Macromolecular Mechanochemistry Polymer Mechanochemistry

MACROMOLECULAR MECHANOCHEMISTRY

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MACROMOLECULAR MECHANOCHEMISTRY Polymer Mechanochemistry Volume 1, Part 1

Cleopatra Vasiliu-Oprea Florin Dan

CAMBRIDGE INTERNATIONAL SCIENCE PUBLISHING

Published by Cambridge International Science Publishing Ltd 7 Meadow Walk, Great Abington, Cambridge CB1 6AZ, UK http://www.cisp-publishing.com

First published 2006

© Cleopatra Vasiliu-Oprea and Florin Dan

Conditions of sale All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library

ISBN 189832672X Printed and bound in the UK by Lightning Source Ltd

The authors

Cleopatra VASILIU-OPREA held the post of Professor of Monomer and Polymer Technology and Polymer Mechanochemistry at the Gh. Asachi Technical University, Iasi, Romania. She received a chemical engineer degree at the Polytechnical Institute of Iasi, Romania, and PhD degree from the Techniche Hochschule für Chemie, Merseburg, Germany. Prof. Vasiliu-Oprea is PhD supervisor in the fields of Polymer Chemistry and Technology and Material Science. During 45 years of scientific activity she published over 450 professional papers and holds more than 40 patents, with special emphasis on polymer degradation and mechanochemical synthesis, mechanochemistry of polymer and composites fracture and deformation. She is the author or coauthor of over 20 monographs, books, and book chapters, including Mechanochemistry of Macromolecular Compounds; Polymers. Theory and Applications; Polymers. Structure and Properties; Polymers Fracture. Theory and Applications; Mechanochemical Polycondensation and Polycomplexation in Polymer Kinetics and Technology, Mechanochemistry of Polymer Deformation and Fracture Process in Elastomer Technology Handbook, Monomer and Polymer Technology. She is a member of the Romanian Society of Polymer Science, the Romanian Society of Chemistry and Chemical Engineering, Romanian Society of Inventors, and of the International Federations of Inventors Associations, IFIIA-WIN, Geneva. For her scientific activity Prof. Vasiliu-Oprea received several awards, as follows: Gh. Spacu Prize of Romanian Academy, 1981 (for research in the field of Polymer Mechanochemistry), title of Evidenced Professor of the Romanian Education Minister, 1984, Elite Inventor award of Romanian Society of Inventors, 1991, 1992, 1994, Henry Coanda gold and silver medals of Romanian Society of Inventors, gold medals and diplomas from the EUREKA-Brusseles, 1994–1996. In 2003, she has been honored with Opera Omnia prize and medal for excellence in scientific research by Romanian Minister of Education and Research.

Florin DAN is a lecturer of Monomer and Polymer Technology and Polymer Processing at the Gh. Asachi Technical University, Iasi, Romania. Prior to this post he served as a chemical engineer in the rubber and plastic processing industry, UAMT-Oradea, Romania. He received his B.Sc. and Ph.D (supervisor C. VasiliuOprea) degrees from the Gh. Asachi Technical University. He then spent a year as a Postgraduate Fellow in Polymer Science at the Institute of Macromolecular Chemistry of Prague, Czech Republic, with J. Stehlicek. This fellowship was followed by a year and a half as a

Postdoctorate Fellow at the TotalFinaElf and a year and a half as an associate researcher at the National Research Council of France at the Blaise Pascal University of ClermontFerrand, France, with J.P. Grolier. His research interests focus on anionic polymerization of lactams in organic media, electroactivated stimuli responsive polymer gels, combined techniques for on-line monitoring of chemical processes, with an emphasis on the use of reaction calorimetry. Dan has authored more than 30 research papers, two invited book chapters, and holds one patent.

Preface Mechanochemical phenomena are implied both in fundamental processes of life and in many branches of science and technology. Notable progress in areas such as solid body resistance, physico-chemical mechanics of materials, colloidal chemistry, polymers physics and chemistry, biophysics, chemical kinetics, theory of molecular capacity of reactions, molecular acoustics, shock waves detonation and propagation, friction and transfer, heterogeneous catalysis and adsorption, inorganic technology, metal corrosion, generally allow us to define and organise the mechanochemistry object, particularly in polymer mechanochemistry. Presently, within the specialised scientific medium, the capacity of mechanical energy to modify into a specific manner, in accordance with the nature of co-existent environment, the relation between polymer structure and properties is unanimously recognised. The mechanisms of irreversible mechanochemical processes are clearly proved. In polymers, the mechanisms of deformation and fracture are studied and discussed in accordance with their physical state, as these ones are concretised in polymer synthesis, processing, and exploitation. Unfortunately, in industrial practice these results are not yet fully utilised. Very promising results have been obtained in the last two decades in the field of reversible mechanochemical processes. The exploitation of the principle of stimulation of conformational changes from the natural or artificial macromolecular structures and the release of chemical and physical processes producing the mechanical work, as well as the assurance of the required feedback of these processes, and not in the last instance the obtaining of new polymeric materials, characterised by very short time response at the applied stimuli, constitute major contributions to the further implementation of this new source of energy in practice. The high efficiency of conversion of chemical energy into mechanical work, and the ability of self-adapting of waste-free and quiet chemo-mechanical systems are some of significant advantages, allowing the fulfillment of one of the major objectives: the discover and use of some alternative energies. These contributions determine the contour of macromolecular mechanochemistry.he names of well-known schools, such as those led by H. Staudinger, H. Grohn, W.F. Watson and R.J. Ceresa, N.K. Baramboin, W. Kuhn and A. Katchalsky, R.S. Porter, and not in the last instance by U. Murakami and Y. Osada made possible the progress in this field. The contributions of the Romanian school of polymer mechanochemisty are ranging among the trajectory of these researches. For of sixteen years, Professor C.I. Simionescu initi-

ated and stimulated the investigations in this field and an optional discipline with this object of study was introduced the education programme of the undergraduate students of Department of Technology of Macromolecular Compounds, Faculty of Industrial Chemistry-Iasi. Our book Macromolecular Chemistry presents from the theoretical and experimental point of view the main problems of this field, including the results obtained in more than a century of research. It is organised in two volumes: Polymer Mechanochemistry and Polymers with Chemomechanical Functions, respectively. The present volume (which is in two parts) deals with: Chained Multistage Character of Mechanochemical Process (1), Mechanochemistry of Polymers Deformation (2); Mechanochemistry of Polymer Fracture (including also the Fracture of Composite Materials) (3), and Mechanochemical processes for Energy Conversion (4). In this framework, the theoretic and experimental material is organised in correlation to the reaction mechanism, the type of mechanical solicitation, and the nature of environmental medium. This book is to be considered as a guideline and not an encyclopedia. The treatment is not exhaustive and it is opened to adsorption and integration of new data, as well as to the critique analysis and suggestions, for which the authors will be indebted. The book is addressed to professors, students, and researchers involved in the field of polymer science, to the engineers from the industry of synthesis and processing of plastic materials, elastomers, and fibres, as well as to the specialists from all technical domains that exploit the polymer-based materials. They will find inside treatment of the theoretical, experimental, and applicative problems and a wide access to the basic literature of this field. The authors are grateful to Mrs. eng. Brandusa Vahnoveanu for the constant help during the make-up of this book.

Authors

Contents Preface Introduction .............................................................................................................. 1 1. CHAIN MULTISTAGE MECHANISM OF THE MECHANOCHEMICAL PROCESS ........................................................................................................... 7 Bibliography Part 1 ................................................................................................... 37 2. MECHANOCHEMISTRY OF POLYMER DEFORMATION .................. 39 2.1. On the local character of polymer deformation ................................................. 39 2.1.1. Basis of the theory of local character of deformation ............................. 41 2.2. The local character of polymer fracture ............................................................. 43 2.3. Deformation and fracture – interconnected processes ....................................... 50 2.4. Mechanochemical mechanism of polymer deformation .................................... 70 2.5. Kinetic aspects ................................................................................................... 81 2.5.1. Kinetics of the mechanochemical reactions in constant mechanical fields .................................................................................................................. 82 2.6. Mechanochemistry of polymer deformation under creep conditions .............. 101 2.7. Chemical stress relaxation ............................................................................... 117 2.7.1. Mechanocracking of the chemical bonds from the main chain ............. 118 2.7.2. Mechanism of mechanocracking of chemical bonds from the main chain ................................................................................................................ 122 2.7.3. Mechanocracking of cross-bridges (transversal bonds) ........................ 126 2.7.4. Interchange reactions............................................................................. 126 2.7.5. Multiple mechanocracking of polymer networks [201,202] ................. 135 2.7.5.1. Scission of the cross-bridges and along the main chains .................. 135 2.7.5.2. Reticulation reactions ........................................................................ 137 2.7.6. Applications of chemorheology ............................................................. 141 2.7.6.1. Control of thermal stability of polyolefin-type hydrocarbonate networks 142 2.7.6.2. Characterisation of some thermosetting networks for ....................... 145 varnishes and adhesives .................................................................................. 145 2.7.6.3. Characterisation of some thermosetting resins .................................. 146 2.7.6.5. Some aspects of the chemorheology of linear .................................... 154 amorphous polymers ....................................................................................... 154 Bibliography Part 2 ................................................................................................. 163 3. MECHANOCHEMISTRY OF POLYMER FRACTURE ............................ 170 3.1. Theories concerning polymer fracture ............................................................. 170

3.1.1. Basis of the theory of the local character of deformation .................... 170 3.1.2. Griffith’s theory ................................................................................... 171 3.1.3. Kinetic theories of fracture .................................................................. 179 3.1.4. Generalised theory of polymer fracture. Andrews’s theory .......................... 182 3.2. Chemical bond strength ................................................................................... 184 3.3. Mechanochemical mechanism of fracture ....................................................... 190 3.3.1. Irreversible conversion of mechanical energy into chemical energy ......... (The nonequilibrium process) ........................................................................ 190 3.3.2. Nature of the primary active centers of mechanochemical reactions .. 194 3.3.3. Chained mechanism of macromolecular chain splitting ...................... 201 3.3.3.1. Initiation ........................................................................................... 202 3.3.3.2. Propagation ...................................................................................... 208 3.3.3.3. Interruption. Stabilization of destruction active fragments .............. 213 3.3.3.4. Types of homolytical mechanodegradation mechanism of some ........... usual polymers ............................................................................................... 215 3.3.3.5. Heterolytical mechanism .................................................................. 226 3.4. Kinetics ............................................................................................................ 227 3.5. Factors that influence the mechanodegradation process .................................. 253 3.5.1. Structural factors ................................................................................. 256 3.5.1.1. Macromolecular chain characteristics ............................................ 256 3.5.1.2. Characteristics of supramolecular–morphological structure ......... 267 3.5.2. Temperature ......................................................................................... 277 3.5.3. Reaction medium ................................................................................. 292 3.5.3.1. Inert media ....................................................................................... 292 3.5.3.2. Radical acceptors ............................................................................. 296 3.5.3.3. Organic liquids compatible with the stressed polymer .................... 311 3.5.4. Mechanical regime .............................................................................. 320 3.6. Modification of the structure-properties relationship by polymer degradation and fracture ................................................................................ 323 3.6.1. Modification of the relation between molecular structure and physico-chemical properties of polymers ...................................................... 323 3.6.2.1. Modification of the polydispersity–properties relationship ............. 340 3.6.2.2. Modification of the relation supramolecular-morphological ................ structure – properties .................................................................................... 350 3.7. Physical phenomena that accompany polymer mechanodegradation and ............. fracture .............................................................................................................. 378 3.8. Mechanochemical reactions at fracture surfaces ............................................. 390 3.8.1. Mechanochemical synthesis ................................................................ 390 3.8.1.1. Mechanochemical polymerisation ................................................... 392 3.8.1.1.1. Mechanochemical polymerisation of crystalline monomers ......... 392 3.8.1.1.2. Mechanochemical polymerisation initiated by crystalline ................. inorganic compounds .................................................................................... 402 3.8.1.1.3 Initiation of mechanochemical polymerisation and copolymeris-ation in the absence of mechanoinitiators .............................................................. 409 3.8.1.2. Mechanochemical block copolymerisation and grafting ................. 422 3.8.1.3. Mechanochemical polycondensation ............................................... 432

3.8.1.3.1 Factors that affect mechanochemical polycondensation ................ 433 3.8.3.2 Considerations of the mechanism of mechanochemical polycondensation ........................................................................................... 448 3.8.1.4. Mechanochemical complexation ....................................................... 453 3.8.1.5. Mechanochemical reactions on the surface of polyfunctional acceptors ......................................................................................................... 465 Bibliography Part 3 ................................................................................................. 473 Index ....................................................................................................................... 493

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Introduction

Introduction Mechanochemistry is a science, which might be located and was firstly developed at the border between mechanical and chemistry sciences. At the same time, mechanochemistry is related with physics, and especially the physics of solid body, biophysics, physico-chemistry of polymers, chemistry and technology of inorganic substances, biochemistry and molecular biology, respectively. Generally, mechanochemistry must be regarded as the science of the mutual (reciprocal) transformations of the chemical and mechanical energies, which occur in all kind of substances [1]. In present time, the term of mechanochemistry is used in many fields of activity but having often a different content. For instance, macromolecular mechanochemistry was defined as that part of polymer chemistry in which the initiation and acceleration of chemical transformations, that occur in polystructures, as a result of elastically absorbed energy, is investigated. On the other side, the direct conversion of chemical energy into mechanical work is studied by chemo-mechanics [2]. N.K. Baramboin defined mechanochemistry as the science dealing with the investigation of the chemical transformations of substances that occur under effect of mechanical forces [3]. In biochemistry, molecular biochemistry and physiology the term of mechanochemistry is associated with the production of mechanical energy by chemical reactions, which occur in living bodies. In this meaning, mechanochemistry can be regarded as being the totality of conformational transformations of the supramolecular organised proteins able to produce mechanical work [4]. In order to elaborate a unitary and complete picture (representation) able to reflect the intimate content of mechanochemical process that characterise macromolecular supports the research must be focused on a good knowledge of the constitutive complexity of the object supposed to mechanical stress. The complexity mainly evaluated by the number of structural organised levels, which implies an adequate hierarchy of the movement forms.

1

Macromolecular Mechanochemistry

Mechanical solicitation of polymeric structures, at molecular level with different conformations and configurations and of supramolecular crystalline-amorphous elements, having dimensions varying in a large range and morphologically organised in fibrils and granularly formations implies changes physical and chemical state of the system. In turn, when the support of mechanochemical transformations is the living matter (i.e. cell, tissue, organ, and body) the changes of biologic movement are stimulated. In order to explain the mechano-chemical process the following aspects must be taken into account [5]: 1) Mechanical stress of the bodies occurs in direct relation with medium (natural, specially created for the investigation or the environment into the object made by polymer is working). In some cases, the mechanic energy plays the first place; it release the sequence of mechanochemical transformations and the environment’s constitutive elements act as mechano-initiated active centres. In other situations, the tensions induced in stressed material act as adjacent factor thus facilitates and accelerates the effect of environment. Practically, the two situations are only experimentally delimited. 2) Mechanical solicitation represents a direct energetic action on the polystructure, determining the excitation of chemical bounds, their broken, and reorganisation of the hole structure. As a consequence, any transformation that occurs under mechanical energy action and is accompanied by broken of chemical bounds, even in the conditions of coexistence of other factors (i.e. heat, light, radiation, chemical agents) has a mechano-chemical nature. From this rule are excluded only the breaks which do not imply the broken of the chemical bounds (ex. the cleavage of a piece of paraffin) and that ones occurring in the absence of mechanical field. 3) The field of forces influences the probability of initiation of two or more different reactions, and these ones, in turn, cause the rearrangement of structural elements belonging to different levels of organisation. K. Murakami reconsidered the mechanochemical concept; the author takes into account the change of polymer structures arising by the splitting of non-covalent bounds under mechanical stress. In respect to this concept, the mechanical induced change from one conformational state to other is accompanied by a variation of free energy of the system and represents a mechanochemical transformation [6]. In the last instance, mechanochemical process suppose two as2

Introduction

pects: the mechano-chemical one, defined as the conversion of mechanical into chemical energy, and chemo-mechanical thus consisting in generation of mechanical work as a result of a chemical reaction. Mechanochemical process consists in a sequence of intercalated physical and chemical phenomena, which governs the change of structure and properties/functions of the macromolecular support in which it occurs. The process affects all levels of structural organisation and its complexity increase both with the increasing of complexity of macromolecular support and environment interactions, Fig. 1.

Figure 1. Schematic representation of the mechanochemical process.

In turn, the chemical reactions released under mechanical forces give up a new spatial disposal of atoms, functional groups, macromolecules (conformational changes), supramolecular organised formations and all these changes would assure the reversibility of the process. However, only biomechanochemical processes, which take place in living world, these ones having self-sensing and self-regulating properties, are reversible. In all other cases the mechanochemical process is irreversible. Muscular contraction is one of the most representative biomechano-chemical processes. In this case, the process occurs at 3

Macromolecular Mechanochemistry

the macromolecular level of some specialised proteins, thus being supramolecular organised and mechano-excited by previous cycle. In this state, the involved proteins take place to a sequence of chemical reactions, especially of fermentative type, which occur isotherm and isobar, in interaction with biologic environment. The above mentioned chemical reactions give rise to conformational changes, which are translated in mechanical work (motion) at macroscopic level, Fig. 2.

Figure 2. Schematic representation of the bio-mechanochemical process.

The chemo-mechanic path was demonstrated, in the first place, by W. Kuhn [7] and A. Katschalschy [8] experiments, which designed and constructed the first “chemo-mechanical engine” using artificial systems. In the last two decades, other research teams [9-20] have developed the results of above-mentioned scientists. The obtained results are very important not only for their technical potential, in present being available microenginees, microrobots, drug delivery systems, chemical valves, etc., but also because these processes simulate important biological phenomena such as membrane transport or muscle contraction of which mechano-chemical mechanism have already been proved [21-35]. Alongside mechanochemistry of polymers and biomechano-chem4

Introduction

istry very important studies concerning mechanochemistry and mechano-emission of solid body have also been developed [36-56]. The development of this branch of polymers science is reflected in a number of published books that are given at the beginning of the references [1,2]. Bib lio g r a ph y Biblio liog phy 1. 2.

3. 4. 5. 6.

7. 8. 9. 10.

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

Cr. Simionescu and Cl. Vasiliu Oprea, Mecanochimia Compusilor Macromoleculari, Ed. Acad. RSR, Bucuresti, 1967. * , Entsiklopedia Polimerov, Tom 2, Moscow, 1974, p. 241. * * N.K. Baramboin, Mehanokhimiya Vysokomol. Soedin., Izd. Khimiua, Moscow, 1978, p. 7. M.V. Volkenstein, Obsceaia Biofizika, Izd. Nauka, Moskva, 1978, p. 211. G.M. Bartenev. Iu.S. Zuev, and A.I. Kuzminski, Mehanika Polim., 2 (1967) 255. K. Murakami, Mechanical Degradation in H.H.G. Jellenik (Ed.), Aspects of Degradation and Stabilisation of Polymers, Elsevier Sci. Publish. Company, 1975, pp. 296-392. W. Kuhn, Experimentia, 5 (1949) 318. A. Katschalsky, Experimentia, 5 (1949) 319. H. Hoffman-Berling, Biochem. Biophys. Acta, 27 (1959) 247. S. Lifson, I. Michael, and M. Zwick, Elementary Mechanochem. Processes in H. Wernek (Ed.) Contractile Polymers, Pergamon Press, London, 1960, p. 1. M. Zwick, J. Polym. Sci., 16 (1955) 221. B. Hargitay, A. Katschalsky, and H. Eisenberg, Nature, (1955) 765. A. Rand and D.H. Walters, in Ref. 10, p. 41. D.R. Robinson and W.P. Jecks, J. Amer. Chem. Soc., 87 (1965) 2470. A. Oplatka and J. Yonath, Biopolymers, 6 (1968) 1147. S. Reich, A. Katschalsky, and A. Oplatka, Biopolymers, 6 (1968) 1159. M.H. Sherebin and A. Oplatka, Biopolymers, 6 (1968) 1169. I.Z. Steinberg, A. Oplatka, and A. Katschalsky, Nature, 210 (1966) 568. J. Yonath and A. Oplatka, Biopolymers, 6 (1968) 1129. A. Katschalsky, Equilibrium Mechanochemistry of Collagen Fibers in Structure and Function of Connective and Skeletal Tissue, Butterworth Co. Ltd., London, 1965, p. 31. P.J. Flory, J. Celluler Physiol, 49(Suppl. 1) (1957) 175. V.I. Vorobiev, Biohimia, 11(3) (1957) 597. W. Kuhn, M. Ramel, D.H. Walters, G. Ebenek, and H. Kuhn, Adv. Polym. Sci., 1 (1960) 340. V.I. Vorobiev, Dokl. Acad. Nauk. USSR, 137(4) (1961) 972. V.I. Vorobiev and L.V. Kuhareva, Dokl. Acad. Nauk. USSR, 165(2) (1965) 435. V.I. Vorobiev and L.V. Galenina, Titologia, 5(6) (1963) 672. I.Ia. Frenckel, L.V. Kuhareva, B.M. Ginsburg, K.A. Rasparean, and V.I. Vorobiev, Biofizika, 10(5) (1965) 735. A. Katschalsky and O. Kedem, Biophys., 2 (1962) 53. K. Blumenthal and A. Katschalsky, Biochem. Biophys. Acta, 173 (1969) 51. A. Katschalsky, in Biology and Phys. Sci., Columbia Univ. Press, 1969, p. 1. 5

Macromolecular Mechanochemistry 31. 32. 33. 34. 35. 36. 37. 38. 39.

40. 41.

42. 43. 44. 45. 46.

47. 48. 49. 50. 51. 52.

53. 54. 55. 56.

A. Katschalsky and R. Spangler, Quart. Rev. Biophys., 1 (1968) 127. G. Oster, A. Perelson, and A. Katschalsky, Quart. Rev. Biophys., 6 (1973) 1. A. Katschalsky and G. Oster, in The Molecular Basis of Membrane Functions, D. Tosteson (Ed.), Prentice-Hall, 1969, p. 1. M.V. Volkenstein, in Ref. 4, Chaps. 3 and 6, pp. 96, 211. T.L. Hill, Free Energy Transduction in Biology, Academic Press, New York, Chap. 5, 1977, p. 103. V.V. Boldyrev and E.G. Abbakumov, Uspekhi Khimii, XL, 10 (1971) 1835. P.Yu. Butyagin, Uspekhi Khimii, XL, 11 (1971) 1935. A. Casale and R.S. Porter, Polymer Stress Reactions, Vol. 1 and 2, Academic Press, New York, 1978, 1979. * , Mehanohimiceskie Reaktsii v Neorganiceskih Sistemakh, Izv. Siberskogo, * * Otdelenia Akademii Nauk, USSR, 7 (1979) 3. K. Tavada, S. Kounosu, and F. Ossawa, J. Theor Biol., 45 (1974) 45. E.M. Gutman, Termodinamickeskaya Teoriya Mekhanokhimicheskikh Yavlenii Na Tverdykh Telakh, in Mekhanokhimiya I Mekhanoemissia Tverdogo Tela, Izd. Ilin, Frunze, 1974, p. 40. S.N. Jurkov and V.E. Korsikov, J. Polym. Sci., 12 (1974) 385. S.N. Jurkov and E.E. Tomasevski, J. Tekhn. Fiziki, 27 (1957) 1248. A.M. Leksovschi and V.K. Regel’, Fizika Tverdogo Tela, 12 (1970) 253. V.E. Korsikov and V.I. Vetegren’, Mekhanika Polimerov, 4 (1972) 621. E.H. Andrews, Molecular Structure and Strength of Polymer and Molecular Fracture in Developments in Polymer Fracture, Vol. 1, Chaps. 1 and 2, Appl. Sci. Publish. Ltd., 1979. E.H. Andrews and P.E. Reed, Adv. Polym. Sci., 27 (1978) 3. H.H. Kausch, Polymer Fracture, Spronger Verlag, 1978. R. Hoseman, J. Appl. Phys., 34 (1963) 25. Cr. Simionescu and Cl. Vasiliu Oprea, Cell. Chem. Technol., II, 2 (1968) 155. Cr. Simionescu and Cl. Vasiliu Oprea, Cell. Chem. Technol., III, 4 (1969) 361. Cl. Vasiliu Oprea, Über Mechano-Chemischen Abbau von Polyamiden Während der Schwingmahlung und Herstellung Einiger Neuen Makromolekularen Produkte, PhD Thesis, Technische Hochschule Für Chemie Leuna-Merseburg, R.D.G., 1965. H. Grohn and Cl. Vasiliu Oprea, Rev. Rom. Chem., 11(11) (1966) 1297. H. Grohn and Cl. Vasiliu Oprea, Plasue u Kuatschuk, 13 (1966) 385. Cr. Simionescu, Cl. Vasiliu Oprea, Cl. Negulianu and M. Popa, Plasue u Kuatschuk, 24(10) (1977) 689. A. Peterlin, in Adv. Polymer Science and Engineering, K.D. Pae, D.R. Morrow, and Yo Chen (Eds.), Plenum Press, New York, 1972, p. 1.

6

Chain Multistage Mechanism of Mechanochemical Process

1 CHAIN MULTISTAGE MECHANISM OF THE MECHANOCHEMICAL PROCESS Due to the wide field of application, practically in all technical fields, polymer structural reactions, both as materials or finite objects, are of major theoretical and practical interest. Understanding of polymer structural reactions requires the elucidation of the mechanism through which the polymers respond to mechanical stress in the conditions of their processing and exploitation as well as of the factors that affect this behaviour. Good knowledge of the above-mentioned mechanisms allows us to improve some properties or to predict longer lifetime periods. The multistage character of the mechanochemical process is defined as being the totality of transformations that occur on all structural organisation levels of mechanically stressed polymers. Essentially, three fundamental steps may be distinguished, namely: 1) mechanoactivation (mechanoexcitation), this meaning the deformation of macromolecular chains; 2) mechanocracking, consisting of splitting of chemical bonds from the main chain; and 3) macroscopical cleavage, as a result of supramolecular–morphological reorganisation of the polymeric material [1–3]. Absorption of the elastic energy into the polymer structure is followed by its dissipation on the structural elements and chemical bonds from the main chain which is reflected, in the last instance, in the increase of the chemical potential energy of the system. In this way, the polymer itself passes into an activated ‘mechanoexcited state’ characterised by an excess of energy. This excess is used in a chemical reaction, which consists of breaking a number of covalent bonds. Usually, these covalent bonds are located in a structural defect region which behaves as a stress concentrator. Not all excess energy is used; part of this energy is converted into other forms, such as: thermal, electrical (electrostatic loading, electroemission) and acoustic energy, etc. 7

Macromolecular Mechanochemistry

During the stage of deformation of chemical bonds (mechanoexcited stage), the macromolecules are stretched, chemical bonds elongate, and angles of valence are altered. When a critical value is reached, ‘mechanocracking’ (the second step of the mechanochemical process) starts. This step gives rise to the active centres of linked scission processes (the third stage). The consumption of elastic energy during the above-mentioned steps has, as a net result, the relaxation of the whole structure. It has been proved that the deformation of macromolecular chains has, as the main result, the increase of the potential energy of the system and, consequently, the increase of its chemical reactivity [4]. Thus, when the tensile stress is applied to rubber, it becomes easily oxidised and its vulcanised products are destroyed faster under the effect of ozone. Also, the rate of poly(methyl methacrylate) saponification under tensile stretching is increased [5]. The increase of the reactivity of macromolecular structures in the deformation state can be explained through the appearance of mechanoexcited states and even of free radicals. This fact justifies the terms of ‘mechanoactivation’ or ‘mechanoexcitation’ ascribing the first step of the mechanochemical process. A lot of information and data regarding the activation mechanism of the mechanochemical process have been obtained by comparative studies with those ones dealing with the influence of other physical factors on chemical substances. It was found that radiant energies such as α, γ, β, X, laser, rapid electron beam radiation, etc., are characterised by large amounts of energy typically higher than the dissociation energy of any chemical bond. On the other side, the energy of a light quantum is comparable with the energy of chemical bonds, and the value of elastic energy is well below this level. Consequently, the mechanochemical process must occur through a peculiar mechanism, involving the concentration of mechanical energy on the chemical bonds that are usually located within the area of a structural fault. So, mechanochemical transformation begins by mechanical energy concentration on the structural faults. These faults exist on all levels of the polystructure represented by elementary volumes where the interruption of continuity in structural organisation occurs. The accumulation of an increased number of such formations brings the system into a state of destructibility to form in the system; this state is usually accompanied by an increase of free energy in the system. When the level of free energy is high enough, mechanochemical transformations reach quantitative levels able to accelerate 8

Chain Multistage Mechanism of Mechanochemical Process

up to ten times the possible chemical reactions in the investigated system. In this way, the second stage of the mechanochemical process, so called ‘mechanocracking’ is initiated; this step occurs by a chain radical mechanism [6]. The accumulation of mechanocracking acts leads to mechanodegradation or mechanochemical destruction that are responsible for the lost of functional or endurance properties of polymers. The third stage of the mechanochemical process takes predominantly place on the supramolecular level and determines the reorganisation of the whole structure through the formation of new surfaces. The events involved here also occur by a chain mechanism, as Fig.1.1 shows [7]. The characteristic elementary events are the following ones: 1) initiation that coincides with the appearance of a nascent microcrack and which represents the primary discontinuity in the area of the structural fault. The discontinuity arise by splitting of a large number of covalent chemical bonds, located in the above-

Figure 1.1. Schematic representation of the multistage nature of mechanochemical transformations that occur on the crystalline–amorphous level [7]. 9

Macromolecular Mechanochemistry

mentioned area, which originates in the mechanoactivation stage; 2) microcrack propagation, or microcrack growth, occurs by self-nucleation or coalescence and leads to the formation of cracks (or macrocracks); 3) conversion of macrocracks into a main crack that is large enough to induces at its tip high stresses capable of completing the cleavage of the stressed structural element and the appearance of new surfaces. A succession of molecular processes, that are sequentially chained, takes place in the period of time between the stress application to a polymer sample and its macroscopic fracture [8]. Depending on the physical state and morphology, the mechanical stress applied to a solid polymer causes different responses on the molecular level. Let us suppose, first of all, a linear amorphous polymer below its glass transition temperature. When a load is applied, the statistically coiled macromolecules tend to uncoil and orient in the loading direction. Due to the strong macromolecule interaction as well as steric hindrance, the stress magnitude must be high in order to reach this effect (above the yield limit). The fully stretched macromolecular chains, being less flexible than their neighbouring coiled chains, will support a more important fraction of the stress. The high tensions acting on the covalent bonds have been detected as shifts of vibration frequencies in IR spectra. Taking into account the high values of energy of dissociation of the chemical covalent bonds, dominant intermolecular sliding (flowing) of macromolecules, by destruction in the first place of the secondary bonds, is expected. This pnenomenon is known as the plastic deformation of polymers. When the macromolecular chains are located in the structural matrix of the crystalline regions or belong in strong physical networks having high values of the relaxation time, their movement will be impeded [9]. With the increase of deformation the macromolecular chains will become uncoiled, finally reaching a fully stretched and elastic tensioned state. In the case of oriented fibres, this result is obtained at low strains. Apart from them, high deformations are required in the case of plastically deformed amorphous polymers [10]. When the macromolecules are permanently fixed in position, a highly tensioned state can be attained. Under the combined effect of mechanical energy (mechanical excitation) and thermal fluctuations the splitting of the fully stretched macromolecular chains will occur [11]. The splitting rate is governed by the value of applied stress and temperature. After scission, 10

Chain Multistage Mechanism of Mechanochemical Process

the stress is integrally redistributed and the rate of macromolecule cleavage decreases. Consequently, the process would continue only if the applied stress (or strain) increases in order to bring new macromolecular chains in a fully extended conformation. Since the stress is redistributed only within a restricted area from the stressed body, the already cleaved macromolecules tend to accumulate within a limited volume (microvolume), giving rise to a nascent microcrack [12–15]. In turn, the uniformly distributed microcracks can grow up by the following ways within the entire stressed material: 1) propagation, as result of subsequent cleavage of some macromolecular chains; 2) growth, due to the local flow, this one being favoured by the reduced absorption of the interfacial energy for the outside; 3) coalescence. The growth of a nascent microcrack will induce the appearance of a single main crack, which by propagation will destroy the stressed polymer or, alternatively, will induce the formation of a large number of stable microcracks (microcrazing). The conversion of narrow microcracks directly into the magistral crack, through the annihilation of microcrack propagation, constitutes an intermediate way, which is also described in the literature [16]. The formation or nucleation of the magistral crack is, in fact, only the first step in macroscopic breaking of the polymer body. In order for the above-mentioned process to occur, the propagation of the magistral crack through the sample is required. During this period, new surfaces appear and the dissipation of accumulated energy (by inelastic deformation) takes place. In other words, macroscopic cleavage implies two steps: 1) nucleation of the magistral crack; and 2) its propagation through the stressed polymer. Particularly, when the polymeric material contains pre-existent cracks, the second stage is strongly diminished [17]. Parameters that characterise the fracture of a given sample, its durability and tensile strength will be generally influenced by the material physical and mechanical properties, sample geometry, and testing conditions, such as: the rate of deformation, temperature, nature of the medium, etc. Deformation of a polymer within an external force field releases a structural reaction that is located either on the supramolecular– morphological or configurational level, depending on the position of the mechanical energy concentrating fault. The manner in which a 11

Macromolecular Mechanochemistry

macromolecular material responds to an imposed force is determined unequivocally by its physical state and is expressed by deformation and fracture processes, these ones being in the cause–effect relationship. The multistage character, with all its components, is depicted in Figure 1.2. In the case of ideal structures, such as biostructures, deformation–fracture processes are reversible. In a living body, for instance, after the third stage (III), i.e. the appearance of the magistral crack, the closure of the crack is commanded by the genetic code due to its self-organisation and self-regulation capacity. This transformation is accompanied by the release of mechanical work, which is used partially to displace the involved structural element and partially to transfer the initial structure to the mechanoexcited state which is able to restart the cycle. A very suggestive example, illustrating the reversible nature of the mechanochemical process, on the living matter level, is the tendon. It functions primarily in uniaxial tension as a reinforced cable between the muscle and the bone [18]. By microscopy and Xray diffraction techniques, six levels of structural organisation, which correspond to a hierarchical composite structure, were found, Figure 1.3a. Thus, the collagen fibres are ‘glued’ together by a highly hydrated network, with a complex structure – a gel-like based on the proteoglycan matrix. The required reversible function is due to an uniaxial crimped structure, as shown in Figure 1.3b. Also, the toughness or resistance to damage belongs to the compos-

Figure 1.2. Polystadial character of the mechano-chemical process. 12

Chain Multistage Mechanism of Mechanochemical Process

Figure 1.3. Hierarchical organisation of tendon: a) schematic illustration; b) TEM detail showing the crimped structure of tendon [19].

ite character of its structure. Macromolecules in biosystems are specifically coded to accommodate the self-assembling of the micro-fibrillar structure. Yielding occurs by a strictly localised shear process within the fibre; a selective microfracture process at the suband microfibre level follows this step. Catastrophic fracture arises only after the establishment of the ‘destructibility state’ within the entire composite system. One of the formed microfractures rapidly grows, giving rise to catastrophic fracture that causes the damage. Similar relations between the hierarchical structure and mechanical function were found in intestine, jointed cartilage, inter-verte13

Macromolecular Mechanochemistry

bral disk, aorta, and other connection tissues. An adequate structural model illustrating an irreversible mechanochemical process is that of an oriented semicrystalline polymer which presents all levels of structural organisation. The study of crystalline polymer deformation and fracture implies the knowledge of their structural organisation up to the morphological level. Generally, the proposed models that describe the oriented semi-crystalline polymers have the following common elements: n macromolecules from crystalline zones are highly orientated in the direction of acting force and the formed lamella from folded chains are perpendicular to the fibre axis; n crystalline and lesser oriented zones (so-called crossing zones) alternate; n very rarely amorphous zones include the entire length of a macromolecule, this one being partly enclosed at least into a crystalline; this kind of molecule is called crossing or linking molecule; n linking macromolecules may suffer conformational changes permitting, in this way, partial relaxation of the stress even if their flowing is limited; n linking macromolecules are less frequent than those composing the crystalline regions; n this structural organisation inevitably presumes the existence of faults acting as centres of stress concentration; A model that adequately describes the fibre structure, having the microfibril as the fundamental element, was proposed by A. Peterlin, Figure 1.4 [20]. According to this model, the crossing

Figure 1.4. The model of transformation of a lamella bunch – within a micronecking zone - into a microfibrils bundle densely packed and aligned [20]. The length l sl of the lamellar section determines the microfibril length. 14

Chain Multistage Mechanism of Mechanochemical Process

macromolecules can by intra- or interfibrilar ones, depending on the type of microfibril blocks they bring together i.e. blocks of the same or adjacent microfibrils. The right place of both types of connections is frequently at the external separation surface of the microfibrils [20]. Within the field of forces, the microfibrils will behave as high resistance and rigid structures. Their dense packing characterised by a very high ratio of the lateral surface to the transversal section (about 1000 times) determines the anisotropy of the properties at this structural level. From RES signal anisotropy [21] as well as using easily polymerising monomers [22], able to enter only into amorphous zones, it has been concluded that free radicals appear on the deformation stage, just before cracking, They are mainly located in the so-called disordered zone which is intercalated between the crystalline blocks of consecutive lamellae [23–26]. Uniaxially stretching a polymer, the mobility of macromolecular chains increases both in crystalline and amorphous phases due to the increase of the free volume around the centres of tension concentration [26]. As Figure 1.5 shows, not all the crossing macromolecules that traverse the amorphous phase connecting the crystalline blocks are fully stretched. During the gradual movement of the crystalline blocks, under the action of an external tensile force, the shortest linking macromolecules (A) will be the first ones to be stretched until the molecule reaches its maximal possible length; in this state, the homolytic scission of macromolecular chains occurs, each scission generating a pair of free radicals. Thus, at the same time with the crystalline blocks movement the number of split macromolecules increase. Consequently, the concentration of free radicals increases with the increasing of sample deformation. Stopping the deformation and resuming it once again, new macromolecules will suffer the scission

Figure 1.5. Schematic illustration of a linking macromolecule [19]. 15

Macromolecular Mechanochemistry

Figure 1.6. Radical concentration, [R . ], and its rate of increase in function of deformation, d[R . ]/dε, vs. deformation for a film of highly orientated polyamide 6,6 during three cycles of deformation [21].

