrate the capacity and the prospects of using fractal concepts for the description of macromolecular characteristics of network and linear polymers. The change in the C∞ value induced by variation of vs or Ven implies that an absolutely different polymer can be formed although the chemical composition of the macromolecule has remained almost the same. This ‘new’ polymer would have different molecular characteristics (C∞, D), a different supersegmental structure (Vcl, ϕcl), and other properties Tg, elasticity modulus E, etc). Equation (11.54) gives the maximum C∞ value possible for the given vs (see Table 11.6); the minimum values can be obtained by extrapolating the straight line D(C∞) to D = 1. At present, vitreous network polymers are mainly characterised by the vs value [44]. However, one network polymer with constant vs can possess different properties, for
332
Fractal Analysis of Macromolecules example, different Tg [135]. This is explained by the change in the supermolecular structure of a network polymer during physical ageing, namely, by an increase in the level of local order. This effect has been described quantitatively in terms of the cluster model. In turn, the level of local order determines the fractal dimension df of the supermolecular (supersegmental) structure of the polymer [8]. Thus, it becomes possible to predict structural characteristics (and, hence, properties) of network polymers in the vitreous state based on the degree of chemical crosslinking up to the gelation point. Analysis of the relationship between vs and df for the epoxy polymers considered showed that an increase in the fractal dimension of the framework to the gelation point induces a decrease in the fractal dimension of the supermolecular (super-segmental) structure of the network polymer in the glassy state. It has been noted in Section 11.1 that description of fractal structures requires, at least, two dimensions, ds and df, at a constant d value [27]. However, the fractal concept is a mathematical model, which does not provide identification of the specific features of the polymer structure. Therefore, in order to use the parameters ds and df in practice (for example, in computer t simulation), one has to find out which elements of the polymer structure (in particular, of network polymers) they embody. It is known [56] that ds characterises the degree of connectivity of the framework and df (which might be timedependent) refers to the structure of this framework. The df value can be found from Equation (11.27), which indicates that df is a function only of the Poisson ratio μ (for fixed d). For amorphous polymers, μ is determined by the degree of local order [47]; hence, this structural factor also determines df. As regards the spectral dimension ds, it appears to be related in one way or another to the framework formed by chemical crosslinks. This suggestion was based on the results of two studies by Kozlov and coworkers [118, 136]. In the former study, the relationships between vs and the degree of local order and between ds and df were elucidated. The latter study demonstrated the variation of properties of epoxy polymers with time (during physical ageing) following the change in the level of local order (or df) with vs remaining invariant. The ds value can be calculated from Equation (11.8). For estimating the dimension dw, needed for this purpose, several relationships exist [23, 37, 56, 61, 125, 137, 138]; they give somewhat different (to within ~ 20%) absolute magnitudes of this parameter. If the variant of constant dw, is chosen and the model of ‘lattice animals’ (d = 3) is used for describing branched polymers, the dependence of ds on vs would follow a somewhat unexpected pattern. According to this dependence, an increase in the density of crosslinking points results in lower d s and, hence, in lower connectivity of the macromolecular framework of chemical crosslinks. It is noteworthy that for great vs, the ds value approaches asymptotically the experimental spectral dimensions of epoxy polymers [22, 36, 72]. This finding can be interpreted in terms of the generally accepted models of the structure (or, more precisely, morphology) of network polymers [139]. 333
Polymer Yearbook The main morphological unit of densely crosslinked epoxy polymers is a globule. It is a local thickening of a molecular space network the packing density in which is higher than the average density. During etching of fractured surfaces of epoxy polymers, this thickening is revealed as a discrete particle - a globule. The non-homogeneity of network polymers is due to both the kinetics of formation of a three-dimensional network and the presence of associates in the initial oligomers [139]. Two variants of construction of a supermolecular (globular) structure are possible: (a) accretion globules with a hexagonal or cubic packing form a strong continuous skeleton in which the role of inter-globule defective areas is insignificant; (b) densely crosslinked globules (grains) are located in a sparse-network matrix and do not contact one another directly. The former variant of morphology seems to be more frequently encountered. An increase in the concentration of a crosslinking agent induces simultaneous generation of a large number of chemical reaction centres; this is confirmed indirectly by a decrease in the size and the increase in the number of globules [119]. This results in a smaller size and a greater number of inter-globule defective areas; thus, the connectivity of the skeleton diminishes (defective areas act as sorts of skeletal discontinuities) and, hence, ds decreases. Where the morphology of a network polymer corresponds to the second variant, its structure can be represented as a mixture of arbitrary polymer fractals in the vicinity of the gelation point; the spectral dimension of the globule is ds and that of the inter-globule area is δs. The δs value can be estimated using the relationship [61]: df = ds
(d + 1)(2 − δs ) (2 + ds − 2δs )
As a first approximation, it was assumed in this relationship that the spectral dimensions of the structures of the epoxy polymer and the globules are equal. It was found that the dependence of δs on vs for epoxy polymers shows parallel variation of ds and δs upon the variation of vs provided that ds>δs [61]. This condition indicates that the skeleton in the inter-globular gaps is less connected than the globules themselves because it is more defective. Thus, the density of chemical crosslinking points cannot serve as an index for the connectivity of the macromolecular skeleton of network polymers. This makes it impossible to use vs to characterise the structure of network polymers in a computer simulation, which follows from the results presented previously. The ds value, which provides determination of elastic properties, may serve as a suitable parameter. However, to estimate other properties, one more parameter is required, which would characterise the degree of thermodynamic nonequilibrium of the structures of vitreous polymers. This role can be played by df or the density of the cluster network of physical entanglements Vcl [48], or by the proportion of clusters ϕcl [140] For instance, the necessity to take into account ds, Vcl or ϕcl for calculating
334
Fractal Analysis of Macromolecules the yield point from known elasticity modulus has been demonstrated by Beloshenko and Kozlov [48]. Therefore, the frequently encountered correlations between properties of network polymers and vs can serve only as an illustration. The use of two parameters (for example, ds and df with a constant d) is a mandatory (fundamental) condition which follows from the fractality of intermolecular frameworks of vitreous polymers; in turn, the fractality is a consequence of thermodynamic nonequilibrium of this structure.
11.10 Description of Molecular Mobility Using Fractal Characteristics The problems of molecular mobility in polymers have always received considerable attention [32, 99, 141]. The reasons are obvious — polymers are thermodynamically nonequilibrium solids, their physical properties being determined by molecular relaxation processes occurring in them; these processes, in turn, depend on specific structural features of molecular chains and the structural organisation of polymers [141]. However, there is no consensus regarding the parameters describing these processes. In particular, it is assumed that fast relaxations are determined by the mobility of free chains located between densely packed regions, which are simultaneously the nodes of the network of physical entanglements in a macromolecule. This interpretation fully complies with the main statements of the cluster model for the structure of amorphous polymers [15], which provides quantitative description of structural elements. The relationship between the cluster model and fractal analysis can be formulated as follows: fractal analysis gives general physical parameters, while the cluster model makes them more specific using particular characteristics of polymers. Yet another important aspect is worth noting. The above interpretation of the structure of amorphous polymers refers to elastomers. Extension of these notions to vitreous amorphous polymers implies ‘freezing’ of densely packed regions, i.e., a sharp increase in their lifetimes. The fractal forms of macromolecules, macromolecular coils formed during nonequilibrium physico-chemical processes are retained (remain ‘frozen’) in polymers. This suggests that the main factor determining the molecular mobility in the vitreous state is the mobility of chain fragments between the points of fixing [114]. The fractal dimension D has been chosen as the structural factor characterising the level of molecular mobility [114]; this was done for the following reasons. First, a chain fragment between the points of fixing is a self-similar object having a dimension differing from the topological dimension, i.e., it is a fractal by definition [110]. Second, it was shown [104] that D with the range of variation 1
Polymer Yearbook Figure 11.15 shows the dependence of tan δ on D for several copolymers [114] [the D values were calculated using Equation (11.48)] for a measurement frequency of 1 kHz. The dependence has clearly defined limits. For D = 1, it is extrapolated to tan δ = 0. When D = 2, tan δ is roughly equal to the corresponding value at Tg. Thus, linear dependences with the limiting tan δ values indicated above can be used to predict the fractal dimension. Now we shall consider examples of using the dimension D for the solution of applied problems. When polymer samples are obtained by solid-phase extrusion, the macroscopic (extrusion) draw ratio λe is determined by the ratio [122, 142, 143]: λe =
Ø2b Øe2
(11.60)
where ∅b, ∅e are the diameters of the intermediate product and the extrudate, respectively.
Figure 11.15 Dielectric loss (tangent tan δ) versus fractal dimension (D) of the macromolecule section for copolyethersulfone formals with the content of formal blocks of 1: 0, 2: 5, 3: 10, 4: 30, 5: 50 and 6: 70 mol%. Measurement frequency 1 kHz.