Table 1.1 Comparison between the number of linking macromolecules and free radicals in stressed zones

Chains’ nature

U.M.

Macromolecular chains within crystalline structure Linking macromolecules within amorphous structure Linking macromolecules per volume unit Broken chains per volume unit

-2

cm cm-2 cm-3 cm-3

Concentration 5 x 10-14 5 x 10-13 5 x 1019 2.5 x 1017

phenomenon only when the maximum deformation from the first attempts is reached, Figure 1.6. It should be noted that all the linking macromolecules, stretched until a given critical value, are broken during the first cycle, other ones remaining unaffected. During the subsequent cycles new macromolecules will be broken just after the maximal deformation from the previous cycle is reached and exceeded. The total number of free radicals (Table 1.1) is much lower than the number of linking macromolecules from the sample. This means that the scission of macromolecular chains occurs only where the 16

Chain Multistage Mechanism of Mechanochemical Process

deformation and concentration of applied stress on the linking macromolecules are higher that in the rest of sample. Analysing a crystalline zone from the structural point of view, as standard for ordered organisation, at long distance, on the three dimensions of the space, we can see that it is not a homogeneous one, having some faults for different reasons, as shown in Figure 1.7. Under the conditions of mechanical deformation any structural fault constitutes a centre of stress concentration capable of inducing tensions, that attain critical values able to induce the homolytical scission of a number of chemical bonds. The group of thus formed free radicals limits the smallest discontinuity appeared by cleavage, which is just the nascent microcrack. S.N. Jurkov firstly confirmed the appearance of a nascent microcrack by X-ray diffraction measurements on polyethylene, polypropylene, polyamide-6, etc. He pointed out the two fundamental characteristics of the process: 1) microcracks have finite dimensions; and

Figure 1.7. Hosemann-Bonart’s model of different possible faults in the ordered structure of polymers [19]. 1) monocrystal; 2) monofibrils arose by ‘cold stretching’; 3) assembly of microfibrils appeared by ‘hot stretching’; 4) voids; 5) chain folding in longitudinal direction; 6) short folded chains; 7) ‘linking macromolecules’; 8) chain ends inside the amorphous zone; 9) chain ends inside the crystalline zone. 17

Macromolecular Mechanochemistry

2) their dimensions are strongly related to material’s structure. Particularly, in the case of oriented semicrystalline polymers the transverse dimension of the crack is the same as the microfibril diameter. The first faults that are overloaded by the applied stress are those ones from the amorphous phase, with lower mechanical resistance. However, during the evolution of the nascent microcrack to cracks with greater dimensions, the internal tensions will reach high enough values in order to activate the existent faults within the crystalline phase. Subsequently, the mechanochemical process with all its characteristic steps will evolve here. In the case of semicrystalline polymers, the structural nonuniformity could proceed by preferential orientation of some macromolecules in the direction of applied tension. In this way, the number of fully extended chains is governed by the magnitude of deformation to which the monofilament is subjected. In turn, the degree of nonuniformity derives from polymer’s morphology and depends on the applied physical treatments and many other factors, too. The fibril can be regarded as a structural element having a high level of organisation. Figure 1.8. Such a fibril is composed from parallel microfibrils that appeared during stretching steps, from

Figure 1.8. Microfibrilar model of the fibrous structure [24]. A) intrafibrilary linking macromolecules; B) interfibrilary linking. 18

Chain Multistage Mechanism of Mechanochemical Process

bundles of parallel lamellae, pre-existing within the initial material. The packing of microfibrils into fibrils stimulates two interdependent ways of plastic deformation of the fibrous structure, namely by – 1) movement of fibrils with respect to each to other; and 2) shearing, caused by microfibril sliding. The first mode is responsive for the macroscopically observed deformation as well as for the final fracture, by the formation of longitudinal microcracks. The coalescence of some microcracks leads to physical separation of the individual fibrils. The change of place due to microfibrils shearing tremendous stretches the interfibrillar linking macromolecules, i.e. the macromolecule connecting two fibrils each another. The microfibrils’ ends create, in the microfibrillar network, voids of about 10 –21 m –3 . Under the applied stress these voids grow up generating microcracks. Consequently, the adjacent microfibrils get an overloaded state, being the first ones that will be broken. The microcracks continues to grow, most likely by coalescence, till at least one of them attains the critical dimensions, according to Thomas–Rivlin’s model (a result of Griffith’s criterion). As soon as this dimension is attained, the further increase of the crack became ‘catastrophic’ causing macroscopic fracture. On the other hand, the microcracks may grow up radially, by the cleavage of adjacent microfibrils, or axially, by separation of microfibrils or fibrils. In the first case, all the linking molecules, that cross at least one amorphous zone of each affected microfibril, are broken. In the second case, only those linking molecules that connect the microfibrils situated on the opposite sides of microcrack will be affected, Figure 1.9. In the case of nylon 6, for instance, the routes A 0BA 2 and A 1 BA 3 will be favoured against routes A 0CA 1CA 3 and A 1 CA 2 CA 3 due to the great number of hydrogen bonds existent lengthways C route. In the case of those polymers that do not present strong secondary bonds between the adjacent microfibrils, as the case of polyethylene is, the cracks evolution follows other pathways. Thus, the cleavage of microfibrils between A 3 and A 4 may occur in B ’ and B”. Furthermore, A 4 –A 5 coalescence can only be achieved through scission of two B microfibrils and of existent bonds alongside C pathway. The coalescence of microcracks that initiate at the ends of microfibrils will tend to proceed on the external (separation) surface of fibres, where the majority of chain ends are located (Figure 1.8). This process leads to both the formation of some longitudinal voids alongside the surface of separation and fibrils’ individualisation. 19

Macromolecular Mechanochemistry

Figure 1.9. Schematic illustration of different ways of microcracks growth [20].

Figure 1.10. SEM photo showing the axially splitting of polyamide 6 fibres [20].

Scanning electron microscopy (SEM) has been used for the morphological investigation of fractured nylon 6 fibres and proved their longitudinal splitting, Figure 1.10. Generally, the fracture of highly stretched semicrystalline polymers occurs through their splitting into a great number of fibrils, each fibril independently cleaving, under the assumption of microfibrillar building of fibres [20]. The internal tensions are not uniformly distributed on each mac20

Chain Multistage Mechanism of Mechanochemical Process

romolecule as in the case of ideal crystalline structures (Fασ). In the former case, each molecule supports a greater force (F,αkσ), where k is a factor expressing the concentration of stress that depends on sample geometry and morphology [24, 27]. In the case of polymers, the values of the length, number, and distribution of connection molecules strongly fluctuate. If we assume, in a first approximation, a model of which the main characteristic is the uniform thickness of the amorphous layer (L 0 ), the distribution of the length of linking molecules can be described by the following function [21].

W( h ) =

h

∫ W ( x)dx 0

(1.1)

where h is the total length of chain. If a sample is stressed with a unitary tensile stress σ, macroscopic deformation, ε and medium deformation ε a will be induced. The thickness of the amorphous layer increases to a new value L, given by the equation:

L = L0 (1 − ε a )

(1.2)

The total stress will be supported by the linking molecules having the length h < L. The deformation corresponding to the individual molecules varies in a wide range. Thus, when the molecules subjected to the highest deformation are broken, the tension will be redistributed on the less deformed chains. Depending on both the intensity of the applied stress and the progress of bonds’ scission, macroscopic fracture may occur. One can compute the number of linking molecules involved as well as the stress concentration factor [24]. When applying a constant stress, the phenomenon of relaxation plays an important role, which decreases the rate of free radical formation. The concentration of free radicals, calculated during material’s fracture, clearly proved that the scission of macromolecular chains occurs within the entire volume of the sample being located in minimum resistance zones of the stressed sample. The experimental data that have been obtained in the case of tensioned nylon 6 monofilaments confirmed this assessment [28, 29]. According to the results obtained by De Vries and co-workers [29–31]: 21

Macromolecular Mechanochemistry n the scission takes place almost exclusively to the linking molecules or in that zone having ‘critical’ fault, which alternate with crystalline zones. ‘Critical’ zones consist, at least partly, of linking macromolecules and differ from each another by the number and length of linking molecules; n linking molecules are not uniformly tensioned. A curve can be plotted showing the distribution of stress as a function of the effective length of macromolecules and fibre microstructure. Consequently, the most stressed macromolecules are firstly broken and the stress is redistributed on the intact chains; n the apparent distribution of tensions is influenced by the nature of material, temperature and rate of deformation; n chains scission is a mechanoactivated process; n crack propagation follows the ‘minimum resistance’ path. The crack perimeter passes through the most important structural faults and the broken chains are distributed in the entire volume of the sample. The distribution of the effective length of molecular chains into the fault zones has been described by a mathematical model [30]. The number and length distribution of the chains are related to the mechanical properties of the polymer. The mathematical model is based on the following hypothesis: 1) in the case of macroscopic fracture, the sliding of macromolecules due to the scission of secondary bonds is negligible as compared with the scission of the main chains (covalent bonds); 2) the scission of macromolecular chains from crystalline zones is negligible; 3) Hooke’s law is valuable up to the atomic scale; 4) a macromolecular chain will reach a tensioned state only after that the deformation in the fault zone attains the required values in order to bring the chain into a fully extended and elastic state; 5) the scission of molecular chains can be forecast from the kinetic theory of fracture. The entropic forces as well as effects induced by material viscoelasticity, even if they play an important role, are not considered in this model. The effective distribution of the macromolecular chains is strictly dependent on temperature. In the tensioned state, increasing the temperature increases the relaxation ability of macromolecules. This effect overlaps with the decrease of the energy required for scission. Thus, near the glass transition temperature, the sliding of macromolecules can prevail comparatively over the scission of covalent

22

Chain Multistage Mechanism of Mechanochemical Process

Figure 1.11 . Model of a linking molecule (t) that connects the crystalline lamellae (c) [41]. a – amorphous zone; L 0 – length of amorphous zone; L – length of the linking molecule; t – boundary of crystalline zones.

bonds from the main chain. H.A. Kaush [32–41] proved that the strongest tensioned macromolecules are that ones which are oriented along the direction of applied stress. If the macromolecules do not relax by flowing, i.e. after the intermolecular forces are exceeded, they will pass to an over-stressed state and their scission occurs. The number of overtensioned bonds was found to be proportional to the number of those stretched chain segments that are parallel in relation to the direction of the uniaxial stress. The structural model, illustrated in Figure 1.11, takes into account a linking molecule (t), which belongs to a, (c) lamella that extends from it, perpendicularly on the folded surface of the crystal (I), taking an extended conformation into the amorphous phase (a), and enters into an adjacent crystalline block, to become a part of this block. It has been accepted that the borders between the crystalline zones are clearly delimited and no interactions between the linking molecules and amorphous material are considered. Such kind of macromolecules, fixed between two different crystalline layers, may be detensioned when the involved layers are not concomitantly summited by macrostresses. The total length (l 0 ) consists of two different elastic segments, namely – (l e ) – stretched segment; and (l a ) – coiled segment. The distribution of local stresses acting on this kind of molecules, can be computed as a function of elastic modulus and conformational modifications. The last ones, timedependent, are responsbile for stress relaxation. Any point situated alongside a linking molecule is characterised 23

Macromolecular Mechanochemistry

by its own (z) distribution, with respect of crystal’s border, where z refers to an unstressed molecule. The sliding of molecular point z under stress is described by both function u = u (z) and by the potential corresponding to unit length ν(u). The axial stress (s), acting on the macromolecular chain, decreases with increase of z, mainly due to the force exerting about itself, by the potential energy accumulated in the crystalline zones ν(u). The equilibrium of the forces from each chain’s section is described by the following condition:

ds d ν(u ) = dz du

(1.3)

This relation does not imply any presumption concerning the shape of the function ν(u) as well as of the function s(u). On the other hand, accepting that the segments of the macromolecular chains, from crystallites, may be compared to an elastic spring, and equalising the axial stress, s, with the local deformation of the chain, we get following relationship:

s=k

du dz

(1.4)

which means that:

k

d 2 u d ν (u ) = du dz 2

(1.5)

where k is the constant of chain elasticity (un-normalised with respect to the transverse section). Considering now a semi-infinite crystal and a sinusoidal potential, the function ν(u) becomes ν(u) = ν(1–cos ku(z)). By integration of equation (5), we obtain: 2

ν 1  du    = A − cos ku k 2  dz 

24

(1.6)

Chain Multistage Mechanism of Mechanochemical Process

ν du from the condition =0, dz k corresponding to zero movement, the following equations are obtained:

After determination of

A=

du = 2 ν ⋅ sin k u k z dz

(1.7)

and

u (z) =

(

)

4   arctan exp  k ν z   k k   

The integration constant C is tan

(1.8)

ku (0) and k is 2π divided to 4

repeating unit length. In the case of static mechanical equilibrium both the stress and movements of the atoms from linking molecules in crystallites are only functions of the axial stress s a existing at the crystal’s border (z = 0). For example, the stress and movement of a polyethylene chain within a crystallite, corresponding to a maximum axial stress (s 0 ) of 1.372 nN is illustrated in Figure 1.12. In a crystal without faults, for any stress greater than s 0 , the static equilibrium can not be achieved. In was found that the required force for removing a

Figure 1.12. Decrease of the stress and displacement for a strongly tensioned linking chain into a crystalline lamella of polyethylene, formed by folded chains [42]. 25

Macromolecular Mechanochemistry

linking molecule from the crystal is 15.8 times higher than those required to pull out a monomer unit. Dividing stress s 0 by the transverse section (0.1824 nm 2 ), we obtain the maximum axial stress that a perfect polyethylene crystallite is able to exert on a linking molecule, i.e. 7.5 GN/m 2 . As Figure 1.12 shows, the highest mechanical excitation penetrates about 5 nm in the crystallite. At a distance of 6 nm from the crystal border, mechanical deformation is lower than the average thermal amplitude at room temperature, that is about 0.008 nm. After deriving the equations describing the elastic interactions between the linking chain and the crystallite, for a single potential, under arbitrary boundary conditions, it must be kept in mind that when the structure also contains physical bonds (i.e. van der Waals forces and hydrogen bonds), the intermolecular interaction differs from the crystalline zone to another zone. Thus, in the case of polyamide 6 the intermolecular interaction is stronger in the front of >C=O and –NH groups as compared with –CH 2 – groups. The problem of calculating the elastic movement of a continuous chain that alternatively traverses regions with strong and week interactions may be solved using alternatively the most suitable boundary conditions. For the above-mentioned polymer, the boundary condition requires both chain’s movement and deformation to be continued at those points z i where the potential changes from a weak attraction (v = v 1 ) to a strong one (v = v 2 ) or conversely (Fig.1.13). It was assumed that the difference between the energy of cohesion (U coh ) of polyamide 6 (18.4 kcal/mol) and of polyethylene (6.3 kcal/mol) is caused by the presence of hydrogen bonds correspond-

Figure 1.13. Typical geometry and notations used for the calculation of efforts and displacements for polyamide-6 chains [42]. 26

Chain Multistage Mechanism of Mechanochemical Process

Figure 1.14. Decrease of the stress and displacement for a linking chain into a crystalline lamella of polyamide 6, formed by antiparallel folded chains [42].

ing to the amide groups. This energy excess increases the intermolecular potential v 2 , which is about 12 ± 0.5 kcal/mol and equivalent to 0.369 nN. Chain deformation and the movement of a linking molecule within a polyamide (PA6) crystal are illustrated in Figure 1.14 [42]. The strong attraction effect of the hydrogen bonds results in the rapid decrease of stress in the front of amide groups. In this case, the decrease of both the stress and displacement is faster than in the case of polyethylene. As can be seen in Figure 1.14, at a distance of 2.1 nm from crystal’s extremity, the movement already decreased to the average level of thermal vibration at room temperature. The maximum stress (s 0 = 3.94 nm) is located at the extremity crystalline zone, more precisely at the end of –(CH 2) 5– segment. This stress is only 1.7 times higher than the required force to pull out an amide group from the crystal; so, about 59% of the maximum stress is wasted to break the hydrogen bonds of the first group –CONH–. Furthermore, its value depends on the specific arrangement of the atoms at crystal’s extremity. In the case of an amide group, the highest stress s 0 is about 20% lower that in the case when crystal’s border passes through the middle of –(CH 2 ) 5 – segment [42]. If the value of s 0 is divided by the transverse section (0.176 nm 2), the value of 22.4 GN/m 2 that defines the static resistance of a per27

Macromolecular Mechanochemistry

Figure 1.15. Schematic representation of the stress induced fault [42].

Figure 1.16. Energy of default displacement, W d , within a polyethylene crystal, as function of the displacement of linking chain to the crystal extremity [42].

fect monoclinic crystal of polyamide 6 is obtained. The crystal and molecule movements are thermally activated and the chain atoms vibrate around new equilibrium positions z+n that are described by equation (1.8). The effect of correlated and uncorrelated movements of the atoms on the potential energy could be evaluated only if the dispersion of vibration amplitudes is known [42]. A macromolecular 28

Chain Multistage Mechanism of Mechanochemical Process

chain under the maximal stress s 0 does not resist to translation movement. Even the lowest thermal vibrations will induce additional sliding of the molecule and will decrease the axial stress to the crystal’s extremity. The point of maximum stress will rapidly propagate throughout crystallites, Figure 1.15. The ‘dislocation’ is completely formed whenever u a reaches the value d. Energy W d corresponding to the fault induced in the crystal, by the movement of atoms which belong to a single chain, may be simply calculated as the lump sum of the potential energy of chain atoms and of chain elastic energy. Both are functions of the highest applied stress. In Fig. 1.16, the energy of a dislocation is represented as a function of both movement u a and exerted stress at the crystal’s extremity, s a . It was found that in polyethylene the fault energy spent to displace a chain with d = 0.252 nm is about 32.85 kcal/mol. At stresses lower than s 0 the displacements u a are lower than d/2, the fault energy is lower than W d(s 0 ) and the fault is characterised by a stable position. When the displacements are higher than d/2, the system becomes unstable, because the stress exerted on the molecular chain decreases with the increase of displacement u a . The transitions between the stable and unstable states are challenged by thermal activation. The required activation energy U d is given by the following equation:

ud ( sa ) = 2 Wd ( s0 ) − Wd ( sa ) 

(1.9)

The scission of macromolecular chains from an amorphous matrix, or in a solution, shows that high axial forces may be also achieved in the absence of periodical potentials. These forces arise from the displacement of chains or chain segments relative to the surrounding matrix. If an uncoiled chain is divided into small segments of equal length, L i , this results in the formation of fragments of chains with different conformations. Consequently, both their modulus, E i , and interaction potential will vary. Using the interpolation method in order to obtain the axial displacement corresponding to an arbitrary sequence, it was found that the modification of both stress, σ, and displacement, u, is described by the following equation:

u = u0 exp γ where: 29

z L

(1.10)

Macromolecular Mechanochemistry

ã= n

n

∑ (W L q ) i i

i =1

(1.11)

n is the number of segments of the chain; L i the length of i-th segment; E i is the modulus of i-th segment; W i are the constants of interaction forces between the segments; q is the transverse section of the macromolecular chain. The stress exerted on the chain is determined using equation (1.4) by replacing the elasticity constant of the chain with another constant, which is expressed by a series of elastic elements, equation (1.12). ó = uo ã

∑(L E ) i

i

(1.12)

Thus, the derived equations clearly show that high stresses can arise only when the constants of interaction forces (W i ) are of the same order of magnitude as in the crystal and when the overall modulus of elasticity of the whole chain is high enough. The presence of only one weak segment on the chain will strongly increase the average displacement and reduces the stress. Relaxation of the tensioned macromolecular chains is based both on their sliding with respect to the environmental matrix (enthalpy of relaxation), modification of conformation (enthalpy of relaxation) and/or scission of some chemical bonds. The recovery, by sliding, of the initial state of a macromolecular chain which was tensioned under axial stress follows an exponential rule for stress relaxation. This process is accurately described by the following equation:

Ø=Ø0exp ( −t ô )

(1.13)

If the sliding is determined by the friction coefficient of the monomer unit (ρ 0 ), relaxation time, τ, is given by the following equation:

τ = ρ0

Lmax Eq

(1.14)

where L max is the length of the monomer unit; E is the modulus of 30

Chain Multistage Mechanism of Mechanochemical Process

elasticity of the chain; q is the transverse section of the macromolecular chain. The effect of the conformational changes on the elastic energy of the chain is illustrated in Figure 1.17. The annihilation of four gauche conformations of a polyethylene segment, which corresponds to a length of 5 nm, corresponds to an increase in length of about 0.25 nm. This increase in length (5%) will reduce the axial elastic forces acting on the chain with 0.05 E which means about 10 GN/m 2 . In the case of static deformation, the above-mentioned increase will induce a total cancellation of the axial stress of about 7.5 GN/m 2 . The changes of macromolecular chain conformation have aa a direct consequence a considerable reduction of the axial stresses. The rate of conformational changes, even for the polymers with high glassy temperature or in the untensioned state, is high enough to induce this effect; in addition, the rate increases additionally under stress. For example, in the case of polyamide-6,6 the reversible increases of free –NH bonds (unlinked in hydrogen bonds) and the increase of the average orientation of the chain with the increase of tension was proved [42]. The third mechanism of macromolecular chains’ relaxation implies their scission, by homolytic cleavage of the covalent bonds. This process is thermomechanically activated. Thus, a segment of chain, containing n c weaker bonds with energy U 0 , tensioned at its extremities with a constant stress Ψ 0 will be broken after a period

Figure 1.17. Free energy of an uniaxially deformed crystal of polyethylene [42]. 31

Macromolecular Mechanochemistry

of time τ c . The stress required for splitting is given by the relation [44]. Ψ c (U 0 , U c ) =

(U 0

− R T ln ω c n c τ c ) β

(1.15)

where ω 0 is the vibration frequency of chemical bonds; β is the volume within which the scission is activated. At room temperature, a segment of polyamide 6.5 nm long has an instantaneous resistance of 20 GN/m 2 (U 0 = 188 kJ/mol, ω 0 = 10 12 s –1 , n c = 12, τ c = 4 s, β = 5.33×10 6 m 3 /mol). Considering that the stress is applied for a period of 4 s, the probability of segment cleavage is ~63%. A macromolecular chain in direct contact with the environmental medium can be represented as a system composed by coupled oscillators. The degree of excitation of the individual oscillators is modified in a static manner. In the absence of the external mechanic forces the splitting of chain at the C–C bonds will always occur when one oscillator, representing a stretch vibration of C–C bonds, exceeds a certain critical value, U 0 , which defines the resistance of the C–C bond. The rate of dissociation of the activated oscillators, k b , above the energy barrier U 0 can be calculated from the relation:

kb = ϖ 0 exp ( −U 0 RT )

(1.16)

where ω 0 is the vibration frequency of chemical bonds, R is the universal gas contant, T is absolute temperature, K. The rate of scission of a bond, k c , between the independent and identical n c weak bonds is equal to k c = n c . k b . By applying an external force, the free energy of the mechanoactivated state is modified, with respect to the initial state ∆F *, and becomes ∆F * + ∆F ext ; ∆F ext is a function of Ψ that acts on the macromolecular chain. Replacing this new force in equation (1.16), we obtain:

kc = ncϖ0 exp ( −U 0 + f ( Ψ ) RT )

(1.17)

Based on both theoretical and experimentally accumulated data, it is accepted that Ψ is proportional to σ. In this way, equation (1.17) becomes: 32

Chain Multistage Mechanism of Mechanochemical Process

kc = nc ϖ0 exp ( −U 0 + βσ ) RT 

(1.18)

The above relation describes the rate of scission of all chains which support the same local stress Ψ. In the case of fibres, a mechanism concerning the scission of intermolecular bonds was also proposed. According to this model, a certain number of atoms are simultaneously moved from their position of equilibrium. The above-mentioned atoms attain, in this way, a lower barrier of activation for the reaction that takes place. The calculated energies of activation for the bonds splitting have been compared with those obtained in the case of ‘simultaneous mechanism’. The results proved that the resistance decreases by 10 orders of magnitude for the ‘simultaneous mechanism’; this explains the observed explosive formation of submicron cracks in semicrystalline fibres [45]. The chain mechanism of cleavage is schematically illustrated in Figures 1.18 and 1.19. It supposes the formation of free radicals on all stages of cracks growth, i.e. from the nascent cracks to the magistral ones [46]. The rate of growth of the magistral crack (V) can be expressed by the following equation:

V = C exp (U 0 − ασ RT )

(1.19)

where: C ≈ 10 10 cm . s –1 ; U 0 is the activation energy of magistral crack growth; α is a coefficient that takes into account the stress from the tip of the magistral crack. The value of U 0 is numerically equal to the splitting energy of the chemical bonds, which is another argument in favour of the mechanochemical mechanism for the formation not only of the nascent microcracks but also of the magistral crack, which determines the macroscopic fracture of the sample. If the nascent crack is defined by the number of free radicals that appear by scission of some chemical bonds in the faults zone, in the case of the magistral crack which causes fracture, only radical ends located on the trajectory of fracture are found. The quantitative determination of the functional groups, which formed after the stabilisation of free radicals, gave a value of 0.5 . 10 22 cm –3 . From the order of magnitude viewpoint, this value 33

Macromolecular Mechanochemistry

Figure 1.18. Mechanism of nascent microcrack generation [46]. I – mechanoexcited macromolecules; II – formation of the first free radicals; III – “nascent microcrack” located at the level of a structural fault.

Figure 1.19. Mechanism “nascent microcracks”; II – growing by coalescence showing free radicals on

of magistral crack generation [46]. I – nucleation of – growing by individual nucleation of microcracks; III of several cracks; and IV – magistral crack propagation its front.

corresponds to the total number of chemical bonds from 1 cm 3 of the analysed sample. This implies that the catastrophic fracture practically contains only radical ends on its front. The study of the multistage character of the mechanochemical process, applied for the fibrous materials in the conditions of high intensity deformation into a field of variable forces (e.g. by vibra34

Chain Multistage Mechanism of Mechanochemical Process

tory milling), shown that the determining step is the ‘mechanocrack’, which is finalised through a chained mechanism of mechanodegradation. The most important result of the mechanodegradation is the decrease of the degree of polymerisation which also favours the macroscopic fracture consisting of the decrease of the geometrical dimensions of the particles; this process is so called ‘mechanodispersion’. Thus, the fibres are converted to particles with sizes varying from several microns to tens of microns. At the level of the amorphous–crystalline structure, the amorphisation of material occurs. This phenomenon was proved by X-ray investigations. In other words, mechanodegradation and mechanodispersion are interconnected and chained processes, having as final effects the decrease of the degree of polymerisation, on the molecular level, and the increase of the surface area, on the morphological level. The stage of mechanoactivation takes place at a much lower rate than the other steps of the multistage process and, consequently, it can not be clearly distinguished [47]. A relevant and systematically investigated example is that of cellulose-based materials for which the main stages of the mechanochemical process are depicted in Figure 1.20. In this case, the process can be initiated from any structural fault existent at the polystructure level. Mechanocracking always starts at the level of the macromolecular chain, therefore it belongs to the molecular level of structural organisation. Instead, the nascent microcracks appear on a finite structural element and its formation belongs to the supramolecular level. Irrespective of the stages of the mechanochemical process, a number of free radicals appear; these ones might initiate many chemical reactions such as grafting, block copolymerization, etc. In addition, the stabilisation of free radicals is followed by the formation of new functional groups, which are able to promote the reactions of polycondensation and/or complexation [48].

35

Macromolecular Mechanochemistry

Figure 1.20. Multistage character of the mechanochemical process illustrated on the cellulose model [47]. A – D – mechanodispersion that is finalised by the formation of micron sized cellulose powders; E – cellulose microcrystal cleavage determining the material’s amorphisation; and F – mechanocracking that promotes mechanodispersion.

36

Chain Multistage Mechanism of Mechanochemical Process Bibliography Part 1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

26. 27. 28. 29. 30. 31. 32. 33.

Cr.Simionescu and Cl.Vasiliu Oprea, Plaste und Kautschuk, 18 (1971) 4843. Cl.Vasiliu Oprea, Mehanika Polimerov, 6 (1978) 977. Cl.Vasiliu and F.Dan, Macromolecular Reports, Spec.Issue, (1995) 1095. E.M.Bartenev and Y.S.Zuev, Strength and Failure of Viscoelestic Materials, Pergamon Press, London, 1968. N.K.Baramboim, Mekhanokhimiya Polimerov, Izd. Nauchno-techn. Lit. Moskva, 1961. Cr. Simionescu and Cl. Vasiliu Oprea, Adv. Chem. Ser. 128, Am. Chem. Soc., Washington C, (1973) 687. Cr.Simionescu and Cl.Vasiliu Oprea, Uspehi Himii, 62 (1988) 502. E.H.Andews and P.E.Reed, Adv. Polym.Sci., 27 (1978) 3. H.H.Kausch, Polymer Fracture, 2 nd Ed.Springer Verlag, 1987. A.J.Kinloch and R.J.Young, Fracture Behaviour of Polymers, Appl. Sci. Publ., London, 1983. V.S.Kuksenko and V.P.Tamusz, Fracture Micromechanics of Polymer Materials, Martinus Nijhoff Publ.Hague, 1981, 1325. S.N.Jurkov, V.A.Zakarevskii, V.E.Korsikov and V.S.Kuksenko, J. Polym. Sci., A2 (1972) 1509. S.N.Jurkov and V.E.Korsikov, J. Polym. Sci.; Polym. Phys., 12 (1974) 385. S.N.Jurkov and V.A.Petrov, Dokl. Akad. Nauk. SSSR, 239 (1978) 1316. S.N.Jurkov, Fiz. Tverd. Tela, 22 (1980) 3344. K.J.Kramer, in: Adv Polym. Sci. (H.H.Kausch Ed.) Springer Verlag, Berlin, 1983. H.H.Kausch, in: IUPAC Macromolecules (H.Benoit and P.Rempp Eds.) Pergamon Press, Oxford, 1982, 211. E.Bayer and A.Moet (Eds.), High Performance Polymers, Hanser Publ. N.Y.Oxford Univ. Press, 1991. B.Wunderlich, Macromolecular Physics, Vol.2, Academic Press, N.Y., 1972. A.Peterlin, Macromol. Sci. Phys., B19 (1981) 401; B6 (1972) 583; J. Mater. Sci., 6 (1971) 490; J. Mater. Sci., 8 (1973) 2. G.S.P.Verma and A.Peterlin, Macromolecul. Sci. Phys., B4 (1970) 589. I.Becht and H.Fischer, Koll. Z. Z. Polymer, 229 (1969) 167. I.Becht and H.Fischer, Koll. Z. Z. Polymer, 240 (1970) 775. A.Peterlin, J. Polym. Sci., A2(7) (1969) 1151; J. Macromol. Sci. Phys., 8 (1973) 277; Int. J. Fracture, 11 (1975) 761. K.L.DeVries, B.Lloyd and M.L.Williams, Am. Phys. Soc. Meeting, Cleveland, Ohio, March, 1971; K.L.De Vries and T.Nagamura, Polym. Eng. Sci., 19 (1979) 2. A.L.Volinskii and N.F.Bakeev, Vysokomol. Soedin., A19 (1977) 785; A.L.Volinskii and N.F.Bakeev, Solvent Crazing in Polymers, Elsevier,1995, 12. A.Peterlin, J. Polym. Sci., C32 (1971) 297. B.A.Lloyd, K.L.Devries and M.L.Williams, J. Polym. Sci., A2 (10) (1972) 1415. B.A.Lloyd, K.L.DeVries and M.L.Williams, Rheol. Acta, 13 (1974) 362. K.L.DeVries, J. Polym. Sci., C32 (1971) 325. K.L.DeVries, R.D.Lutz and M.L.Williams, J. Polym. Sci., B10 (1972) 409. H.H.Kausch and C.C.Hsiao, J. Appl. Polym; Polym. Phys., 39 (1963) 4915. H.H.Kausch, J. Appl. Polym. Sci, 38 (1967) 4212.

37

Macromolecular Mechanochemistry 34. 35. 36. 37. 38. 39. 40. 41. 42.

43. 44. 45. 46.

47. 48.

H.H.Kausch, S.R.Moghe and C.C.Hsiao, J. Appl. Phys., 38 (1967) 4212. H.H.Kausch, Z. Materialprufung, 12 (1970) 137. H.H.Kausch, Koll. Z., Z. Polymer, 247 (1971) 768 H.H.Kausch and I.Becht, Rheol. Acta, 9 (1970) 137. H.H.Kausch, Fracture, 1 (1977) 487. H.H.Kausch, Koll. Z., Z. Polymer, 250 (1972) 1048. H.H.Kausch and K.L.DeVries, Int. J. Fracture, 11 (1975) 727. A.D.Chevychelov, Polymer Sci., USSR, 8 (1966) 49. H.H.Kausch and I.Becht, Deformation and Fracture of High Polymers, Plenum Press, N.Y., 1973, 317; H.H.Kausch and D.Langbein, J. Polym. Sci.; Polym. Phys. Ed., 11 (1973) 1101; H.H.Kausch, Polymer Fracture, Springer Verlag, Heidelberg, 1978. W.Pechold, Koll. Z., Z. Polymer, 228 (1968) 1. S.N.Jurkov and V.E.Korsikov, J. Polym. Sci.; Polym. Phys. Ed., 12 (1974) 385. E.V.Deinm, G.B.Manelles and L.P.Smirnov, Vysokomol. Soed., A22 (1980) 1558. M.Popa, Contributii la cunoasterea unor reactii mecanochimice privind prelucrarea si exploatarea copolimerului ternar pe baza de poliacrilonitril, PhD Thesis, I. P. Iasi, 1989. Cr.Simionescu and Cl.Vasiliu Oprea, Materiale Plastice, 11 (1974) 328. Cl.Vasiliu Oprea and M.Popa, Mechanochemistry of Polymers Deformation and Fracture Processes (Chapter 5) in: Elastomer Technology Handbook, Ed. N.P. Cheremissinoff, C.R.C. Press, 1993.