336
Fractal Analysis of Macromolecules However, the structure and properties of oriented polymers are characterised much more adequately by the molecular draw ratio λmol [125]. The following expression relating λe, λmol and D to one another has been obtained [123]: λ mol =
lst λ2e / D Rs
(11.61)
It follows from this relationship that the lower D, i.e., the more ‘frozen’ the molecular mobility of the chain during drawing, the greater λmol (the more efficient the orientation process), all other factors being the same. The limiting draw ratio λ∞ attained by stretching a polymer is determined, in terms of the rubbery high-elasticity theory, by the equality [124]: λ ∞ = n1st/ 2
(11.62)
where nst is the number of statistical segments. This equation has been applied repeatedly to glassy polymers. The following fractal relationship has been obtained [39]: /4 λ ∞ = nD st
(11.63)
It can be easily seen that an increase in D for nst = constant enhances the deformability of polymers. Equations (11.62) and (11.63) are identical when D = 2, i.e., for rubbers. An important difference between Equations (11.62) and (11.63) is that in the former, λ∞ depends on one parameter, which is typical of equilibrium Euclidean objects, while in the latter, it is a function of two parameters, which is typical of thermodynamically nonequlibrium fractal objects. Therefore, the use of Equation (11.62) in the latter case is improper. The relationship between the statistical chain flexibility, characterised by C∞, and the dimension D has been found [144]: D=2−
1 C∞
(11.64)
Using published data for C∞ [94] and Equations (11.27) and (11.49), the lengths of chain sections between entanglements Len were calculated. The results were in agreement with
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Polymer Yearbook
Table 11.7 Characteristic ratios C∞ and Len [134] Polymer
C∞ [90, 132]
Len, nm Calculated
Experimental
13.4
226
208
Poly(n-octyl methacrylate)
10
177
149
Polystyrene
10
104
149
Poly(vinyl acetate)
9. 4
88
136
Poly(n-butyl methacrylate)
9. 1
130
131
Poly(methyl methacrylate)
8. 6
97
92
Polyethylene
6. 8
56
88
Poly(vinyl chloride)
6.7
31
87
Polytetrafluoroethylene
6. 3
41
80
Polyamide-6
5. 3
46
61
Poly(propylene oxide)
5. 1
60
58
Poly(ethylene oxide)
4. 2
45
43
Poly(ethylene terephthalate)
4. 2
21
36
Poly(ether terephthalate)
3. 3
28
30
Polycarbonate
2. 4
29
17
Poly(n-dodecyl methacrylate)
experimental data (Table 11.7). Thus, the increase in the density of the network of macromolecular entanglements following an increase in the statistical chain rigidity was confirmed within the framework of fractal analysis. By combined use of Equations (11.27) and (11.49), one can predict the increase in the number of points of topological fixing of a macromolecule in the vitreous state with respect to the rubbery state [144]. The fractal dimension D of a chain fragment between the points of topological fixing (entanglements, clusters, crosslinks) is an important structural parameter, which controls the molecular mobility and deformability of polymers. Crucial factors accounting for the use of the dimension D are clearly defined limits of variation (1
338
Fractal Analysis of Macromolecules serve only as illustrations. The necessary use of at least two parameters (for instance, ds and df with a constant d) is a fundamental condition, which follows from the fractality of the intermolecular skeletons in glassy polymers.
11.11 Conclusions The fractal properties of a macromolecule in a polymer are predetermined by thermodynamic nonequilibrium and by the presence of a certain deterministic order. Proceeding from this fact, we considered the limitations of the scope of the concept of polymer fractal, developed for polymer solutions, and the Vilgis theory for condensed media (melts and rubbers). The major drawback of these approaches is that they neglect the effects of macromolecular entanglements. It is demonstrated that a description of the fractal properties of macromolecules cannot be physically correct without allowance for entanglements. Examples are given to illustrate the diversity of fractality in polymers. In particular, it is shown that not only macromolecular coils but also sections of macromolecules between the points of topological fixing (crosslinks, entanglements) are stochastic fractals. Conditions required for the fractality to be manifested are discussed. They include the range of scales, self-similarity and fractional dimension. It is shown that a section of a macromolecule between the points of topological fixing possesses configurational fractal properties, caused by the mutual arrangement of fragments of the macromolecule, and conformational fractal properties, conditioned by the state of bonds within a section of rigidity, i.e., statistical segment). In this connection, a model of structure formation in network polymers is considered; this model includes a quantitative determination of the relationship between the crosslinking density and the level of local order of the structure. It is demonstrated that, in addition to the parameters of local order, fractal dimensions of the polymer structure should also be taken into account. Examples of practical use of the fractal dimension of the section of a macromolecule between chemical crosslinking points are given; it is shown that this value can serve as a measure of molecular mobility. The influence of characteristics of molecular and topological levels of the structure of crosslinked polymers on the fractal dimension is noted.
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Polymer Yearbook 35. A.J. Dianoux, J.N. Page and H.M. Rosenberg, Physical Review Letters, 1987, 58, 886. 36. V.A. Bagryanskii, V.K. Malinovskii, V.N. Novikov, L.M. Pushchaeva and A.P. Sokolov, Fizika Tverdogo Tela, 1988, 30, 2360. 37. R. Xie, B. Yang and B. Jiang, Physical Review B, 1994, 50, 3636. 38. G.V. Kozlov, G.B. Shustov and K.B. Temiraev, Vestnik KBGU Khimicheskoy Nauki, 1997, 2, 50, [in Russian]. 39. V.U. Novikov and G.V. Kozlov in Fractals and Applied Synergetics (Abstracts of Reports of the First Interdisciplinary Seminar), Moscow, Russia, 1999, p.124. (In Russian) 40. B.D. Sanditov, V.V. Mantatov, G.V. Kozlov and V.U. Novikov in Baikal Reading on Mathematical Modelling of Processes in Synergetic Systems (Abstracts of Reports of the All-Russian Conference), Ulan-Ude, Russia, 1999, p.36, [in Russian]. 41. B. Chu, C. Wu, D.Q. Wu and J.C. Phillips, Macromolecules, 1987, 20, 2642. 42. S.F. Edwards and T. Vilgis, Polymer, 1987, 28, 375. 43. P.J. Flory, Polymer Journal, 1985, 17, 1. 44. V.I. Irzhak, B.A. Rozenberg and N.S. Enikolopyan, Crosslinked Polymers. Synthesis, Structure and Properties, Nauka Publishers, Moscow, Russia, 1987, [in Russian]. 45. A.S. Balankin, Doklady Akademii Nauk, 1992, 325, 465. 46. A.S. Balankin, Izvestia Akademii Nauk SSSR, Metallyrgia, 1992, 2, 41. 47. A.S. Balankin and A.L. Bugrimov, Vysokomolekulyarnye Soedinenia, Seria A, 1992, 34, 10, 135. 48. V.A. Beloshenko and G.V. Kozlov, Mekhanica Kompozitnyh Materials, 1994, 30, 451. 49. G.V. Kozlov, V.D. Serdyuk and V.A. Beloshenko, Mekhanica Kompozitnyn Materials, 1994, 30, 691. 50. G.I. Sandakov, L.P. Amirnov, A.I. Sosikov, T. Sununanen and N.N. Volkova, Journal of Polymer Science, Part B: Polymer Physics, 1994, 32, 1585.
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Fractal Analysis of Macromolecules 51. V.G. Baranov, S.Ya. Frenkel and Yu.V. Brestkin, Doklady Akademii Nauk, SSSR, 1986, 290, 369. 52. V.G. Baranov and A. Frenkel, Acta Polymerica, 1979, 30, 601. 53. P-G. De Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, USA, 1979. 54. V.N. Tsvetkov, V.E. Eskin and S. Ya. Frenkel, The Structure of Macromolecules in Solution, Nauka Publishers, Moscow, Russia, 1964, [in Russian]. 55. V.E. Eskin and I.N. Serdyuk, Vysokomolekulyarnye Soedinenia, Seria A, 1969, 11, 372. 56. M.E. Cates, Journal of Physics, 1985, 46, 1059. 57. W. Hess, T.A. Vilgis and H.H. Winter, Macromolecules, 1988, 21, 2536. 58. B.B. Mandelbrot, Fractals: Form, Chance and Dimension, Freeman, SanFrancisco, CA, USA, 1977. 59. Y. Gefen, S. Aharony and A. Alexander, Physical Reviews Letters, 1983, 50, 77. 60. P.J. Flory, Principles of Polymer Chemistry, 2nd Edition, Cornell University Press, Ithaca, NY, USA, 1979. 61. T.A. Vilgis, Physica A, 1988, 153, 341. 62. T.A. Vilgis, P. Haronska and M. Benhamou, Journal of Physics II, 1994, 4, 2187. 63. D. Lhuillier, Journal of Physics, 1988, 49, 705. 64. T.A. Vilgis, Journal of Physics, 1988, 49, 1481. 65. H.J. Stapleton, J.P. Allen, C.P. Flynn, D.G. Stinson and S.R. Kurtz, Physical Review Letters, 1980, 45, 1456. 66. J.T. Colvin and H.J. Stapleton, Journal of Chemical Physics, 1985, 82, 4699. 67. E. Young in Fractals in Physics, Eds., L. Pietronero and E. Tosatti, Proceedings of the Sixth International Symposium on Fractals in Physics, ICTP, Trieste, Italy, North-Holland Physics Publishing, Amsterdam, The Netherlands, 1985, p.168. 68. J.S. Helman, A. Coniglio and C. Tsallis, Physical Review Letters, 1984, 53, 1195.