38

Mechanochemistry of Polymer Deformation

MECHANOCHEMISTRY OF POLYMER DEFORMATION

2

Under the action of low intensity forces exerted for prolonged periods on polymeric materials, both the elongation of chemical bonds and the modification of valence angles take place determining the increase of the potential energy of the system and, consequently, the increase of its chemical reactivity. Whenever the stressed macromolecules belong to a supramolecular-organised structural formation, the prevailing effect is the cancelling of some physical interactions. It was established that a direct relation of the cause-effect type exists between deformation and fracture, both of them being released by the local concentration of mechanical energy [1–48]. 2.1. ON THE LOCAL CHARACTER OF POLYMER DEFORMATION The study of mechanical energy effects on the polymers stressed in the conditions of their service life as well as the analysis of microphenomena that compose the fracture process clearly shows that both the materials and objects made from polymers are subjected to complex strains. In these conditions, the tension induced by mechanical actions brings about a complex process of deformation that occurs in the neck area of the stressed specimen, at the crack border, during flowing and during oriented crystallisation or recrystallisation. The deformation process takes place by a complicated mechanism, which also includes the mechanism of formation of residual stresses. It was established that even in the case of the uniaxial stretching of a cylindrical sample, plastic local deformation occurs just before fracture. This process is accompanied by the redistribution 39

Macromolecular Mechanochemistry

of the value of the stress tensor components in the proximity of a considered point, from the stressed specimen. Whenever the object loses its equilibrium stable shape under the action of mechanical force, new components of the stress tensor appear. These components are determined by the sharp increases of transverse deformations which essentially modify the tensor field of stresses. The theory of complex stressing of elastoplastic materials has three important components: 1) mathematical theory of plasticity; 2) mathematical theory of flow; and 3) theory of local character of deformation. The last theory is strongly related to the subsequent development of the fracture of polymeric materials. If the tensioned state is analysed for a point located in the hexadimensional space of tensions, the stress will be represented, in this space, as a curve that represents its trajectory. In a similar way, the deformed state as well as the deformation trajectory may be depicted. If the stress is applied in the unstressed and undeformed state of the material, both the curves of stress and strain start from the origin of the co-ordinate axes. Their relative position depends on the material properties and represents a specific feature of the materials. Since the number of stress and strain trajectories as well as the number of required experiments for its evaluation may be infinite, a series of hypotheses and postulates have been formulated in the field of polymer mechanics which allowed the elaboration of some laws and theories. These theories are very useful for establishing the limits of utilisation of these materials. In order to generalise the data that characterise the relation between the deformation and stress trajectories, the postulate of materials isotropy and the law of delayed deformation have been considered. Both of them have been deduced from mathematical theory of plasticity that was established from incompressible materials [49]. In the virtue of the materials isotropy postulate, to a symmetric trajectory of stress corresponds a symmetric trajectory of strain. On the other hand, the law of delayed deformation shows that this one is characterised by a delay as compared with those determined by simple deformation. The length of the segment corresponding to the retardation of deformation is a characteristic of material and does not depend on the shape of the stress curve. However, for compressible materials as well as for polymers the above mentioned assumption are not sufficient and require some corrections.

40

Mechanochemistry of Polymer Deformation

2.1.1. Basis of the theory of local character of deformation Small or finite deformations which appear around the stressed point in a material are described by the strain tensor ε i,j (i, j = 1,2, ...). The values of components depend on the manner in which the coordinates axes are chosen and are accordingly modified by their rotation, Figure 2.1:

εα ,β = εi , j ⋅ lαi ⋅ lβi ,

εi , j = εα,β ⋅ liα ⋅ liβ

(2.1)

where l αi is the cosine of angles between the basic coordinate axes i,j = 1,2,3 and auxiliary axes α,β = x,y,z. According to tensor theory, when the indexes from the right hand part of equation (2.1) are idential they are summed up. The components of the strain tensor are determined by the different positions of the auxiliary co-ordinate axes, but by their translation to the main system of the co-ordinates, using equation (2.1), the same values of the components of the deformation tensor are obtained:

εi , j =

1 n

n

∑ εα β l α l β n n i

n j n

(2.2)

where n defines the position in space of the axes x, y, z (n times summing and subsequently dividing by n gives a value that remains constant in these operations). Also, it is assumed that one of the system's auxiliary co-ordinate axes, for instance z, which continuously modifies its position in space, describing a sphere, is described by the following equation:

Figure 2.1. Systems of co-ordinates axes used for tensor analysis of strains [95]. 41

Macromolecular Mechanochemistry

εi , j =

1 εαβliαliβ dS Ss

εi , j =

1 εαβ liα liβ dS 4π S

∫

(2.3)

or

∫

taking into account that for any position of the z axis, the x axis also changes its position, the following function is obtained: π

εi , j =

2π

+π 2

1 εαβ liα liβ d ϕ3 sin ϕ1 d ϕ1 d ϕ2 SN 0 −π 2 0

∫

∫

∫

(2.4)

where j 1 , j 2 , j 3 are Euler ’s angles; S is the surface of the unitary sphere. The relation between stress and strain, expressed as a tensorial series, is the following one:

εαβ = aαβγδ σγδ + aαβγδθϕ σ γδ σθϕ + ....

(2.5)

The above equation physically substantiates equations (2.2) and (2.3) and allows determination to be carried out with the desired precision, by introducing a reasonable number of terms and coefficients into the tensor series. On the stress trajectory, in the area of residual strains, complicated phenomena occur due to the different state of material, on the different axes of the co-ordinates. The abovementioned strains are induced by different work that is supported by the stressed material either by the prolongation of increasing the stress (loading) or by its decrease (discharging). In particular, in the case of simple axial stress, when all components of the stress tensor are proportionally modified with respect to a given parameter, for a certain point of the stressed specimen, two boundary states, i.e. loaded and discharged, are possible. For multiaxial stress, for the same point, the increase of values of local stress for the first system of coordinates and their decrease for the other system may occur. This is the fundamental difference between the two modes of stressing. Consequently, for

42

Mechanochemistry of Polymer Deformation

a multiaxial stress two different functions are required to describe the strains, i.e. equation (2.6) under loading and equation (2.7) under discharging, respectively:

′ σ γδ + aαβγδ ′ θ σ γδ σθϕ + ... ε′αβ = aαβγδ

(2.6)

'' ′′ σ γδ + aαβφδθϕ ε′′αβ = ε*αβ + aαβγδ σγδσθϕ + ..

(2.7)

ϕ

The overall deformation is obtained as the arithmetical average of developed deformations developed on all other systems of coordinates, and the relation describing the local character of deformation is the following one:

εij =

1 1 '' ε'αβliα l jβdS + εαβ liαl jβ dS 4π ' 4π ''

∫

∫

S

(2.8)

S

Similar equations can be described for stresses [98]:

σij =

1 ' 1 σαβliα l jβ dS + σ''αβ liα l jβ dS SS S ''

∫

∫

(2.9)

S

' ' σ'αβ = Aαβγδ ε γδ + Aαβγδθϕ ε γδεθϕ + ...

(2.10)

'' '' σ''αβ = σ*αβ + Aαβγδ + Aαβγδθϕ ε γδ εθϕ + ...

(2.11)

The local character of deformation is quantitatively expressed by the localisation function for which the literature indicates some methods of computation [94–96, 98–100]. 2.2. THE LOCAL CHARACTER OF POLYMER FRACTURE The study of the fracture process must clarify two fundamental problems, namely: 1) the type of bonds that split during mechanical stressing of a polymer with the given chemical and supramolecular–morphological structure; and 2) the type of mechanism that the process follows. The elucidation of these 43

Macromolecular Mechanochemistry

problems will allow the researchers in the synthesis field to design the most adequate chemical structures in order to obtain highperformance polymers, will indicate to the manufacturers the proper type of supramolecular–morphological suprastructure they have to obtain, and, finally, will permit the users of these materials to select those ones corresponding to the desired aim. Supposing that no changes occur in the physical state during mechanical stressing, particularly for linear polymers, the force causing fracture is directly proportional to the rate of microcrack growth, v, and also depends by the term e U/RT of equation (2.12) [50]:

σr = k1 v eU

RT

(2.12)

where: σ γ is tensile strength; v is the rate of microcrack growth; U is internal energy, a measure of polymer ’s resistance; k 1 is a constant; R is the universal gas constant; T is temperature in Kelvin.

Figure 2.2. Variation of tensile strength with temperature for a linear polymer (polycarbonate): a) Strain rate: 1) 500 mm/min; 2) 50 mm/min; and 3) 5 mm/min, respectively; b) Variation of tensile strength with strain rate at different temperatures [50]. 44

Mechanochemistry of Polymer Deformation

For the linear polymers, the data plotted in Figure 2.2 are in good agreement with the above relation. In the case of polymer networks, equation 2.12 becomes:

σr − σ x = k1 v eU

RT

(2.13)

where σ x is the tensile strength corresponding to the deformation under quasi-equilibrium conditions, Figure 2.3 [50]. The relation connecting the rate of microcrack growth and deformation is as follows:

v = Av1n + f (σ n )

(2.14)

where A and n are parameters depending on the fault dimensions and relaxation properties of the polymer; f(σ n ) is a function that is usually neglected. Equations (2.12) and (2.13) show that polymer fracture, when it is not accompanied by secondary chemical reactions, occurs under the action of deformation forces and thermal fluctuations. The main particularity of polymer fracture, which makes the difference between this class of materials and the low molecular weight compounds, consists in the release of a complex of transformations that are conditioned by the flexibility of macromolecules. These transformations determine, before deformation, the values of the parameters from equations (2.12) and (2.13) to a greater extent even than structural characteristics and relaxation of the material. At the same time, with an increase of deformation the tension,

Figure 2.3. Variation of tensile strength with deformation rate for crosslinked polymers [50].

45

Macromolecular Mechanochemistry

which causes the fracture, also increases; for a given domain of temperature, the values of U diminishes concomitantly with the intensification of stressing (the increase of σ). It was found that U is equal to the amount of energy required for an elementary step of activated fracture [53]. The simultaneous scission of a number of bonds, which oppose the destruction of material’s continuity, occurs at this moment. The forces acting to keep the material in shape can be chemical or valence forces (FC) as well as intermolecular interaction forces (FI). Depending on the nature of stressed material, either FC or FI can govern the elementary step of fracture. Since the fracture of a polymer material occurs through scission of some chemical bonds and formation of other new bonds, this process can be regarded as a reaction in which the kinetic and structural units are not macromolecules, but rather certain elementary volumes that defines the fault’s area, rather belonging to supramolecular level of organization. Under the action of certain amount of mechanical energy, Ω, that is absorbed by the bulk of elementary volume, X 2 , following the mechanical loading of the sample, its fracture in two parts takes place. X2 + Ω → 2X '

(2.15)

where X′ is the bulk of the substance belonging to the individual parts formed by fracture. The proposed analogy between the fracture process and a chemical reaction does not simply reduce only to the scission of FC and FI bonds, respectively, but it can also be extended to the elementary steps composing the two processes. Thus, in the case of chemical reaction, the molecules of reactants get close each to other consuming from kinetic energy reserve and this fact contributes to the increase of potential energy of the system. The initial configurations of the atoms pass to the final ones, through an intermediate critical state for the given system. Critical configuration appears at the maximum level of the accumulated potential energy and governs the nature/structure of the formed active intermediate/ complex. This supposes either the scission of FC bonds (in the case of a chemical reaction) or the scission of FI bonds, in the case of polymer fracture accompanied by the viscous flow) depending on the specific conditions. The accumulated energy is distributed on all degrees of freedom of oscillation, translation, and rotation 46

Mechanochemistry of Polymer Deformation

movements, accordingly to the requirements of newly formed configurations. This means that the kinetic element practically spontaneous losses a part of the stored energy. In the case of the fracture process, the role of reacting molecules is played by the elementary volume of fracture (VEF). Its potential energy increases as a result of mechanical loading of the stressed body. At the structural level, the potential energy is nonuniformly redistributed. According to the nature of polymer nature and its relaxtion properties, it is located more extensively on certain microvolumes than on other ones. When enough energy required for transition to a new state is absorbed within a given volume, in order to overcome the potential barrier, the elementary step of fracture process will occur. At this moment, a part of the bonds, which oppose the fracture process (i.e. FC or/and FI), will be broken. A part of the accumulated energy within a microvolume will be converted to surface energy. Absorption of mechanical energy also determines the redistribution the energy reserve on the chemical and physical bonds, this fact assuring the structural continuity of material. The non-uniformity of energy redistribution is determined by the relaxation properties of polymers, structural non-uniformity, and the shape of the stressed sample. The irreversible displacement of the elementary volume of fracture, in the sense of its conversion from volume to a new-formed surface (under the action of deformation stress), is analogous to irreversible displacement of chain segments during the viscous flow caused by polymer stretching. It is known that in this case the following equation is valid:

η = Be Evisc

RT

(2.16)

where η is viscosity; E visc is the activation energy of the viscous flow. In the case of axial deformation of a polymer, under the action of stress σ with speed v, equation (2.16) becomes:

σ = v B1 e Evisc

RT

(2.17)

This equation is similar to the equation deduced from the theory of absolute reaction rates, namely:

47

Macromolecular Mechanochemistry

 vhN −∆S ++ R  ∆H ++ e σ= e  V 

RT

(2.18)

where V is the molar volume; N is Avogadro’s number; ∆H + + is the entropy change; ∆S + + is the enthalpy change; h – Planck’s constant. The validity of Boltzman’s law of distribution as well as the constancy of ∆H + + within the studied temperature range can be experimentally established from the linear equation ln σ = f (1/T). Equation (2.18) can be also deduced taking into account the analogy between the fracture process and viscous flow. By comparison with equation (2.12) it may be written:

k1veU RT 1 σr = = k2 σ  hN −∆S ++ R  ∆H ++ e   ve  V 

RT

(2.19)

where k 2 is the stress concentration coefficient, which shows how many time the stress from the tip of the growing crack is greater than the nominal stress in the rest of the sample. At the constant volume, the change of enthalpy when passing from the initial state of VEF to those corresponding to the maximum of potential energy, ∆H + + , to the constant volume, can be equal to the experimental value of activation energy, E exp . In other words, it can be written: U = Eexp = ∆H ++ . Since there is a linear dependence between lnσ r and 1/T, ∆S + + can be considered constant. k 2 depends on the shape and dimensions of the fault as well as on the type of function of energy distribution on the macromolecular chains. After replacing in equation (2.12) the value obtained from equation (2.19) and expressing v by the strain rate v 1 , the following equation is obtained:

 hN −∆S ++ R n  U e Av1  e σ r =  k2  V 

RT

(2.20)

Equation (2.20) physically describes the fundamental relation between the structural characteristics of the polymer, temperature, and rate of deformation. Since both the structure and relaxation 48

Mechanochemistry of Polymer Deformation

Figure 2.4. Dependence of the energy required for realisation of elementary steps on applied stress [50].

properties of the fractured polymer are different from those of the unstressed polymer, the value of U expresses not only the properties of material but also the real conditions of fracture, Figure 2.4. In fact, parameter U must be considered as a function of σ r [U = f(σ r )], which for the relatively small range of σ r values can be considered as being linear. Even in this case, the slope of straight line (U = U 0 – ασ r ) is modified; the value of α for a given value of tension corresponds to VEF multiplied by k 2 . For example, in the case of polystyrene it has been proved that the molar volume in which elementary fracture steps occur is V = 130 cm 3 proving that about 20 bonds (representing FC and FI) are broken, instead of only one. So, from the kinetic point of view, polymer fracture must be regarded as being a process that implies the scission of a certain number of bonds, within an elementary volume having a maximum potential energy, which has accumulated under mechanical stress conditions. In order to characterise the state of destructibility, an object or a polymer material, subjected for a long period to the action of an external mechanical force, is considered. Thus, irreversible transformations occur within its structure which through local accumulation gives rise to the destructibility state. Tensorial computations have proved that the mechanical properties of the stressed body can be used to establish the function 49

Macromolecular Mechanochemistry

characterising the local development of the fault. In this aim, the term of durabulity was proposed to characterize the behaviour of polymeric materials constrained to normal stress conditions [146]. 2.3. DEFORMATION AND FRACTURE – INTERCONNECTED PROCESSES Establishing the progress of fracture, considered a modality of interruption of continuity within a tensioned body, and of deformation, regarded as totality of regrouping phenomena at the atom-molecular and supramolecular–morphological level, is of great theoretical interest. This, especially, in order to clarify the causes that release the primary process and practically for explanation of the nature of mechanical properties of polymers. From the published papers, with kinetic character, is clear that both the deformation and fracture are characterised by equal energies of activation. This assessment was proved by many studies made on the most different classes of materials, namely: metals, polymers, semiconductor crystals, etc. [49–55]. Analysing the two phenomena, which seem to be interdependent, a problem arose, namely – the necessity to ascribe the primary role, causative, to one of them. A series of conclusive results have been obtained studying the uniaxial stretching of oriented polymers. It was proved that irradiating with ultraviolet rays a tensioned polymer, by stretching, has as result a considerable increase of the stationary creep rate. It is already known fact that the action of ultraviolet rays on the macromolecular structures takes place by scission of chemical covalent bonds. The cumulative effect induced by the increase of the rate of deformation reveals that both stressings, i.e. photochemical and mechanical, occur at the atommolecular level through a common mechanism. Consequently, under creep conditions material deformation is caused by the splitting of covalent or secondary bonds [31]. Interdependence of deformation and fracture processes is also manifested on different levels of supramolecular organisation [33, 34]. Thus, the study of uniaxial stretching of oriented crystalline polymers offers many interesting informations in this sense. The results were obtained by investigation of the structure, fault energy, structure and distribution in the crystal, as well as by studying the nature of surfaces resulted from splitting of the formations of supramolecular structures. Using polarised light electron microscopy for stressed 50

Mechanochemistry of Polymer Deformation

polyethylene it was established that concomitantly with the gradual increase of applied load, plastic deformation starts on those fragments whose axial orientation of the constituent filaments coincide, at least approximately, with the direction of stretching. In Figure 2.5 the darker parts represent the plastically deformed domains; this Figure allows almost rigorous to discern the zones where transformations of microstructure occurred. Under experimental conditions, the plastic deformation, even at high enough values, does not affect the fibrous formations which maintain their individuality, Figure 2.6. In turn, cracks form even from low values of stretching in the middle of spherulites; the cracks grow with the increase of deformation, by coalescence, passing to magistral fracture that causes fracture. Fibrils formed by stretching of spherulites are nothing else but fascicular formations of macromolecules, free of weak interactions that kept them shape in the former suprastructure, Fig. 2.7. This behaviour confirms the existence of certain weak surfaces along which the sliding of elements of the supramolecular structure is possible.

Figure 2.5. Initial stage of spherulite deformation [55]. Figure 2.6. Initial stage of spherulite deformation and crack formation in its center [55]. 51

Macromolecular Mechanochemistry

Information concerning the relation between deformation and fracture was also obtained studying the contact zone between two adjacent spherulites. One may ascertain that whenever the fascicles belonging to two adjacent spherulites show parallel orientation in the contact area, fracture occurs without significant traces of plastic deformation, Figure 2.8. In the case of their normal orientation, significant elongation can be seen at the contact boundary. This elongation is several times greater than the spherulite diameter and it is related to the plastic deformation of internal formations. Figure 2.9 clearly shows that inter-spherulitic fracture started from a microcrack. This one appeared in the first moments of deformation as a result of local separation (by sliding) of filaments. Correlating the above observations, one can conclude that tangential orientation of filamentary fascicles (inside of spherulites), under the action of external mechanical forces confers upon these formations a marked anisotropy of mechanical properties. The localisation of primary centres of fracture at the separation surface of spherulites as well as in area of primary centres of spherulite

Figure 2.7. Fibrils debounding during deformation [55]. Figure 2.8. Character of interspherulitic fracture as a function of filamentary formations orientation at the detachment limit [55]. 52

Mechanochemistry of Polymer Deformation

Figure 2.9. Internal fracture initiated by the crack appeared in the spherulite center.

fracture is just a consequence of mentioned anisotropy. Anisotropy is the factor that governs both the laws of non-uniformity of deformation (local character) and the genesis and development of nascent microcracks which initiate the fracture. It is well known that the formations of fascicular type are based on lamellar crystals – consisting of sheets of extended chains folded periodically through 180°, thus reversing the chain direction. The full crystal consists of the packing together of these sheets. This means that these formations are characterised by high plasticity along the crystallographic axis c, which coincides with the direction of macromolecules. An adequate model for the structure of polymer crystals, physically and crystallographically sustained, is depicted in Fig. 2.10. It is assumed that the succession of crystalline lamellae along the c axis is realised by winding formations that are helically screwed. An important property of this model is that each spiral (volute) of helix can be regarded as a lamellar crystal, in which a section in direction of the chain axis was made and that some parts of the crystal are slightly displaced along this section. Correlating this representation with the data regarding the ‘mosaic’ 53

Macromolecular Mechanochemistry

Figure 2.10. (a) Schematic representation of the spiral development of stratified monocrystal; (b) Model of helical crystal showing an spiral axial dislocation; (c) Schema of a surface composed by helical crystals; (d) Schema of twisting and sliding of helical crystals; (e) Flexing crystallography of crystalline lattice by crystal compression along the c axis; (f) Schema of elastic deformation of an helical crystal [55].

structure of polyethylene (PE) single crystals and with the presence in their structure of dislocations, it can be supposed that any volute-lamella of the helix has a similar structure. This structural concept allows understanding the mechanism of plastic deformation and the genesis of nascent microcracks, the primary active centres of fracture. Plastic deformation occurs by a dislocation mechanism. The circular orientation of the crystals in spherulites is responsible for the initiation of deformation on those of its fragments where the cleavage planes (lateral sides of lamellar crystals) present a favourable orientation, i.e. are located close to the direction of applied force, Figure 2.10b. The data of small angle X-ray diffraction shows an insignificant increase of the ‘long period’ with increasing deformation. Therefore, the polymer property of passing into the oriented state is related to the existence of helical crystals, uniaxially deformed along the c axis as well as their high capacity to favour the cleavage on the lateral faces of the crystals (Figure 2.10c). This model also explains the origin of polymer fracture in the stressed state. The fracture process is controlled by the rate of rupture of macromolecular chains due to thermal fluctuations [56]. Experimental determination of the energy required for fracture gives a value that by far overtakes those exclusively required for scission of chemical bonds. The crystallographic sliding favoured by 54

Mechanochemistry of Polymer Deformation

the existence of dislocations, causes critical values of flowing on the local level but the mechanical load does not reach the level required for the scission of chemical bonds. Since the deformation is strongly related to the displacement of crystalline junctions, it is required to overcome the energy barrier to which thermal activation also contributes. This means that under the influence of the thermal fluctuations, the sliding in the crystal can be started at external stresse lower than those required for reaching the flow limit. In the presence of dislocations, this process is located in the area of the physical nucleus of the dislocation. Due to the sliding of crystalline knots in the proximity of the dislocation trajectory, the resistance to displacement rapidly decreases. Under these conditions, the thermal fluctuations may actively contribute to the initiation of movement within the planes composing the nucleus of the dislocation. Furthermore, the crystallographic sliding process itself is accompanied by heat emission, which, in turn, accelerates the displacement of structural elements. Due to the lower thermal conductivity of polymers, it seems that the cleavage process is almost an adiabatic one and, consequently, it locally favours the thermal scission of chemical bonds. In other words, the fracture process of stressed polymers is based on the thermofluctuating mechanism of dislocations. This explains why, even at low stresses, the stress–strain relation is a non-linear one. Subsequent evolution of the two processes, deformation and fracture, is governed by the increase of the number and dimensions of the cracks former in the previous stage. One can ascertain that concomitantly with the increase of stress (σ) the crack concentration becomes increasingly greater (Figure 2.11, curve no. 1) and the progress of the deformation process agrees with the above-mentioned behaviour (Figure 2.11, curve no. 2). As Figure 2.11 shows, the deformation proportionally increases with the increase of stress up to a certain value, but it strongly accelerates after the appearance of cracks. Removing the load determines, after a certain period of time, complete recovery of the initial dimensions of the sample, and X-ray investigations proved that the cracks close up during relaxation. Subsequent stressing again determines the growth of the cracks, but the growth rate is much higher (Figure 2.12a, curve no. 2). These results clearly demonstrate that in the first case the fracture of material took place, whilst only re-opening of the existent cracks took place in the second case. Following the variation of deformation, one can see that it increases much more rapidly af55

Macromolecular Mechanochemistry

Figure 2.11. The increase of submicron crack concentration with the progress of deformation process in the case of oriented poly(ε-caprolactam) concomitantly with increase of applied stress: 1) crack concentration, N; and 2) relative strain, ε%).

Figure 2.12. The increase of crack concentration (a) and the development of strain (b) in time, in the case of oriented poly(ε-caprolactam), under the conditions of combined stress: 1) the first run; and 2) the second run, after the complete removing of the load after the first stressing.

ter the second stressing (Figure 2.12b). So, in this way, not only the interrelation between deformation and fracture but also the causal character of fracture were demonstrated [58]. Crack formation is therefore caused by the destruction of the continuity of the stressed body and investigation of the new generated surfaces gives valuable indications, not only regarding the distribution of these centres of fracture but also concerning the prehistory of the fracture process. There is a strong interconnection between the formation of the 56

Mechanochemistry of Polymer Deformation

fracture surface and the mechanism of its generation [59–73]. The existence of three characteristic zones of fracture was established: 1) the ‘mirror’ zone, defined by the surface of the initial crack and characterised by circular delimitation (Figure 2.13); 2) the zone with a fine relief with hyperbolic or parabolic delimitation (Figure 2.14); 3) the zone with a coarse relief resulting from the branching of cracks, under the conditions of high fracture rates (Figure 2.15) [57]. In the first zone, the rate of crack propagation is low and the stress state is maintained up to the moment of fracture. Therefore, the stretching force is parallel to the axis of action of the structural units, macromolecules, and supramolecular formations. The displacement of the crack front is determined by the displacement of the borders between the macromolecular chains containing the broken bonds and the molecules from its vicinity. The latter are characterised by a reserve of energy and are ‘prepared’ for the

Figure 2.13. The mirror zone formed in fractured poly(methyl methacrylate), magnification 12× (a) and the internal structure of the mirror zone, magnification 50×, (b) [57].

Figure 2.14. Hyperbolic zone of fractured poly(methyl methacrylate) [57].

57

Macromolecular Mechanochemistry

Figure 2.15. Superficial structure of fracture at high deformation speed [57].

scission of their own bonds. In the ‘mirror’ zone, the fracture process is preceded by the process of orientation [69, 70]. The rate of crack growth increases concomitantly to the displacement of its front away from the centre of initiation. Since the crack front always contains a rigid zone, as a result of the local orientation of some parts of macromolecular chains, the fluctuation of local stresses will lead not only to conformational modifications but also scissions of chemical bonds. This process will accelerate the displacement of the fracture front in subsequent stages of crack propagation. In the ‘mirror ’ zone, the oriented field of forces destroys the spherulitic formations; due to high load supported by these structures their component elements are oriented in the loading direction. In the transition zone, where the rate of crack propagation is strongly increased, the displacement of spherulites is realised by the formation of the hyperbolic shape of the structural element. The displacement of the crack from the incipient moment of its genesis up to catastrophic fracture does not occur at a constant speed. To overcome different ‘obstacles’ from which the trajectory of its displacement extends, i.e. macromolecules, bundles of chains, formations of supramolecular structure, micropores, inclusions, etc., crack propagation requires different periods of time and the crack perimeter becomes sinusoidal. On the whole, the perimeter of the crack front and the border between different formations is controlled by the established equilibrium between mechanical and physico–chemical forces; the displacement of the crack front is achieved by destruction of this equilibrium. Considering now that, at a given moment, the elastic forces are in the equilibrium position on the whole perimeter of the crack; therefore these forces just finalised a step of fracture. For the 58

Mechanochemistry of Polymer Deformation

process to proceed a specific period is required to annihilate further ‘obstacle’. During this period, the selective displacement of the crack front takes place. However, the overcoming of some ‘obstacles’ is locally impeded by the existence of other neighbour faults on which the mechanical forces did not yet caused the fracture of the structural elements. Redistribution of the stresses on the whole crack perimeter leads to rapid destruction of all ‘obstacles’. In this way, the elastic energy is accumulated at the crack perimeter and an overload appears at the crack–polymer interface that is materialised in an energy pulse. The elastic field of stresses and the pulse energy displace the crack perimeter in a brittle or quasi-brittle manner. The value of this displacement is governed by the total energy reserve exactly at the moment of ‘crack jump’. This mechanism is subsequently repeated. The fundamental problems that must be clarified are related to the shape of cracks, the mechanism of their propagation as well as the quantitative characterisation of the fracture process of the polymers in different states of aggregation [74–85]. The images of the fracture surfaces taken by optical microscopy are directly connected to the mechanochemical mechanism of the fracture of brittle polymers. The genesis of a new surface starts by the development of most dangerous fault that is located with the highest probability on the specimen surface. Concomittantly with propagation of the primary crack, the average pressure increases on the remaining surface and the induced tensions in the closest faults also attain critical values. The development of secondary cracks starts exactly from these points. Through the intersection of primary cracks with secondary ones, the hyperbolic or parabolic delimitations of the relief appear in the advanced stages of the ‘mirror’ zone formation. We consider the two cracks, located in two very close planes, which move towards each other with the same rate v of the crack front. The centre of one crack is located in the origin of the co-ordinate system and that of the second one is on the Ox axis, i.e. point x 0 (Figure 2.16) [85] The equations describing the crack parameters are:

x 2 + y 2 = (v t )

2

( x - x0 )2 + y 2 = v 2 (t - t )2

59

(2.21) (2.22)

Macromolecular Mechanochemistry

Figure 2.16. Hyperbolic intersection of the primary and secondary cracks.

where t is the period from the initial moment of crack growth; τ is the period from which the growth of the second crack starts. Eliminating the time from the above equations, we get the intersection point of the two curves:

(

)

(

) (

)

4 x02 - v 2 t 2 x 2 + 4 v 2 t 2 y 2 + 4 x0 x02 - v 2 t 2 x - x02 - v 2 t 2 = 0

(2.23)

Equation (2.23) describes a hyperbole having its top towards the origin of the co-ordinate axis, i.e. towards the centre of the initial crack. The intersection point of the hyperbole with the axis Ox is located at distance x m2 from the origin: x0 + v t (2.24) 2 Angle ϕ between the tangents of the hyperbola can be calculated, using the following relation: xm =

2

æx ö tan j = ± ç 0 ÷ - 1 è vtø

(2.25)

Experimentally, it was established that the delimitation is of the hyperbolic type when the rates of propagation of primary and secondary cracks are equal; when the above-mentioned rates differ from each other, the delimitation zone is parabolic. The realisation the first stage of crack growth is, in the first place, a consequence of the development of stresses in the stressed body, but the contribution of other factors, such as chemical reagents, must also be considered. In the second step of fracture, so called ‘mat’ zones appear; it is the result of ramification of the cracks formed in the first stage. 60

Mechanochemistry of Polymer Deformation

During this stage, one of primary cracks grows at a high rate by coalescence with the other ones, attaining during propagation the critical dimensions and causing the splitting of the stressed specimen. An important parameter is surface energy, which changes during cracking, as well as its dependence on temperature and time [81, 82]. Since the mathematical analysis of crack propagation is difficult to realise, for the most general case, one can use the same simplified hypothesis to obtain models describing certain types of cracks. Analysis of the results still allows establishing a mathematical expression that correctly characterises the fracture process. In particular, for rubber considering a spherical or cylindrical geometry of the crack and applying the specific thermodynamic equation of the given system and process, it was possible to establish analytical results that express the dependence of the crack process versus the nature of applied stress [76, 81, 83]. In principle, starting from Griffith’s data [84] and assuming that the investigated sample is a linear viscoelastic and incompressible material, it is possible to establish the fracture–time dependence. In turn, this dependence enables us to calculate critical stress (σ cr ). For the formation of a crack, having the length equal to 2e, which appears in an infinite elastic sheet that is biaxially and uniformly strained in the entire sample, the following equation can be written:

s cr =

2 E gc = p C

2 p

gc /C D

(2.26)

where γ c is the energy required by the new surface to overcome cohesion; D = 1/E is tensile compliance. Considering a cylindrical crack, with the diameter equal to 2a, under the same conditions we found the relation:

s cr =

2 gc /a 4 2 Dcrp (t ) - Dg

(2.27)

where D crp (t) is tensile creep compliance which takes the value D g at the limit of glass transition. For short strain periods tending to zero: Dcrp (0) º Dg . 61

Macromolecular Mechanochemistry

The numerical similarity between equations (2.26) and (2.27) is

2 / p 2 / 4 and the criterion of time dependence (D), for this particular case, can be expressed by equation 2D crp (t) – D g . Thus, the equation that allows the calculation of σ cr for a crack formed in a viscoelastic linear material during a loading step, is: quite evident, since

s cr =

2 gc /C p 2 Dcrp (t ) - Dg

(2.28)

However, equation (2.28) is only approximate due to the simplified hypothesis of A. Griffith, namely: 1) incompressibility of the material; 2) uniform stressing of the material; 3) symmetric propagation of the crack, circularly and in two directions; and 4) time interdependence of the energy of cohesive fracture (γ c ). An important contribution to the generalisation of this problem has arisen from the application of the conditions of thermodynamic equilibrium. Expressing the equality of the rate of stressing of the system ( I ) by the sum of the rates of energy accumulation ( F ), of energy dissipation (2D), of conversion into kinetic energy ( K ), and of formation of new surfaces ( S ) [81], equation (2.29) is obtained: (2.29) I = F + 2 D + K + S Replacing in the above equation the explicit values of each term, we obtain: ∨

I = T ⋅ ni

∫

(2.30)

A t

. d σi E i dtdV F + 2 D = dt V 0

∫∫

(2.31)

t

. d ρ . ni dtdV K = dt V 0 ni

(2.32)

d γ c (t ) dA S = dt A

(2.33)

∫∫ ∫

where A (t) and V (t) are the surface area and volume, respectively; 62

Mechanochemistry of Polymer Deformation

both of them are time-dependent during crack growth. Equation (2.33) gives the possibility calculation of γ c as a function of time, which becomes γ c (t), and defines the contribution of cohesive energy to the formation of a new surface. The term γ c (t) differs from the term γ a which represents the contribution of adhesive energy. Using equations (2.30)–(2.33) and considering the value of the stresses n(b, t) ≡ n 0 g(t) applied to long cracks (a << b→∞), the thermodynamic condition, valid for the critical state and expressed as a function of relaxation modulus E rel (t), may be written in the form: 2 b6  n   a  2aγ c (t ) − 4 4  0  a b  

2g  ×  Eg g ( ξ ) + 0 2ξ 

∫

t

∫

ξ

o

 ∂Erel ( ξ − τ ) I b4  g ( τ ) d τ d ξ − n0 2 g 2 (t ) = 0 ∂ (ξ − τ ) 2 a  

(2.34)

where a (t ) = 0 corresponds to the moment of crack initiation; by summing the terms in the brackets, by cancellation of the terms in the brackets, the condition of crack propagation as a function of time at a given moment t[a(t)], is obtained. The calculations made with the model of the spherical crack are simplified. The only model close to reality is the one treating the crack in the cylindrical co-ordinates. However, it presents some difficulties when performing analytical calculations. The calculations for vitreous polymers show that the experimentally determined energy of fracture is 1000 times greater than the theoretically deduced values. This is because to finalise the fracture both the activation energies of the viscous flow and of cracking must be overcome. It should be expected that together with a decrease of plastic deformation is limited due to ‘obstacles’ that appear in polymer (pendant groups, displacement of macromolecular chains, etc.), the energy of fracture should diminish, tending towards the theoretical value; this one is the amount of energy required exclusively for breaking atomic bonds. In practice, this tendency has not been confirmed. Research made on a series of vitreous polymers, such as: CH3 O CH3

63

n

Macromolecular Mechanochemistry

O

CH3 O

O

C

S O

CH3

n

Polyphenylene oxide, T g = 210 °C Polysulfone, T g = 191 °C O

CH3 O

O

C

C

CH3

n

Polycarbonate, T g = 144 °C H

CH3

C

C

H

C O

OCH3

n

Poly(methyl methacrylate), T g = 105 °C proved that the energy required for fracture continuously increases with the decrease of temperature to –50°C. In the case of poly(phenylene oxide), polysulphone, polycarbonate the fracture energy increases concomitantly with the decrease of temperature to attain a maximal value of –85 °C. This temperature must be related to the general modifications of the viscoelastic properties in the region of vitreous transition. In the same temperature range, a monotonous variation of energy was obtained for poly(methyl methacrylate). It may be possible in this case as the maximal value of energy is shifted to much lower temperatures. Extrapolation to 0 K of the data concerning the fracture energy of the three polymers shows that at boundary conditions this parameter tends to the theoretical value, Figure 2.17. In conclusion, either in intensely deformed zones, under the action of high speeds, in the zones deformed at the low speed, but for a long period (the force being concentrate on small surfaces), due to tension cumulation, especially at the edge of submicroscopic 64

Mechanochemistry of Polymer Deformation

Figure 2.17. Dependence of the fracture energy of the vitreous polymers with temperature [82].  ) polyphenylene oxide; ∆) polysulfone; l ) polycarbonate; ™ ) poly(methyl methacrylate).

cracks or on flaws, flow processes take place. These ones are accompanied by the fracture process that consists of scission of chemical bonds. Usually, these processes do not occur simultaneously on the entire stressed area, but their propagation with very high speeds through successive steps. Mechanical stressing of the polymeric materials is a complex phenomenon, implying the following elementary steps [86]: 1) The formation of stresses and development of elastic strains; 2) The genesis and statistical distribution of submicron cracks; the true centres of initiation and fracture propagation; 3) The occurrence of molecular displacement into the stretched domains of the polymer when the temperature at which mechanical stressing occurs may assure the progress of microBrownian movements. This leads to the annihilation of critical tensions and all submicron cracks are closed; 4) The formation of new surfaces which are characterised by specific energies and accompanied by the scission of a large number of physical and chemical bonds; 5) The reaction of macromolecular species from the proximity 65

Macromolecular Mechanochemistry

of the stressed area, which especially in the case of very fast deformation impedes stress propagation over a large range; 6) The conversion of a part of elastic energy into a wave which travels moved at the velocity of sound stimulating in turn the propagation of fracture; 7) The formation of fracture accompanied by creep into amorphous domains and the development of brittle fracture into the crystalline zones. The established ratio between deformation and fracture can also be explained kinetically. In this case, a qualitative criterion of fracture evaluation is the durability and strain rate of strain cumulation. The rate of strain cumulation is defined as the inverse values of the relaxation time [87]:

e =

{

1 = e 0 exp - (Q0 - as ) / kT tr

}

(2.35)

The logarithmic form of this equation gives the linear dependence between the applied stress σ, corresponding to the occurrence of inelastic deformation, and the temperature and strain rate, respectively:

sD =

e Q0 kT ln a a e 0

(2.36)

where Q 0 is the activation energy of the relaxation process; α, τ are the constants of the polymer (α is the activation volume); k is Boltzmann’s constant. A similar relation, Jurkov’s relation, correlates under load the polymer durability, τ r, with the temperature and applied stress [41]:

{

t r = t 0 exp - (U 0 - gs ) / kT

}

(2.37)

where U 0 is the activation energy of the scission of chemical bonds; γ, τ are polymer constants (γ is a structural parameter). The logarithmic form of the above equation expresses breaking stress τ r , as a function of temperature and durability:

66

Mechanochemistry of Polymer Deformation

sr =

U 0 kT t r ln g g t0

(2.38)

Therefore, the stress required for inelastic deformation to take place, σ D , and the stress required for the scission of chemical bonds, σ r , have common expressions; this fact suggests the interdependence of the two processes. However, equations (2.36) and (2.38) proved their validity only in narrow ranges of temperature and strain rates, especially at high values of these parameters. The fact that inflections appear on the curves σ D = f(T) and σ r = f(T) (Figure 2.18 and 2.19) suggests that the terms U 0 , α and Q 0 are not constants in the whole investigated range, as it was assumed. The position of the two inflections does not depend on the polymer strain state, but on its chemical nature and physical state. Using NMR spectroscopy it was established that the slope changes, due to the modification of the constants in equations (2.36) and (2.38), occur just to the temperature that stimulates the oscillation and rotation movements of some groups of individual molecules or chain segments. Consequently, modifications of the volume of activation of deformation, α, of the structural parameter, γ, and of U 0 and Q 0 take place; both the deformation and fracture processes imply important modifications of the polymer structure. The structure recovery firstly depends on the applied regime of deformation (stress or strain rate). The two processes are characterised by different values of activation energy or of the magnitude of kinetic elements, which are involved in the elementary act of deformation or fracture. Supposing that during that no structural modifications take place during deformation, the parameters from equations (2.36) and (2.38) remain constant in the

Figure 2.18. Dependence of σ r on temperature for poly (methy methacrylate) at different deformation rates: 1) 3 × 10 –1 cm/s; 2) 5 ×10 –4 cm/s [87]. Figure 2.19. (right) Dependence of σ D on temperature poly (methy methacrylate) at different deformation rates: 1) 3 × 10 –1 cm/s; 2) 5 ×10 –4 cm/s [87]. 67

Macromolecular Mechanochemistry

whole deformation period. In turn, if some scissions or only conformational changes take place, the parameters are changed and inflections appear on the characteristic curves. The data concerning the creep of polymers, obtained at different temperatures, show that two different components of the stress are responsible for deformation and fracture. In order to illustrate

Figure 2.20. Mechanically stressed macromolecule.

this, let us consider a stretched macromolecule subjected to a tensile stress, σ, Figure 2.20. The level of structural unit can be divided into two components: the normal one, σ n, modifies the valence angle ϕ and the tangential one σ t acting in the same direction with the chemical bond, elongates it. Converting to polar coordinates, the normal component becomes the observation part of the stress tensor, i.e. tangential stress (t m ), while the second component becomes the spherical component of the stress tensor (σ 1 ). It may easily be noted that tangential stresses are responsible for polymer deformation, by increasing the valence angle. Q 0, expressing the activation energy of deformation, constitutes the sum of all interactions preventing the elementary development of this process (inter- and intramolecular bonds), so: Q0 =

å qi

(2.39)

thus

{ (åq -a×t )/ kT}

e = e exp -

i

m

(2.40)

With high tensile strains, irrespective of whether fracture is 68

Mechanochemistry of Polymer Deformation

brittle or ductile, it is the spherical component of the stress tensor that is responsible for polymer durability.

{

t r = t 0 exp - (U 0 - g × s1 ) / kT

}

(2.41)

Let us suppose that there is no connection between deformation and fracture – both being different, independent physical processes – taking place simultaneously in the stressed body. Under stress σ the process that develops faster becomes dominant. Consequently, the way in which the stressed polymer will evolve is governed by the ratio of the two competitive processes. The fracture rate may be deduced by asserting that it is the reverse of durability. n=

{

1 exp - (U 0 - g × s1 ) / kT t0

}

(2.42)

The ratio of these two rates will be imposed on the one hand by Sqi and U 0 and, on the othed hand, by the tangential and normal stress ratio (β = t m /σ 1 ). With linear, rigid polymers, at low stress values deformation takes place mostly by the displacement of macromolecules or of their associations which becomes possible by de-

creasing the interaction force among them (Sqi ) . If, however, the sum of these interactions is higher than U 0 (chemical bond energy), the deformation will not be able to occur without chemical bond splitting, having very low values at the moment of fracture. The normal and tangential component ratio of the stress, β, offers information on polymer deformability under various mechanical regimes. Thus, at elongation, β = 0.5 because under these conditions σ 1 is obviously higher t m . At torsion, due to equivalence of the two stresses, β = 1. However, when the sample is in a compression state, when σ 1 is practically zero, β→∞; inducing a high strain capacity, without fracture. Fracture is an irreversible process being based on the scission of chemical bonds; by tensile stressing, the polymer resistance might be expected to decrease. Experimentally, a reverse phenomenon can be noticed. In this way, by stressing the polymers at higher temperatures, due to the decrease of Sqi , the deformation rate increases very much, so polymer deformation acquires a high value while the local stresses, expressed by parameter γ, decrease. 69

Macromolecular Mechanochemistry

This is an effect of the conformational changes of macromolecules that have the tendency to uncoil themselves and orient in the sense of stress action. In this way, the loading of chemical bonds from the unitary cross-section becomes more uniform. The immediate effect is the increase of strength expressed as durability. Consequently, deformation and fracture are interconnected phenomena and the inflection points on the curves σ(T) and ε(T) coincide, as it was experimentally proved [88]. These conclusions are also verified in the case of polymers in different physical and aggregation states and having quite different chemical structures. Thus, the deformation of linear polymers, rigid at low temperatures, is directly dependent on fracture, its low values being attributed to elastic deformation in the proximity of the microcrack tip. The explanation lies in the fact that the deformation activating energy is in this case very high exceeding by far the energy of the chemical bond (U 0 ); therefore, its fracture becomes more probable [89]. The same phenomenon happens with linear, highly oriented polymers subjected to tensile stresses. Since this case the majority of macromolecular chains are already perfectly stretched, there are no other possibilities of conformational modifications; Σq i becomes extremely high and, as a consequence, the deformation undergone by these polymers is due to chemical bond fracture. Referring to highly reticulated polymers loading, it must be stated that their chemical bond splitting, under the action of the tangential stress tensor, cannot be avoided. In this case, the mechanochemical act will occur, because there are few possibilities of conformational changes, due to the high frequency of cross bonds between the macromolecular chains. The thermofluctuation nature of fracture and deformation has been proved from the structural and kinetic viewpoints. Their activation energies are practically equal (see Refs. 90 and 91). 2.4. MECHANOCHEMICAL MECHANISM OF POLYMER DEFORMATION [54,92,93] The nature of mechanochemical transformations that occur in a polymer-based body can be understood by analysing the mechanism of elastic energy concentration on individual chemical bonds or, alternatively, in small local volumes. In a constant field of forces, the conversion of elastic energy into chemical energy follows a mechanism base on the deformation 70

Mechanochemistry of Polymer Deformation

of electronic level of reacting particles (changes of interatomic distances, valence angles, etc.). This process has an equilibrium character since the equilibrium of the energy distribution with respect to the degrees of freedom is maintained in the system. The above mentioned distribution is described by a Maxwell–Boltzmann function, as follows:

U def =

r

òr

f u dr

or

U def =

0

V*

òV

* 0

s u dV *

(2.43)

where: f u and U u – force and tension, respectively, that act on the chemical bond; r and r 0 – length of initial and after-deformation bonds; V * = rs * (s * - the effective section of the molecule or bond with respect of applied stress). In order to calculate the deformation energy and fracture activation energy, the equation of the Morse potential curve is often used. The relation connecting the fracture activation energy and the value of force f u is the following [94]:

U f f = 1 - U - U ln U0 F0 F0

1+ 1-

fU F0

1- 1-

fU F0

(2.44)

Figure 2.21. Representation of the function U(f U ). Number of bonds on the deformed fragment of chain: 1) ∞; 2) 100; 3) 50; 4) 20; and 5) 10 [95]. 71

Macromolecular Mechanochemistry

where F 0 is the tensile strength of the bond. Graphical representation of the function U(f U ) is presented in Fig. 2.21 (curve no.1) [95]. This curve, in fact, describes the simplest case of conversion of mechanical energy into chemical energy. It is currently used for the explanation of mechanical fracture of stretched bonds in the simplest case. In the case of more complicated molecules, it is required to take into account also the deformation of valence angles, internal contraction, and interaction of physical interactions between atoms. For thermal activation, the activation energy from Arrhenius’s equation coincides with bond energy U 0 [96]:

k = k0 exp (( -U 0 / RT )

(2.45)

where k is the destruction rate constant; k 0 is the pre-exponential factor, having the value of 10 12 –10 13 s –1 . For the mechanically stressed bodies, U 0 can be replaced with U(f U):

(

k = k0 exp -U ( f u ) / RT

)

(2.46)

In the case of reversible processes, mechanical stresses act only to decrease the energy barrier of thermal destruction. Pure mechanical fracture of chemical bonds, without any contribution of thermal fluctuations, is possible only when stresses exceed the resistance of the bond F o , acting for smaller periods than the oscillation period, i.e. 10 12 –10 13 s –1 . For a typical bond length of about 10 –10 µm, the rate of stress distribution is approximately the same as the speed of sound. This boundary case of pure mechanical fracture of chemical bonds happens only in very hard conditions, for instance, under the action of impact waves:

W=

10 -10 » 102 - 103 mm × s -1 10 -12 - 10 -13

(2.47)

The existence of stressed bonds on the main chain bonds, during polymer mechanical stressing, under a constant field of forces, was proved using IR spectroscopy [97–100], as Fig. 2.22 shows. It can be observed in this Figure that mechanical deformation changes the shape of the line at 975 cm –1 , corresponding to mac72

Mechanochemistry of Polymer Deformation

Figure 2.22. Modification of the absorption band from 975 cm –1 contour (a): 1) σ = 0; 2) σ = 65; and 3) σ = 80 kg/mm 2 , respectively, and the shape of the tensions on the chemical bonds (b), in the case of oriented polyethylene under load [92].

romolecule skeleton oscillation in uniaxially oriented polypropylene. Under loading, the position of the absorbance maximum is displaced only slightly, but the line contour is appreciably broader and displaced slightly towards higher wavelengths. These data indicate the permanent existence of a certain number of overstressed chemical bonds. In the case of uniaxially stressed polypropylene, the range of frequencies between 940 and 950 cm –1 is typical for the most deformed bonds. The distribution function of the external force on the chemical bonds that was obtained by analysing the shape of the absorbance curve at 84 kgf/mm 2 is depicted in Figure 2.22b. It is extremely asymmetric, being far extended towards the range of high tensions (value of maximal tension is about 1.000 kgf/mm 2 ). Therefore, the constant of the fracture rate increases with an increase of real stress, following an exponential growth (equation 2.46); splitting must practically develop only on the bonds loaded with the highest stresses. The scission of fragments/segments of a chain occurs homolytically through free radicals. Using RES spectroscopy, the free radicals have been directly identified during uniaxial stretching of some polymers or during cold stretching of fibres, respectively [22, 95, 101–107]. Low tensile stresses applied to some polyoxoamides-type fibres (I and II) at temperature are accompanied by red coloration of the sample. After removing the load the coloration disappears. This behaviour is related to the prior history of production of the fibres. Thus, when the fibres are obtained from very viscous melts, at the 73

Macromolecular Mechanochemistry

temperatures ranging from 200 to 300 °C, the effect is present. The red coloration during mechanical deformation of polyoxoamide fibres strongly depends on temperature and the presence of oxygen does not affect the colour. It can be noticed that after ‘coloration’ the fibres becomes insoluble in m-crezol [103].

NH

CH2

CH2 CH2 NH

CH2

O

O

C

C

n

Polyoxoamide I

NH

O

O

C

C

CH2 CH2 CH2 NH

n

Polyoxoamide II The specific macroradicals appeared after stretching of polyoxoamide fibres have been studied by ESR spectroscopy. P. Matties et al assumed the primary formation of mechanoexcited stages that subsequently undergo the following transformations [103]: 1) splitting of the main chain; 2) splitting of a hydrogen atom or of a pendant group; 3) splitting of an electron that is immobilised in the solid structure of the polymer, for instance, in the proximity of a carbonyl group. Depending on the external conditions, the radicals can be stabilised by different reactions. In the presence of air, at room temperature, a reaction characterised by an activation energy of about 9 kcal/mol was detected. This value was ascribed to oxygen diffusion into the bulk of the polyamide material, since the reaction between oxygen and macroradicals must occur spontaneously, without energy consumption. DeVries, Roglance, and Williams applied tensile stresses to various polymers, such as poly(methyl methacrylate), poly(vinyl chloride), polystyrene, and polyethylene, polyamide and polyester fibres. The investigated materials were processed by casting, extrusion, injection and spinning. The most unexpected result concerns the fibre behaviour as compared to other types of materials. Thus,

74

Mechanochemistry of Polymer Deformation

when the tensile stress was increased 10 times, the free radicals concentration was 10 17 µp/cm 3 with respect to the situation of all other materials, i.e. 10 11–13 µp/cm 3 . The smaller number of free radicals found in the samples obtained by casting, injection, or extrusion should be explained either by the presence of some impurities inside of these materials (residues of stabilisers) or structurally. The number of broken bonds along the fracture surface can be lower in the case when the crack during its propagation avoids the nodes that arose by chains coiling without producing their scission. Otherwise, fracture occurs with the highest probability on the directions that imply the lowest number of obstacles. This should be a possible explanation for the observed particular behaviour of highly oriented fibrous materials. A series of interesting phenomena were observed when stressing rubbers. Thus, during determination of the tensile stress for natural rubber, at 120 °C, a foaming phenomenon on the sample surface was observed [106]. Rubber without filling reagents was oriented by 100% stretching at room temperature; by cooling at –120 °C it was transferred into the vitreous (glassy) state and tensile stresses were measured at low strain rates (0.2 cm/s). After removing the load and gradual heating to the ambient temperature it was observed that its surface was rough and covered with bubbles which sometimes were noisy when bursting. After a certain number of hours, all traces of foam disappeared and small craters formed in the bulges. Using GC and mass spectroscopy techniques, it was established that the emitted gas is pure hydrogen. Andrews et al explained this phenomenon by mechanical splitting of macromolecular chains into free radicals. They react with neighbouring chains eliminating hydrogen that favours foam formation [108]. The authors eliminated the reticulation hypothesis; measuring the swelling degree and calculating M c (this represent the average molecular weight of the chain segment between two knots of the polymer network) from the Flory–Rehner equation, they proposed the following mechanism: H

H

H

CH3

C

C

C

C

H

H

•

•

CH2 + CH2

75

Macromolecular Mechanochemistry

•

CH2 +

•

2H

C

H

H

C

H

H

C

H

C

CH3

C

H

H

C

H

CH2

C

H

C

CH3

+

•

H

H2

According to this mechanism, a hydrogen atom is eliminated in every act of splitting. Considering that only one scission occurs in one fragment of the polyisoprene chain, fixed between two crosslinks, the fraction of the number of broken bonds, indirectly expressed by M c (which in this case decreases from 6650 to 4900) represents 35% of the total number of network chains. Therefore, into an orthogonal network only one third of the total number of macromolecular chains is loaded during the uniaxial stretching test. The variation of the foaming effect with the applied force and stress is illustrated in Figure 2.23 [108]. Thus, no foaming occurs until the point A and only in the range A–C a ‘fracture wave’, located on the main chain, traverses the sample giving rise to a small amount of hydrogen (0.48 cm 3 /g). From point C, the second stage of foam formation starts over a much wider stress range persisting several hours at room temperature. During this period,

Figure 2.23. Dependence of foaming effect by the applied stress and strain [108].

76

Mechanochemistry of Polymer Deformation

the whole sample surface is covered by thick strips of foam, the amount of released hydrogen attaining the value of 1 cm 3 /g. R. Natarajan and P.E. Reed extended this research from sulphur vulcanized to dicumylperoxide vulcanized polyisoprene rubber and polychloroprene rubber. The formed macroradicals were also investigated by ESR spectroscopy. The research area, comprising the basic characteristics of the investigated system, is presented in Figure 2.24 [109]. These investigations reveals three distinctive zones of the mechanical behaviour characterised by stress–strain curves. In the first zone, above 160 K, the material is ductile and its behaviour is similarly to that of other vitreous polymers. With decreasing temperature the load rapidly drops; this behaviour is associated with material destruction by necking. After that, a postflow process occurs, related to ‘cold’ stretching. No elimination of gaseous bubbles was observed during this period. The formation of free radicals was found to start on the postflow zone. They can be evidenced only by conducting the stretching test directly in the RES spectrophotometer; this proves their short lifetime. Below 160 K, the brittle behaviour is characteristic (curve A 1 in Figure 2.25) [109]. ESR spectra were taken at 110, 200, 220, and 270 K, respectively, for a mechanically stressed sample at 95 K. It was found that their shape does not change even by keeping the sample for two days at the liquid nitrogen temperature. In other words, at low temperatures the macroradicals are stable. By heating above 190 K as the temperature approaches the vitreous temperature, the peak intensity diminishes, disappearing at 270 K. The RES spec-

Figure 2.24. Characterisation of investigation area [109].

77

Macromolecular Mechanochemistry

Figure 2.25. Stress–strain curves [109].

trum taken at 110 K (Fig. 2.26) is highly asymmetric and composed of five lines corresponding to several types of radicals, as the following scheme illustrates:

:setart

H

CH3 H

H

CH3 H

C

C

C

C

H

C

H

H

CH3 H

H

H

CH3 H

H

C

C

C•

C

C

C

H

H

C

H

•

C

H

C H •C

H

CH3 H

H

H

CH3 H

H

C

C

C

C

C

H

H

C

C •

H

In the case of samples vulcanised with cumyl the stress–strain curves are similar but the shape of ESR curves is completely different [109]. The spectrum recorded below T g contains only one singlet that suggests a chemical reaction which occurred above the glassy transition when free rotation around the main chain easily occurs. Hydrogen is also eliminated, in measurable amounts, generating whitish zones that cover the sample. Macroradicals obtained by stretching the vulcanised polyisoprene with cumyl have also been evidenced using stable radicals, such as [110]:

78

Mechanochemistry of Polymer Deformation tBu

tBu

O

tBu

CH

OH

tBu

tBu

tBu

tBu

O

tBu

tBu •

CH

O

tBu

tBu

tBu

Hydrogalvinoxyl

Galvinoxyl

The first compound acts in the absence of oxygen, the second one in its presence. Free radicals formation corresponds to the stress relaxation period and they appear by the scission of a number of strongly tensioned chemical bonds. The second step is dominated by the fast consumption of the stable radicals. An important role was ascribed to the macromolecules’ excited states that are generated by double bond stretching and modification of the tetrahedral angle respectively: In the presence of oxygen and hydrogalvinoxyl the following sequence of reactions occurs: CH3 H

H

H

CH3

C

C

C

C

H

H

CH3 H

H

H

CH3

C

C

C

C

H

H

C

C

Force

CH3 H

H

H

CH3

C

C

C

C

H

H

tBu

+

O

C

tBu

tBu

CH

tBu

•

O

tBu

tBu (I)

H

CH3

C

C

C

H

H

CH3 H C

C

•

tBu

+

O

tBu

tBu

CH

tBu

tBu

tBu ( II )

79

OH

Macromolecular Mechanochemistry

CH3 C

CH3

CH3 CH

CH2 CH2

C

CH

CH3 C

CH

C

CH2 + O2

tBu

CH

CH2

•

OO +

O

CH3 C

C

CH

CH2

OO

•

•

CH2 + CH2

C

CH

CH2

CH3 •

CH3 C

CH2

CH3

CH

CH2

CH

tBu

tBu

CH

tBu

tBu

tBu

tBu

OOH + O

OH

( II )

tBu

tBu •

CH

tBu

•

O

tBu

tBu (I)

Figure 2.26. ESR spectrum recorded at 110 K for the natural rubber vulcanised with sulphur, stretched at 93 K [ 109 ].

When σ = constant, the radical formation rate is proportional to the rate of overtenstressed bond splitting and varies with applied stress according to the following equation [102]: 80

Mechanochemistry of Polymer Deformation

d [ R×] = B exp (bt ) dt where B and β are constants.

(2.48)

d [ R⋅] was found to be in good agreement with the rate of fracture dτ over a wide range of the variation of the external parameters (σ, T). 2.5.

KINETIC ASPECTS

Mechanochemical transformations differ from other physically initiated reactions by the fact that these reactions require low values of energy in the unit volume of the mechanically stressed material. Thus, by comparing with the photochemical processes, where the quantum energy is of the same order of magnitude with electronic excitation energy, or the case of the reactions occurring under the action of ionising radiation, when the available energy by far overtakes the bonding energy, the elastic energy is lower than bonding energy. We can conclude that the mechanochemical reactions occur as a consequence of a specific mechanism of mechanical energy concentration on the individual bonds or in small volumes. Apart from photochemistry, where the evaluation of the reaction rate is made taking into account the overall quantum yield or in radiochemistry where the rate of transformation is regarded as the change of reactants concentration due to the absorption of a specific amount of energy, in mechanochemistry the direct correlation between the reaction rate and mechanical energy is made onlu very rarely. There are many causes that explain this fact, such as: 1) difficulties in experimental measurement of absorbed energy; 2) evaluation of the actual stres that releases the chemical transformation is not possible; and 3) ignorance of the mechanochemical reaction that take place. The kinetics of the mechanochemical reactions covers two distinct cases: 1) the rate of the whole process, which is determined by the rate of the primary mechanochemical reaction; and 2) the limiting stage of the process, i.e. mechanical energy absorption. Thus, the fundamental kinetic criterion for distinguishing the mechanochemical reactions is the ratio between the rates of elastic energy absorption and the mechanochemical activated reaction, respectively [92]. 81

Macromolecular Mechanochemistry

The first case refers to material deformation in a constant field of forces. Under the action of constant load, the elastic energy is quickly absorbed; the stage of elastic deformation is well delimited in time, due to the subsequent chemical transformations that slowly occur. The mechanochemical reaction rate is governed by the rate of primary steps, which are initiated by induced elastic tensions. The value of the reaction rate constant depends on external parameters, in fact on the particularities of the elementary stage. The second case deals with material deformation in a variable field of forces. In this case, the rate of elastic energy absorption is by far lower than the rate of the reaction which is thus activated. This situation is realised in different cases of the fatigue process, during the milling of solid state polymers, in irradiation with ultrasound, the destruction of material surfaces by friction, etc. 2.5.1. Kinetics of the mechanochemical reactions in constant mechanical fields In this case, the typical process is that of uniaxial stretching under constant tension of polymer films or filaments (Fig. 2.27).

Figure 2.27. (a) Variation of force and free radicals variation in time for the fibers based on poly(p-hydroxyethoxy benzoic acid); (b) Variation of strain and free radicals variation in time for the fibers based on poly(p-hydroxyethoxy benzoic acid) [92]. 82

Mechanochemistry of Polymer Deformation

According to the kinetic concept of polymer resistance, material’s fracture occurs as a result of the splitting of stretched macromolecules [92, 111–113]. The rate of this process is described by the following equation:

1 1 v = = e −U 0 −γ σ / RT ≈ k τ τ0

(2.49)

where v is the rate of fracture; U 0 and γ are material’s constants determining its resistance properties; τ is the average lifetime of bonds; 1/τ 0 = ν 0 is the thermal oscillation frequency of groups of entities which are involved in the splitting and remaking of chemical bonds; k is the mechanocracking rate constant; σ is mechanical stress. If an ideal situation is assumed, when stresses are uniformly distributed in the whole stressed material (σ = constant), the number of chains supporting the load will decrease in time, in accordance with an exponential law:

N º N 0 exp [ - k t ]

(2.50)

where N is the number of chemical bonds at the moment t; N 0 is the number of initial chemical bonds; k is the mechano-cracking rate constant of the macromolecular chains; τ is material’s durability. Mechanocracking follows a first order kinetics. In its general form, the equation describing the rate of variation of N is:

dN / dt = - Nk( s , N ,T )

(2.51)

where k is the mechanocracking rate constant; σ is the stress tensor; T is temperature in Kelvins. If we accept that the decrease of polymer resistance under load occurs by splitting and remaking of certain chemical bonds, equation (2.52) may be written as:

dN / dt = - Nk0 + ( N 0 - N ) k r

(2.52)

where k 0 and k r are splitting and remaking rate constants of 83

Macromolecular Mechanochemistry

chemical bonds. Both of them are considered to be constant in time. Starting from the above-mentioned considerations as well as from the fact demonstrated here that the fracture process is controlled by the thermal–fluctuational fracture of chemical bonds, the process activated by the applied mechanical stress, the kinetic of scission accumulation can be described by a differential equation similar to a first order chemical reaction [114]:

- dN / dt = - N n1 + ( N 0 - N ) n 2

(2.53)

where ν 1 and ν 2 are the frequencies of splitting or remaking of chemical bonds, respectively. Using the notations: k = ν 1 + ν 2 and ϖ = Nν 2 , equation (2.51) becomes[73]:

dN / dt = kN + v

(2.54)

The frequency of splitting of chemical bonds is determined from the inverse value of durability given by Jurkov’s equation (2.49):

N = C exp - kT + v / k

(2.55)

where C is a constant which can be determined under the following boundary conditions: at t = 0; N = N 0 , so:

C = N0 - v / k and finally: N =  N 0 - v / k  exp( - kT ) + v / k

(2.56)

Analysing the last equation, it can be noted that the ratio ω/k has a physical sense, namely it represents the number of bonds N at a very long period of stressing (t → ∞). Using the notation N ∞ = ϖ/k, equation (2.56) becomes: N - N¥ = e - kT N0 - N ¥

(2.57)

In order to simplify the calculations, the uniform repartition of 84

Mechanochemistry of Polymer Deformation

the normal force component, on all chemical bonds of the stressed body (considered homogeneous), is assumed. In this way, the force fraction acting on each chemical bonds is σ i and taking σ ∞ = σ i N ∞ ; σ 0 = σ i N 0 ; σ max = σ i N, we obtain: s max - s¥ = e - kT s o - s¥

(2.58)

where σ max is the stress at which fracture occurs. Both σ max and σ 0 are experimentally determined (σ max is the limit of material resistance, i.e. the value toward which the material resistance asymptotically tends in the conditions of unlimited increase of deformation rate or of applied load). The ratio: N - N¥ s max - s ¥ = =N so - s ¥ N0 - N ¥

(2.59)

signifies the number of active bonds, which are, at a given moment of the process, under load. In these conditions, Jurkov’s equation may be written as: æ s - s¥ ö t = ln ç 0 t 0 exp U 0 - gs / kT  è s max - s ¥ ø÷

(2.60)

Introduction of this factor infirms the assertion of ‘spontaneous destruction of the body’ that could formally appear when in above equation σ = 0. Reanalysing equation (2.50), one can see that catastrophic destruction of the sample starts when is fulfilled the condition, kτ ≈ 1. The period to sample fracture (durability) is given by the relation, τ = 1/k. In other words, the period until to the fracture of the sample coincides with the required period for mechanocracking of stretched bonds. Furthermore, the durability determination under different loading conditions (medium, temperature, and applied tension), in principle, allows clarifying the nature of the primary mechanochemical step. For instance, in the case of thermoplastic elastomers such as linear polyurethanes, i.e. an urethanic polyester based on 4,4’diphenyl methane diisocyanate, working at different temperatures 85

Macromolecular Mechanochemistry

a family of straight lines, with different slopes, have been obtained (Figure 2.28) [115]. The investigated temperature range was between 323 and 238 K. It may be noted that in the range of positive temperatures, T = 0–50 °C, polyurethane film fracture occurs at relatively low forces, ranging from 10 to 40 MPa. Fracture is preceded by a considerable strain. In this temperature range, the fracture is mainly ductile. In turn, at the temperatures near the vitreous temperature, T g , i.e. –37 °C (lines 7 and 8 in Figure 2.28), when the macromolecules almost completely lost their mobility, fracture becomes brittle. In this case, the unitary force, required for polymer fracture, is higher and the line slope is close to 90 °. Based on the experimental data and considering τ 0 = 10 14 s [116], the values of the constants U 0 and γ have been calculated and collected in Table 2.1 [115]. It can be seen that the value of γ, given by the line slope, constantly increases from 5 844.803 × 10 –10 m 3 mol –1 (at T = 323 K) to 18 430.856 × 10 –6 m 3 mol –1 (T = 233 K) when the straight line becomes almost vertical (tan α = 84°) [117]. The values of U 0 are also lower as compared with the characteristic values of some semicrystalline polymers stressed in the same conditions, such as: high density polyethylene (HDPE), low

Figure 2.28. Curves log τ vs. σ for different temperatures in the case of uniaxial tensile stress under creep conditions, of a thermoplastic polyurethane elastomer: 1) 323 K; 2) 313 K; 3) 303 K; 4) 293 K; 5) 273 K; 6) 268 K; 7) 238 K; 8) 233 K [ 115 ].

86

Mechanochemistry of Polymer Deformation Table 2.1. Values of U 0 and γ calculated from the experimental data for the polyurethane elastomer based on 4,4’-diphenyl diisocyantate, at different temperatures [115] Temperature (K) 323 313 303 293 273 268 238 233

γ 10-6 (m3.mol1) 5050.526 5844.803 6921.266 8495.337 10 687.201 12 636.473 14 079.390 18 430.856

U0 (kJ.mol-1) 94.746 92.892 92.245 92.847 93.304 95.239 96.608 100.825

density polyethylene (LDPE), polypropylene (PP), and oriented polyamide-6 (PA-6) whose corresponding values of U 0 are 113, 117, 125 [117], and 184 kJ/mol [118], respectively. Most likely, in the case of a thermoplastic polyurethane elastomer scission occurs to the C-heteroatom bonds, which are characterised by lower dissociation energy than the energy corresponding to the C–C bonds from polyolefins bonds. The values of U 0 (see Table 2) clearly evidence that with a decrease of temperature below 0 °C, the energy barrier of mechanocracking release increases, mainly due to the rigidity of the macromolecular chains and, consequently, to the increase of mechanical resistance [120]. On the other hand, a slightly increase of U 0 is observed for temperatures higher than 40 °C. This behaviour is related to thermal plasticizing of the polyurethane elastomer. This process firstly occurs by the scission of intercatenary physical bonds, which requires higher forces to overcome the energy barrier than the energy required for splitting the covalent bond from the main chains. Stressing the same polymer film under creep conditions and at constant temperature (20 °C) in different gaseous media, inert or active, durability–stress kinetic curves presented in Figure 2.29 were obtained [119]. When the experiment was carried out in an electron acceptor medium (in the presence of NO), curve 1, sample fracture occurs at lower values of the applied force than in air, curve 2. It appears that NO favours the fracture, blocking the radical active centres and, in this way, impeding the recombination of free radicals that appeared by homolytic scission of the chemical bond from the main chain. The same result is also obtained in the presence of air, when the oxygen present in the air plays the role of the radical accep87

Macromolecular Mechanochemistry

Figure 2.29. Curves log τ vs. σ for different gaseous media in the case of thermoplastic polyurethane elastomer: 1) NO; 2) air; 3) vacuum; 4) nitrogen [115].

tor. In inert media (vacuum or nitrogen) fracture starts at lower forces and the durability of the sample increases for the same unitary stress [115]. Equation (2.50) establishes the relation between the durability and the mechanocracking rate constant of chemical bonds. A rigorous kinetic equation has to take into account the multiple aspects of the phenomenon, such as material’s structural inhomogeneity and the shape of the function of stress distribution in its volume, the dependence of the mechanocracking rate constant on the average degree of polymerization, stress values acting in side radical reaction and the probability of chained destruction. Investigation of the activation process, mechanocracking and bonds remaking in the case of mechanically stressed polymers shows that the increase of temperature, which is accompanied by an increase of the kinetic energy of structural units from the chain, determines the decrease of the number of intermolecular bonds bearing the mechanical load. In Figure 2.30 the relation between durability (τ ≈ 1/k) and temperature is illustrated. Clearly, for any material, in a wide range of temperature and stress σ, the function τ = f(T, σ) is in good agreement with Jurkov’s relation: 88

Mechanochemistry of Polymer Deformation

Figure 2.30. Dependence of tensile strength with temperature and time [112]: I – sodium chloride, 1) 400 °C; 2) 500 °C; 3) 600 °C; II – polycrystalline aluminium, 1) 18 °C; 2) 100 °C; 3) 180 °C; III – polyamide fiber (Capron), 1) – 180 °C; 2) –120 °C; 3) –75 °C; 4) +20 °C; 5) +80 °C.

t = t0 exp (U 0 - gs / RT )

(2.61)

where R = 8.314 J mol –1 K –1 ; τ 0 = 10 –12 –10 –14 s; U 0 and γ are material constants. γ is related to the sample nature and prehistory and is termed the structural factor. It characterises the degree of concentration degree of the stress in the chain. Table 2.2 gives the calculations of U 0 obtained measuring the durability at σ = constant. The Table also contains the data concerning values of the sublimation energy of metals (E), as well as the activation energy of thermal destruction for some polymers. Figure 2.31 illustrates the graphical method used for the determination of U 0 . It can be noted that U 0 has the same order of magnitude as the chemical bond energy. The good agreement between τ 0 and U 0 , on the one side, and the molecular constants, on the other side, once again confirms that the kinetic parameters of the mechanochemical processes under the effect of a constant mechanical field are governed by the particularities of the primary chemical reaction. Jurkov’s equation shows that the time τ required for polymer deformation and fracture results from the direct competition between the induced effects by thermal motion, defined by RT, and the energetic barrier U. Thermal motion tends to split the chemical bonds and the energetic barrier expresses the strength of the 89

Macromolecular Mechanochemistry Table 2.2. Comparison of the value of U 0 with the heat of sublimation of metals and activation energy of thermal destruction of polymers [112] Substance

U0 (kcal/m ol)

E (kcal/m ol)

120 100 81 53 30 68 75 56 45 35

127 97 80 55 31 76 58 43 32

Platinum Iron C opper A lum inium Zinc Sodium chloride Poly(tetrafluoroethylene) Polypropylene Polyam ide (C apron) Poly(vinyl chloride)

Figure 2.31. Dependence of the effective energetic barrier U = RT . ln τ/τ 0 on tensile strength [112]: 1) sodium chloride; 2) polycrystalline aluminium; 3) polycrystalline platinum; 4) Capron fiber.

chemical bonds:

U = U 0 - gs

(2.62)

The role of mechanical stresses is to create the field of forces able to decrease the maximal energetic barrier U 0 . The efficiency of mechanical field action depends on the physical state of the material characterised by the structural factor γ. Experiments confirm that equation (2.61) has been rigorously verified for a series of polymers with different chemical structures. However, the same deviations from linearity have been observed. Thus, in the case of irreversible deformation, the rate of 90

Mechanochemistry of Polymer Deformation

mechanocracking of the bonds determines the rate of the irreversible deformation process. This rate, in turn, is conditioned by the faults and cracks growth rate. For certain polymers, the rate of irreversible deformation, v, depends on the stretching rate, v 1 , according to the following relation:

v = Av1n

(2.63)

where A is the rate of deformation redistribution under tension; n is a parameter that depends on the fault dimensions and polymer relaxation properties. Under stationary conditions v 1 = constant, the ultimate strength is strongly related to the crack propagation rate v by the equation:

(

s r = kv exp U 0' - abg / RT

)

(2.64)

where U′0 is the fracture activation energy; α is the elementary volume of fracture; β is the stress coefficient. When α, β and U′0 depend on T and v, the functions σ r = f(1/ T) and α r = ϕ (ln v) must be linear. For the majority of polymers there is a range within which α and β depend on T and v. Analysis of the durability dependence on time and temperature shows that the structural parameter γ might be related to T and v also following a Jurkov-type relation. However, equations (2.61) and (2.64) are not identical. These equations show that, depending on the deformation regime (τ = constant or γ = constant), reorganisation of the polymer structure follows different paths. In these cases, the process is characterised by different values of the activation energy and of kinetic events, which are involved in the primary stage of fracture. When the polymer structure does not change until fracture, the parameters from equation (2.61) remain constants allowing a rigorous and relatively simple determination of the values of U 0 and τ 0 . When some conformational changes take place during deformation, the parameters from Jurkov’s equation are established as functions of T, v, and σ r . In this case, the additional use of the functions U 0 = f(σ r , T), γ = f ′ (σ r , T) and τ 0 = f′′ (σ r , T) is required. Parameters U 0 and U 0 ′ from the two equations were compared with each other using the activation energies that characterise dif-

91

Macromolecular Mechanochemistry

ferent types of destruction (thermal, mechanical, etc.). It can be concluded that the activation energy U 0 has not only the simple meaning of the activation energy of chemical bond splitting but it must be regarded as the maximum energy required for fracture activation and reorganisation of the whole structure of the investigated specimen. During deformation and fracture processes both the physical and chemical structure undergo important changes. The initial molecular and supramolecular structure of the polymer as well as the conditions of its final reorganisation, i.e. temperature, strain rate, etc., determine the different polymer capacity to counteract fracture, in other words, determine their mechanical resistance [120]. Jurkov and co-workers have used the IR-spectroscopy that allows establishing the concentration of final functional groups which appear by stabilisation reactions of the macroradicals formed by mechanocracking. The dependence of the concentration of the final functional groups on the loading time is illustrated in Figure 2.32. Quantitative analysis of the curves in this Figure, for instance in the case of high-density polyethylene and polypropylene, suggests that these curves are most adequately described by a first order kinetic equation:

Figure 2.32. Time dependence of the end-groups concentration for low-density polyethylene stressed: at room temperature (a): 1) σ = 20 kgf/mm 2 ; 2) σ = 23 kgf/ mm 2 ; 3) σ = 20 kgf/mm 2 ; and at constant stress, σ = 20 kgf/mm 2 , (b): 1) 340 K; 2) 319 K; 3) 293 K [121]. 92

Mechanochemistry of Polymer Deformation

dc / dt = k ( c* - ct )

(2.65)

where c t and c * are functional groups concentrations at time t and t → ∞, respectively; k is the constant of the final functional groups generation rate. By integrating equation (2.65), the dependence of the final functional groups concentration on loading time is obtained: ct = c* (1 - exp { - kt } )

(2.66)

It was established that c * can be considered as constant and the dependence of the rate constant on temperature, at σ = constant, can be deduced from Arrhenius’s relation (Figure 2.33). As expected, the applied stress changes the slope of straight lines suggesting modification of activation energy E *. The activation energy decreases proportionally with increasing stress and, consequently, the functional groups form more easily. The dependence of activation energy on stress is expressed by a linear equation:

E* = E A - as

(2.67)

and by its substitution in Arrhenius’s equation, the constant k can be determined:

{

k = k0 exp - ( E A - as ) / RT

}

(2.68)

The value of these studies is manifested in the possibility of

Figure 2.33. Dependence of rate constant k (a): 1) 223 K; 2) 239 K; 3) 340 K and of end-group concentration at room temperature (b) on applied stress [121].