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Polymer Yearbook 69. A. Maritan and A.L. Stella in Fractals in Physics, Eds., L. Pietronero and E. Tosatti, Proceedings of the Sixth International Symposium on Fractals in Physics, ICTP, Trieste, Italy, North-Holland Physics Publishing, Amsterdam, The Netherlands, 1985, p.151. 70. R. Kopelman in Fractals in Physics, Eds., L. Pietronero and E. Tosatti, Proceedings of the Sixth International Symposium on Fractals in Physics, ICTP, Trieste, Italy, North-Holland Physics Publishing, Amsterdam, The Netherlands, 1985, p.156. 71. P. Meakin and H.E. Stanley, Physical Review Letters, 1984, 51, 1457. 72. P. Meakin, I. Majid, S. Halvin and H.E. Stanley, Journal of Physics A, 1984, 17, L975. 73. M. Muthukumar, Chemicheskay Physika, 1985, 83, 3161. 74. J. Vannimenus, Physica D, 1989, 38, 351. 75. B.H. Zimm and W.H. Stockmayer, Journal of Chemical Physics, 1949, 17, 1301. 76. G.R. Dobson and M. Gordon, Journal of Chemical Physics, 1964, 41, 2389. 77. A.G. Kokorevich, Ya. A. Gravitis and V.G. Ozol’-Kalnin, Khimia Drevesiny, 1989, 1, 3. 78. J. Isaacson and T.C. Lubensky, Journal of Physics, Letters, 1980, 41, L469. 79. T.C. Lubensky and J.J. Isaacson, Physical Review A, 1979, 20, 2130. 80. M. Daoud and J.F. Joanny, Journal of Physics, 1981, 42, 1359. 81. S. Bantle, H.W. Hasslin, H-U. Ter Meer, M. Schmidt and W. Burchard, Polymer, 1982, 23, 1889. 82. A. Boukenter, E. Duval and H.M. Ropanberg, Journal of Physics, C, Solid State Physics, 1988, 21, 541. 83. Y. Lin, M.C. Nelson and D.M. Hanson, Journal of Chemical Physics, 1987, 86, 1586. 84. P.W. Schmidt, A. Hohr, H-B. Neumann, H. Kaiser, D. Avnir and J.S. Lin, Journal of Chemical Physics, 1989, 90, 5016. 85. P.W. Klymko and R. Kopelman, Journal of Physical Chemistry, 1983, 87, 4565.
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Fractal Analysis of Macromolecules 86. D.C. Prevorsek and B.T. De Bona, Journal of Macromolecular Science – Physics, 1981, B19, 605. 87. C.S. Henkee and E.J. Kramer, Journal of Polymer Science, Polymer Physics Edition, 1984, 22, 721. 88. B. Qian, Z. Wu, P. Hu, J. Qin, C. Wu and J. Zhao, Journal of Applied Polymer Science, 1991, 42, 1155. 89. V.N. Belousov, G.V. Kozlov, A.K. Mikitaev and Yu. S. Lipatov, Doklady Akademii Nauk, SSSR, 1990, 313, 630. 90. V.P. Lebedev, Uspehi Khimii, 1978, 47, 127. 91. B.M. Smimov, Uspeki Fizicheskih Nauk, 1986, 149, 177. 92. A.G. Mikos and N.A. Peppas, Journal of Chemical Physics, 1988, 88, 1337. 93. S.M. Aharoni, Macromolecules, 1983, 16, 1722. 94. V.P. Budtov, Physical Chemistry of Polymer Solutions, Khimiya Publishers, St. Petersburg, Russia, 1992, [in Russian]. 95. P.J. Flory, British Polymer Journal, 1976, 8, 1, 1. 96. P.J. Flory, Pure and Applied Chemistry, 1984, 56, 305. 97. A.S. Balankin, Doklady Akademii Nauk, SSSR, 1991, 319, 1098. 98. D.S. Sanditov and G.M. Bartenev, Physical Properties of Disordered Structures Nauka Publishers, Novosibirsk, Russia, 1982, [in Russian]. 99. G.V. Kozlov, V.N. Belousov, D.S. Sanditov and A.K. Mikitaev, Izvestia Vysshyh Uchebnyh Zavedeniy, Severokavkazskogo Region, 1994, 1-2, 86, 64. 100. V.N. Shogenov, G.V. Kozlov and A.K. Mikitaev, Vysokomolekulyarnye Soedinenia, Seria A, 1986, 28, 2436. 101. A.B. Mosolov, Zhurnal Tekhnichestoy Fiziki, 1991, 61, 57. 102. A.B. Mosolov and F.M. Borodich, Doklady Akademii Nauk, 1992, 324, 546. 103. P.V. Goi’dshtein and A.B. Mosolov, Doklady Akademii Nauk, 1991, 319, 840. 104. G.V. Kozlov, V.A. Beloshenko, M.A. Gazaev and V.N. Varyukhin, Fizika i Tekhniko Vysokih Davleniy, 1995, 5, 1, 74.
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Polymer Yearbook 105. V.A. Beloshenko, G.V. Kozlov and V.N. Varyukhin, Fizika i Tekhniko Vysokih Davleniy, 1994, 4, 2, 70. 106. G.V. Kozlov, M.A. Gazaev, V.U. Novikov and A.K. Mikitaev, Fractal Physics of the Formation of Topology and Structure of Polymers, article deposited at the VINITI No.3072, Moscow, Russia, 1995, [in Russian]. 107. S. Havlin and D. Ben-Avraham, Physical Review A, 1982, 26, 1728. 108. V.P. Privaiko and Yu. S. Lipatov, Vysokomolekulyarnye Soedinenia, Seria A, 1971, 13, 2733. 109. G.V. Kozlov and V.U. Novikov, Prikladnay Fizika, 1997, 1, 77. 110. E.J. Kramer, Polymer Engineering and Science, 1984, 24, 761. 111. D.S. Sanditov, G.V. Kozlov, V.N. Belousov and Yu.S. Lipatov, Ukranian Polymer Journal, 1992, 1, 241. 112. J. Heijboer, Journal of Polymer Science, Part C: Polymer Symposia, 1968, 16, 3755. 113. J.L. McCauley, International Journal of Modern Physics, 1989, ?3, 821. 114. G.V. Kozlov, K.B. Temiraev, R.A. Shetov and A.K. Mikitaev, Materialovedenie 1999, 2, 34. 115. G.V. Kozlov, V.A. Beloshenko and V.N. Varyukhin, Prikladnay Mekhanika I Tekhnicheskay Fizika, 1996, 37, 115. 116. G.V. Kozlov, V.A. Beloshenko, V.N. Varyukhin and V.U. Novikov, Zhurnal Fizicheskih Issledovaniy, 1997, 1, 204. 117. H.H. Kausch, Polymer Fracture, Springer Verlag, Berlin, Germany, 1978. 118. G.V. Kozlov, V.A. Beloshenko, E.N. Kuznetsov and Yu.S. Lipatov, Doklady Nation Academy Nauk Ukrainy, 1994, 12, 126. 119. A. Peterlin, Journal of Macromolecular Science – Physics, 1975, B11, 57. 120. D.S. Sanditov, G.V. Kozlov, V.N. Belousov and Yu.S. Lipatov, Fizika i Khimia StekIa, 1994, 20, 3, [in Russian]. 121. F.B. Mosolov and O.Yu. Dinariev, Problemy Prochnosti, 1988, 1, 3.
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Fractal Analysis of Macromolecules 122. V.A. Beloshenko, G.V. Kozlov, V.N. Varyukhin and V.G. Slobodina, Acta Polymerica, 1997, 48, 181. 123. G.V. Kozlov, M.A. Gazaev, V.A. Beloshenko, V.N. Varyukhin and V.G. Slobodina, Ukrainskyi Fizicheskyi Zhurnal, 1995, 40, 883. 124. G.V. Kozlov, V.A. Beloshenko and M.A. Gazaev, Ukrainskyi Fizicheskyi Zhurnal, 1996, 41, 1110. 125. M.P.C. Watts, A.E. Zachariades and R.S. Porter, Journal of Materials Science, 1980, 15, 426. 126. S.M. Aharoni, Macromolecules, 1985, 18, 2624. 127. S. Wu, Journal of Polymer Science, Part B: Polymer Physics, 1989, 27, 723. 128. G. Porter, Group Interaction Modelling of Polymer Properties, Marcel Dekker, New York, NY, USA, 1995. 129. G.V. Kozlov, V.A. Beloshenko, M.A. Gazaev and V.U. Novikov, Mekhanika Kompozitnyh Materialov, 1996, 32, 270. 130. A.I. Olemskoi and A. Ya. Flat, Uspehi Fizicheskih Nauk, 1993, 163, 12, 1. 131. Y.C. Jean, T.C. Sandreczki and D.P. Ames, Journal of Polymer Science, Part B: Polymer Physics, 1986, 24, 1247. 132. V.A. Beloshenko, G.V. Kozlov and Yu.S. Lipatov, Fizika Tverdogo Tela, 1994, 36, 2903. 133. G.V. Kozlov, V.A. Beloshenko and V.N. Varyukhin, Ukrainskyi Fizicheskyi Zhurnal, 1996, 41, 218. 134. R.F. Boyer and R.L. Miller, Macromolecules, 1977, 10, 1167. 135. I.I. Perepechko and A.V. Maksimov, Vysokomolekulyarnye Soedinenia, Seria B, 1989, 31, 54. 136. G.V. Kozlov, V.A. Beloshenko, I.V. Stroganov and Yu. S. Lipatov, Doklady National Academii Nauk Ukrainy, 1995, 10, 117. 137. V.U. Novikov and G.V. Kozlov, Materialovedenie, 1997, 4, 6. 138. V.U. Novikov, G.V. Kozlov, M.A. Gazaev and A.K. Mikitaev, Behaviour of Dissipative Structures in Deformed Polymer Matrices, article deposited at the VINITI No.2944, Moscow, Russia, 1995.
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Polymer Yearbook 139. V.U. Novikov and G.V. Kozlov, Materialovedenie, 1997, 6-7, 42. 140. G.V. Kozlov, V.A. Beloshenko, V.N. Varyukhin and M.A. Gazaev, Prikladnay Mekhanika i Tekhnicheskay Fizika, 1998, 39, 160. 141. G.M. Bartenev and Yu.V. Zeienev, The Physics and Mechanics of Polymers, Khimiya Publishers, Moscow, Russia, 1983, [in Russian]. 142. V.A. Beloshenko, G.V. Kozlov, V.G. Slobodina, E.V. Prut and V.G. Grinev, Vysokomolekulyarnye Soedinenia, Seria A, 1995, 37, 1089. 143. G.V. Kozlov, V.A. Beloshenko, V.G. Slobodina and E.V. Prut, Vysokomolekulyarnye Soedinenia, Seria B, 1996, 38, 1056. 144. G.V. Kozlov, V.U. Novikov and A.K. Mikitaev in Synergetics (Abstracts of Reports), Moscow, Russia, 1996, p.226.
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12
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites G.V. Kozlov and Yu.S. Lipatov
12.1 Introduction This chapter considers a study of two types of composites based on polyhydroxyether and graphite with various amounts of a filler. Using various methods it is possible to estimate the adhesion characteristics and interfacial layer, including its thickness and tensile strength and the interdependence between these values and the adhesion properties. The results were treated on the basis of the theory of irreversible aggregation, cluster theory of the polymer structure and fractal analysis. It was established that all the important characteristics of adhesion, the interfacial layer and mechanical properties are interconnected by the fractal dimensions of the surface of the aggregates of filler particles and of the polymer matrix, whose structure is distorted under the influence of the filler surface. Adhesion at the interface of the polymer-solid is a determining factor for the physical and mechanical properties of polymer composites. Many properties of particulate-filled composites are determined by the adhesion level at the filler-matrix interface. The problems involved in adhesion are very complicated and adhesion cannot be described by any single theory [1]. Many properties of particulate-filled composites are determined by the adhesion level at the filler-matrix interface [2]. However, no theory allows calculation of the adhesion strength of joints from the data on the nature of substrate and polymer or reliable calculation of the energy of the adhesive interaction. The reason for it is the number of factors that influence adhesion [3-9]. In the present review, an attempt will be made to consider some of the structural aspects of interfacial adhesion using modern physical models: the cluster model of the amorphous structure of polymers [10], fractal analysis [11, 12] and the model of irreversible aggregation [13]. Fractal analysis allows consideration of the surface structure of the filler particles, which are characterised by its fractal dimension (dn) and by the self-similarity interval. Because the polymer structure is also described in the framework of the fractal analysis, it becomes possible to consider the interaction between the filler surface and polymer matrix, including the interfacial layers, based on the analysis of their fractal dimensions. Application of the model of irreversible aggregation allows description of the processes of aggregation of the filler particles in a particulate filled composites. This aggregation causes changes
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Polymer Yearbook in the adhesion and adhesion strength; aggregation leads to an increased value of dn and in such a way as to exert a marked influence on the interaction between filler and matrix and adhesion.
12.2 Experimental In this study composites based on poly(hydroxyether) (PHE) and graphite have been used. Poly(hydroxyether) was obtained from diane resin and has the following chemical structure:
PHE (0.5% solution in chloroform) has a reduced viscosity of equal to 0.044 m3/kg at 295 K. PHE was dissolved in the mixture of two solvents: 1,4-dioxane and N,N-dimethyl acetamide with a ratio (by weight) of 1:1. To the solution with a concentration of 17% of polymer, flaky graphite was added in the necessary amount and after this procedure the dispersion was poured into water. In such a way a powder with a volume concentration of graphite (ϕF) of 0.0088, 0.018, 0.044, 0.088 or 0.176 was obtained which was dried in vacuum at 333 K to a constant weight. The blend obtained was extruded using the screw extruder and granulated. The specimens of composites with dimensions 4 x 6 x 50 mm have been prepared by moulding at 433 K. Two series of graphite-filled polymers were used in the following experiments: with nonactivated graphite (I) and with graphite activated by the mixture of sulfur and nitric acid in the ratio 1:1 by volume. To investigate the structure of filled polymers transmitting electron microscopy (EMMA-4 electron microscope) was used. A two-step replica from the specimen chip was obtained either at the room temperature or at the temperature of liquid nitrogen. Replicas were investigated using transmitting electron microscopy. The methods of the experimental determination of the fractal dimensions (dn) of the surface of aggregates of filler particles from microphotographs of the chips were described in detail in [14, 15].
350
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites The measurements of the dielectric characteristics of composites were carried out at a frequency of 104 Hz using an alternating current bridge P-5058. The specimens prepared had a disc-like shape with a diameter equal to the diameter of the electrode (15-18 mm). The thickness of the specimen was about 1 mm. The temperature dependencies of the dielectric permeability (ε) and of the tangent of the dielectric losses (tan δ) were found at the heating rate 3-4 K/min. In [16] it was proposed to characterise the degree of polymer-filler interaction (adhesion level) by the following parameter: A=
1 tan δ c −1 1 − ϕ c tan δ m
(12.1)
where tan δc and tan δm are the dielectric losses of the composite and polymer matrix, respectively. Strong interactions between the filler and the polymer matrix at the interface, diminish the molecular mobility in the vicinity of the interface [1] as compared with the bulk matrix. The result of this reduction is to diminish tan δc and A. A low value of parameter A, indicates a high degree of interaction at the interface, or adhesion between two components of polymer composite [16]. The parameter A is a measure of the adhesion level between the aggregation of the filler particles in the matrix. Traditional methods of the determination of adhesion [17] cannot be applied in this case due to variations of the structure of the particle aggregate surface as compared to the surface of the initial filler particles. This method is sensitive to particle aggregation and does not need special specimen preparation. Impact toughness according to the Charpy method for specimens without a notch and with a sharp notch of length a = 0.22 mm have been performed using a pendulum driver with piezoelectric detector, whose signal was directly transmitted to the oscilloscope trace. Such a device allows the load-time diagram (P – t) to be obtained and the calculation of the elasticity modulus (E) [18], strength (σC) and yield stress (σY) [19]. The notches were made by the indentation of sharp blade into the sample, their length at the surface being controlled using optical microscope (with an accuracy of 0.02 mm). All the measurements were performed at 293 K [20]. Values of the tensile strength of the interfacial layer (σat) in the composites under investigation were taken from [21]. This value was found from equation proposed by Leidner and Woodhams [22]: σ C = (σ1 + 0.83τ M ) + σ1K(1 − ϕ f )
where σC is the composite tensile strength, σI is the tensile strength of an interfacial layer the τM is the shear strength of a matrix and K is a coefficient of stress concentration. This
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Polymer Yearbook equation is valid for good bonding between polymer and filler. The existence of such a bonding in these systems is proved by the dependence of the elastic modulus (E) on the volume fraction of a filler (ϕf), which is described by the Kerner equation [23]. Value τM was taken to be equal to the shear yield strength of polymer matrix (τY) which may be easily found from the macroscopic yield stress (σY) as: τ M = τY
σY 3
The value of K does not depend on the particle size and may be taken as a constant equal to 2.
12.3 Results and Discussion In the course of the experimental works many physical values were determined describing the properties of composites. All these values are given in Table 12.1.
12.3.1 Description of the Aggregation of Particles in the Framework of the Models of Irreversible Aggregation As it was stated previously, the problems connected with the filler particle aggregation are important because aggregation changes their surface structure, that is characterised by the fractal dimension (dn) as compared with the fractal dimension of initial particles [15, 21]. The importance of this factor will be discussed later. It was shown [24, 25] that aggregates of filler particles in polymer matrix (for example, nickel particles in epoxy polymers) are fractal objects with a dimension close to 2. This implies that the process of aggregation proceeds according to the theoretically and experimentally investigated mechanism of irreversible aggregation of cluster-cluster type [26]. Therefore it is possible to elucidate the factors affecting this process [27]. In [26] a relationship was proposed to describe the change in the radius of the particle aggregate RaT in the aggregation process proceeding according to cluster-cluster mechanism:
RaT
⎛ 4c kT ⎞ ~⎜ 0 ⎟ ⎝ 3ηm 0 ⎠
1/ D
t1 / D
(12.2)
where c0 is the initial fraction of particles, k is the Boltzman constant, η is the viscosity of the medium, m0 is the particle mass, D is the fractal dimension of the particle aggregate, t is the aggregation time (equal to the processing time).
352
22.5 38.0
0.088
0.176 2.40
2.33
2.26
2.20
2.16
2.68
2.60
2.53
2.45
2.32
dn Eqn. 12.7
83
59
58
36
32
148
107
98
56
52
Nu, rel. units Eqn. 12.10
0.36
0.36
0.39
0.40
0.44
0.16
0.32
0.25
0.29
0.35
Δd, Eqn. 12.11
1.80
1.35
1.30
0.65
0.35
2.95
2.70
2.30
1.80
0.80
A, Eqn. 12.1
10.2
12.2
13.8
18.5
22.6
6.0
8.6
10.4
18.0
18.4
σ a, Eqn. 12.14
Note: values R a and li were found from the electron microscopic data. PHE-GR-I: PHE with a non-activated graphite filler. PHE-GR-II: PHE with an activated graphite filler.