93

Macromolecular Mechanochemistry

making a correlation between easily determined kinetic parameters with the behaviour of polymers, under the stress conditions, expressed as the durability:

{

t = (1/ k0 ) exp ( E A - as ) / RT

}

(2.69)

and the ultimate tensile strength:

s r = ( E A / a ) [1 - ( RT / E A ) / ln kt ]

(2.70)

Analysis of equations (2.69) and (2.70) also leads to the conclusion that mechanical fracture is in its essence a thermally activated mechanocracking process. In the first step, the main role of the mechanical stress is to distort the interatomic bonds that has as a consequence a decrease of activation energy of chemical bond splitting from U 0 to U * = U 0 –γσ. By increasing the stress concentration on chemical bonds the probability of polymer fracture under load also increases and its durability and mechanical resistance decrease. Another kinetic equation has been derived by Manelis [122]. The author also starts from the hypothesis of the reversibility of the fracture process, considering that in addition to the mechanocracking rate of chemical bonds the recombination rate of these bonds must also be considered. Supposing that the recombination rate does not depend on stress, the variation rate of the broken bonds concentration will be described by the equation: é ù as dN / dt = k1 exp ê ú f1 ( N ) - k2 f 2 ( N ) ëê RT (1 - N / N p ) ûú

(2.71)

where N is the concentration of bonds at the moment t; N p is the concentration of broken bonds; α is the activation volume of fracture; σ/(1 – N/N p ) is the actual stress at the chemical bond level; k 1 is a constant of the mechanocracking rate; k 2 is a constant of bonds remaking; f 1(N) is the mechanocracking kinetic law; f 2 (N) is the kinetic law of restoration of chemical bonds. The first term in the righthand member of equation (2.71) describes the mechanocracking rate and the second one the remaking rate of the chemical bonds. Making the substitution π = N/N p 94

Mechanochemistry of Polymer Deformation

(the increase of the degree of mechanocracking), equation (2.71) becomes:

dp 1 æ m ö F (p) × = exp ç è 1 - p ÷ø f1 ( p ) d t d

(2.72)

where µ = αγ/RT is a parameter characterising the mechanical m2 −m1

field; δ = ( k1 / k2 )

N p is a parameter defining the correlation

between the constant of mechanocracking and remaking rates of − chemical bonds; m 1 and m 2 are reaction orders; τ = k1 N ( 1 ) is the measured period; F(π) = f 2 (π)/f 1 (π). Term π represents, in fact, the concentration of the broken bonds which, for a stationary regime, i.e. mechanocracking rate = chemical bonds restoration rate, can be calculated solving the following equation: m 1t

exp (m /1 - p st ) = F pd

(2.73)

where π st is the stationary concentration of broken bonds that must be calculated. Starting from Jurkov’s equation and taking into account the parameters of thermal degradation (E – activation energy; k – thermal degradation rate constant), Ratner established a relation between U 0 , γ and t 0 . The author considered that polymer thermal degradation occur in two steps – the first one related to splitting of secondary bonds and second one associated with the splitting of the covalent bonds (–C–C–) from the main chain. The characteristic parameters of the above-mentioned steps are k 1 , E 1 and k 2 , E 2 , respectively. Calculations show that mechanodegradation depends on k 2 and E 2 not being affected by k 1 and E 1 . It was also found that U 0 (mechanocracking activation energy) is equal to E 2 . In turn, the values of parameters γ and τ 0 are not affected by the kinetic parameters of thermal degradation (γ depends on the polymer structure and loading time, τ 0 – is the same for all investigated polymers) [123]. Starting from Jurkov’s studies, in his theoretical research concerning fibre fracture, Bartenev proposed the following equation for calculating durability [124–127]:

95

Macromolecular Mechanochemistry

ìU - vb(0) ü L - lk t ( s ,T ) = j ( s ,T ) exp í ý+ (2.74) kT vk î þ where ϕ(σ, T) is the preexponential factor (σ and T slightly influence the value of ϕ as compared to the influence of the preexponential term the above equation. Thus, ϕ is practically constant in the whole investigated range); ω = λλ π λ m is the microvolume within which the thermal fluctuation splitting of chemical bonds occurs (λ is the elementary path covered by the crack top at each fluctuation that leads to the splitting of the chemical bond; λ π is the elementary circumference of the fracture front consisting of many chemical bonds; λ m is the length of the chemical bond just before its scission); β (0) is the coefficient of stress concentration; L is the sample breadth; l k is the crack critical length at the moment of passing from the thermalfluctuation mechanism of fracture to the isothermal one, when the rate of crack propagation becomes constant. In equation (2.74) the first term describes the thermal-fluctuation stage of fracture and the second one the isothermal stage, respectively. The theory introduces the notions of limit stress for crack initiation (σ 0 ) and critical stress (σ cr ), which have been confirmed in practice [128, 129]. In the range of low stresses, for the brittle state that is characterised by small deformations, a deviation of the function log τ (σ) from linearity was found. Durability increases asymptotically tending to the vertical line σ = σ 0 . For high stresses, (σ > σ cr ) a tendency was observed to reach a limiting value of σ cr ≈10 –6 s (for L = 1 cm). This behaviour is related to the establishment of the maximum crack growth rate, v cr , as is depicted in Figure 2.34. Starting from this general equation, Bartenev developed a general theory of durability, the so called complete isotherm of polymer fibre durability, which was subsequently verified on many specific examples. The fundamental element of the supramolecular structure of the fibres is the microfibril with a diameter of about 100–200 Å diameter. Microfibrils are composed from parallel disposed macromolecular chains and their most important inhomogeneity is the amorphous–crystalline border. During uniaxial stretching of fibres, with stress σ, the amorphous zones are the first to be overstressed. Here, some discontinuities appear, thus generating the nucleus of a sub-micron crack. This crack has usually a disk-like shape (penny-shaped crack), perpendicularly to the direction of the force which causes brittle fracture of the material. 96

Mechanochemistry of Polymer Deformation

Figure 2.34. Durability’s isotherm for an amorphous polymer [120].

Overstress σ * appears in the crack proximity that is able to activate the scission of a chemical bond. According to the thermal fluctuation theory, the following relation describes the crack fracture rate: æ U - vs *0 ö év * * ù vl ,s ,T  = 2k un 0 exp ç ÷ sinh ê kT s - s 0 ú kT ë û è ø

(

)

(2.75)

where ν 0 is the thermal oscillations frequency which causes the splitting and restoration of chemical bonds (υ 0 ≈ 10 13 s –1 ); σ* is the overstress in the microvolume ϖ and σ 0* is the limiting stress in the microvolume ϖ (σ 0 * = αλ/λ m ). For a microcrack with a disk-like shape, having axial symmetry, within a sample stretched in the direction of its axis with constant force, the overstress can be calculated using the following equation:

s* = b (r0 ) s r / r0

(2.76)

where r(t) is the crack radius at the moment t; r 0 is the initial radius; β( r0 ) = 0.5 r0 x is the coefficient of stress concentration in the crack proximity. Knowing that the critical stress is given by the 97

Macromolecular Mechanochemistry

equation: s cr =

U vb0

(2.77)

finally, we obtain:

ì æ U ö é ù ï 2 l 0 exp çè - RT + as 0 ÷ø sinh ë a s r / r0 - s 0 û vs ,r ,T  = í ïv î cr





for s 0 £ s £ s cr for s 0 ³ s cr

(2.78) The durability of the fibre, considering that the fibre radius is r, stretched with tensile stress σ ranging from σ 0 to σ cr is expressed by the relationship: t = t0

rct

dr

0

vs ,r ,T 

òr

+

R - t cr vcr

(2.79)

where the second terms give the isothermal contribution to the fracture. Integrating, we obtain: æ U - vb0s ö R - t cr t = t j + t cr = j ( s, T ) exp ç ÷+ kT vcr è ø

ì 2 r0 f 0 ï ln as ï 0 j ( s, T ) = í ï0 ïî f0 =

¥

(2.80)

s 0 £ s £ s cr s ³ s cr

(2.81)

1

å 2n + 1 exp éë -2na (s - s0 )ùû

n =0

(2.82)

Decreasing the applied stress σ → σ 0 and f → ∞. Consequently, the function τ(σ) asymptotically tends to the axis σ = σ 0 . In the range of higher stresses, σ > σ 0 and f 0 ≈ 1. The influence of the preexponential factor is negligible as compared with the contribu98

Mechanochemistry of Polymer Deformation

tion of the exponential factor. In practice, the function τ(σ) is linear in this stress range which corresponds to the usual range of durability, i.e. from 10 –3 to 10 8 s. In this range, the durability can be calculated using the equation: t = tj =

æ U - vb0 s ö 2 r0 exp ç ÷ kT ln 0as è ø

(2.83)

Concomitantly with the increase of σ, (σ ϕ →σ cr ) and the second term from equations (2.82) and (2.83) begins to have an essential contribution. In this case, the critical durability, τ cr, is given by the relation: t cr =

R - rcr R - 4lb0 = vcr vcr

(2.84)

or, in other words, in this stress range the function τ(σ) runs parallel to the abscissa. Taking into account that fracture activation energy, U, depends on temperature, two distinct situations must be considered – namely: a) for σ 0 < σ < σ cr t=

U 0 - vb0s R - t 2 r0 f 0 exp ( - q / k ) cr + exp ln 0as kT vcr

(2.85)

b) for σ > σ cr t cr

R - 4 l éb  0  ù ë û = vcr

2

(2.86)

Equation (2.85) describes efficiently a series of experimentally established cases concerning the dependence of fibre durability on temperature in the stress range from σ 0 to σ cr , when f 0 _ 1. Equation (2.86) was also verified in practice; molecular and structural significance of the terms in this equation is given below:

t0 = j ( s, T ) exp ( - q / k ) ;

g = vb0

(2.87)

The validity of the durability isotherm in the case of polymer fibres 99

Macromolecular Mechanochemistry

was proved for many concrete cases, such as: polyamides [130], polypropylene [131], polyethylene [132], cellulose triacetate [133, 134] at different temperatures. In the case of oriented polyamide-6, the distance between adjacent chains, theoretically calculated, is the same with intermolecular distance (4 Å), when all chains are oriented in the same direction with the fibre axis. Thus, λ = λ 0 = 4 Å. The value of λ m is of the same order with the length of C–C bonds, i.e. approximately 1.5 Å. Computing the above data for the oriented fibres, we obtain a thermal-fluctuation volume, ϖ, equal to 2.4·10 –23 mm 3 . The initial crack radius can be calculated using the relation r 0 = 4λβ (0) , where β (0) was experimentally determined. The fibre diameter was 2 µm and the crack growth rate was 800 m/s. Finally, the limiting and critical stresses were calculated. All these parameters, corresponding to four types of fibres, are collected in Table 2.3. The curve representing the durability isotherm has a distinctive shape, but in accordance with the theoretical equation, is very illustrative being the curve obtained for polyamide-6 fibres, Figure 2.35. Four distinct domains can be distinguished, namely: 1) σ < σ 0 – domain of brittle fracture; 2) σ 0 < σ < σ ϕ – domain of thermalfluctuation fracture; 3) σ ϕ < σ < σ cr – domain of transition in which the isothermal mechanism prevails; 4) σ < σ cr – domain of the isothermal mechanism of fracture. The interval from σ 0 to σ strictly delimits the range of their judicious exploitation which is determined by durability. Concomitantly with the increase of temperature this range becomes narrower but the range σ ϕ –σ cr , where the isothermal mechanism of fracture is dominant, increases. Very important is the knowledge of the influence of macromolecule orientation on the parameters of the durability equation [132]. It was demonstrated that the value of γ depends on the polymer orientation degree, its change meaning the modification of fibre rigidity. Taking ω = 2.4×10 –20 mm 3, we obtain β = 7.6. This value is close enough to the characteristic ones for oriented polyamide fibres β (0) = 9. Comparatively, for unoriented fibres ωβ (0) = 1.3× 10 –18 mm 3 , thus β (0) = 9.3 is close to the value β (0) = 10 found for the vitreous polyamide [135]. Apart from U 0 which is not affected by the fibre orientation, γ is slightly influenced by orientation. Experimental values of critical stress β (0)cr = U 0 /γg = 25 kg/mm 2 and 173 kg/mm 2 were obtained in 100

Mechanochemistry of Polymer Deformation Table 2.3 Durability parameters for some polymer fibres [128]

Parameter U0 (kcal/mol) γ = ωβ(0) (mm3) β l0 (cm) αλ (erg/cm2) σ cr(0 ) (kgf/mm 2 )

Polyethylene 26 1.44 x 10-19 6 6 x 10-6 35 140

Type of fibre Polypropylene Polyamide-6 30 9.60 x 10-20 4 3 x 10-6 30 222

45 1.81 x 10-19 7.5 4 x 10-5 45 170

Cellulose triacetate 45 8.30 x 10-19 35 3 x 10-4 40 38

Figure 2.35. Durability isotherm of polyamide-6 [128]: (a) T = 163 °C; (b) T = 291 °C [128].

the case of non-oriented and oriented fibres, respectively (from the durability equation, the calculated values for the two types of fibres are 30 and 189 kg/mm 2 , respectively). It is clear that the breaking limit increases with orientation, concomitantly with the decrease of γ that is in fact determined by the decrease of β (0) . 2.6. MECHANOCHEMISTRY OF POLYMER DEFORMATION UNDER CREEP CONDITIONS Under mechanical stressing the polymers show a viscoelastic behaviour that is characterised by creep and relaxation phenomena. Creep means here the continuous increase of deformation in time, under the action of constant stress. Relaxation is defined as the stress decrease in time, keeping the strain constant [54]. Therefore, the creep represents a manifestation of polymer material viscoelasticity being strongly related to the stress and temperature. 101

Macromolecular Mechanochemistry

Apart from metals, in the case of polymers creep may even occur at room temperature. Normally, in unloading creep must cease and the stressed body tends to regain its initial shape. Practically, creep accompanies all simple stresses but the most investigated case is that of the uniaxial tensile stress. Creep tests consist of maintaining the sample in the stressed state, at constant temperature, continuously measuring the deformation and period until the sample fractures. This period is called durability [115]. The test is usually carried out using simple devices, by loading the investigated sample with calibrated loads and continuous measurement of the time dependence of strain. The stress is axially and instantaneously applied avoiding any shock. In the case of uniaxial tensile stress, a typical experimental creep curve shows four distinct zones: 1) zone of elastic deformation, instantaneous (OA); 2) zone of primary or retarded creep (AB); 3) zone of secondary or stabilised creep (BC); and 4) zone of tertiary or accelerated creep, when the creep rate increases up to fracture (CD), Figure 2.36 [111]. By removing the load, for instance, at point E, reverse creep occurs, firstly almost instantaneously place (EF) followed by its delayed return (FG). The creep phenomenon may have the following consequences: 1) sample fracture occurs almost instantaneously after applying the stress; 2) the sample fractures occurs after a certain period; and 3) the sample withstands the applied load for an indefinite period. The molecular mechanism of creep, the equations describing this process, and the adopted models have been studied in detail and are well known [54]. The studies dealing with the mechanochemical aspects of this process, irrespective of the physical state of the investigated polymers [54, 112–124], are less numerous,

Figure 2.36. Typical creep curve of uniaxially stretched polymers [115]. 102

Mechanochemistry of Polymer Deformation

especially for linear amorphous polymers at temperatures below T g . Among these one might note the studies concerning poly(vinyl chloride) (PVC) [136, 136–139]. Creep of PVC was studied to obtain the creep equations, to clarify the character of fracture as well as the change of some physical–chemical properties induced by stress. Mechanical stress was applied in an original testing stand (see Ref. 136) at stress values ranging between 100 to 400 daN/ cm 2 , at the environment temperature and humidity. The experimental rheologic curves have the typical shape of the creeping curves, emphasising the viscoelastic behaviour of the material (Figure 2.37), i.e., elasticity, creep, and reverse creep. Consequently, the suggested rheological model is a variant of the Burgers model. The elasticity of the material due to a change in the atom position and valence angle in macromolecules (Figure 2.38) is expressed by the E 1 spring. The viscoelasticity expressed by the retarded elasticity is conveyed by the Voight’s generalised model where the springs E 2k express the modification of macromolecule deformation while the piston cylinders λ 2k express the reaction of the environment. The element λ 3 characterises the motion of the macromolecule segments provoked by the shape changes but especially by the destruction of some chemical bonds which leads to the appearance of irreversible viscous deformation. The processing of the experimental results allowed the computation of the coefficients and exponents from the rheological equation corresponding to the proposed model; thus, for the studied case the equation has the form:

Figure 2.37. Experimental (full line) and theoretical creep curves (dotted line): 1) σ = 105; 2) 193; 3) 249; 4) 364; and 5) 400 daN/cm 2 , respectively [136]. 103

Macromolecular Mechanochemistry

Figure 2.38. Rheological model of PVC [136]. t × ) + s1.63 ù e(%) = 10-4 é0.5 × s1.83 + 10s(1 - e -510 ëê ûú -6

(2.88)

A good correlation between the theoretical equation (dotted line) and the experimental creeping curve has been demonstrated (Figure 2.37), thereby confirming that the proposed rheological model is the proper one. Similarly, creep equations have been derived for the polymer modified with benzidine or subjected to accelerated ageing under the action of high temperature and UV rays. These equations have the following form which also demonstrates a good correlation with the experimental creep curves, specifically for: 1. The benzidine-modified PVC

(

)

é1 1 ö 1.65 ù × -6 æ e ( % ) = 10-4 ê lg (1 + s ) + s 1 - e - t / 310 çè 0.5 + ÷ø + 0.01256s ú 6 t × 10 + 1 ë2 û (2.89) 2. Heat-treated PVC for 150 h at 70 0 C

(

) (

)

e ( % ) = 5 ×10-4 é s 0.31 + 2s -0.058 × th 2 × 10-5 × t + 2 0.3 + 0.8 ×10-7 t ù (2.90) ë û 3. PVC subjected to heating (above-mentioned conditions) combined with UV-ray treatment

104

Mechanochemistry of Polymer Deformation

(

) (

)

e ( % ) = 5 × 10-4 é s 0.29 + 2s -0.087th 2 × 10-5 t + 2 0.3 + 0.8 × 10-7 t ù (2.91) ë û 4. Benzidine-modified PVC subjected to the combined action of heat and UV rays

(

) (

)

e ( % ) = 5 ×10-4 é s 0.25 + 2 s 0.186th 2 × 10-5 t + 2 0.3 + 8 ×10-7 t ù (2.92) ë û PVC modification by two-roll processing in the presence of benzidine results in structure strengthening manifested at the level of the physico–chemical properties, namely, the reduction of the values of the instantaneous elastic deformation and of residual deformation, respectively, for the same stress. The process of polymer ageing acts similarly, being caused by heating and especially by the simultaneous action of heat and UV rays. Both the witness polymer and polymers modified chemically or by physical treatment undergo important changes during creep which affect their structure at all its organising levels. The first effect of the stress action is the partial shape change of the macromolecules in their elongation and orientation, which lead to an increase of the polymer packing degree and to the adequate modification of some physical properties. Thus, the material density increased as a result of stress intensification at the same stress duration (Figure 2.39). Accordingly, the behaviour in specific swelling agents (acetone, toluene) is also affected. The increase of the packing degree of the stressed macromolecules leads to intensification of the interactions between them. Consequently, the swelling agent penetrates with more difficulty in the polymer while the maximum swelling degree and the swelling constant rate, respectively, are reduced with the applied stress. This phenomenon has been observed for all studied PVC types, represented by benzidine-modified PVC in Figure 2.40. The mechanical energy absorbed by the polymer, concentrated in the fault zones of the structure, is consumed almost to the extent of deformation of both the chemical bonds and the valence angles, so that the polymer passes into the mechanoexcited state. During stress relaxation, part of the accumulated elastic energy is used up for the homolytical splitting of the chemical bonds and for the formation of free radicals which, by stabilisation, lead to the

105

Macromolecular Mechanochemistry

Figure 2.39. Variation of density with applied stress [136].

Figure 2.40. Maximum swelling degree – static tensile stress profiles for PVC modified with benzidine (1) and swelling constant rate – static tensile stress profiles (2), [139].

accumulation of some reduced molecular weight fractions; therefore, the polymer solubility in specific solvents must increase, an effect evidenced in Figure 2.41. The lower solubility of benzidine-modified PVC compared to that of the unmodified one is the result of some crosslinking reactions produced during synthesis [114, 115, 117, 120]. However, this solubility has superior values in the mechanically stressed polymer due to the reduction of the molecular weight caused by the mechanochemical degradation reaction induced by the stress (curve 2 compared with curve 3). The prolonged action of stress (even lower than that required for fracture) causes polymer fracture. To provide information on the 106

Mechanochemistry of Polymer Deformation

Figure 2.41. Variation of dissolved polymer amount with time: 1) PVC blank sample; 2) PVC modified with benzidine, stressed (σ = 25.3 N/mm 2 ); 3) PVC modified with benzidine (unstressed), [139].

fracture type of this rigid material, some samples were subjected to a stress of σ = 400 daN/cm 2 . Macroscopic fracture took place after 70 to 80 h and the fracture surfaces were analyzed by electron microscopy (Figure 2.42 a–c). Their marked relief leads to the conclusion that the material response to mechanical stress is of brittle type. A careful analysis also shows stages of the mechanochemical process up to the sample fracture. Thus, the splitting of the chemical bonds takes place in microvolumes which become destructive centers. Under the combined action of stress, thermal fluctuations, and mechanoradicals generated in the incipient stages, splitting of a large number of bonds in microvolumes leads to the appearance of a discontinuity in the material (i.e., the microcrack, obvious if we analyze Figure 2.42 a). The microcracks continually grow, either by macromolecule splitting or by coalescence, up to some critical dimensions. In this stage, the stress values are below those of the breaking one, so that the relaxation times are comparable with the stressing time. Consequently, the macromolecules can be rearranged under stress so that the relief of the fracture surfaces is less marked. The appearance of the main crack is the first stage of macroscopic fracture. Because the stress is lower than the one required for macroscopic fracture, the main crack propagates slowly through the sample, making new surfaces with a relatively coarse aspect. The stored elastic energy is partially dissipated in the material by inelastic strains which do not imply the splitting of the 107

Macromolecular Mechanochemistry

Figure 2.42. Microphotographs of the fracture surfaces of modified PVC with benzidine (σ = 45 N/mm 2 , 75 hours, ×9900), [139].

chemical bonds. When the sample section attains a critical value and the stress is comparable with the fracture stress, the propagation of the main crack is accelerated, thus becoming ‘catastrophic’. In this stage, the chemical bonds split almost exclusively because of the mechanical stress, the participation of the thermal fluctuations being strongly diminished. Although the propagation of the crack is rapid, it is controlled by the inelastic properties of the polymer. As the relaxation times are now higher than the stressing time, the overstressed macromolecules cannot rearrange themselves under stress; therefore, the relief of the breaking surface becomes very coarse (Figure 2.42 b), characteristic for the rigid polymers which do not show any energy losses due to their plasic and viscoelastic properties. The transition from the regime characterized by the slow propagation of the crack to that with rapid propagation becomes evident from the analysis of microphotographs. A clear delimitation of two zones, which constitute the front of the main crack at the moment when its ‘catastrophic’ propagation starts, is clearly shown in Figure 2.42c. These results prove that the deformation and fracture of PVC under prolonged static stress at temperatures lower than the vitreous transition are based on the mechanochemical act and pass compulsorily through all the stages of the polystage chain mecha108

Mechanochemistry of Polymer Deformation

nism specific to the mechanochemical processes. Owing to its outstanding practical importance, the time dependence of polymer capacity of being subjected to constantly applied mechanical stresses has been thoroughly studied [140–143, 145,146]. Only few studies approach the creep of semicrystalline polymers used as yarns and fibers and even fewer refer to the elucidation of the molecular aspects implied to this process. Among these, the ones referring to the behaviour of polypropylene, poly(ethylene terephthalate), polyamide-6, and copolymer based on acrylonitrile-vinyl acetate-α-methyl styrene are worth mentioning [46, 144, 147–161]. Thus, using IR spectroscopy for the study of polypropylene monofilament creep, important data concerning the stress distribution in chemical bonds have been obtained. This fact allowed the determination of the fraction of the chemical bonds passing to the mechanoactivated state, previous to fracture, at a certain stress value (Figure 2.43). The results of a monofilament creeping study based on poly(acrylonitrile-co-vinyl acetate-co-a-methyl styrene) were used to plot experimental rheologic curves, as well as study the monofilament behaviour at different stages of production technology: after spinning, wet stretching, dry stretching [46]. These curves are shown in Figure 2.44 for monofilaments with 6-denier fineness, stressed at a constant stress in their range of viscoelastic behaviour on the 0 to 60 min interval. It should be mentioned that the typical shape of creep curves for all analysed samples but also differences in some of their characteristics are evident. Thus, the instantaneous strain as well as the residual strain decrease in value from the fibre which is immedi-

Figure 2.43. Stress distribution in chemical bonds in isotactic polypropylene [148]. 109

Macromolecular Mechanochemistry

ately sampled after spinning to the stretched and dried one, pointing out the tendency of increase of structure rigidity with the applied mechanical treatment. The same effect is manifested by increasing tendency of some rheological parameters, which are calculated on the basis of the creep equation having the form:

e = A + B × t - C × D -t

(2.93)

with their values collected in Table 2.4. The increase of the crystallinity index of the orientation factor

Figure 2.44. Experimental creep curves of poly(acrylonitrile-co-vinyl acetate-coα-methyl styrene) (6 den finesses) at different stages of their obtaining technology [46]: 1) after spinning; 2) after wet stretching; 3) after avivage; 4) after stretching and drying.

as well as of the heat of dissolution along with stretching – a wellknown effect – suggests at the same time the occurrence of structure stiffening by intensification of intermolecular interaction due to the increase of the packing degree of the macromolecules. The existence of the strain plastic component, even in the case of the dry-stretched monofilament (curve 4 in Figure 2.44), proves also that macromolecule fracture takes place in the polymer during stressing. Nevertheless, the splitting of these bonds is not so frequent as to be indicated by a molecular weight decrease. To establish whether the studied copolymer undergoes mechanochemical reactions under the tensile creeping conditions, experiments were carried out with stressing of some monofilaments immersed in a radical acceptor solution. Thus, it has been found out that after 60 min stressing under a constant load in the presence of DPPH, the monofilaments become coloured on the area immersed in the solution, with the colour being resistant to repeated 110

Mechanochemistry of Polymer Deformation Table 2.4. Rheological parameters calculated from experimental creep curves of monfilaments with finesses of 6 den [46]

Processing step

Type of relaxation, θr (s)

Spinning Wet stretching Avivation Stretching-drying

242 273 296 460

Rheologic parameters Modulus of high Modulus of elasticity, G1 visco-elasticity (gf/mm2) (gf/mm2) 1.714 2.000 2.107 2.727

0.75 2.83 4.09 7.50

Viscosity η x 10-4 (gf.s/mm) 2.64 3.96 4.16 5.94

extractions with methanol. Similarly, the monofilaments stressed in a methanol solution of aromatic diamines acquire a shade specific to the micromolecular compound which remains even after dissolution and reprecipitation of the copolymer; this fact becomes an outstanding proof that the diamine has been chemically bonded to the copolymer chains. An argument in this favour might also be the possibility of diazotizing and coupling of the free aminic groups from the chemically bonded aromatic diamine with phenolic compounds (resorcinol, naphtol) which causes the appearance of colours specific to the formed azo-dyes. Filaments reacted with benzidine could also be directly dyed in weak shades with acid dyes. Although it was not possible to accomplish a quantitative correlation between the used radical acceptor and the value of deformation obtained at different creeping times, experimental results are worth mentioning. The colour of the monofilaments stressed for short periods (10 to 20 min) is very faint and it intensifies along with increasing stressing time. After 50 min of creeping its intensity remains constant. By correlating this result with the creep curve shape, it becomes obvious that the mechanodegradation intensity depends to a lesser degree on the stress value and is more evidently dependent on the strain which remains practically steady after 30 min of stressing. Similar results have been also obtained for some other types of fibres, for instance, the ones based on poly[p-2hydroxy-ethoxy)benzene carboxylic acid] (140,141) or nylon 6 [142]. It may be concluded that, during the static stress of a semicrystalline polymer of poly(acrylonitrile-co-vinyl acetate-comethyl styrene) type in the monofilament form, there appear mechanochemical reactions which finish with free radical formation even at strains that are lower in comparison with the macroscopic fracture strain. This monofilament deformation mechanism is thus 111

Macromolecular Mechanochemistry

of the mechanochemical type, behaving in this way in the whole stress period up to their fracture. Elastomer creep has not been widely studied because these polymers do not show a residual strain component; when the force action stops, the deformation is totally recovered. The discovery and wide utilisation of thermoplastic elastomers such as polyurethanes in recent years has determined detailed investigations of their behaviour under different mechanical conditions. One such linear polyurethanic elastomer is Estane 5707, a urethane-ester synthesised from 4,4’-diphenyl methane diisocyanate, poly (tetramethylene adipate) end-capped with hydroxylic groups ( M w = 2000) and 1,4-butanediol as a chain extender. Blocks of polyester and urethane segments alternate therefore on its chain. The creep of this polymer was studied on films achieved by solution deposition, at definite values of the stress in inert or active gaseous media, sometimes in solution of radical acceptors or vinylic monomers [143, 145]. The creep curves for different gaseous media at a stress of σ = 42.2 MPa are shown in Figure 2.45. The values of three strain components calculated from these curves (Table 2.5) show considerable differences. It may be noted that in active media (air, NO, vinyl chloride) all the strain components and also the overall strain have higher values than in inert media. The static tensile stress in the presence of NO and vinyl chloride resulted in rapid fracture of the samples (after 22 and 65 h, respectively). Both substances in the gaseous state can react with the macroradicals formed by chemical bond scission of the polymer, thus preventing their stabilisation through specific reactions (recombination, disproportionation). The relative increase of strain in active media is mainly due to the increase of the viscoelastic and flow components. Knowing that the flow strain is the main consequence of molecular fracture, it is obvious that the mechanochemical process intensifies in the presence of active gaseous substances. Thus, the experimental results obtained in the study of urethane polyester creep are good arguments for a radical mechanism of the deformation and fracture processes. The different behaviour of the statically stressed polymers in the presence of NO and vinyl chloride compared with the sample stressed in an inert medium is therefore the consequence of some of its reactions with the above-mentioned micromolecular compounds, activated by load. The polymer IR spectra, subjected to creep, point out some considerable changes (Figure 2.46). Thus, 112

Mechanochemistry of Polymer Deformation

Figure 2.45. Creep curves of polyesterurethane, ε – log t in different gaseous media: 1) air; 2) nitrogen; 3) vacuum; 4) vinyl chloride; 5) NO [143]. Table 2.5. Deformation values calculated from creep curves for various gaseous atmospheres (σ = 42.20 MPa) [143] Type of deformation Instantaneous elastic deformation (mm/min) Retarded elastic deformation and of flowing (mm/min) Total deformation (mm/min)

air

vacuum

3.25

3.10

1.84 5.09

Medium nitrogen

NO

vinyl chloride

3.00

3.50

3.45

1.60

1.55

2.50

2.15

4.70

4.55

5.95

5.65

the spectrum characteristic of the sample stressed in the presence of NO, curve 2 in Figure 2.46 shows an intensification of the absorption band from 1360 cm –1 specific to the R–NO group. At the same time, the bands from 1600 and 620 cm –1 are intensified, being attributed to the R–ONO group, which is made up through the nitrogen oxide reaction with the radicals obtained as a result of the ester groups splitting from the polymer chains. The presence of the band from 700 cm –1 (curve 3) also shows the linkage of vinyl chloride to some macromolecules. Its missing from the spectrum of the unstressed polymer (curve 1) is also an argument for the vinyl monomer reaction with the macroradicals. Conclusions on the deformation and fracture mechanism of the polyurethane elastomer have also been obtained by studying the 113

Macromolecular Mechanochemistry

creep in a liquid medium, in the presence of some radical acceptors and vinylic or dienic monomers. Thus, it was observed that when stressing the film in absolute ethyl alcohol the film does not fracture macroscopically and the deformation becomes practically constant after 20 hrs (Figure 2.47, curve 1). On the other hand, in alcohol solutions of DPPH, acrylonitrile, and isoprene, macroscopic fracture takes place after 8, 48, and 149 hrs from the beginning of stressing. These outcomes also

Figure 2.46. IR spectra of the polyurethane elastomer under creep conditions: 1) unstressed; 2) stressed in NO atmosphere; 3) stressed in vinyl chloride atmosphere [143].