max
22.0
0.044
0.176 15.0
41.5
0.088
0.018
30.5
0.044
8.5
30.5
0.018
0.0088
18.5
0.0088
PHE-Gr-I
PHE-Gr-II
6.0
ϕf
Composite
Ramax × 103, nm
10.5
23.8
10.9
9.0
4.9
42.3
24.0
16.8
11.6
6.5
li, × 103, nm
80
36
51
42
38
137
143
103
84
69
acrit. × 103, Eqn. 12.22
0.14
0.15
0.16
0.17
0.20
0.10
0.11
0.14
0.14
0.17
εloc
Table 12.1 Measured values characterising adhesion and fracture of adhesion joints
0.95
1.34
1.47
1.68
2.24
0.38
0.38
0.55
0.69
0.90
GIC, kJ / m 2
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
353
Polymer Yearbook Let us consider the methods of evaluation of parameters in Equation (12.2). In the simplest case it will be assumed that all the particles of initial filler powder are of the same size and mass, and then c0 ≅ ϕf. The value of T is the temperature of the moulding in the extruder, i.e., T = 493 K. The viscosity of the melt of a composite may be measured directly by a number of methods. However, for our case the crosslinking of the matrix is possible in the course of the moulding and viscosity measurement, which may deteriorate the results of the measurement [25]. Because of this we have used the theoretical estimation of the viscosity using the equation proposed by Mills [28]: η 2.5ϕ f = 1+ η0 1 − ϕf
(12.3)
where η0 is the viscosity of the melt of polymer matrix; we have accepted η0 = 1, that means that value of η is the characteristic of a relative viscosity of a composite [25]. Value m0 in Equation (12.2) was calculated in the following way. Taking, according to the electron microscopic data, that the diameter of a filler particle is about 10 μm and assuming spherical shape of the particles, the volume of a particle is calculated and then, from the known density of graphite (≈ 2265 kg/m3) [27], m0 is easily found. Fractal dimension of the particle aggregates was taken to be equal to 2 [25]. The time of processing which is equal to the time of aggregation was found experimentally by using a coloured composite marker and measuring the time t1, taken for it to pass through the extruder, value t being constant and equal to 2 minutes. From these data the value RaT may be calculated according to Equation (12.2) in conditional units. Maximum experimental values of the radius of particle aggregates, Rmax were estimated a from the data of electron microscopy as an average from 10 measurements. The comparison of values of RaT and R amax (Figure 12.1), shows that they obey an approximately linear correlation passing through the origin. The interrelation between the two values is described by the expression: Ramax = 2.74 ⋅ 108 RaT , μm
(12.4)
Under the conditions of a given experiment only two variables enter into Equation (12.2): ϕf and η, whereas other parameters are taken as constants. Variation intervals of ϕf and η are very different; by changing ϕf 20 times, value η changes only 1.5 times. From Equation (12.2) it follows that RTa ~ Co1/D ~ ϕf1/D. As D = 2 it follows that RTa ≈ ϕf1/2 should be valid. Figure 12.2 presents the dependence of Rmax calculated according to a Equation (12.4) on ϕf which really has expected linear character and may be approximated in the following way [26]:
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Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
Figure 12.1 The relationship between the experimental value of Ramax and that calculated from Equation 12.2, (RaT) is the radii of filler particles for composites 1: PGE-GR-I and 2: PGE-Gr-II.
Ramax = 9.7 ⋅ 10 4 ϕ1f / 2 , μm
(12.5)
As is known [21] the fractal dimension of the aggregate surface is a function of the degree of aggregation of the filler particles, being increased with ϕf. The simplest variant of this dependence may be written as: d n = 2 + C ln Ramax
(12.6)
because increasing the degree of aggregation manifesting itself on the growth of Ramax leads to the increasing dn. Number 2 means the equal for all initial powder values of d 0 = 2. Logarithm function is chosen because of better fitting of theoretical and experimental data [26]. The difference in values d0 for composites PHE-Gr-I and PHEGr-II may be eliminated by replacing the constant 2 in Equation (12.6) on dn = d0. At a minimum value of Ramax = 5 μm the following equality should be carried out: dn = d0. Because of it, more correctly Equation (12.6) should be presented in as in Equation (12.7) [25].
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Polymer Yearbook
Figure 12.2 Dependence of the maximum radius of aggregates of the filler particles Ramax on the filler volume fraction, ϕf1/2 for 1: PHE-Gr-I and 2: PHE-Gr-II.
⎛ ln 5 ⎞ d n = d0 + ⎜1 + ⎟ ln Ramax ⎠ ⎝
(12.7)
where Ramax is given in μm. Figure 12.3 presents the comparison of the values dn calculated from Equation (12.7) (solid curves) and of experimental values [15, 21]. A good agreement between the two values is evident. Thus the method proposed allows estimation in a quantitative way of the effect of aggregation on the value of the fractal dimension dn of the aggregate surface.
12.3.2 Effect of the Surface Structure of the Filler on Adhesion The roughness of the filler surface [7, 29] essentially determines the properties of the interfacial layer. However, during recent years it was discovered that a great deal of dispersed materials, including fillers, have the surfaces possessing fractal properties in rather broad interval of a linear scales [30]. This circumstance gives us the possibility to describe quantitatively the adhesion characteristics in the framework of the fractal analysis [31]. Besides, this possibility allows the development of a new approach to the adhesion
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Figure 12.3 Dependence of the fractal dimension (dn) of aggregate surface on the volume fraction of a filler, (ϕf), for PHE-Gr-I (1, 3) and PHE-Gr-II (2, 4). Calculated from Equation 12.7 (1, 2) and experimental values (3, 4) taken from [15].
problem in particulate-filled composites where fractal properties are inherent to both polymer and filler surfaces. It was shown [32] that the interaction of two fractals is possible at a definite linear scale, which depends on the both fractal dimensions of a filler surface (dn) and of a polymer (df). The structure of the filler particle surfaces and of the polymer surface characterised by their fractal dimensions, affects the interfacial adhesion in composites. To explain the structural effect let us introduce the concept of the ‘accessibility’ of the sites on these surfaces to form adhesion joints (physical or chemical). As a first approximation the degree of such accessibility may be defined as a difference of the fractal dimensions of two surfaces. The higher is this difference the lower is the accessibility of the surface and the less is the adhesion [21]. Suppose that the filler particle has a very rough surface with dimensions which are close to the Euclidean dimension d = 3 (for example, Al2O3 particles) [33], whereas the polymer surface is very smooth, i.e., dp = d = 2. In this case the contact between two surfaces is possible only at the apexes of the rough surface of the filler and the result could be very low adhesion. In other words, the disparity of the dimensions determines the inaccessibility of the greater part of the filler particle for the formation of adhesion bonds [21].
357
Polymer Yearbook A more strict approach to the characterisation of the effect under consideration is the concept of the unscreened perimeter of any object introduced in [34], for a filler. This perimeter is a measure of the accessibility for the formation of adhesion bonds [34]. The particulate-filled polymers at a definite values of ϕf may be considered as percolation clusters with the first percolation threshold ϕfC = 0.15-0.17 [35]. Because the maximum value of ϕf for the composites considered in this paper is equal to ∼ 0.176, one can believe these systems are below the percolation threshold and from them the following relationship is valid [34]: d u = (d n − 1) + (d − d n ) / d w
(12.8)
where du is the fractal dimension of the unscreened surface, dw is the dimension of the trajectory of the filler particles that form aggregates. Value dw may be estimated as [36]: dw = dn + 1
(12.9)
The number of the sites available for the adhesion joints at the particle surface, Nu, is given as [34] N u ≈ Rda u
(12.10)
The value of the fractal dimension of the surface of a fractal object is taken to being equal to the corresponding parameter of its structure [21] and because of it for the polymer matrix may be taken as fractal dimension of the polymer dp. In such a way the degree of accessibility of the filler particles may be characterised by one more parameter: Δd = d p − d n
(12.11)
Figure 12.4 gives the comparison of two parameters, Nu and Δd (taken from [21]) for the composite PHE-Gr. As it was supposed, increasing Δd leads to the diminishing of the number of available sites; at Δd = 0.5 the formation of the adhesion joints is not generally expected (Nu ≅ 0). The extrapolation of the dependence of Nu on Δd to Δd = 0 gives the maximum value of Nu ≅ 195 relative units. Using this figure in Equation (12.10) we can find that it may be valid for value dn = 3 at the maximum value of Ra = 42 μm, For lower values of Ra the condition (12.10) cannot be realised because gives the value dn > 3 which has no physical meaning. This example shows the effect of the particle aggregation on the formation of the adhesion joints [21]. The values of Nu presented in Figure 12.4 were calculated per aggregate of the filler particles. To estimate this parameter
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Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
Figure 12.4 Dependence of a number of non-screened points at the surface of a filler particle Nu on the difference of fractal dimensions of the filler surface and polymer, Δd, for 1: PHE-Gr-I and 2: PHE-Gr-II.
for the whole composite this value should be normalised to the volume content of a filler, ϕf. The dependence of the parameter A, calculated according to Equation (12.1) on Nu/ϕf is given in Figure 12.5. As it should be expected, increasing Nu/ϕf leads to the diminishing A, i.e., to the increasing adhesion. At comparable values of Nu/ϕf value A is less for composites PHE-Gr-II. It is evident that besides the structural factor, N u/ϕ f there are other factors that affect value of A. In the case under consideration, one can suppose that for composite PHE-Gr-II during chemical treatment of the filler surface by the mixture of the sulfuric and nitric acids, some chemically active groups may be formed at the filler surface. These groups may adsorb bisphenol-A as a result of interaction of the hydroxilic groups of bisphenol A with the surface groups of the treated filler. This may lead to the increasing adhesion (diminishing A) for PHE-Gr-II as compared to PHE-Gr-I. Using values of dn allows us to obtain for both composites the correlation between A and dn, which is shown in Figure 12.6.
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Figure 12.5 Dependence of the adhesion parameter A on normalised number of nonscreened points on the filler surface, Nu / ϕf for 1: PHE-Gr-I and 2: PHE-Gr-II.
It is worth noting that at the minimum value of dn = 2, value A becomes negative. That means, in accordance with Equation (12.1), that tan δC < tan δM. In other words, at small dn (smooth surfaces of the filler particles) the packing of the polymer molecules at the interface may be more dense compared with the bulk. This fact leads to the diminishing molecular mobility in the interfacial layer [1, 37, 38] Extrapolation of the dependence of A on dn to maximum value of dn = 3 gives the limiting value of A ≈ 4.5. This value meets the value A ≈ 4.2, that was derived from the extrapolation of the volume of the interfacial layer on dn to dn = 3 [39]. Thus, this analysis allows an estimation of the structural factors influencing formation of the adhesion joints. The main factors are: fractal dimensions of the particle surface, dn and of the polymer df, which determine adhesion at the polymer-filler particle interface.
12.3.3 Interfacial Adhesion and the Strength of the Interfacial Layer For composite PHE-Gr, it was shown [23] that the dependence of the elasticity modulus (E) on ϕ f is well described by the Kerner equation which assumes strong interactions at the interface. Because of it we can suppose that by fracture of a composite there exists the possibility of transfer of the applied stress through the interfacial border. The tensile strength of the composite in the given case should be the function of the shear strength of the
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Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
Figure 12.6 Dependence of the adhesion parameter (A) on fractal dimension (dn) of the filler surface for 1: PHE-Gr-I and 2: PHE-Gr-II.
matrix, τ M and of the strength of the interfacial bond σa. The latter value may be calculated from the Leidner-Woodham equation [21, 22]. Figure 12.7 shows the dependence of σa on A. It should be expected, that the strength of the interfacial layer diminishes with weakening of adhesion, characterised by the value A. At A ≅ 4.3 the tensile strength of the interfacial layer drops to zero. In the given case the calculation of σA has been done in the following way. It is known [40] that the degree of the local ordering (relative fraction of the regions of the local orders, clusters) ϕcli in the interfacial layer changes from zero at the interface to the value of the bulk, ϕcl. This allows the definition of ϕcli in the following way: ϕ Icl = ϕ cl / 2
(12.12)
To calculate the tensile strength of the interfacial layer σat, the next equation has been used [41]: ⎛ ⎞ ϕ icl σ ti = 1.4 ⋅ 105 ⎜ ⎟ ⎝ 2N A Sl0C ∞ ⎠
5/6
, Pa
(12.13)
where NA is the Avogadro number, S is the cross-section of a macromolecule, equal to 30.7 Å for PHE [20], l0 is the length of the skeleton bond of the main chain (l0 = 1.54 A, [42], C∞ is the characteristic ratio taken from [43]. 361
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Figure 12.7 Dependence of the strength, (σa), of an interfacial layer on adhesion parameter A for PHE-Gr-I (1, 3) and PHE-Gr-II (2, 3). 1, 2: calculated from Equation 12.13, 3: from Leidner-Woodham equation at K= 2 [22].
Values ϕ cl for the composites under consideration were given in [44]. To estimate the shear strength of the interfacial layer σa the formula [45] has been taken as: σa =
σ at 3
(12.14)
The extrapolation of the dependence of σa on A to A = 0 gives the value σa = 24 MPa which corresponds to the shear strength of initial PHE (about 23.2 MPa, [20]). Figure 12.7 presents dependence σa on A (line 3) where values σa were calculated using LeidnerWoodham equation for constant value of coefficient of stress concentration K = 2 [22]. This dependence gives qualitatively reasonable shape of the dependence of σa on A, although the calculation methods give lesser absolute values. It is interesting to compare the dependence of the strength of interfacial layer on its structural characteristics for the polymer-polymer and polymer-high-modulus filler. For the first type of systems with increasing li there is observed the growth of adhesion [17]. 362
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
Figure 12.8 Dependence of the adhesion parameter (A) on the thickness of the interfacial layer (l1/2 i ), for 1: PHE-Gr-I and 2: PHE-Gr-II.
Figure 12.8 gives the dependence of the parameter A on the value of the thickness of an interfacial layer li1/2 for composites of PHE-Gr. It is seen that increasing A (diminishing adhesion) with increasing the thickness of an interphase layer lI is observed. The comparison with the data given in Figure 12.7 also shows that increase in li diminishes the strength of the interfacial layer, which is characterised by σa. Thus the dependencies of interfacial adhesion A and strength of interfacial layer as functions of li for two types of systems are in reverse correlation. These distinctions are explained by the different mechanisms of the interphase formation in two systems. For a polymer-polymer system the interfacial layer is formed due to diffuse interpenetration of molecules of both polymers [17]. In the polymer- high-modulus filler system this layer arises as a result of the modifying action of the fractal surface of a filler on the adjacent layer of a polymer [1] and role of diffusion is negligible. Besides, at the polymerfiller interface there is possibly the formation of an macroscopic structural defect, whose length acrit increases with diminishing adhesion [46, 47]. Modification of the graphite surface diminishes the adhesion (Figure 12.6), acrit and, what is especially important, diminishes the fraction of clusters in the interfacial layer, ϕicl. As a result, σa diminishes (Figure 12.7). 363
Polymer Yearbook Adhesion may be also characterised by the critical strain energy release rate in the interfacial layer, Gi, which depends on the thickness of the interfacial layer, li. Value Gi is a function of some variables [48]:
Gi =
πa crit σ 2a Ei
(12.15)
where Ei is the elastic modulus of an interfacial layer. Following from Equation (12.15), at high growth of acrit, the value of Gi may increase when σa diminishes. Because of this effect, in order to characterise the strength of an interfacial layer it is desirable to use the shear strength of an interfacial layer, σa.
12.3.4 The Level of Interfacial Adhesion and Mechanical Characteristics of Composites The interphase region in polymer composites is often the place of the origin of destruction [7, 46, 47]. In spite of this fact, there are few data on the correlation between the structure of an interfacial layer and composite properties [21]. Now we try to elucidate the role of an interfacial layer in the macroscopic properties of composites. Figure 12.9 shows the dependence of the shock impact toughness Ap of specimens of PHE-GR without a notch on the values of A-1/3. Such functional forms, Ap = f(A-1/3) were taken for the following reasons. It is supposed [20] that increasing A, denoting the diminishing adhesion, should diminish Ap, i.e., both values are in a reversed dependence. Preliminarily estimations have shown that linear correlation may be achieved if Ap is a function of A to the power 1/3. As may be seen from Figure 12.9, corresponding dependence is really a good approximation. The empiric correlation between these two values is [21]: Ap ~
19 3
A
, kJ / m 2
(12.16)
As is seen, the interdependence of two values is rather weak. The modification action (‘disturbance’) of the graphite surface (increasing A) leads to facilitating fracture of an interfacial layers, and, as a consequence, to increasing the size of critical structural defect, acrit [46, 47]. Figure 12.10 shows that the correlation of acrit to (A) meets the above concept.
364
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
Figure 12.9 Dependence of the impact strength (Ap) on parameter (A–1/3) for specimens without incision for 1: PHE-Gr-I (1) and 2: PHE-Gr-II
The correlation is linear and begins at a point of origin in accordance with equation [21]: a crit ≈ 49.5 A, μm
(12.17)
Figure 12.11 shows the dependence of the local deformation in plasticity zone, εloc, on A for the composites under consideration. The value of εloc was determined from the following equation [49]: ⎛ rp + δ c ⎞ ε loc = ln⎜ ⎟ ⎝ rp − δ c ⎠
(12.18)
where rp is the length of the local plasticity zone and δc is the critical crack opening displacement. Both of these values were found from relationships of linear mechanics of elastic fracture [48] (Equation (12.19)).
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Figure 12.10 Dependence of the critical structural defect length (acrit) and adhesion parameter (A) for 1: PHE-Gr-I (1) and 2: PHE-Gr-II
rp =
π K2IC 8 o2Y
(12.19)
δc =
K2IC σ YE
(12.20)
where E is the elasticity modulus and KIC is the critical stress intensity factor equal to [48]: K2IC = πaσ 2c
(12.21)
The data given in Figure 12.11 show that, as expected, the worsening of adhesion (growth of A) leads to decreasing εloc, i.e., to harsh failure of the polymer martix in the local plasticity zone. Let us now consider the reasons for a weak dependence of the impact toughness A p on A (see Figure 12.9 and Equation (12.16) The length of the critical structural defect according to the modified Brown equation [50] is:
366
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites
Figure 12.11 Dependence of the local plastic deformation (εloc) in adhesion parameter (A) for 1: PHE-Gr-I (1) and 2: PHE-Gr-II
a crit =
GIC BD L d 72U
(12.22)
where GIC is the critical strain energy release rate, B and D are the width and thickness of the specimen, Ld is the distance between the device bearing and U is the fracture energy of a specimen without notch. By dividing the numerator and denominator by BD (specimen cross-section), after regrouping, we have: GIC ≈ A pa crit
(12.23)
Taking into account Equations (12.16) and (12.17) we obtain: GIC ≈ A2 / 3
(12.24)
In other words, Equation (12.22) derived in the framework of the mechanics of continuous media implies the increase in GIC (composite plasticity) with decreasing adhesion level (growth of A).
367
Polymer Yearbook However, as the experimental data show [20] for PHE-Gr-II there was observed a diminishing GIC from 2.23 to 0.95 kJ/m2 in the range of ϕf = 0.0088-0.176. Therefore, the scaling relationship 12.24 does not correspond to the experiment. The reason for it may be the invariance of the structure of polymer matrix that does not depend on the volume fraction of filler according to the postulate of mechanics of continuous media [51]. As it was shown in [52], the value GIC may be expressed as: GIC = νeff U act
(12.25)
where νeff is the effective chain density crossing the fracture plane and having entanglements with both sides of this plane and Uact is the activation energy of conformational changes and nonelastic deformation of the polymer chain in the course of its fracture. In the first approximation, value of Uact may be accepted as a proportional to εloc, i.e., to nonelastic deformation. In this case we can write [53]: GIC ≈ νeff ε loc
(12.26)
Figure 12.11 shows the diminishing of values of εloc which decrease approximately 1.33 times for the specimens of PHE-Gr-II. GIC is decreased 2.5 times, according to Equation (12.26), supposing that the diminishing νeff ª 1.9 times in the ϕf interval 0.0088-0.176. The same value of diminishing density of the cluster network of entanglements νeff, which characterises the structure of a polymer matrix, was obtained for PHE-Gr-II in [44, 54] and for PHE-Gr-I in [20, 44, 54]. This fact is very important. It confirms the conclusion, made many years ago by Lipatov [1, 29, 55] that the filler surface exerts a disturbing action on the matrix structure in the interfacial layers.