prove the radical character of the mechanism of polymer deformation and fracture processes and the capacity of newly formed macroradicals to initiate the graft and block copolymerisation reaction of the vinylic and dienic monomers, which are present in the medium. The DPPH reaction with the stressed film can be also seen when visually examining the sample; there appears a violet colour on its active sector – a characteristic of the radical acceptor – which is resistant to washing and repeated extractions in methanol. The appearance of the absorption band at 350 nm in the UV spectrum of the same film also proves its reaction with the micromolecular compound. The acrylonitrile chemical bonding to the stressed polyurethane has been proved by IR spectroscopy (Figure 2.48). The spectra exhibit a new absorption band at 2350 cm –1 attributed to the –C=N group. Studying the influence of the duration, the stressed film was kept in acrylonitrile after macro114

Mechanochemistry of Polymer Deformation

Figure 2.47. Creep curves of the polyurethane in different liquid media: 1) absolute alcohol; 2) isoprene; 3 – DPPH (alcohol soln. 0,5%); 4) acrylonitrile [143].

scopic fracture; we can notice that the amount of the chemically linked monomer increases with the post-reaction time pointed out by the intensification of the band from 2350 cm –1 . The increase of the acrylonitrile content in the stressed film with time is the consequence of the increase of the grafted chain length, when the concentration of the macroradicals initiating the reaction is kept practically constant. The behaviour of the polyurethane elastomer with different cross-

Figure 2.48. IR spectra of the polyurethane films stressed in the presence of acrylonitrile for different periods of postreaction: 1) blank polyurethane; 2) stressed for 24 hrs; 3) 48 hrs; 4) 72 hrs; 5) 96 hrs; 6) 120 hrs, respectively [143]. 115

Macromolecular Mechanochemistry

linking degrees at the static tensile stress is also described by typical creep curves (see Refs. 140 and 145). The value of the overall strain and of its components depends on the cross-linking degree, indirectly expressed by constant M c . This represent the average molecular weight of the chain segment between two knots of the polymer network and it is expressed by the relation [162]: E=

3RrT MC

(2.94)

where E is the dynamic elasticity modulus; R is the universal gas constant; ρ is polymer density and T is temperature. For the tested samples, M c varies from 5500 to 7700. Interesting conclusions can be obtained if we consider – to make the comparison easier – the ε–t curves corresponding to five polyurethane elastomers, based on 4,4’-diphenyl methane diisocyanate polyurethane elastomers with different cross-linking degrees within the range 0 to 120 hrs (Figure 2.49). The sample with the lowest cross-linking degree has, as expected, the highest strain value, with the strain decreasing as M c is reduced (signifying the cross-linking degree increase). Although strong and numerous, the interactions between the linear macromolecules, determined by the presence of the –CO–NH– groups in the chain, allow nevertheless structural changes under loading and the manifestation of high elasticity, respectively. However, the in-

Figure 2.49. ε – t curves of five polyurethane elastomers characterised by different cross-linking degrees:1) M c = 7700; 2) 7100; 3) 6600; 4) 6000; 5) 5500. 116

Mechanochemistry of Polymer Deformation

troduction of some chemical cross bridges reduces the possibility of the linear segment structural change, stiffening the structure thus contributing to the strain decrease. On the other hand, it may be noted that an increase in the cross-linking degree results in a decrease of the polymer durability, expressed by the time between the stress application and macroscopic fracture. We can find the explanation in the structural changes caused by the cross-bridge introduction of the allophanate type, which remove the macromolecules one from the other, reducing the hydrogen bonds frequency. During mechanical loading these cross-bridges are the first ones to break or induce the splitting of the neighbouring chemical bonds from the main chain. As a result, the resistance to creep decreases with an increase of the degree of cross-linking degree. The loading of some samples submitted to accelerated ageing determined by UV irradiation and simultaneous heating at 60 °C leads to greater strains compared to the reference sample, for the same duration of mechanical loading. Thus, a pronounced increase of the irreversible strain component may be observed (i.e., the flow component), an evident consequence of the intensification of the chemical bonds splitting from the main chain, as well as of the cross-links, Table 2.6 [143]. Also noted is the intensification of the microcrack formation process, which can be detected by the visual observation of the stressed samples. The acceleration of elastomer deformation and of the fracture process during simultaneous thermal and UV stressing is a good argument for the common mechanism of the mechano-chemical, photochemical, and thermal destruction. At its basis lies the macroradical formation by homolytic splitting of the chemical bonds from the polymer main chain. 2.7. CHEMICAL STRESS RELAXATION The measurement of stress relaxation as a function of time, in the case of the elastomers maintained under constant strain, was firstly considered by A.V. Tobolsky as a useful method for the investigation of the mechanochemical reactions that take place in polymer networks [163]. Varying the temperature and duration of deformation allowed also the study of the viscoelasic component. All these studies have been defined using the generic term of chemorheology [163–178]. The phenomenon of chemical stress relaxation was discovered during the investigation of vulcanised elastomers. In the range of temperature from 100 to 105 °C these 117

Macromolecular Mechanochemistry Table 2.6. Characteristic deformations obtained during concomitant stressing under creep conditions and ageing of a crosslinked polyurethane (M c =5500) σ = 9.0 MPa [143] Type of deformation (mm/min)

Control sample

With accelerated ageing

Instantaneous elastic deformation, ε0 Retarded elastic deformation and of flowing Maximal deformation, εmax

0.880 0.255

0.885 1.435

1.135

2.320

polymers show a strong decrease, almost to zero, of the stress at constant strain. For the cross-linked polymers low stress relaxation could be anticipated, at least from the theoretical viewpoint. In this way, the observed phenomenon was ascribed to the scission of the network chemical bonds. It was proved that molecular oxygen plays an essential role in this process. By avoiding its presence an important decrease of the relaxation rate was observed. The relative curves of stress decrease f(t)/f(0) [f(t) – stress value at time t; and f(0) – initial stress value] do not depend on the strain magnitude at which the sample was maintained, when its values are higher than 200 % (straining ratio α = 3). The typical curves for vulcanised natural rubber are depicted in Figure 2.50. In may be noted that the presence or absence of black carbon (Figure 2.51) does not affect the stress decay. 2.7.1. Mechanocracking of the chemical bonds from the main chain The structure of cross-liked elastomers can be represented in two manners, namely: as a uniform lattice (Figure 2.52 a) and as the random distribution of chains (Figure 2.52 b). A.V. Tobolski [173] as well as J.P. Berry and W.F. Watson [172] established the equations that describe the relation between the total number of broken main chains from 1 cm 3 , q m (t) and the relative stress f(t)/ f(0) under the assumption of the chains’ length in the network. From the statistical theory of rubber elasticity, the tensile stress f(0) that deforms an elastomer until a certain strain ratio α is given by the following equation [174–177].

(

)

(

f (0) = n (0) × RT × a - a -2 = N (0) × kT a - a -2

)

(2.95)

where n(0) and N(0) is the number of moles and network chains 118

Mechanochemistry of Polymer Deformation

Figure 2.50. The effect of elongation on the chemical relaxation of the stress in the case of natural rubber vulcanised with sulphur at 100 °C [171].

Figure 2.51. Curves of stress chemical relaxation in air and purified by oxygen nitrogen, respectively, in the case of natural rubber vulcanised with sulphur [171].

in 1 cm 3 , respectively; R is the universal gas constant; k is Boltzman’s constant and T is Kelvin temperature. If at time t occur q m (t) scissions and there are n(t) moles of chains (or N(t) chains) that are tensioned under the stress f(t), we have:

(

)

(

f (t ) = n (t ) × RT × a - a -2 = N (t ) × kT a - a -2

combining equations (2.95) and (2.96) results: 119

)

(2.96)

Macromolecular Mechanochemistry

Figure 2.52. Chain length distribution in a polymeric network: a) uniform distribution; and b) random distribution [171].

f ( t ) n (t ) N (t ) = = f ( 0) n ( 0) N ( 0)

(2.97)

A. Berry-Watson equation [172] The authors consider that the initial number of active chains, of length x, into a structure having a random distribution is:

N x (0) = N (0) × p × (1 - p )

x -1

(2.98)

where N(0) is the total number of chains; p is the reverse of the chain average length. Considering now that the probability of a structural unit undergoing a scission at the time t is β, the number of remaining chains, of length equal to x, is:

N x (t ) = N (0) × (1 - b )

x

(2.99)

If the probability β is the same for all structural units of the chains, irrespective of their length, then equations (2.98) and (2.99) can be combined and summarised, giving: N (t ) p (1 - b ) = N (0) p + b (1 - p )

where: N (t ) =

¥

å N x (t )

.

X =1

120

(2.100)

Mechanochemistry of Polymer Deformation

Equation (100) is known as the Berry–Watson equation. B. Yu equation [77, 178] Another approach belongs to Yu. According to author's assumptions, if q m(t) is the total number of randomly broken bonds, at a given time t, that occurred in the unitary volume of the network, then the number of scissions occurring on the chains of length x, is: qm, x (t ) = qm ( t )

xN x (0) ¥

å xN x

(2.101)

x =1

Consequently, the number of unbroken chains of length x can be calculated as: é 1 ù N x (t ) = N x (0) ê1 ú êë N x (0) úû

where:

qm , x t 

(2.102)

1 is the probability of one of these chains to undergo N x (0)

scission. Substituting equation (2.98) into equation (2.102), we obtain the Yu equation: N (t ) = N ( 0)

p é pq ( t ) ù exp ê m ú + p - 1 ë N ( 0) û

(2.103)

C. Tobolsky equation The author considers the case of a uniform chain distribution, when the following equations may be written:

N x (t ) = N (t )

(2.104)

(2.105) N x ( 0) = N ( 0) Noting with M 0 the number of structural units from the unitary volume, i.e. 1 cm 3 , in expressing β by:

121

Macromolecular Mechanochemistry

b=

qm (t ) M0

(2.106)

and replacing the equations (2.104–2.106) in equation (2.100), we obtain:

é é q (t ) ù N (t ) q (t ) ù = 1 - ê m ú = ê1 - m ú N ( 0) ë M0 û ëê x × N (0) ûú x

x

(2.107)

When the average chains length x between two knots of a network is enough high, equation (2.107) can be approximated with:

é q (t ) ù é q (t ) ù N (t ) = 1 - ê m ú exp ê - m ú N ( 0) êë N (0) úû ë M0 û

(2.108)

qm (t ) N ( 0) = p ln M0 N (t )

(2.109)

x

therefore:

Equation (2.108) is known as Tobolsky’s equation. 2.7.2. Mechanism of mechanocracking of chemical bonds from the main chain Considering a lattice with uniform chain length and using Tobolsky’s equation, the following relation is obtained:

( ) = N (t ) = exp æ - q

f t'

f ( 0)

N ( 0)

ç è

(t ) ö N (0) ÷ø m

(2.110)

from here: qm (t ) = - N (0) ln

122

f (t ) f ( 0)

(2.111)

Mechanochemistry of Polymer Deformation

Equation (2.111) allows to express q m(t) as a function of relative stress f(t)/f(0). If we assume that the number of supplementary scissions is q m (t) (i.e. 8 in Figure 2.53) occurring in the interval of time ∆t and that the number of scissions taking place in the region of unbroken chains (full lines, i.e. 2, in Figure 2.25) is ∆N(t), then ∆N(t)/q m(t) (therefore ¼ of the total number of chains in Figure 2.53) will be given by the ratio xN(t)/xN(0) or by the following equation:

-

Dn ( t ) N (t ) = Dqm (t ) N (0)

(2.112)

The place of scission x is included in each unbroken chain only once. Even if any of these chains can suffer another scissions, after the first splitting they are not considered as unbroken. The most general expression of the equation (2.112) is the following one: dN (t ) N (t ) = dqm (t ) N (0)

(2.113)

æ N (t ) ö f (t ) = - N (0) × ln qm ( t ) = - N (0) × ln ç ÷ f ( 0) è N ( 0) ø

(2.114)

-

and after integration:

Experimentally was often found that the splitting rate is approximately constant [179,180]. Therefore, equation (2.114) becomes:

qm (t ) @ qot

(2.115)

where q 0 is the number of scissions that occur on the main chain per time unit. By replacing equation (2.115) in equation (2.110) we obtain: f (t ) @ e k1t f ( 0) 123

(2.116)

Macromolecular Mechanochemistry

Figure 2.53. The mechanism of network chains splitting: x – splitting place; ∆q m (t) – total number of splitting places [179].

Equation (2.116) shows that when mechanocracking occurs on the main chains, the chemical relaxation can be approximated by an exponentially decreasing curve of the Maxwell type. This behaviour was proved for many elastomers, such as: natural, poly (butadiene-co-styrene, neoprene), and isobutylene rubber (Fig. 2.54). For all the above-mentioned polymers it was possible to obtain complete description of the temperature effect on the decrease of stress, according to the next relation: f (t ) = F (k ' t ) f ( 0)

(2.117)

where k′ is affected only by temperature. The dependency of k′ on temperature is usually expressed by an Arrhenius-type equation:

k ' = A exp ( - Ea / RT )

(2.118)

and its value can be easily obtained from graphical representation. The curves calculated using on equation (2.118), in coordinates log f(t)/f(0) – t, at different temperatures and experimental ones, are illustrated in Figure 2.55. In the case of those rubbers having 124

Mechanochemistry of Polymer Deformation

Figure 2.54. Curves of stress decay for different vulcanised elastomers at 100 °C [180]. 1) natural rubber; 2) Bunas; 3) Butil B-3; 4) Neopren GN.

Figure 2.55. Temperature effect on the stress decay in the case of vulcanised natural rubber (the curves are drawn based on equations (2.117) and (2.118), respectively, and the plots correspond to the experimental values) [171].

the behaviour as described by the curves depicted in Figure 2.55, it was found that E a = 127 kJ/mol [163]. Therefore, the chemical relaxation must be regarded as a useful physical method for measuring the chemical bonds scission in polymer networks. The mechanocracking rate is considered as being unaffected by the forces acting on the network, including the strain force, until very high values of these forces. However, there are some cases when the stress chemical relaxation is not described by Maxwell-type curves. Both the vulcanisation reagents and vulcanisation mechanism can play an important role in the observed deviations from the Maxwell-type shape of curves [181–188]. Some aspects concerning the chemical relaxation of different 125

Macromolecular Mechanochemistry

vulcanised elastomers, especially in the presence of oxygen, at different temperatures have been widely analysed. Important contributions to the development of this field of mechanochemistry are due to A.V. Tobolski [180], W.F. Watson and co-workers [172], J.P. Berry, R Murakami, and S. Kamura [189–191]. 2.7.3. Mechanocracking of cross-bridges (transversal bonds) If it is accepted that the splitting takes place exclusively in the transversal bonds of the macromolecular network and noting with C(0) the initial number of cross-bridges, q c (t) – the number of scissions occurring after a given period, t, and k – the proportionality constant, it can be written:

dqc ( t ) = k éëC (0) - qc (t ) ùû dt

(2.119)

and therefore:

(

qc (t ) = C (0) 1 - e - kt

)

(2.120)

Denoting with f(t)/f(0) the relative stress and with n(0) the initial chain density, and considering that the splitting takes place exclusively in the transversal bonds, we have:

f ( t ) / f ( 0) = 1 - 2 qc ( t ) / n (0)

(2.121)

In the case of the ideal lattice:

2C (0) = n (0)

(2.122)

and thus: (2.123) f (t ) / f (0) = e- kt In accordance with equation (2.123), the stress relaxation curve is also of the Maxwell decreasing type. 2.7.4. Interchange reactions The importance of interchange reactions was proved studying the stress relaxation in the case of a polysulphuric rubber that undergoes a faster relaxation process in a stream of n-butyl

126

Mechanochemistry of Polymer Deformation

mercaptan than in air (Figure 2.56), due to the following chemical reaction which takes place: R

S

S

R + Bu

SH

R

SH + Bu

S

S

R

Such reactions are also possible between the polymer macromolecules, which are referred to as interchange reactions. The following types of chemical bonds are found in polysulfonic rubbers [192,193]: CH2CH2

S

S

CH2CH2

S

S

ethyl disulphuric elastomer CH2CH2OCH2CH2

S

S

CH2CH2OCH 2CH 2

S

S

diethyl eter disulphuric elastomer

Figure 2.56. Curves of stress chemical relaxation in the case of polysulphuric rubbers in atmosphere of n-butyl mercaptan [164]:  – air; l – n-butyl mercaptan.

Although the disulphide bonds are the main type of bonds, in networks there are also monosulphide –S–, trisulphide –SSS–, and tetrasulphide –SSSS– bonds, respectively. The junction points (network knots) are usually three functional ones and at the chains extremities of the network the characteristic functional bonds are of –SH bonds type as well as the reduced number of other groups such as: –S – ….Pb + …. – S–, and –S – …. + Na. In this case, the interchange reactions become important if the elastomer is kept up at a certain deformation for a long period of time, being illustrated below:

127

Macromolecular Mechanochemistry

The catalysts indicated in the scheme are ionic compounds (i.e., acids, bases, or salts) which remained included in the polymer during synthesis or vulcanisation processes. R

S

a)

S

R

R

+ R'

S

S

R

S

H

b) S

S

R

S

Na

R'

S

S

R

S

Pb

R'

S

S

R

S

H +

R'

R'

S

S

R

S

Na

+

d)

R

R'

Catalyst

R'

S +

R'

+

c)

S

Catalyst

R'

+ R'

R'

S

S

R

R

S

S

R'

Pb

+ R'

S

S

R

S

R'

+ S

R'

R'

S

R and R' - macromolecular chains

Such reactions appear not only in the polysulphuric elastomers but also in those based on silicone: CH3 Si CH3

CH3 O

Si CH3

CH3 O

Si

O

CH3

In this case, the proposed mechanism for the interchange reaction is the following one:

128

Mechanochemistry of Polymer Deformation

R

O

Si

R

+ R'

O

R

O

R'

Si

Catalyst

Si

R'

Si

R

O

R'

+

Once again the catalyst is an acid, base or salt substance left over from polymerization or vulcanisation [94, 195]. In addition, the interchange reactions may also occur on the transversal bridges. For instance, salt-type bonds are very labile and can be implied into interchange reactions, which should occur in two steps: scission and restoration, in other parts of the network, of chemical bonds, the rates of the two reactions being the same.

O

O C

O

Me++

-O

C

On the other side, the transversal bridges, which are continuously broken and remade, can also be of physical nature, especially hydrogen bonds. In the case of polymers, the physical interactions at long distances are well described by ‘complex entanglement’. Thus, the physical knots act as temporary transversal bonds; thus, an equilibrium between their scission and remaking is established. Just after deformation of the initial state of chains, the stress f(0) is given by the following equation: (2.124) f (0) = N (0)kT (a - a -2 ) where N(0) is the effective number of chains per cm 3 at the time zero. Supposing that the elastomer is maintained at constant length, only N(t) chains from the total number N(0) will be affected by the interchange reactions, at a given time t. It was accepted that a chain participating in an interchange reaction is relaxed with respect to the sample length and, consequently it will not be

129

Macromolecular Mechanochemistry

stressed, therefore:

(

f (t ) = N ( t ) × kT a - a -2

)

(2.125)

the interchange reaction rate can be expressed as:

-

dN ( t ) = k ' n1m2 N ( t ) dt

(2.126)

where n 1 is the average number of bonds on each available chain for interchange reactions (i.e., the total number of di-, three-, and tetrasulphuric bonds); m 2 – number of terminal bonds – S – …. + Na per cm 3 and k′ is the rate constant. At boundary conditions, for t = 0; N(t) = N(0) and by integration we obtain: (2.127) N (t ) = N (0) × e- kt = N (0) × e - t / t where k = k’n 1 m 2 and t = 1/k. Replacing the equation (2.127) in equation (2.125) and dividing it by equation (2.124), the following expression is obtained: f (t ) = e - kt = e -t f ( 0)

t

(2.128)

Clearly, for the interchange reactions, the stress relaxation is also described by a Maxwellian decay. For more accuracy, if a vulcanised elastomer undergoes mechanocracking under stress, we have to take into account both the cross-bridges scission and their subsequent recombination [196, 197]. Considering now the probability γ as a structural unit to be bonded at a cross-bridge, which exist at a given moment t, then the probability to find out a chain consisting from x units, in which x–1 units are not vulcanised, at time t, will be γ(1–γ) x–1 . The Sn

C

C

C O2

C

Sn

OO

•

C

Scission

•

Sm + • Sm C

Recombination S n - polysulphuric chain; m
130

Mechanochemistry of Polymer Deformation

number of chains N x , composed from x units, is:

N x = N (t ) × g (1 - g )

x -1

(2.129)

where N(t) is the total number of chains. Considering that the number of cross-bridges in the system is C(t): g = g ( 0) ×

C (t ) C (0)

(2.130)

where γ = γ(0) and C(t) = C(0) at t = 0. Ignoring the chain-end effects, we obtain: N (t ) C (t ) = N ( 0 ) C ( 0)

(2.131)

where N(0) is the total number of chains at the initial moment, t=0. Thus:

é C (t ) ù é C (t ) ù N x = N ( 0) × g ( 0) × ê ú × ê1 - g ( 0) ú C ( 0) úû êë C ( 0) úû êë 2

x -1

(2.132)

On the other hand, the splitting of hydrocarbonate bonds may occur simultaneously with the reticulation reaction. Taking p, the scission probability, at the time t, the probability of a chain of length x to remain unchanged is then: γ(1 – γ) x–1 (1 – p) x–1 ; 1–p is the probability of the scission not occurring. Consequently, the number of chains with length x, existing at the time t, will be:

é C (t ) ù é C (t ) ù N x = N ( 0 ) × g ( 0) × ê ú × ê1 - g (0) ú C (0) úû ëê C (0) ûú êë The total number of chains: 2

x -1

é C (t ) ù é C (t ) ù Nt = N ( 0 ) × g ( 0) × ê ú × ê1 - g (0) ú C (0) úû ëê C (0) ûú êë x =1 2

å

é C (t ) ù N (0) × g ( 0) × ê ú C ( 0) û ë = C (t ) g ( 0) × +p C ( 0)

x -1

× (1 - p )

x -1

× (1 - p )

x -1

(2.133)

=

2

(2.134)

131

Macromolecular Mechanochemistry

According to the theory of elasticity: f (t ) N (t ) = f ( 0) N ( 0)

(2.135)

for a given strain, the relative stress is:

é C (t ) ù g ( 0) × ê ú C ( 0) û f (t ) ë = C (t ) f ( 0) g ( 0) × +p C ( 0) 2

(2.136)

When p = 0, equation (2.136) is compatible with equation (2.131). In order to calculate the number of cross-bridges in the system, at any time, the recombination reaction must be considered. Thus, any broken bond from a network segment may participate with the same probability in recombination; it is estimated that usually there are about 100 segments for a cross-bridge and that from kinetic point of view the recombination reaction is a first order reaction. Considering that A, B, and C are the possible structures from the above scheme and the involved chemical reactions: k1 A + O2 → B

k

2 ®C B ¾¾

k

3 ®A C ¾¾

where k 1 is the oxidation rate constant; k 2 the splitting rate constant and k 3 the recombination rate constant. The corresponding kinetic equations are the following: dA = k3C - k1 A dt

(2.137)

dB = k1 A - k2 B dt

(2.138)

dC = k2 B - k3C dt

(2.139)

132

Mechanochemistry of Polymer Deformation

Due to the fact that A and B are cross-linked structures:

C (t ) = A + B

(2.140)

These equations lead to the relation: C (t ) æ k ö æ 1ö = A1 ç 1 + 1 ÷ - ç ÷ (a + k1 ) A2 expat C ( 0) è k 2 ø è k3 ø æ 1ö - ç ÷ (b + k1 ) A3 expbt è k3 ø

(2.141)

where:

A1 =

1 + C0 k k 1+ 1 + 1 k 2 k3

é 1 ê 1 + C0 ê k3C0 - ( k1 + b ) a0 + A2 = k k a -b ê 1+ 1 + 1 êë k 2 k3

(2.142) ù ú ú ú úû

é ù ê 1 1 + C0 ú ê k3C0 - (k1 + a ) a0 + ú A3 = k1 k1 ú b-a ê 1+ + êë k2 k3 úû

(2.143)

(2.144)

1é a = - ê(k1 + k2 + k3 ) + 2ë

(k1 + k2 + k3 )2 - 4 (k1k2 + k2k3 + k3k1 ) ùú (2.145)

1é b = - ê(k1 + k2 + k3 ) 2ë

(k1 + k2 + k3 )2 - 4 (k1k2 + k2k3 + k3k1 ) ùú (2.146)

û

û

where a 0 is the initial fraction of cross-bridges that did not react in structure A; C 0 is the initial fraction of broken bonds in structure C. If 4(k 2 k 1 +k 2 k 3 + k 3 k 1 ) > (k 1 + k 2 + k 3 ) 2 , 133

Macromolecular Mechanochemistry

C (t ) æ k ö cos vt é k1 - d) A2' + A3' ùû + éë(k1 - d) A3' - vA2' ùû sin vt ×t -dt = A1 ç 1 + 1 ÷ ( ë C ( 0) k3 è k2 ø

(2.147) where:

A2' = a0 -

1 + C0 k k 1+ 1 + 1 k 2 k3

A3' = (d - k1 ) a0 + k3C0 -

(2.148)

(1 - C0 ) d 1+

k1 k1 + k 2 k3

(2.149)

2d = k1 + k2 + k3

(2.150)

2w = 4 (k1k2 + k2k3 + k3k1 ) - (k1 + k2 + k3 )

2

(2.151)

The estimation of number of scissions and of their positions can be made by determining the swelling degree at equilibrium, as was proposed by Horiks [198] and Charlesby [199]. Stress decrease is not necessarily caused only by oxidative splitting, it should also be related to knots relaxation by the interchange reactions. The measurement of the swelling degree takes a long time until the therodynamic equilibrium is reached; Murakami and coworkers [200] proposed a simple method that combines Horiks’s equations with mechanical ones. For the main chain splitting they proposed the equation: 12 f (t ) é 1 - S (t ) ù ú =ê f (0) ê 1 - S (0)1 2 ú ë û

2

(2.152)

In the case of cross-bridges splitting: 2

1 2ù é f (t ) g (t ) ë1 - 2 S (t ) û = f ( 0) 12 2 g (0) é1 - S (0) ù ë û

134

(2.153)

Mechanochemistry of Polymer Deformation

When the splitting is selective and occurs near the reticulation centres: 12 f ( t ) é 1 - 2 S (t ) ù ú =ê f (0) ê 1 - S (0)1 2 ú ë û

2

(2.154)

where S(0) and S(t) are soluble fractions, initially t = 0 and at the time t, respectively; γ(0) and γ(t) is the average number of transversal bonds (cross-bridges) per main chain. Charlesby’s equation can be only applied in the case of random distribution of the primary chains [177]:

1 g = S + S1 2

(2.155)

in this case the equation (2.154) becomes: 2

1 2ù é 1 2ù é f (t ) ë S (0) + S (0) û × ë1 - S (t ) û = f ( 0) é 12 2 12 1 - S (0) ù é S (t ) + S ( t ) ù ë û ë û

(2.156)

Using the equations (2.154–2.156), mechanocracking of any vulcanised rubber can be easily determined. Thus, the soluble fractions are measured to the determined intervals of time and the slope of strength line from equation (2.156) is expressed as a function of time. The stress relaxation curve is then drawn and is used in order to find again the previously obtained values. 2.7.5. Multiple mechanocracking of polymer networks [201,202] 2.7.5.1. Scission of the cross-bridges and along the main chains In order to avoid the concomitant splitting of the main chain and of the cross-bridges, Murakami and co-workers have prepared a natural rubber reticulated with tetramethyl thiuram disulphide (TMDT) rubber whose density of reticulation being denoted with n(0). They also considered a second model, i.e. an ethylene-copropylene ternary rubber (EPTR) that was also reticulated with TMTD. In the given conditions the scission occurs only to the cross-bridges. Their initial density of reticulation is n(0) and the scission number q c (t) is given by the relation:

(

qc (t ) = C (0) × 1 - e - kt 135

)

(2.157)

Macromolecular Mechanochemistry

Finally, the authors studied a third model, which was natural rubber, vulcanised by irradiation. In this case, scission takes place only on the main chain. Its density of reticulation was noted with n′(0) and the number of scissions is given by the following equation: qm (t ) = - n ' (0) ln

f (t ) f ( 0)

(2.158)

If the chemical relaxation of the three samples is studied in the same conditions, i.e. in air, at 109 °C, we have:

Q ( t ) = qm (t ) + - n ' (0) ln

n '' (0) f (t ) n '' (0) × qc (t ) = n ' ( 0) ln + × C ( 0) 1 - e - kt = n ( 0) f ( 0) n ( 0)

(

f (t ) n '' ( 0) 1 - e - kt + 2 f ( 0)

(

)

)

(2.159)

where Q(t) is the total number of scissions on the main chain and cross-bridges of natural rubber, vulcanised with TMTD. In this case, Q(t) can be determined using the experimental results obtained for EPT rubber, vulcanised with TMD, and by irradiation-vulcanised natural rubber. In addition, when the scissions of the main chain and of the cross-bridges occur concomitantly, the following equation can be used:

é f (t ) Q (t ) ù 4k ( t ) x Q ( t ) 2x = 1× × exp ê × ú+ f ( 0) k (t ) + 2 x M 0 ëê k ( t ) + 2 x M 0 ûú +

é Q (t ) ù 2k ( t ) x Q ( t ) 4 x2 × × exp ê ú k (t ) + 2 x M 0 êë k (t ) + 2 x M 0 úû

(2.160)

where: k (t ) =

qc (t ) / C0 qm (t ) / M 0

M 0 = x × n (0)

(2.161) (2.162)

M 0 is the total number of structural units per cm 3 of the reticulated polymer and x is the number of structural units between two knots. 136

Mechanochemistry of Polymer Deformation

For the natural rubber vulcanised with TMTD, the experimental values of Q(t), q c (t), M 0 and k(t) are collected in Table 2.7, and the relation f(t)/f(0) – t is represented in Figure 2.57. It can be seen that only a small difference appears between the theoretical and experimental curves, respectively; the experimental data are lower than the calculated ones. Most likely, the main reason for the observed deviation is the segment modification resistance nearby the reticulations. Particularly, the chemical structure of cross-bridges of this polymer diminishes the oxidative scission. 2.7.5.2. Reticulation reactions Study of the stress chemical relaxation, at the temperatures ranging from 100 to 150 °C, showed that some vulcanised rubbers, such as butyl-rubber, gradually become soft and other ones, such as poly(butadiene-co-styrene) rubber, are continuously strengthened. Finally, there is a third category and the natural rubber belongs to it. In this case, the rubber is firstly softened and after that its toughness increases. Based on these observations, it was concluded that at high temperatures the mechanocracking and

Figure 2.57. Curves of stress chemical relaxation in the case of natural rubber [202]. 1) theoretical; 2) experimental. Table 2.7. Experimental values of q c (t), q m (t), Q(t) and the calculated values of f(t)/f(0) obtained from equation (2.160) [203] Time (hr)

qc(t).10-7 (mol/mol)

qc(t).10-8 (mol/mol)

Q(t).10-8 (mol/mol)

f(t)/f(0)

0 0.5 1 1.5 2 3 4 5 6

0.00 0.05 0.16 0.31 0.62 1.24 1.86 3.09 4.02

0.0 4.7 8.0 9.8 11.7 14.8 18.2 21.6 25.0

0.0 4.7 8.0 9.8 11.8 14.9 18.4 21.9 25.4

1.000 0.963 0.937 0.925 0.909 0.888 0.863 0.839 0.817

137

Macromolecular Mechanochemistry

reticulation concomitantly occur; their rates are not affected by the stress or strain values. By performing some intermittent measurements of the stress, it was possible to evaluate the combined effect of the mechanocracking and reticulation [163, 164]. Thus, the so-called TMM method, for continuous measurement of stress relaxation, in order to determine the cross-bridges in the elongated state and at low strains, was developed by S. Ore [164]. Another method is based on the simultaneous measurement of continuous and intermittent relaxation, SMCIR [203]. This method has some advantages, such as: it minimises the measurement errors; it enables determination of cross-bridges determination in the tensioned state; and it gives information concerning the effect of the reticulation reaction on the measured stress. By representing the relative stress in time, it was found that the relative stress initially increases rapidly and latter it tends to a constant value. This means that after a given period of time, the equilibrium is installed in the system and other mechanoradicals, able to enter in new recombination reactions, do not appear, Figure 2.58. The relation between the density of reticulation, n(∞) and temperature is illustrated in Figure 2.59. n(∞) was determined by holding the above mentioned samples for three hours at different temperatures. As it can be seen in Figure 2.59, the radicals that appear by mechanocracking enter in recombination reactions at a

Figure 2.58. Curves of intermittent stress relaxation in the case of vulcanised rubber [190]. 138

Mechanochemistry of Polymer Deformation

Figure 2.59. Crosslinking density at equilibrium; n(∞), as a function of temperature for natural rubber [190].

Figure 2.60. Representation of the relation n(∞)/n(0) vs. ε in the case of natural rubber [204].

constant ratio irrespective of temperature. Therefore, the number of formed radicals is not affected by temperature and is practically constant. Analysing the graphical representation of the ratio n(∞)/n(0) in function of elongation (ε), Figure 2.60, one can see that in the presence of radical acceptors the ratio of reticulation densities is lower than in their absence. Irrespective of the initial value of reticulation density n(0), all curves can be approximated with 139

Macromolecular Mechanochemistry

Maxwell-type curves. In the case of vulcanised elastomers, such phenomena have been evidenced not only at low temperatures but also at higher temperatures than room temperature [204,205]. Other studies deal with the effect of new formed cross-bridges, during stress relaxation, on chemical relaxation [166, 206–211]. Thus, Murakami and co-workers established the role of additional reticulations on the continuous chemical relaxation under stress in the case of a reticulated polyester. The respective polyester was synthesized by maleic anhydride esterification with ethylene glycol and its subsequent reticulation with divinylbenzene. The authors investigated the effect of temperature, elongation and of initial density of reticulation during stress relaxation [205,212]. It was found that the peaks of chemical relaxation curves diminish with the increase of temperature, Figure 2.61. As seen in Figure 2.62, for a density of reticulation n(0) = 1.3×10 –3 mol/cm 3 and a given temperature, 190 o C, the peak of the relaxation curve is proportional to strain ε. Similarly, it was proved that the peak value on the continuous stress relaxation curves is inverse proportionally to the reticulation density, under the conditions of constant deformation and temperatures, Fig.2.63. The sample vulcanised at 190 oC for 10 hours is practically completely reticulated and the corresponding curve is a descending one. Therefore, the supplementary reticulations may contribute to

Figure 2.61. The effect of temperature on the stress relaxation in air [205].

140

Mechanochemistry of Polymer Deformation

Figure 2.62. The effect of strain ε on continuous stress chemical relaxation in air [205].

Figure 2.63. The influence of crosslinking initial density n(0) on continuous stress chemical relaxation in air [205].

the more accentuated increase of the chemical stress relaxation peak, under the conditions of a constant applied stress. 2.7.6. Applications of chemorheology Chemorheology can be regarded as a precise method for the investigation of the chemical modifications that take place in 141

Macromolecular Mechanochemistry

physical or chemical networks. It is an extremely useful tool for the kinetic studies carried out in the case of some systems in which the mechanical properties are strongly related to the chemical reaction. In this sense, the vulcanised rubbers appear to be most suitable for chemorheological applications. In principle, chemorheology of elastomer networks is based on the rubber elasticity theory, according to which the modulus is determined exclusively by the network chains density. In the case of certain solid polymers, without containing transversal bridges, the physical relaxation of the macromolecules plays an important role and a general treatment of the relaxation process that is accompanied by the chemical reaction becomes difficult, because the visco-elastic response on the different reaction steps must be known. Another limitation of chemorheology appears in the case of the heterogeneous systems. The rate of chemical reactions generally differs in different stages, this rendering more difficult the correlation between the mechanical properties and the chemical reaction. Thus, detailed morphological studies are required before the application of the chemorheological method (for instance, for crystalline or filled polymers). In spite of these limitations, chemorheology has some doubtless advantages in the following chemical reactions. In the first place, in chemorheological studies the stress values are often very close to those encountered in practical conditions. Consequently, the experimental data, obtained in laboratory, can be directly transferred to the technological scale. On the other hand, this method is a nondestructive one. 2.7.6.1. Control of thermal stability of polyolefin-type hydrocarbonate networks An interesting application of chemorheology was developed by Shaw and co-workers and refers to the investigation of the thermal stability of hydrocarbonate networks in the temperature range from 300 to 350 o C. The authors used in these experiments reticulated high or low-density polyethylene and ethylene–propylene ternary polymer, vulcanised with peroxides. The measurements of stress relaxation were performed under vacuum or in the nitrogen atmosphere [213]. The chemical stress relaxation curves, for the temperatures of 300, 325, and 350 o C, respectively, are illustrated in Figs. 2.64– 2.66. 142

Mechanochemistry of Polymer Deformation

The above-mentioned temperature range practically covers the relaxation times range for all the experimentally investigated samples. At the temperatures well below 300 o C relaxation is negligi-

Figure 2.64. Stress relaxation in the case of hydrocarbonate networks of polyethylene-type at 300 °C under vacuum [213].

Figure 2.65. Stress relaxation in the case of hydrocarbonate networks of polyethylene-type at 325 °C under vacuum [213].

143

Macromolecular Mechanochemistry

Figure 2.66. Stress relaxation in the case of hydrocarbonate networks of polyethylene-type at 350 °C under vacuum [213].

ble. In turn, at temperatures higher than 350 o C the degradation process occurs so fast that the measurement becomes impossible. For all the investigated polymers, except the ethylene-propylene terpolymer, the relaxation curves are concave ones. This shape indicates a decay of the relative stress that occurs more slowly than thT corresponding to an exponential decrease. This effect is more evident at low temperatures. The network theory imposes that the irreversible scission of the main chain bonds as well as of the cross-bridges bonds should be expressed by an exponential relaxation curve or even more srapidly descending curves than the exponential ones. It was supposed that some secondary effects affect the behaviour of these networks. The experimental results lead to the conclusion the networks of saturated hydrocarbonate polymers, vulcanised with peroxides or by irradiation, are thermally decomposed at measurable rates by chemical stress relaxation in the temperature range from 300 to 350 o C. Thus, using the chemical relaxation data, the following series of thermal stability was established:

Vulcanised EPT >

Low-density polethylene High-density polethylene Low-density polethylene > > reticulated with peroxides reticulated with peroxides reticulated with irradiation

144

Mechanochemistry of Polymer Deformation

It was concluded that the hydrocarbonate networks stability is directly dependent on the density of network’s three-dimensional structure. The number of transversal bridges is higher in the case of more amorphous polymers, i.e. EPTR or low density polyethylene, and it confers superior characteristics to these networks. 2.7.6.2. Characterisation of some thermosetting networks for varnishes and adhesives The majority of polymers used as varnishes or adhesives are resins that are strengthened by heating. Their structure corresponds to a three-dimensional network, which offers good mechanical properties, chemical and thermal stability. At high temperatures, these materials show similar characteristics to those of vulcanised rubbers, i.e. their modulus is proportional to the number of crossbridges. The relaxation, under stress, of acrylic thermosettings in hot water has been investigated by Hakozaki [214]. Epoxy resins and melamine were used as vulcanisation reagents and the working temperatures varied from 140 to 160 o C. After a preliminary treatment in boiling water for 90 min, the behaviour to stress relaxation was followed. The relative stress is expressed by the relation [177]: f (t ) / f (0) = A exp ( − k1 t ) + B exp ( −k 2t ) + C exp ( − k3t )

(2.163)

The rate constants of the stress decay factors and the pre-exponential terms, which characterise the acrylic resins with different contents of epoxy resins, are collected in Table 2.8. Equation (2.163) can be particularised for different values of the epoxy resin content. Thus, for the acrylic resin without epoxy resin or with 5% epoxy, only a single exponential term is required to describe with sufficient accuracy the variation of the relative stress. For those mixtures containing 10% and 20% epoxy resin, two or event three exponential terms are required. The contributions of different types of reticulated structures are reflected in a discrete set of the relaxation times, equation (2.163). Figure 2.67 compares the stress-relaxation curves determined in air and water at 98 o C. The faster decay of the relative stress in water was explained by the hydrolysis reaction that occurs at the reticulation centres. In air the observed behaviour was ascribed to thermal degradation. The stress decay rate increases concomitantly with the increase 145

Macromolecular Mechanochemistry Table 2.8. Rate constant and the pre-exponential factors corresponding to equation (2.163) [214] Epoxy resin content (%)

A

k 1 x10 2

t1

(min -1 )

(min)

k 2 x10 3

B

t2

C

k 3 x10 4

t3 (min)

(min) 0 5 10 20

1 1 0.284 0.180 0.023

1.63 1.44 1.23 1.18 8.82

61 69 82 88 11

0.708

1.18

848 0.795

2.81

3580

Figure 2.67. Stress relaxation curves of epoxy resins in air and water, respectively, at 98 o C [214].

of the epoxy chain length, i.e. with decrease of the network density, Figure 2.68. The determined value of the activation energy was 130 kJ/mol, this being an argument in the favour of macromolecular chain splitting hypothesis. 2.7.6.3. Characterisation of some thermosetting resins TBA method (torsional braid analysis) elaborated by Gillham and co-workers [215] and modified by Naganuma and co-workers [216] has been used for the characterisation of rigidity increase during the reticulation of some resins used for varnishes and adhesives. The changes of Young’s modulus examined during the reticulation reactions of some commercial cyanoacrylates and in Figure 2.69 [217]. It was established that only 70% of the reaction occurred up to the gel-point and, in fact, the post-reticulation reaction occurring subsequently has the main role in the resin mechanical properties 146

Mechanochemistry of Polymer Deformation

Figure 2.68. The influence of the initial molecular weight of epoxy resin on the shape of stress-relaxation curves in the case of epoxy-acrylic resins in boiling water. The epoxy resin content is 10% and the average molecular weights of Epon 828, 1001, and 1004 are 390, 1000, and 1850, respectively [214].

Figure 2.69. Crosslinking reactions of trade cyano-acrylates adhesives, at 20 °C, studied by the dynamic spring analysis (DSA) technique [217].

[71]. In this way, chemomechanical studies of the post-reticulation process are very important, the most representative cases being those of epoxy resins reticulated with amines [218]. Arridge has studied in detail the dependence of relaxation on the degree of reticulation. According to the data depicted in Figure 2.70, the maximal values of tan δ and T increase with the increase 147

Macromolecular Mechanochemistry

Figure 2.70. Modification of γ-relaxation with the reticulated state for aminoepoxy resin [218]. Figure 2.71 (right). The dependence of elasticity modulus with temperature for different reticulations. Vulcanisation temperatures for Esant A, B and C resins are 19 o C, 84 o C, and 159 o C, respectively [ 218 ].

of the reticulation degree. The change of the elasticity modulus (transversal) with the vulcanisation degree is illustrated in Figure 2.71. Elasticity modulus γ increases concomitantly with the evolution of the reticulation process and it was proposed that its value, both below and above the transition γ, represents the quantitative measure of reticulation in the post-reticulation region, Figure 2.72. 2.7.6.4. Characterisation of some textile fibres The application of chemorheological methods to the characteris-

Figure 2.72. The elasticity modulus as a function of vulcanisation period for 3 different reticulation temperatures: × – 120.8 °C; ˜ – 132,8 °C;  – 145.6 °C [218]. 148

Mechanochemistry of Polymer Deformation

ation of textile fibres was generally limited, the majority of them being obtained from linear polymers which, for the abovementioned reasons, are less suitable for this kind of experiments. However, wool fibres as well as those based on poly(vinyl alcohol) fibres, insoluble in water, show an adequate behaviour for the chemorheological characterisation. Thus, in the case of woollen fibres, the intercatenary cysteine bonds are of the disulphide type and they play an important role in the stabilisation of the α-cheratine structure of the native fibres. The splitting of these bridges and their remaking are deeply reflected in the mechanoelastic properties of the wool fibres and this behaviour constitutes the basis of application of chemorheological methods [219–224]. The chemical stress relaxation of the wool fibres was measured in water and in aqueous solutions of sodium disulphite of different concentrations. It was found that sodium disulphite acts as a selective reducing reagent with respect to the cysteine groups. The decay of the relative force rate, f(t)/f(0), in aqueous solutions of NaHSO 3 increases with the increase of NaHSO 3 concentration. However, at a low NaHSO 3 concentration it is not affected by the salt content. Similar results were obtained in the presence of thioglycolic acid, cystine, and NaCl, respectively. The chemical stress relaxation rates of the woollen fibres were significantly increased in the presence of reducing reagents, but these curves remained practically unaffected in the case of nylon based fibres, Figure 2.73. A kinetic study concerning the chemical stress relaxation of

Figure 2.73. Effect of NaHSO 3 addition on the detensioning of the following fibers: open circle – wool; half-filled circles – silk; full circles – nylon, respectively, in water at 30 °C. The arrows indicate the moment when NaHSO 3 was added [220].

149

Macromolecular Mechanochemistry

wool fibres was performed on the reactions of cysteine solutions with the chemical bonds from the macromolecular support. The investigated parameters were the cysteine concentration, pH, and temperature, respectively. The possible chemical reactions are presented bellow: R

S

S

R + Cys

R

S

S

Cys + Cys

k1

SH

k2 SH

R k3 k4

S Cys

Cys + R

S S

S

SH

Cys + R

SH

where: Cys-SH cystine

When deriving the kinetics equations, the following hypotheses were considered: 1. The reticulation reaction, which is characterised by the rate constant k 2 , does not influence stress decay; 2. The cysteine concentration is maintained constant during the reaction period due to its large excess; 3. The difference f(t)–f(∞) is proportional to the cysteine content (where f(t) and f(∞) is the stress at the time t and at the equilibrium, respectively). The above-presented hypotheses are sustained by a rigorous analysis of the cysteine content. It was found that f(∞) corresponds to the stress induced by the physical bonds. The reaction follows a first order pseudokinetic, according to the following equation:

(

)

éë f (t ) - f ( ¥)ùû / f (0) = (1 - f (¥)) / f (0) exp k1 [Cys - SH ]0 t (2.164) The graphical representation of equation (2.164) leads to the curves presented in Figure 2.73. It can be noted that the reaction rate decay, at low values of pH, is related to the low values of the dissociation constant of the sulphydryl group from cysteine, in these conditions. The heat and entropy of activation were 72 kJ and 8.8 e.u., respectively. A series of technological operations can be explained in the terms of chemorheology, for instance, the ‘fixation’ process. Thus, the action of water vapours on the wool fibres has two effects, depending on the period of contact; the stressed fibres, to a given stretching force, under tensioned state and in the presence of water

150

Mechanochemistry of Polymer Deformation

vapours suffer: 1) supra-contraction, at short periods of vapours action (2 – 3 min); and 2) ‘wool fixation’, at longer periods of water action (25 – 30 min). The mechanism of water vapours action on tensioned wool is not so simple. It occurs at the level of hydrogen bonds, but especially at the cysteine bridges level. These bridges are converted in two acidic components, i.e. cysteic and sulfenic acid, respectively, as the following scheme shows: CO

NH

CH

CH2

S

CH2

S

CH

H+ -OH

CO

NH

CO

NH

CH

CH2

SH + HOS

CH2

CH CO

NH Sulfenic acid

Cysteic acid

By treating the woollen fibres with water vapours, in stretched state, for short periods, the α-conformation of the native keratin passes in β-conformation. Removing the applied load the fibres contraction takes place, with about 30% of initial length; this phenomenon is called “supra-contraction” and is illustrated bellow: Model of the reversible transition of α- into β-cheratine CHR

o

OC

NH

NH

HN

CO

RCH

RHC CO

NH

5.1 A

HN CHR

o

CHR RCH CO OC

OC

NH NH

HN

CO

RHC

RCH

CO HN

151

10.3 A

Macromolecular Mechanochemistry

Schematic representation of the folded model of α -cheratin and its transition into β -cheratin.

In the contracted state, the macromolecules are in the α-keratin conformation, more coiled, due to the scission of a certain number of hydrogen bonds. In the fibres tensioned for a long period (20– 30 min) and under the action of water vapours the macromolecules pass in the strengthened conformation of β-keratin. After removing the load, the fibre remains in the elongated state, with respect to its initial state. The length difference represents a measure of ‘wool fixation’. The relaxation rate was analysed in correlation with the second order vitreous transition temperature (T g ), which was considered the inferior limit of fixation treatment. Below T g relaxation was ascribed to the reversible transformations of the native keratin and above this limit the process was associated with irreversible bond splitting. Detailed studies concerning the behaviour during unloading in boiling water have been carried out by Weigman [225]. The author concluded that this process consists in two steps. The first one faster occurs, requiring a lower activation energy and it is mainly based on the relaxation of secondary bonds. The second sage much slowly occurs. The recorded curves, in phosphate buffer solutions, at pH = 7, are presented in Figure 2.74. The second stage prevails at high temperatures. The relaxation modulus, at 10 s after elongation, is presented in Figure 2.75. The experiments were made in the presence of N-ethyl maleinimine, NEMI, a reagent that is recognised as a blocking reagent of the 152

Mechanochemistry of Polymer Deformation

Figure 2.74. The values of the relaxation modulus in time for the wool fibres into the phosphate buffer, pH = 7 [225].

Figure 2.75. The relation between relaxation modulus of wool fibres and temperature. The relaxation modulus E r(10) was determines 10 s after elongation, pH = 7, and elongation 20%, (500%/min) [225]..

sulfhydril groups. The intense relaxation, observed in the second step, occurs at 70 o C, above the transition temperature. The reaction is greatly delayed by adding the NEMI. This process is well approximated by a simple relation of the Maxwell type and its activation energy corresponds to a value of 96 kJ/mol. This value suggests that the mechanism of relaxation in this stage is based on the sulfhydrilsulfure reaction. In water, the occurrence of the above-mentioned reaction is also justified by the mechanodynamical data. The chemorheological methods have been widely used for the 153

Macromolecular Mechanochemistry

elucidation of the nature of different intercatenary reactions of keratin fibres that constitute the wool [224, 226]. Other textile fibres have also been characterised by chemorheological methods. Nevertheless, the use of this method to other fibres than the woollen ones is limited due to the absence of intercatenary chemical bonds from their structure. Among the problems of practical importance which could be solved in this way, it is worth mentioning the estimation of the capacity of access of different reagents to the crystalline–amorphous biphase structures. The behaviour of different natural or synthetic fibres in distilled water, with or without chemical reagents, was different. Thus, nylon relaxation occurs rapidly concomitantly with the increase of the amount of HCl, but the specific curves, obtained for polyester fibres, remained unchanged in the presence of this reagent. In the case of cellulose fibres rapid relaxation was observed in 0.1 N HCl aqueous solutions. This behaviour was explained by the scission of glycozidic bonds from the cellulose macromolecules [227]. Lemiszha estimated that HCl relative accessibility with the respect to different zones of cellulose fibres can be evaluated as a function of extrapolated interruptions of the linear parts of the curves f(t)/f(0). Thus, the obtained values are in good accordance with those furnished by other methods. This fact demonstrates the potential of the relaxation method to the estimation of reagent accessibility. The following equation:

f ( t ) / f ( 0) =

s

å Ane- k t n

n =1

(2.165)

is empirically applied to describe the relaxation of cellulose fibres, induced by diluted HCl aqueous solutions. A n and k n are specific parameters when the relaxation fraction and frequency are of the order n. The physical meaning of this equation has been clarified by Canter [228]. Quantitative estimation of the water effect on relaxation was also realised for other fibres, such as cellulose diacetate or poly(acrylonitrile) fibres [229]. 2.7.6.5. Some aspects of the chemorheology of linear amorphous polymers The chemorheology of linear polymers is more difficult to be treated from the theoretical point of view, because the molecular

154

Mechanochemistry of Polymer Deformation

flow by diffusion is generally faster than the relaxation or flow caused by chemical reactions. Apart from polymer networks where physical relaxation is negligible, in the case of linear polymers in their rubbery-flow range range, it is necessary to take into account both the chemical and physical relaxation. Tobolsky and co-workers have derived equation (2.108) and the box distribution of relaxation times with respect to the relaxation modulus E r (t) in the rubbery flow region of amorphous polymers.

{

}

Er (t ) = E0 Ei ( - t / t e ) - Ei ( - t / t m )

(2.166)

where E 0 is the height of the box-shaped relaxation spectrum; τ e and τ m are the minimum and maximum relaxation times in the rubbery flow range, respectively; E i (–x) is the integral exponent, which can be expressed by the relation:

Ei ( - x ) = -

¥

ò (e

-U

)

/ U dU = ln x + g - x + ( - x ) / r + ..... α (2.167)

x

r

where γ is Euler’s constant, equal to 0.5772. In the case of polystyrene degradation, in the presence of some peroxides, one assumed a first-order reaction, where k 1 is the rate constant and M (t ) and M (0) are the molecular weights after time t and at t=0, respectively, the following equations will be valid: - d M (t ) = k1M (t ) dt

(2.168)

M (t ) = M (0) e - k1t

(2.169)

It is well-known that τ m – the average relaxation time – is proportional to the 3.4 th power of the molecular weight. Thus, τ m of the polymer is given by:

{ } (t ) = k {M (t )}

t m ( 0) = k2 M ( 0) tm

3.4

3.4

2

(2.170) (2.171)

Substituting the ratio of τ m (t) to τ m (0) into equation (2.168), equation (2.172) is obtained: t m (t ) / tm (0) = e -3.4 k1t

155

(2.172)

Macromolecular Mechanochemistry

Again, substituting the time dependence of τ m(t) for τ m in equation (2.166) for chemical degradation and physical relaxation, respectively, for a linear amorphous polymer gives:

{

(

Er ( t ) = E0 Ei ( - t / t e ) - Ei - t / t m (0) e3.4 k1t

)}

(2.173)

Additional information has been obtained by comparing the measured and predicted theoretical values. Stress relaxation was measured varying the molecular weight, thus determining E 0 , τ m, τ e and k 1 . The investigated samples were monodisperse samples of anionically polymerised styrene and two samples of polydisperse polystyrene (differing from each other by values of M η and M ω , respectively. In order to measure the chemical relaxation at 120 o C, samples containing 2, 3 and 5 parts of dicumyl peroxide, respectively, were cast from dichloromethane solutions and dryed in vacuum for two weeks. The stress relaxation curves of the monodisperse and polydisperse polystyrenes are given in Figures 2.76 and 2.77, respectively. The master curves for physical relaxation are shown for the reference temperature of 120 o C. The stress relaxation decay increases with an increase of the dicumyl peroxide amount for the samples containing dicumyl peroxide at 120 o C in a N 2 stream.

− ln

M (t ) vs. time and logE r (t) vs. time are plotted in Figures M (0)

Figure 2.76. Physical and chemical relaxation of monodisperse polystyrene at 120 °C in nitrogen atmosphere [224]. 156

Mechanochemistry of Polymer Deformation

Figure 2.77. Physical and chemical relaxation of polydisperse polystyrene at 120 °C in nitrogen atmosphere [224].

Figure 2.78. Variation of ln[M(t)/M(0)] with time at 120 °C in nitrogen atmosphere for monodisperse polystyrene with dicumyl peroxide [230]:  – 5 parts DCP, k 1 = 2.04×10 –3 min –1 ; – 3 parts DSP; ˜ – 2 parts DCP.

2.78 and 2.79, respectively. Since straight lines are obtained for both polystyrenes containing 5 parts of dicumyl peroxide, the rate constants of decomposition can be calculated as K 1 =2×10 –3 min –1 for monodisperse polystyrene and as K 1 =2.04×10 –3 min –1 for polydisperse polystyrene, respectively [230]. The results indicate a fast decomposition followed by a slower process of decomposition for both mono- and polydisperse samples. The time required to reach the second decomposition process increases with increasing dicumyl peroxide concentrations. For the sample containing 5 parts of dicumyl peroxide it takes about 600 min; however, the first-order kinetics appear to be followed over 157

Macromolecular Mechanochemistry Table 2.9. Kinetic parameters calculated from equation (2.173) [224]. Polystyrene sample

E0 (dyne/cm2)

τm (min)

τc (min)

k1 (min–1)

monodisperse polydisperse

1.09 × 106 1.09 × 106

1.96 × 104 4.34 × 104

6.43 × 10 –2 6.43 × 10 –2

2.10 × 10 –3 2.04 × 10 –3

Figure 2.79. Representation of logE r (t) vs. time for polystyrene using the method x [230]: half-filled circles – monodisperse polystyrene, τ m = 1.96×10 4 min; open circles – polydisperse polystyrene, τ m = 4.34×10 4 min.

the entire time range. In this experiment, the values of the rate constant are almost constant and independent of the molecular weight distribution. The kinetic parameters calculated according to equation (2.173) are listed in Table 2.9. The comparison of curves calculated from theoretically determined constants with those calculated from measured values is shown in Figures 2.80 and 2.81. It can be seen that the measured curves deviate considerably from the calculated ones for polydisperse polystyrene, in contrast to those for monodisperse polystyrene, with the exception of the sample containing 5 parts of dicumyl peroxide. The above-mentioned experimental results show that the sample containing 5 parts dicumyl peroxide the measured values are smaller than the calculated ones; however good agreement was obtained for the sample containing 2 parts of dicumyl peroxide for both polystyrenes. The melting point of dicumyl peroxide is 39 oC, so it will be liquid and will affect the plasticity appreciably. This is the reason why the relaxation is greater for the sample containing 5 parts 158

Mechanochemistry of Polymer Deformation

Figure 2.80. Comparative representation of the (——) - calculated and ( ____ ) experimentally obtained relaxation curves for the monodisperse polystyrene [230]. E 0 = 1.09×10 6 dyne/cm 2 ; τ m = 1.96×10 4 min; τ e = 6.43×10 –2 min; K 1 = 2.10×10 –3 min.

Figure 2.81. Comparative representation of the (——) - calculated and ( ____ ) experimentally obtained relaxation curves for the polydisperse polystyrene [230]. E 0 = 1.09×10 6 dyne/cm 2 ; τ m = 4.3×10 4 min; τ e = 6.34×10 4 min; K 1 = 2.04×10 –3 min

dicumyl peroxide than that for the others. Equation (2.174) adequately describes the rubbery flow region of monodisperse polystyrene:

{(

Er (t ) = Er (0) exp - (t / t )

B

)}

(2.174)

where E r (0) is the value of modulus on the rubbery flow region; τ defines the period of E r (t) decay until to E r (0)/e; B is the specific parameter for the rate of modulus decay, which governs the shape 159

Macromolecular Mechanochemistry

of the rubbery flow region. Starting from equation (2.174) that describes the stress chemical and physical relaxation and taking into account that the parameter E r (0) and B are constants, and τ depends on time t [217,218], the following equation is obtained:

{

Er (t ) = Er (0) exp - (t / t (t ))

B

}

(2.175)

τ was found to follow equation (2.172), when expressed in seconds, for modulus curves at 115 o C, and is calculated as follows:

{ }

t115 (t ) = 1.4 × 10-14 M (t )

3.4

(2.176)

from the equations (2.175), (2.176) and (2.169) one obtains the equation:

(

ì Er (t ) = Er (0) exp í - éê t /1.4 × 10-14 M ( t ) î ë It was established that:

)

3.4 ù -3.4 kt ü

úû e

ý þ

(2.177 )

for M w / M n = 1.05 B = 0.608 and for M w / M n = 2.53 B = 0.275 By interpolation and extrapolation of the values of M w / M n for all polystyrene types investigated, the values E r (0), τ(0) and B thus calculated are collected in Table 2.10 [231]. The curves of chemical relaxation for both monodisperse and for two polydisperse polystyrene samples, established in the presence of 2 parts DCP were recorded at 120 o C, in the nitrogen atmosphere, are presented in Figure 2.82–2.84. Three arbitrary chosen theoretically curves, i.e. one for each value of k (k = 0.00064 min –1 ; k = 0.0021 min –1 ; k = 0.0450 min –1 , respectively) have been obtained using equation (2.177). These curves were compared with the experimental value of PS–2 (Figure 2.82). It can be noted the good agreement Table 2.10. Characteristic parameters of equation (2.177) [231] Polystyrene Monodisperse Polydisperse Polystyrene PS-2

log Er (0) (dyne/cm2)

τ0 (min)

B

6.96 7.20 7.03

2884.00 301.99 150.00

0.488 0.258 0.229

160

Mechanochemistry of Polymer Deformation

Figure 2.82. Calculated and experimental curves of chemical relaxation for monodisperse polystyrene in the presence of DCP at 120 o C in nitrogen atmosphere [232].

Figure 2.83. Calculated and experimental curves of chemical relaxation for polydisperse polystyrene in the presence of DCP at 120 °C in nitrogen atmosphere [232].

Figure 2.84. Calculated and experimental curves of chemical relaxation for polystyrene PS-2 in the presence of DCP at 120 o C in nitrogen atmosphere [232].

161

Macromolecular Mechanochemistry

between the theoretical and experimental curves for the two polystyrene samples, Figures 2.83 and 2.84. On the basis of these results, one can conclude that equation (2.177) most adequately describes the phenomenon than equation (2.173).

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169

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MECHANOCHEMISTRY OF POLYMER FRACTURE

3

E.H. Andrews defined the fracture as the formation of new surfaces in a solid body [1]. Even, in appearance, this phenomenon seems to be simple one, it is very comprehensive, including not only the fluctuation occurring under the action of the external forces, but also those occurring either by thermal fatigue (having at their base the internal forces) or by cohesion (which implies the energy released by chemical reactions). Furthermore, even the fracture process that occurs, as result of mechanical stressing, is not independent by the thermal processes that take place into the stressed body. Particularly, in the case of polymers the fracture is strongly related to their chemical structure, physical state, and to the nature of environmental medium. 3.1. THEORIES CONCERNING POLYMER FRACTURE 3.1.1. Basis of the theor y of the local cchar har acter of def or ma tion theory haracter defor orma mation After the publication of the first theoretical studies of Tobolsky and Eyring [2], the most probable mechanism of polymer fracture has been considered, so-called “intermolecular” mechanism. This mechanism supposes the “sliding” of macromolecules each to other. It starts from the hypothesis that the secondary bond energy is very low as compared to the energy of covalent bonds; so, the assessment that the first type of bonds are easier split, under stress conditions, appears to be valuable. According to Eyring and Halsey, the polymer fracture take place by dislocation of the macromolecules that are retained by second170

Mechanochemistry of Polymer Fracture

ary valence bonds, as a consequence of the thermal activation of the chain segments rotation [3]. The fracture would also occur by a progressive decay of the chains number from the stressed sample transversal section. In the case of the long chains that pass several times through the fracture section, due to their high coiling degree, some ‘knots’ may appear. Under the action of the applied force is possible for such ‘knots’ to be pulled out from the above-mentioned section, leading to a decrease of the number of chains that traverse the section and, consequently, the concentration of mechanical energy on the remained chains. By continuing loading, the sliding of the ‘knots’ is followed by chains scission. The maximal deformation that can be reached by a given polymer without to be fractured depends on the number of the ‘knots’; in turn, this number is conditioned by the different ways of macromolecules twisting. Thus, the perfectly stretched chains suffer a minimal deformation while the statistically coiled ones permit a maximal deformation, without macromolecule scission. In the latter case, the applied stress is converted to mechanical work used for the separation of the clews bonded by van der Waals forces. Real polymers show an intermediate behaviour as a result of greatly different mechanisms of chains coiling which determines, even in the same material, a very broad distribution of the clews dimensions. This distribution will affect the behaviour to the fracture at high deformation and the load will be transferred on the most stressed knots; these ones will be unknoted, usually causing an increase of material mechanical resistance. The temperature and many chemical reagents also affect polymer behaviour to fracture [4]. The intermolecular mechanism of polymers fracture has been accepted until the more efficient techniques of structure investigation, i.e. ESR, IR, mass spectroscopy, etc., proved that during stress application, the scission of covalent bonds from the polymer’s backbone takes place. It was established that the scission of covalent bonds is the elementary act of the polymers’ fracture. 3.1.2. Gr if y Grif ifffith’ ith’ss theor theory It is well known that in condensed state, the atoms are in the equilibrium positions around of each they effectuate vibration movements. As is seen in Figure 3.1, these positions are characterised by a minimal energy [5]. Under stress the atoms are shifted from the equilibrium positions, thus storing an certain amount of energy. After the stress is removed, this energy is wasted and the atoms recover their initial state. On the whole, the system 171

Macromolecular Mechanochemistry

Figure 3.1. Interatomic potential energy [5].

suffers elastic deformation. If the applied stress is characterised by high values and it is accompanied by the action of thermal vibrations, the atoms will pass into a new equilibrium position. However, sometimes to reach this position the interatomic distance is so much increased that the chemical bond splitting occurs. In this way, new atomic configurations appear. By transposing all these individual atomic events at the macroscopic scale, the plastic deformation results. It reflects the totality of mechanochemical phenomena that occur into a mechanically stressed system. The tensile strength of a stressed chemical bond is given by the following equation: σm ≅ E ⋅ εm

(3.1)

where E is Young’s modulus, characteristic for the considered solid body; ε m is the deformation corresponding to the applied stress. For the majority of the chemical covalent bonds ε m = 0.1–0.2 and the tensile strength of the bond becomes: σm = α ⋅ E

(3.2)

where 0.1 < α < 0.2. For an ideal elastic solid, the tensile strength is given by the resistance of its individual atomic bonds, therefore:

σ f = σm = α ⋅ E 172

(3.3)

Mechanochemistry of Polymer Fracture

where σ f is the macroscopical tensile strength. The above relation defines the theoretical resistance of the stressed body. It was deduced for a continuous and uniformly stressed body, under the assumption that the stress is uniformly distributed on the chemical bonds and also neglecting the fact that this body ‘works’ in certain conditions of temperature. The net result of the action of σ f should be the complete dissociation of the atoms, in a similar way as the passing of a liquid to the gaseous state at its critical temperature. Generally, the solid bodies and especially the polymers do not accomplish the above-mentioned conditions. Thus, the experimentally determined results are far from the theoretical ones; the proportionality factor, α, having values ranging from 10 –2 to 10 –4 . Griffith explained the differences between the predicted values by equation (3.3) and the measured ones by the inevitable preexistence of some cracks inside of the stressed body [6]. These ones grow during the stress application, giving the possibility as the local force to increase very much as compared to the normal applied one, which acts in the rest of the stressed body. Let us considering a sample from a stressed body, of unitary thickness, that is crossed by an elliptical crack, having its semiaxes denoted with a and b, respectively (Figure 3.2), and the stress, σ 0 , acting perpendicularly on the crack’s length. According to the theory of elasticity, the maximum stress is located at the crack tip:

b

σ = σ 0 1 + 2a / b

g

Figure 3.2. Preexistent elliptical crack [7]. 173

(3.4)

Macromolecular Mechanochemistry

where: (1 + 2a/b) is the stress concentration factor The ellipse curvature radius is given by: (3.5) ρ = b2 / a by substituting the Eqn. 3.5 in Eqn. 3.4, the following relation is obtained:

b g

1/ 2

σ = σ0 1 + 2 a / ρ

(3.6)

which in the case of a >> ρ becomes:

b g

1/ 2

σ = 2σ 0 a / ρ

(3.7)

Under the assumption that σ = σ m and by replacing it in equation (3.7) the expression for real tensile strength, σ f , is obtained:

σf =

b g

σm ρ/ a 2

1/ 2

(3.8)

Relation (3.8) can be in a small measure applied since its utilisation supposes the knowing of curvature radius. This difficulty was overtaken working in terms of mechanical work. Thus, if the cleavage of a monocrystal (Figure 3.3) is considered and supposing

Figure 3.3. Monocrystal subjected to stretching stress σ m [7]. 174

Mechanochemistry of Polymer Fracture

its ideal behaviours, i.e. a linear stress vs. deformation behaviour, the mechanical work, W cr , consumed for atom separation is given by the relation:

Wcr = 1 / 2σ m d 2ε m d = 1 / 2σ m d 3 ε m

(3.9)

where d is the interatomic distance; ε m is the maximum deformation of the chemical bond. In the fracture plane, the mechanical work on the surface unit area is equal to: 2 ε m σ md 2 σ m d = 2 2E

(3.10)

The left hand term of Eqn. (3.10) is the twice the surface energy, S, due to the fact that during crystal’s fracture the energy of fluctuation is equally distributed on the two faces. Therefore:

S=

σ m2 d 4E

(3.11)

by replacing σ m from relation (3.11) in Eqn. (3.8) the following expression is obtained:

LM E ⋅ S ⋅ ρ OP N a dQ

1/ 2

σf =

(3.12)

In the case of monocrystal plane cleavage, it is assumed that ρ = d, and finally we obtain:

LM E ⋅ S OP Na Q

1/ 2

σf =

(3.13)

Equation (3.13) expresses the quantity of effort required for the fracture of a body containing cracks with a length equal to 2a. A similar equation was deduced considering the lost of elastic accumulated energy into a tensioned lamellae with an elliptical crack having its long semiaxis equal to e. The new generated sur175

Macromolecular Mechanochemistry

face accumulates on the unit surface an amount of energy, S, which is obtained by multiplying the interatomic bond energy by the number of bonds traversing the surface unit. Correspondingly, the stored mechanical work in the fracture section is equal to 4 . e .S. At the moment of crack opening a decay of mechanical work occurs than can be expressed by the following equation:

Wcr =

πe 2 σ 2 E

(3.14)

where σ is the uniaxial stress; E is the elastic modulus. The amount of energy changed in the system is:

Wt = 4eS −

πe 2 σ 2 E

(3.15)

The above equation allows the calculation of the value of the elliptical crack semiaxis, c cr , when fracture propagates in the absence of thermal energy: dWt / dc = 0

(3.16)

and therefore:

ccr =

2E ⋅ S πσ 2

knowing c cr , σ f can now be calculated:

σf =

2E ⋅ S π ⋅ ccr

(3.17)

Equation (3.17) is practically identical with equation (3.13). According to the results of calculations, the surface energy (S) represents a half of the required energy for the fracture of unitary surface which contains interatomic bonds passing through the plane during the propagation of the existing bonds. At the boundary conditions, in equation (3.17), when c → 0, c cr must be replaced by (c + d), where d is the interatomic distance. 176

Mechanochemistry of Polymer Fracture

The importance of Griffith’s theory is the fact that it expresses the fracture energy (or the resistance of the chemical bonds) in terms of surface energy S. The limits of this theory are related to the assumption that the material is considered as a continuous ideal solid, having an elastic behaviour. It does not take into account the irreversible deformations, with other words the energy damages that prevail in crack’s proximity, which depend on time and temperature. Consequently, the Griffith’s equation predicts the lower fracture force than those experimentally measured, even for the brittle polymers. Two approaches have been proposed to improve this model. In the first one, Orowan have generalised the term S in order to include the contribution of dissipation energy on the new generate surfaces [8]. This modified ‘surface energy’ has been designed as ‘surface work’, ℑ . Its main shortcoming is that ℑ can not be correlated with the physical parameters of the solid body. Even if this value is constant for a given material, it still depends on many factors, such as: temperature, deformation rate, sample thickness, etc. In the second approach, Irwin characterised the stress field which surrounds an existent crack in a stressed body, by a field parameter, k, so-called ‘stress intensity factor’. The fracture occurs just in the moment when k reaches a critical value, k cr. Unfortunately, this parameter also can not be correlated to the physical characteristics of the stressed body [9]. Although the Griffith theory played an important role in the knowledge of the atomic–molecular basis of fracture, this theory is not valuable in the case of polymers. Even after the already mentioned improvements made by Orowan and Irwin, the above theory remains an empirical one, due to the operation with parameters T and k cr , which can not be correlated to the material physical properties and, consequently, they can not be predicted. The theory of continuous solid that analyses the stress–strain dependence in the voids or crack proximity and leads to some crack stability criteria, by considering the energetic balance, is known as ‘the theory of mechanic fracture’. The main result of Griffith’s theory is the statement that as a result of a preexistent crack increase, the energy also increases. By equalising the stored elastic energy decay, dU, with the superficial energy, σdA, required for the increase of a crack of infinitesimal area, dA, the following relation is obtained:

177

Macromolecular Mechanochemistry

ó* = ( 2óc ×E/ð×a )

1/2

(3.18)

where: σ* – the macroscopic uniaxial stress; σ c – the parameter of surface mechanical work; a – the length of the elliptical crack; E – Young modulus. It results that the dimension of the biggest fault of the stressed body, together with its physical characteristics (modulus of elasticity and surface mechanical work) exceeds the mechanical resistance of the body; i.e. the value of uniaxial macroscopic stress, σ*. When this value is attained, the initiation of the magistral crack and the catastrophic propagation of fracture takes place. Application of the continuous solid theory to the visco-elastic bodies, particularly to polymer materials, is limited on one side by the deviations from the conditions of infinitesimal deformation and on the other side by the pronounced dependency with the time both of the stress and deformation. The extension of Griffith’s theory to the visco-elastic materials with a linear behaviour is due to contributions of William [10], Knauss [11], and Nikitin [12]. Its application to the study of polymers’ mechanical resistance evidenced a series of supplementary effects, such as: rotation, elongation, and broadening of the existent faults [13, 14]. Their shape and orientation modification has as a consequence the change of voids effect as centres of stress concentration. Thus, those voids become less dangerous in the parallel direction to those of orientation (z) and more critical on the perpendicular direction to the voids (x). If the growth of the elliptical crack only parallel to the orientation direction is taken only, then the expression for lateral mechanical resistance σ x , derived from equation (3.18) is as follows:

b g

σ x = 2σ c E 1 + λ π ⋅ a

1/ 2

(3.19)

where λ is the stretching ratio. In the case of statistical distribution of crack orientation, taking into account different geometric shapes, a complete calculation – in the tridimensionally space – concerning effects of fault rotation and broadening on the axial and lateral mechanical resistance of the stressed body, have been performed [15]. For instance, in the case of polystyrene with moderate average molecular weights and stretching ratios smaller than 1.5 was found a deviation of about 20% for the predicted values [16]. At the higher values of the 178

Mechanochemistry of Polymer Fracture

molecular weight and stretching ratio the deviations can exceed 70%. In order to characterise the visco-elastic behaviour of the solid polymers, the model of ‘wrapping fracture’ has been developed. It assumes that if the fracture criterion refers to the limits of material ability to support a given effort, at the level of its molecular structure, than the representation of the tensile stress at the fracture vs. deformation, for different experimental conditions, leads to a single master curve, which is just the ‘wrapping fracture’. This concept was verified on for a great number of elastomers sumitted to the same type of mechanical stressing. It allows the extrapolation of the behaviour during the fracture process in portions, which have an unknown solicitation level with respect to deformation rate, duration, and temperature. Latter, this model was extended, by Fedors, to the fracture of uniaxially stressed elastomers [17]. The discrepancy that appears between the ‘wrapping unfolding fracture’ values, for different types of deformation, can be solved by expressing the generalised energetic function as a constitutive part of the multiaxial deformation equation [18]. Thus, in the case of uniaxially stretching and compressing, and of shearing of the natural and poly(butadiene) rubber, the simultaneous description of the stress–strain curves, using four material constants, was achieved.