Conclusions The analysis of experimental data on adhesion, adhesion strength and tensile strength of an interfacial layers shows that all important properties of particulate-filled composites may be described in the framework of the theory of irreversible aggregation of the filler particles, cluster theory of the structure of amorphous polymers and fractal analysis. The analysis is based on the consideration of the filled polymer as the totality of two or more fractal. Adhesion is determined by the structure of an interfacial layer that also represents a fractal. An interfacial layer is formed as a result of interaction between two fractals: of the surface of the aggregated filler particles (dn) and of polymer matrix (df), the latter being in the perturbed state under the effect of the filler surface. The fractal dimension (dn) depends on the aggregation of a filler particles. Using the model of irreversible aggregation and fractal approach it becomes possible to establish the
368
Structural Aspects of Adhesion in Particulate-Filled Polymer Composites interconnection between the number of sites on the surface of aggregate available for the formation of adhesion joints. It was established that the most important characteristics of the particulate-filled composites are determined by the difference of two fractal dimensions. Thus the value of this difference is the most important factor that determines the adhesion, structure of an interfacial layer and mechanical properties of composites.
References 1.
Y.S. Lipatov, Polymer Reinforcement, ChemTec Publishers, Toronto, Canada, 1995.
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S. Ahmed and F.R. Jones, Composites, 1988, 19, 277.
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J.J. Bikerman, The Science of Adhesive Joints, Academic Press, New York, NY, USA, 1968, p.350.
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B.V. Deryagin, N.A. Krotova and V.P. Smilga, The Adhesion of Solids, Nauka, Moscow, Russia, 1973.
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A.A. Berlin and V.E. Basin, The Basis of Polymer Adhesion, Khimiya, Moscow, Russia, 1974.
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V.E. Basin, The Adhesion Strength, Khimiya, Moscow, Russia, 1981.
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S. Wu, Polymer Interface and Adhesion, Marcel Dekker, New York, NY, USA, 1982, p.492.
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W.C. Wake, Adhesion and Formulation of Adhesives, Applied Science Publishers, London, UK, 1982.
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A.I. Kinloch, Adhesion and Adhesives-Science and Technology, Chapman and Hall, New York, NY, USA, 1988.
10. G.V. Kozlov and V.U. Novikov, Uspekhi Fizicheskikh Nauk, 2001, 171, 737. 11. V.U. Novikov and G.V. Kozlov, Uspekhi Khimii, 2000, 69, 378. 12. V.U. Novikov and G.V. Kozlov, Uspekhi Khimii, 2000, 69, 572. 13. T. Vicsek, Fractal Growth Phenomena, World Scientific Publishing, Singapore, 1989. 14. G.V. Kozlov, Y.G. Yanovskii and A.K. Mikitaev, Poverkhnost, 1999, 8, 43, [in Russian].
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Polymer Yearbook 15. G.V. Kozlov, Y.G. Yanovskii and A.K. Mikitaev, Mechanics Composite Materials 1998, 34, 539, [in Russian]. 16. J. Kubat, M. Rigdahl and M. Welander, Journal of Applied Polymer Science, 1990, 39, 1527. 17. R. Schnell, M. Stamm and C. Creton, Macromolecules, 1998, 31, 2284. 18. G.V. Kozlov, R.A. Shetov and A.K. Mikitaev, Polymer Science, 1987, A29, 1109. 19. G.V. Kozlov, R.A. Shetov and A.K. Mikitaev, Polymer Science, 1987, A29, 2012. 20. G.V. Kozlov, A.M. Abaev, V.I. Novikov and A.S. Komalov, Materialovedenie, 1997, 5, 31. 21. V.I. Novikov, G.V. Kozlov and O.Y. Bur’yan, Mechanics of Composite Materials, 2000, 36, 3. 22. S. Ahmed and F.R. Jones, Journal of Materials Science, 1990, 25, 4933. 23. G.V. Kozlov, A.M. Abaev, A.S. Komalov, A.A. Beev, V.D. Serdyuk, D.S. Sanditov and D.A. Magaeva. Plasticheskie Massy, 1995, 6, 28. 24. M.V. Shamurina, V.I. Roldugin and T.D. Pryamova, Kolloidnyi Zhurnal, 1995, 56, 451, [in Russian]. 25. M.V. Shamurina, V.I. Roldugin and T.D. Pryamova, Kolloidnyi Zhurnal, 1995, 57, 580, [in Russian]. 26. D.A. Weitz, J.S. Huang, M.Y. Lin and J. Sung, Physical Reviews Letters, 1984, 53, 1657. 27. G.V. Kozlov, E.N. Ovcharenko and Y.S. Lipatov, Reports of the National Academy of Sciences of Ukraine, 1999, 11, 128. 28. N.J. Mills, Journal of Applied Polymer Science, 1971, 15, 2791. 29. Y.S. Lipatov, Interfacial Phenomena in Polymers, Naukova Dumka, Kiev, Russia, 1980, [in Russian]. 30. D. Avnir, D. Farin and P. Pfeifer, Nature, 1984, 38, 5959, 261. 31. D. Avnir, D. Farin and P. Pfeifer, Journal of Colloid & Interface Science, 1985, 103, 112.
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Structural Aspects of Adhesion in Particulate-Filled Polymer Composites 32. H.G.E. Hentschel and J.M. Deutch, Physical Review, 1984, A29, 1609. 33. D. Avnir, D. Farin and P. Pfeifer, Journal of Chemical Physics, 1983, 79, 3566. 34. P. Meakin, A. Coniglio, H.E. Stanlet and T.A. Witten, Physical Review, 1986, A34, 3325. 35. A.I. Bobryshev, B.N. Kozomazov, L.O. Babin and V.I. Solomatov, Synergetics of Composite Materials, NPO ‘ORIUS’, Lipetsk, Russia, 1994, p.153, [in Russian]. 36. M. Sahimi, M. McKarnin, T. Nordahl and M. Tirrell, Physical Review, 1985, A32, 590. 37. Y.S. Lipatov, E.G. Moisya and G.M. Semenovich, Polymer, 1975, 16, 582. 38. V.A. Dovgyalo, E.V. Pisanova and O.R. Yurkevich, Polymer Science, 1989, A31, 708. 39. H.H. Mashukov, V.U. Novikov, G.V. Kozlov and O.Y. Buryan, Materialovedenie, 2000, 3, 35. 40. V.U. Novikov and R.A. Tkalenko, Mechanics of Composite Materials, 1996, 32, 467. 41. G.V. Kozlov, B.N. Belousov and Y.S. Lipatov, Reports of the National Academy of Sciences of Ukraine, 1990, 6, 50. 42. S.M. Aharoni, Macromolecules, 1983, 16, 1722. 43. V.U. Novikov and G.V. Kozlov, Mechanics of Composite Materials, 1992, 35, 269. 44. G.V. Kozlov, A.M. Abaev, V.D. Serdyuk, D.A. Nagaeva, D.S. Sanditov, A.A. Beev and R.Z. Oshroeva, Plasticheskie Massy, 1999, 11, 27. 45. A.S. Argon and M.I. Bessonov, Philosophical Magazine, 1977, 35, 917. 46. G.V. Kozlov, V.A. Beloshenko and A.K. Mikitaev, Physico-chemical Mechanics of Materials, 1999, 35, 116. 47. G.V. Kozlov, V.U. Novikov and O.Y. Buryan, Materialovedenie, 1999, 11, 13. 48. C.D. Bucknall, Toughened Plastics, Applied Science Publishers, London, UK, 1977. 49. M.I. Baskes, Engineering Fracture Mechanics, 1974, 6, 11.
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Polymer Yearbook 50. V.N. Belousov, G.V. Kozlov and A.K. Mikitaev, Polymer Science, 1984, B26, 563. 51. T.S. Chow, Polymer, 1991, 32, 29. 52. A.G. Mikos and N.A. Peppas, Journal of Chemical Physics, 1988, 88, 1337. 53. G.V. Kozlov and V.U. Novikov, Applied Physics, 1997, 1, 94, [in Russian]. 54. G.V. Kozlov and A.K. Mikitaev, Mechanics of Composite Materials and Constructions, 1996, 2, 144, [in Russian]. 55. Y.S. Lipatov, Physical Chemistry of Filled Polymers, Translator, R.J. Moseley, Rapra Technology Ltd., Shrewsbury, UK, 1979.
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13
Change of Microgel Structure on Curing Epoxy Polymers in Fractal Space G.V. Kozlov, A.A. Bejev and I.V. Dolbin
13.1 Introduction This chapter considers the reasons for a variation of microgel structure characterised by its fractal dimension, D, formed in the cure of epoxy resin systems. Quantitatively, change of D during the increase of reaction time is well described within the framework of mechanism of aggregation cluster – cluster. The fractal space, in which the reaction curing proceeds, is formed by a structure of the greatest cluster in system. Kozlov and co-workers [1] showed that the occurrence of epoxy polymers curing in Euclidean space characterised by a condition D = constant (where D is the fractal dimension of curing the macromolecular coil-microgel) and in fractal space by the condition D = variant. This chapter will discuss causes of the variation of D in the latter case. In this case, in a part of the kinetic curve a degree of conversion (the time of reaction (Q-t) almost up to a gelation point the continuous change of microgels structure characterised by its fractal dimension D occurs), there is a monotonous increase D. Such a variation of D, the curve D(t) which has the qualitative differences from a similar curve for curing epoxy polymers in Euclidean space, namely, on the previously mentioned part up to a gelation point (Q<0.8) the linear growth Q as function t is observed practically. The purpose of the present chapter is the study of the reasons and mechanism for the variation of microgels structure on an example of halogen containing oligomers basis of hexachlorobenzene [2] with using the representations of the fractal analysis [3] and irreversible aggregation models [4].
13.2 Experimental The kinetics of a halogen containing oligomer cured with hexachlorobenzene (EPS-1) have been investigated. This oligomer is cured by 4,4´-diaminodiphenylmethane (DDM) at stoichiometric ratio DDM:EPS-1 [2]. The curing kinetics of system EPS-1/DDM was studied by a method of inverse gas chromatography [2]. The basic parameter determined from processing of experimental data, was a degree of conversion Q, as function of curing time t, determined for a part of kinetical curve up to t ≤3 x 103 s. Ketones (methyl ethyl ketone, 1,4-dioxane, cyclohexanone) were chosen as standard substances, and argon was used as the carrier gas.
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Polymer Yearbook The curing temperature of system EPS-1/DDM was 393 K. Values of fractal dimension D of microgels varied within the limits of 1.61-2.38 [1].
13.3 Results and Discussion The previously mentioned interval of a variation D assumes that the process of formation of microgels proceeds by the mechanism cluster – cluster, i.e., the large microgels are formed out of smaller, ones instead of directly from oligomer units [5]. In this case for dimension D of the large microgel which is formed out of two smaller ones with dimensions D1 and D2 (D1>D2) the following relationship [6] is correct: D=
3(2D1 − D2 )
3 + 2( D1 − D2 )
(13.1)
It follows from the Equation (13.1) that in the case of absence of microgel distribution on their fractal dimensions, i.e., in the case D1=D2=...=Di, the large cluster differs from smaller ones which form it, only by sizes and Equation (13.1) D= D1=D2=...=Di. Equation (13.1) shows that the distribution of the values of Di, i.e., small microgels (analogues of macromolecular coils for linear polymers) should have different dimensions of D, i.e., D1≠D2≠D3≠...≠Dn. Theoretically we can estimate the possible variation of D(t) in the following way. If we assume that at the moment of time (ti) the distribution of D of microgels is equal to Di-1-Di+1, according to the Equation (13.1) it is possible to calculate Di=D under condition Di+1=D1, Di-1=D2. The interval of time Δt=t1-ti-1=ti+1-ti is accepted as equal to 500 s. As Di-1, Di+1, the appropriate experimental values of D were accepted. In Figure 13.1 the comparison of the experimental and calculated by the previously discussed technique, of D(t) for system EPS-1/DDM is given. As it is possible to see the mechanism of aggregation cluster – cluster quantitatively explains an experimentally observable variation of D(t). As has been mentioned before [1], the reason for a variation of D(t) is of course the curing reaction in fractal space. This process in the physical sense is similar to the formation of a cluster with dimension D on fractal lattices with dimension Dlat [7]. In paper [1] it was supposed that Dlat=D. The relationship between D and Dlat is given by the following equation [7]: D = Dlat
2 + 2d l − ds 4d l − ds
(13.2)
where dl and ds, are the chemical or ‘spreading’ and spectral dimensions of a cluster (microgel), respectively.
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Change of Microgel Structure on Curing Epoxy Polymers in Fractal Space
Figure 13.1 Dependence of the fractal dimension D (Dlat) of microgels on reaction time (t) for system EPS-1/DDM. 1: calculation D according to the equation (13.1); 2: calculation Dlat according to the equation (13.2); 3: experimental values D
Between the dimensions D, dl and ds there is the following relationship [8]: D = ds
ds =
d+2 ds + 2
2d l dl + 1
(13.3)
(13.4)
where d is a dimension of Euclidean space in which fractals are considered (obviously, in our case d = 3). It follows from the Equations (13.2)-(13.4) that the condition Dlat=D is realised only at the following values of the mentioned dimensions: D≈1.67, dl=1 and ds=1. The latter condition means that the microgel is formed by linear macromolecule [9]. However, in the process of curing there is branching of a polymeric chain and it results in an increase
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Polymer Yearbook of ds [9]. In turn, it follows from the Equation (13.4), that it will cause the corresponding increase of dl . If we accept that ds is a value of this dimension for the branched polymeric chain (ds=1.33 [9]), and dl is the value of this dimension determined for cluster – cluster modelling (dl =1.42 [8]) formed by mechanism, then the following equation results: D ≈ 0.807 Dlat
(13.5)
The relationship (13.5) determines the following condition: Dlat > D
(13.6)
for the branched (crosslinked) polymers. The condition (13.6) allows us to assume that a cluster forming a fractal space in curing process of system EPS-1/DDM, is the greatest cluster in the system (Figure 13.1). As shown previously [10], during the increase of molecular weight of the macromolecular coil (microgel) an increase of D is observed. Such tendency was found out from the graph of Figure 13.1. After a gelation point such cluster is the spanning cluster, i.e., cluster extending from one end of the system up to another [10]. Such a cluster has dimension D≈2.5 [10] which is shown in Figure 13.1 by a horizontal dashed line. In paper [1] the curves Q(t) were described in terms of the scaling approaches for low molecular substance reactions [11]. Let us consider the reaction in which particles P of chemical substance are diffused in the environment containing randomly located nonsaturated statistical traps T. At the point of contact of a particle P with trap T the particle disappears. Nonsaturation of a trap means that the reaction P+T→T can be repeated an infinite number of times. It is usually considered that if the concentration of particles and traps is large or the reaction proceeds at intense stirring, the process can be considered as classical reaction of the first order. However, if the concentration of the randomly located traps is small, with necessity there exist areas of space, practically free from traps. The particles that are in these areas, can reach traps only for rather long time and, hence, the fall of their number with time grows slower in comparison with the reaction of the first order. The formal analysis of this problem shows that the concentration of particles falls down under the law [11]:
(
C(t) ≈ exp −Btd /(d +2)
)
(13.7)
which is dependent on the dimension of space d (B is constant). In paper [1] it was shown that the dependence C(t)=(1 – Q) on td/(d+2) is not linear and it is possible to linearise it by use of value D in the Equation (13.7) instead of d. It has
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Change of Microgel Structure on Curing Epoxy Polymers in Fractal Space
Figure 13.2 Dependence of (1 – Q) from parameter tD/(D+2) in logarithmic coordinater according to equation (13.7), for system EPS-1/DDM
formed the basis for the assumption that the curing reaction proceeds in the fractal space. In Figure 13.2 is shown the dependence ln (1 – Q) on tD/(D+2) for system EPS-1/ DDM which also has appeared to be linear. Together with the previously stated reasons, the data of Figure 13.2 assume that the curing reaction of system EPS-1/DDM proceeds in fractal space with dimension Dlat. We should note that at t = 3 x 103 s a deviation is observed (given in Figure 13.2) of dependences on linearity. From the comparison with the data of Figure 13.1 it is seen that this deviation corresponds to Dlat = 3, i.e., transition to nonfractal behaviour at Dlat=d, as should have been expected.
13.4 Summary Thus, the results given in the present chapter have shown that the main reason of a variation of microgel structure characterised by its fractal dimension D, is the distribution of values D. Quantitatively, change of D during the increase of mechanism of aggregation cluster – cluster. The fractal space in which the reaction curing proceeds, is formed by the structure of the greatest cluster in system.
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Polymer Yearbook
References 1.
G.V. Kozlov, A.A. Bejev and G.E. Zaikov in New Perspectives in Chemistry and Biochemistry, Ed., G. Zaikov, Nova Science Publishers, New York, NY, USA, 2002, p.27-33.
2.
A.A. Bejev, Epoxy Oligomers, Polymers and Composite Materials with Improved Characteristics and their Synthesis, Khimiko-Technologicheskii Institut, Tashkent, SSSR, 1991. [PhD Thesis]
3.
G.V. Kozlov and V.U. Novikov, Synergetics and Fractal Analysis of Cross-Linked Polymers, Klassika, Moscow, Russia, 1998, [in Russian].
4.
B.M. Smirnov, Uspekhi Fizicheskikh Nauk, 1986, 149, 2, 177.
5.
A.G. Kokorevich, A.Ya., Gravitis and V.G. Osol-Kalnin, Khimiya Drevesiny, 1989, 1, 3-24.
6.
H.G.E. Hentschel and J.M. Deutch, Physical Reviews A, 1984, 29, 3, 1609.
7.
J. Vannimenus, Physica D, 1989, 38, 2, 351.
8.
P. Meakin, I. Majid, S. Havlin and H.E. Stanley, Journal of Physics A, 1984, 27, 8, L975.
9.
S. Alexander and R. Orbach, Journal de Physique Lettres, 1982, 43, 17, L625.
10. R. Botet, R. Jullien and M. Kolb, Physical Reviews A, 1984, 30, 4, 2150. 11. Z.B. Djordjevic in Fractals in Physics, Eds., L. Pietronero and E. Tosatti, Mir Publishers, Moscow, Russia, 1988, p.581-585.
378
14
Levels of Fractality in Polymers G.V. Kozlov and G.E. Zaikov
14.1 Introduction It has been found that the basic elements of structure of initial and deformed polymers are homogeneous fractals that can be characterised by their fractal dimension. Examples of such elements are macromolecular coil, supermolecular organisation as seen in the cluster structure and a stable crack in film samples of polymers. These examples are given as examples of the possible variants of the term ‘multifractality’ with reference to polymers. Current thinking indicates [1] that condensed phase systems self-organise in the scaleinvariant into multifractallic forms and are a consequence of the fundamental principles of thermodynamics of an open system. Any structure can be proved analogously to consist of N of elements at N>BN(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)
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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].
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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
381
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.
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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).
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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.
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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)
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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.
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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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