3.1.3. Kinetic theor ies of fr actur theories fractur acturee Generally, the continuous visco-elastic models start from the theory of elastomer elasticity as well as from the principle of time– temperature superposition. These models recognise the molecular origin of the polymer materials, their visco-elastic behaviour, but do not make any explicit correlation with the material’s structural parameters, such as: macromolecule length, anisotropy of the mechanical properties or molecular force distribution, and of stored mechanical energy. Apart from the theories that consider the bodies as continuous solids, the kinetic–molecular theories of the fracture recognise the fact that these bodies, and especially the polymers, are composed by distinct particles. According to these theories the macroscopic fracture is regarded as a kinetic process, whose main steps are controlled by the thermally activated primary and/or secondary bonds scission. In addition, the accumulation of these scissions in limited areas causes the apparition of the nascent cracks that finalises through the macro179

Macromolecular Mechanochemistry

scopic fracture of the stressed body. Based on the Glasstone, Laidler, and Eyring theory [19], which assumes that the liquid movement and diffusion phenomena are based on thermally activated jumping of molecules over a given energetic barrier that, at equilibrium, delimits the initial and final positions, respectively, a series of concepts concerning the polymer fracture have been postulated. The fluids’ flow represents the result of irreversible thermodynamic movement of its molecules each to other. The displacement of a molecule from its initial equilibrium position to a neighbouring one occurs only if their thermal energy is high enough in order to reach the activated state, i.e. the maximal value of the energetic barrier that separates the initial and final position of equilibrium. In the absence of the external forces, the equilibrium initial and final states have the same potential energy and the rates of particles’ movement over the potential barrier that separate the two states are the equal on the two directions. In the presence of the external forces, a local field of force arises. Thus, a particle that moves in the direction of molecular stress application, Ψ, on o distance λ/2 stores on amount of energy, W, equal to:

W = Ψ⋅

λ ⋅q 2

(3.20)

where q is the average transversal section occupied by this particles on the normal direction to the movement. In the case when the movement is in opposite site of the effort’s direction, the particle will lose the same amount of energy. The particle flow rates over the energetic barrier in the two opposite directions are influenced by the local applied stress. The expressions of flow rate constants are the following:

b g = k expb −W / kT g

k1 = k 0 exp W / kT

(3.21)

k1

(3.22)

0

where: k 0 – constant of molecular collision frequency; k – Boltzman’s constant; and T – temperature, in Kelvin degrees. The net result of the flow rate is given by:

180

Mechanochemistry of Polymer Fracture

b

k = k1 − k 2 = 2 sin h W / kT

g

(3.23)

Starting from the original concept of liquid flow, many theories concerning to polymer fracture have been developed. Thus, Tobolsky and Eyring regard the decay of the number of secondary bonds as the governing factor of fracture process [20]. S.N. Jurkov [21–23] and F. Bueche [24–26] considered that the fracture of solid bodies as an accumulation process of interatomic bonds splitting, in the conditions of mechanical solicitation, and under the action of the thermal fluctuations, putting in this way the bases of fracture kinetic theory. They found that the poly(methyl methacrylate) and poly(styrene) durability, under the conditions of uniaxial stress application, at the temperatures below their glassy temperature can be expressed by an exponentially relation, which implies three kinetic parameters:

b

τ = τ 0 exp U 0 − γ ⋅ σ 0 / RT

g

(3.24)

Based on the available data, the three parameters are interpreted as: U 0 – activation energy of chemical bond splitting; τ 0 – the inverse of molecular oscillation frequency; and σ – structural parameter. Equation ( 3.24 ) is considered as being the general expression that reflects the kinetic nature of the material splitting. It has designed as the time–temperature relation of durability and was particularised for several classes of materials, in a very broad range of applied force and temperature, respectively [26–28]. Thus, the strong influence of the potential energy of interaction between the segments of the same macromolecular chain, the faults caused by the chain ends, and the splitting of valence bonds on the neighbour bonds mechanical resistance have been proved [29–33]. Hsiao and Kausch evidenced the effect of the local deformation on the overall splitting rate of the macromolecular chains [ 34–36]. On the other side, Holzmüller [37], Bartenev [38], and Salgonic [39] have analysed the amount of thermal energy and the direction of relative displacement of the segments in the deformation’s proximity that statistically fluctuates. The statistic of molecular faults accumulation was also investigated and by mathematical simulation valuable informations regarding the generation, growing, interaction, and faults’ coalescence have been obtained [40–42]. Later, Volonis combining the role of density of deformation energy with the stochastic nature of the fracture process and with kinetic theory, developed a new energy theory [43]. 181

Macromolecular Mechanochemistry

Bueche–Halpin theory is based on the study of elastomers’ tensile strength [44]. The authors considered that the visco-elastic deformation of the macromolecular fascicles of rubber, at their maximal strain, determines the kinetic of crack propagation into an elastomer-based material. Bueche proposed a structural model, in

Figure 3.4. Bueche’s model of an ideal polymer network [44].

the shape of network formed by isotropic knots, Figure 3.4. The ideal resistance of this network is given by the product n . f b – the force that determines the scission of n segments of chain, which cross the unitary surface perpendicularly orientated in the stress direction [45–47].

 ρ NA  σ b = n ⋅ fb =    3Nc 

2/ 3

 2M c  ⋅ fb 1 − M  

(3.25)

where: ρ – polymer density; N A – Avogadro’s number; M c – molecular weight of the chain segment between two knots; M – polymer average molecular weight.

y ymer fr 3.1.4. Gener alised theor y of pol Andreews’ ws’ss theor theory Generalised theory polymer fractur acturee. Andr actur E.H. Andrews introduced as characteristic parameter of fracture process, the fracture surface energy or the surface mechanical work [1, 48]. The fracture surface energy is defined, as the total energy required for the formation of a fracture of unitary surface by the propagation of the magistral crack. It is equal with a half of quantity of available energy in the moment of starting the crack propagation. Since the real materials do not present ideal elasticity a part of this energy is consumed for the scission of interatomic bonds, for the generation of new surfaces, and another part is dissipated as a result of the competitive occurrence of some irreversible processes, 182

Mechanochemistry of Polymer Fracture

such as the plastic flow. According to this theory, it may be written:

 T , ε0 ) ℑ = ℑ0 Ö ( c,

(3.26)

where: ℑ0 – the surface energy, defined as a half of required energy for unitary surface fracture of the interatomic bonds, which are located into a perpendicular plane of the fracture surface; Φ – a function of losses, which depends on the material nature, the rate of crack propagation, c, temperature, T, and on the overall deformation of the stressed . body, ε 0 . Loss function Φ is reduced to unit in the case of a perfectly elastic body, but in other cases it takes explicit shapes and values, which are related to both the real distribution of the deformation energy into the stressed body and characteristic losses of the solid. Equation (3.26) can successful be applied in the case of cohesive fracture of some polymers presenting large deformations, such as: butadiene–styrene rubber, ethylene–propylene rubber, plasticized poly(vinyl chloride), and low density polyethylene. By measuring ℑ and calculating Φ, from the data concerning the deformation distribution around the propagation cracks, a good accordance was established with the date obtained from different deformation rates. The values of ℑ 0 have been determined as being the smallest values of the fracture energy at high temperatures and low deformation rates, therefore for an ideal elastic body when Φ tends to zero [49]. Because ℑ 0 may be expressed as a function of the applied stress and sample’s geometry, it appears that equation (3.26) reflects a direct correlation between the macroscopic fracture strength and ℑ 0 ⋅ ℑ 0 is a parameter of molecular interactions, directly governed by polymer’s chemical and supramolecular structure, being roughly proportional to the dissociation energy of the C – C chemical bonds. By means of this parameter the fracture kinetic theory can by correlated to the solid body theory. According to the kinetic theory, the required energy for valence bonds splitting depends on the splitting frequency, ν, and temperature, T:

b g

ℑ0 = ℑ ν, T

(3.27)

and may be considered as being proportional to the bond dissociation energy, U:

183

Macromolecular Mechanochemistry

b

ℑ0 = λU = α G AB − kT ln ν / ν0

g

(3.28)

where: G AB – bond fracture energy in the absence of stress; ν 0 – bond fracture energy, which is proportional to temperature, T; k – Boltzman’s constant; α – proportionality coefficient. By replacing equation (3.28) in equation (3.26) the following expression is obtained:  T , å0 ) ℑ = á [G AB − kT ln ν 0 / ν ]Ö (c,

(3.29)

In the case of materials with an elastic behaviour, the dependence of fracture rate with temperature is given by the first term of equation (3.29), in the following conditions: – the applied effort of deformation to tend to zero (ε 0 → 0); – a reduced crack rate; and – very low or high temperatures with respect to the glassy temperature of the investigated polymer, T g. In the conditions of rapid crack growth, of high applied stresses, and of moderate temperatures in the above-mentioned range, the value of the loss function depends on temperature and decisively affects the rate of fracture. The values of ℑ 0 depends on the two factors: the transversal area of macromolecules (Vincent’s relation) and the number of valence bonds, contained between the network’s knots, in accordance with Lake and Thomas theory [1]. The fracture theoretical strength of polymer macromolecules can be calculated using the interatomic bonds strength from the main chain on the unitary surface. Mark reported this value as equal to 15 000 MN/m 2 and Vincent values range from 6 000 to 30 000 MN/ m 2 for the majority of solid state polymers. Vincent defined the ‘critical fracture strength’ as the yielding stress to the material transition from the vitreous to plastic state. He found a linear dependence between this parameter and the number of bonds from the main chains on the surface unit. Therefore, using the binding energies, in certain conditions, the evaluation of solid polymers fracture becomes possible. The restrictive conditions require the absence of inelastic deformation processes and of structural faults or cracks, which represent centres of stress concentration. 3.2. CHEMICAL BOND STRENGTH The potential energy of an arbitrary chemical bond A–B into a polyatomic molecule is represented in Figure 3.5. 184

Mechanochemistry of Polymer Fracture

Figure 3.5. Schematic representation of an arbitrary bond energy into a polyatomic molecule: D – dissociation energy; E – intrinsic bonding energy; P – sum of promotion, hybridisation, and polar and steric rearrangements energies; U 0 – activation energy of bond dissociation; γ 0 – bond length at equilibrium; hν/ 2 – vibration energy of zero point [50].

In the case of polyelectronic atoms, the atom’s valence state must be situated below the base level, since in this state bond formation is not possible. When the atoms collide each to other their potential energy increase. At a given interatomic distance the system’s atoms will reach the energy corresponding to their valence state (dotted line in Figure 3.5); consequently, a transition in the binding state will occur. The intrinsic binding energy, E, represents the difference between the initial state energy and that of the valence state, at an infinite atomic distance. Dissociation energy D is lower than E and it is equal to zero point of vibration energy (hν/2) and with the sum of promotion, hybridisation, and polar and steric rearrangement energies (P), required to achieve the valence state. The difference between the zero point of energy and the maximum of the potential energy curve is just the activation energy of bond dissociation, U 0 . For the molecules with three or more atoms the assignment of the energetic increment specific to a given bond is complicated by the existence of the term P that characterises the electrons promotion and reorganisation. This occurs by the formation of delocalised electrons and is due to the fact that the initial similar bonds energies after their successive splitting become different each to other. Thus, in the case of methane decomposition, CH 4 , is accepted that the four hydrogen atoms are identical and the energies of all C–H bonds are the same. These ones are formed by the participation of the hydrogen’s electronic orbital and the carbons sp 3 orbitals [50]. The removing of the first hydrogen atom requires an amount of energy of 425.8 kJ/mol and converts the methane into methyl radical. For symmetry reasons which have been confirmed 185

Macromolecular Mechanochemistry

by ESR spectroscopy, the resulting methyl radical is planar, with its unpaired electron located into an orbital 2p of the carbon atom. Dissociation energies of one C–H bond are equal to 477.3, 418.7, and 341.7 kJ/mol, for the second, third and fourth bonds, respectively. The experimentally determined dissociation energies of some small molecular groups are presented in the left upper part of the Table 3.1 [51]. In the case of these molecular fragments the bonds splitting activation energy and the dissociation energy are considered to be the same. In the right-hand lower part of this Table, the data concerning the dissociation energies, obtained for the bonds with hybridisation state sp 2 and sp 3 , respectively, are presented. In addition, the dissociation energies of the bonds R 1 – R 2 have semiempirical been calculated, by extrapolation of the data corresponding to the compounds R – X, where X represents H, F, Cl, Br, and I [51, 52]. The term of valence bonds strength, from the viewpoint of quantic chemistry, refers to the excentricity of one atomic orbital (hybrid or not), which is measured as the maximal angular intensity of the wave function by comparison to an orbital s, with spherical symmetry. In technical sense, the valence bonds strength means the required force to split the stressed bond. In the chase of a covalent bond, the change of electron distribution affects the bond strength. Electronic excitation of a network of macromolecular bonds can be caused by electromagnetic (light, α, β, and γ) or UV radiation. The energy transfer from this radiation to the electrons leads to an excited state. In the case of the light from visible spectrum, the photons or a radiation having, for instance, the wave length of 330 nm have enough energy for splitting a C–C bond. In order to be efficient a photon must be absorbed or to interact with an electron of the bond. This interaction takes place directly or indirectly by energy transfer. The curves of potential energy, corresponding to different excitation states of a molecule that is composed by two carbon atoms, Figure 3.6 illustrate the effect of electronic excitation on the bond energy. Dissociation energies of different molecular states are located in the range of 110 to 350 kJ/ mol, being lower than those caused by the electronic excitation. The excited state of the carbon atom are noted with s, p, d. Since, two atoms in excited states can combine each another in different modes, it exists only a single molecular state characterised by the same atomic state. 186

Mechanochemistry of Polymer Fracture Table 3.1. Values of the primary bonds dissociation energies in the case of organic molecules and macromolecular chains HFCl HO O=CH NH2 N≡C -

431 453 352 381 314 331 461

406 444 339 381 297 327

394 440 339 385

373 427 331 381

323

323

CH 3

CH3 CH3

CH 2

H 3C CH 3 CH

C(CH3)3

436

507

360

427 245 205

360

469

365

344 427

419

411

CH 2

CH

CH 3

CH

C

O

O

C

347 377 285

300 448 314 356

419 545 H3C

H3C

427 524 419 469

O

C O

H

N

O C

C

451 R

CH2 C

CH2

O

CH2

H2C R' HC CH 3

276

HC

355

CH

CH2

302

260

230

293

264

210

377

O

323

199

324

364

C

427 NC

CH 2

348

327

499

423

377

←

355

432

316

↓ 297

251

H3C C O O

379

H3C C O

344

323

H3 C O

335

335

339

HC

C

419

457

432

H2 C

CH

377

377

356

339

(H3C) 3C

335

314

306

293

(H3C) 2CH

348

327

318

H3C CH2

356

337

H3C

423

306 314

H C O

381

385 290

251

311 336

126

311

251 327

345

328

142

326

461

342

423

298 433

377

301 270

224

369

←

328

272

↓

254

285

R CH2

NH (CH 2)n

R (CH 2)2

R

CH

R (CH 2)3

R

CH 2 CO

R (CH2)4

O

R CH2

C

R CH2 CH R'

O

CH3

C

RO CH2

206

NH R

Transitions from an initial state of a macromolecule into an excited state usually occurs from a bonding orbital, having s or p electrons, to an non-bonding orbital (σ* or π*). Table 3.2 presents the electronic transitions for some usual polymers. The electronic excitation of a polymer network causes the decay of bonding energy. Consequently, the mechanical stability of the polymer decreases, contributing to the splitting of some macromolecular bonds or favouring crack propagation. Completely removing of an electron from a molecule (ionisation 187

Macromolecular Mechanochemistry

Figure 3.6. Interatomic energies of the excited states of a two carbon atoms contained in a macromolecule [72]. Table 3.2. Electronic transitions in some polymers a [53] Polymer

Polyethylene Polybutadiene Polystyrene Poly(methyl methacrylate) Poly(ethylene terephthalate) Poly(ethylene terephthalate)

λmax, nm

hυmax kJ/mol

kcal/mol

Transition

< 150 180 187 – 260 214 290 240

> 802 670 461 – 645 561 415 502

> 191.5 160 110 – 154 134 99 120

σ →σ * π →π * b π →π * π →π * b

a – thin films; b – the system of π electrons is implied in this transition.

process) requires a higher amount of energy than the electronic excitation and has a stronger effect on the dissociation energy. Thus, the dissociation of a bond R 1 – R 2 in two ions R –1 and R +2 requires an amount of energy with 672 kJ/mol greater then the required energy for homolytic splitting in radicals R ⋅1 and R ⋅2 , respectively. The strength of a bond that binds together two carbon atoms, one of them possessing an unpaired electron (e ⋅), is determined by de interaction of sp 2 and sp 3 orbitals. The energy of a bond formed by superposition of a hybrid orbital sp 3 with an orbital sp 2 is higher than those formed by two hybrid orbitals sp 3 . This conclusion has been drawn knowing that the dissociation energy of the C–C bond in the compounds with the general structure R–CH 2 –CH 2 –R′ is 337 kJ/mol and in the case of the compound R–CH 2 –C 6 H 5 it is 381 kJ/mol. 188

Mechanochemistry of Polymer Fracture

The C–C bond from the α position with respect to the unpaired electron is rarely stronger than in the initial molecule. Instead, the C–C bond from the β position is weakened by the molecule’s electronic reorganisation. In the case of chemical and thermal degradation these bonds will be preferentially split. Those reactions that involve the scission of a macroradical usually lead to the formation of a double bond: R1

CHX

CH2

•

CX

CH2

R2

R1

+

•

CHX

CH2

CX

+

CH2

R2

The data concerning to the considerable amount of energy, determined for different states, in the case of polyethylene macroradicals splitting are illustrated in Figure 3.7. In addition, a series of dissociation activation energies, D, for some usual polymers are collected in Table 3.3. Nevertheless, the mechanocracking reaction requires an activation energy considerably higher as the values D from Table 3.3. The tensile strength of polyethylene, polypropylene, and polyamide-6 (the last one stressed in the shape of fibres at 77 K) decreases with the increasing of free radicals number, which were stimulated by Xray irradiation. Thus, polymers’ mechanical strength decreases with coefficients whose value varies in the range from 1.54 .10 –20 to 5 . 10 – 20 MPa for each new formed radical on the macromolecular chains [53]. In Figure 3.7 the change of potential energy of two atoms, bounded each to other by an interatomic bond of length r, is qualitatively represented. The exact shape of the electronic potential can be in principle achieved by calculating the total electronic energy, E, of the molecule as a function of r. However, in the case of polyatomic molecules E(r) can not be determined with enough precision. This is why the potential functions are often described using some empirical equations, for instance the Morse potential function.

o b

g

b

U = D exp −2a r − r0 − 2 D exp − a r − r0

189

gt

(3.30)

Macromolecular Mechanochemistry Table 3.3. Activation energies of bond splitting in the case of some usual macroradicals [53] Polymer

Polyethylene Polypropylene Polyisobutene Polystyrene Poly(α-methylstyrene) Poly(vinyl chloride)

Activation energy kJ/mol 118 102 76 85 95 87

Polymer

Poly(vinyl fluoride) Poly(vinylidene fluoride) Poly(tetrafluoroethylene) Poly(vinyl acetate) Poly(methyl methacrylate) Polyamide-6

Activation energy kJ/mol 116 131 147 118 85 117

Figure 3.7. Schematic representation of enthalpy in the case of polyethylene macroradical splitting [74].

3.3. MECHANOCHEMICAL MECHANISM OF FRACTURE 3.3.1. Ir sib le con ver sion of mec hanical ener g y into cchemical hemical Irrrever ersib sible conv ersion mechanical energ ener g y (T he nonequilibr ium pr ocess) energ (The nonequilibrium process) The mechanochemical reactions are developed not only in the case of stressed bodies, but also during load removing or tensions redistribution when the elastic energy is converted into caloric one [54–56]. In a stressed material, the backbone bonds are deformed in the first place, which supports the main mechanical charge. In discharging conditions, just on these bonds, the fluctuating 190

Mechanochemistry of Polymer Fracture

oscillatory energy will be distributed. Consequently, the macromolecules will suffer a contractile effect that causes the oscillatory excitation of the main chain bonds. Subsequently, the oscillatory excitation energy is redistributed on the all system’s freedom degrees. Since the whole flux of elastic energy, which is dissipated as thermal energy, traverses the main chain’s bonds, it results that into a determined period of time τ * , the bonds pass into an oscillatory-excited state. At the level of the deformed bonds, the conversion of elastic into thermal energy may be written as:

U def → ∆U osc → Q

(3.31)

where: ∆U osc – oscillatory excitation energy of the deformed bonds. Under the stationary conditions, the concentration of oscillatory excited bonds, A * , is given by the relation:

A* = τ* dU def / dτ

(3.32)

In a solid body, the life-period of oscillatory excited states is very short one, of about 10 –10 s; after the time τ * , the oscillatory energy either passes on other freedom degrees of system or is released as mechanochemical reaction. Noting with τ chem – the characteristic time of mechanochemical reaction, it follows that the expression τ * /τ chem controls the reaction probability in function of the magnitude of the oscillatory-excited state. Thus, always when τ * /τ chem = 1 the excitation will release the chemical reaction. A quantitative evaluation of the parameter τ chem may be achieved accepting that the elastic energy dissipation brings into the excited state an enough large range, able to permit the use of the notion of oscillatory temperature T *. The above condition being accomplished * the approximation RT * ≈ Uosc should be admitted; therefore in the case of chemical bonds splitting, for ∆U osc > RT it can be written [54–56]:

τ chem ≈ τ 0 exp

FG U IJ H ∆U K 0

osc

or, in the most general case:

191

(3.33)

Macromolecular Mechanochemistry

τ chem = τ 0 exp

R|U f bU g U| S| ∆U V| T W osc

(3.34)

and for the inequality τ * /τ chem ≥ 1 it is imposed as:

* ∆U osc ≥

b g

U f U ln

τ* τ0

(3.35)

* This means that the dissipation of a higher energy that ∆Uosc leads to the scission of chemical bonds. The critical energy, ∆U *osc , required for bonds splitting after the time τ * is lower than the bonding energy U 0 ; for instance, for τ * = 10 2 τ 0 we obtain ∆U *osc ≈ 0.2U. The mechanochemical reaction rate is proportional to the oscillatory-excited chemical bonds concentration [A * ] and also to the elastic energy dissipation rate:

dU def dC ≈ τ* dτ dτ

(3.36)

The essential future of the irreversible mechanism residues in the fact that the mechanochemical reaction rate is determined by the elastic energy relaxation rate in system. The mechanism of irreversible mechanochemical reactions can be confirmed either directly by spectral techniques or indirectly by carrying out some chemical reactions, which are initiated just by the mechano-exited states and by the active particles that appeared their subsequent decomposition, respectively. The both methods have been widely used in the polymers mechanochemistry field, in present being available a vast experimental material sustaining this mechanism [1, 5, 48, 57–94]. The fracture of oscillatory-excited macromolecules leads to the apparition of the “hot” free radicals that subsequently are able to initiate chemical reactions, even at those temperatures at each thermally activated chemical reactions do not occur. A relevant example refers to the decomposition of polyisobutene and poly (formaldehyde), reactions accompanied by the formation of low molecular weight compounds by vibratory milling at –78°C, Figure 3.8. 192

Mechanochemistry of Polymer Fracture

Elastic deformation and non-equilibrium excitation represent component stages of the same process. The essence of irreversible mechanism consists in the fact that elastic energy dissipation, started in a solid body, is lower than that one required for its fracture. As result, some unstable excited states should appear which consist mainly in mechanocracking macromolecules. In few cases, the mechanochemical transformations are exclusively the result of elastic energy action. In some mechanochemical processes, such as ultrasonic treatment, tribochemistry, and shock waves chemistry, the mechanism of the above-mentioned transformation is more complicated. It involves the development of elevated temperatures and/or pressures, electrostatic effects or electronic emissions that are released by the local concentration of the elastic energy, either within the whole volume or in superficial layers of the body. The existence period of the maximal local concentration domains of the mechanical energy is of about 10 –3 –10 –4 s and their radius vary from 10 –8 to 10 –7 cm. The high pressures and temperatures as well as the electrical phenomena developed in such small domains can initiate, on their turn, new chemical reactions. The existent theories concerning the conversion of elastic energy in other forms of energy in small local domains offer actually well argued conclusions, especially in the case of shock waves propagation and cavitation. Under the action of shock waves, the chemical and physico– chemical transformations are extremely fast (τ << 10 –6 s) attaining higher rates as compared to those corresponding to the growth of a new phase or of diffusion mechanisms in the condensed phase. It was assumed that at the developed pressures, in the front of shock

Figure 3.8. Decomposition into low molecular weight compounds (corresponding monomers) of polyisobutene and polyformaldehyde by vibratory milling at –78 °C [56]. 193

Macromolecular Mechanochemistry

wave, due to the high degrees of compression the polymer is brought into an activated complex state, similar to the metallic state. After shock wave propagation, a decompression effect occurs and the specific state of matter, corresponding to the dilatation degree attained at the moment of activated complex decomposition is stabilised. Such effect can be explained under the assumption that the electrons transfer is more rapid then the atoms reconstruction. In a similar manner, the polymorphous transformations of graphitediamond type that occur under the high intensity shock waves action were explained, too [95]. Mechanical processing of solid bodies determines beside of temperature and pressure increasing, some phenomena of exo- and mechanoemission. The exo-electrons do not exceed the energy value of 1 eV instead the mechanoelectrons energy can reach values of several KeV. This explains the apparition in the mechano-stressed body of some ‘micro-condensers’, whose plates are just the new opened surfaces through material’s fracture. The electrons tunneled the energetic barrier due to the existence of an intense electric field. On their turn, the electric phenomena causes triboluminescence effects. The nature of the extremely complicated physico–chemical phenomena released during the mechanochemical transformations are explained, to some extent, by the ‘magno-plasma’ model [96]. According to this model, the energy generated into a variable field of forces (under shock waves action or by friction) determines not only strong local overheating but also brings the polymer into a new state, composed by ions, radicals, electrons, i.e. the plasma state. Under the action of shock waves, especially developed in the case of vibratory milling or utrasonic irradiation, some ‘microexplosions’ should be released that contribute to the installation of the plasma state, Figure 3.9. 3.3.2. Na tur ve center hanoc hemical Natur turee of the pr primar imary activ centerss of mec mechanoc hanochemical imar y acti reactions A fundamental problem, namely that of the analysis of the elementary act of different mechanochemical reactions – deals with the establishing of the active particles’ nature or with the nature of surface centers, appeared as result of the elastic energy conversion into chemical energy. The first results have been obtained by studying the mechanical scission of the macromolecules, of some organic substances, in 194

Mechanochemistry of Polymer Fracture

Figure 3.9. ‘Magno-plasma’ model of mechanochemical processes [96].

some reactions carried out in the ultrasound field. Latter the research had been extended to all types of mechanochemical processes. If the ideal case is admitted, i.e. the fracture under vacuum of the most different chemical bonds, from the nonpolar to the pure ionic ones, we can conclude that from the electric point of view the highest probability is obtained in the case of neutral particles formation. These particles seem to be the most suitable from energetic considerations. In principle, as it is illustrated below, there are possible two-limit situations [56]. •

A

B

A• + B (I)

UA-B

A+ + - B ( II )

UA-B + (IA - IB)

In the first case, the energy consumption is equal to the bond resistance A–B, but for the second one the introduction of a additional amount of energy, which is equal with the difference between the ionization potential of the fragment – A, I A, and the affinity for the electron of the particle B – (AB), is imposed. Therefore, it is expected, as under the action of the mechanical energy, that the majority of macromolecular or organic compounds will be split into radicalic particles or molecules and generate only a small number of active ionic centers. However, Sakaguki and co-workers have proved that during polymer fracture, in the solid state, along with free radicals some ionic species appears too. Different polymers were stressed under vibratory milling, at 77 K in dark, in the presence of tetracyanoethylene, TCNE, as powder. The formed TCNE -. anion-radicals were detected by ESR spectroscopy as is shown in Figure 3.10. Their formation can be explained by the pulling out of the electrons by TCNE molecules, which acts as ‘an electron trap’ for the 195

Macromolecular Mechanochemistry

formed anions by heterogeneous splitting of – C – C – bonds from the main chain of some polymers such as: polyethylene(PE), polypropylene(PP), polytetrafluoroethylene(PTFE) and poly (vinylidene fluoride)(PVDF), Table 3.4 [97–112]. Based on the obtained results, the following splitting mechanism was proposed:

R

R

2 R•

Homolytical scission of C

C bond

R

R

R - + R+

Heterolytical scission of C

C bond

R- + TCNE

R • + TCNE -•

–

Electron abstraction

–

When the splitting occurs in vacuum, at 77 K, under the conditions of photoirradiation the following reaction take place: R- + TCNE

hν

Electronpromoted abstraction promoted b R • + TCNE -• Electron abstraction by photoenergy

Figure 3.10. ESR spectra for polypropylene, PP, (all ESR spectra were observed at 77 K and 2 µW): (–⋅–⋅) spectrum of fractured PP; (___) spectrum of PP fractured with TNCE; (----) ESR spectrum after photoillumination for 20 min of PP fractured with TCNE. DPPH = 1,1–diphenyl–2–picrylhydrazyl [109]. Table 3.4. Yields of mechanoions in mechanically fractured polymers [112] Polymer

PVDF PP PE PTFE

Molecular structure

-(CF2CH2)n-[CH2CH(CH3)]n-(CH2CH2)n-(CF2CF2)n-

196

Yield of mechanoanion (%) 85 37 27 16

Mechanochemistry of Polymer Fracture

where: R ⋅ , R – , and R + are the mechanoradical, mechanoanion, and mechanocation, respectively [100–103]. The mechanoions yield is presented in Table 3.4. Based on the above-mentioned study it was concluded that at least 37% of C–C bonds are heterolytically broken. Most complicated is the analysis of the primary active centers in solid state mechanochemistry. In this case is necessary to study not only the splitting of individual bonds but also the formation behaivour of crystals or other types of supramolecular formations that characterize the newly formed surface (by fracture). The active states generated in solid bodies are investigated by absorption, electronic emission, luminescence, ESR spectroscopy, and holography techniques, respectively. Table 3.5 presents the active centers investigated by ESR method for some solid bodies. Since in the case of the solid bodies with complicated structures the interpretation of these spectra is a difficult process, very often indirect method are used, such as the analysis of physical and chemical properties. Some times, the potential energy changes, Figure 3.11, of the crystalline substances under the action of mechanical energy and allows faults generation which become the centers of mechanical energy concentration, Figures 3.12 and 3.13, and consequently the initiation centers of the mechanical degradation process. The formation of the active centers to the fracture surfaces is accompanied by secondary effects, such as: electrostatic phenomena, luminescence, and electronic emission. The most important types of active centers as well as mechanisms generating these centers, which contribute to the completion of mechanochemical transformation, are presented in Table 3. 6. The primary active center widely used for the explanation of the overwhelming majority of reaction mechanisms in the polymers’ mechanochemistry is the free radical; this one being the direct result of mechanical stressing is called the mechanoradical. The chemical reactivity of the mechanoradicals is governed by the existence of an unpaired electron at the scission place, but the reactivity also depends on its macromolecular dimension. Thus, a high macroradical length implies a reduced motility, which will determine the subsequent possibilities of conversion. In principle, knowing the bonding energies in polymer mechanochemistry the right place of chain splitting can be foreseen and also the mechanoradical structure. However, the mechanoradicals do not always represent the most 197

Macromolecular Mechanochemistry Table 3.5. Nature of the paramagnetic centers recorded during mechanical destruction of some solid bodies [56] Substance Cellulose Deoxyribonucleic acid Proteins Graphite Silicon Silicon carbide Quartz Germanium dioxide Barium sulfate

Free radicals

Charged states

+ + + + ? + ? -

+ +

advantageous particles from energetic viewpoint. Thus, in the first moments of the process many types of particles with different energetic levels can coexist in a resonance state. These ones subsequently suffer intramolecularly rearrangements, passing into the more stable states, which from the thermodynamic point of view are in concordance with the system state. Supplementary particularities appear during the solid state mechanocracking process. Solid state structure imposes itself kinetic

Figure 3.11. Modification of potential energy during the fault formation: (a) – passing from a network knot to another; (b) – passing from network knots to internodal space; and (c) – passing from an internodal space to another [113]. 198

Mechanochemistry of Polymer Fracture

Figure 3.12. Structural faults in crystal: (a) after Schottky; and (b) after Frenkel [113].

Figure 3.13. Active centers into crystalline lattice [114]: center V formed by electron delocalization in the proximity of negative charge; center F formed by electron delocalization in the proximity of positive charge.

characteristics to the reaction that occurs in this phase [114]. Thus, for a chemical reaction to occur, the active centers must approach each other. Apart from liquid or gaseous states, in the solid state the lifetime of particle pairs and their contact time are high enough. An equilibrium, on all degrees of freedom, is established between two particles. In these conditions each pair of active centers makes up a particle having its own independence. The pairs represent en199

Macromolecular Mechanochemistry Table 3.7. Types of primary active centers in polymers mechanochemistry [115] Nature of primary active center Free radical

Mechanism of active center formation

Mechano-cracking of the covalent bonds from linear polymers and chemical networks under the action of any type of mechanical energy Free ion Mechano-cracking of the covalent or ionic bonds from polymers and ionic crystals. Destruction of atomic and crystalline networks, accompanied by simultaneous ionization Ion-radical Destruction of some materials containing covalent and mixed bonds F-center Destruction of ionic-crystalline lattices and electron immobilization in the lattice’s knot corresponding to the vacancy of negative ion G-center Destruction of ionic-crystalline lattices and electron immobilization in the lattice’s knot corresponding to the vacancy of positive ion Free electron Electronic emission that accompanies the fracture of solid bodies; destruction of the adhesive contacts between the phases with different densities; destruction by cavity or by friction processes Active atom Destruction if atomic crystalline lattices and atoms release on germs, edges or other faults, accompanied by atomic forces decompensation Active molecule Destruction of molecular packages on faults fragments and unpackaged domains, accompanied by intermoleculare forces decompensation Addenda vacancy Complexes destruction to the coordinative bonds

Energy of active center 50 – 100 Kcal/mol

Depends on the nature of active particles Idem ≅ 3 eV ≅ 3 eV Depends on the source > 1 eV -

-

Depends on the complex type 80 – 90 Kcal/mol Active Depends on the Spontaneous redistribution of the shock energy on intermediate state the chemical bonds followed by its subsequent level of shock “Mechano-excited conversion into one of aforementioned active centers energy and the type state” of chemical bonds. Is lower then the bonding energy

tities with high lifetime and until to the occurrence of the chemical reaction, these ones are implied in a series of elementary physical steps that are related to the realization of rotation, translation, and orientation movements. In other words, a strong interdependency exists between the kinetics of solid state chemical reactions or molecular movement kinetics, on one side, and the structure and properties of solid body, on the other side. The elementary steps of a transfer motion that occurs in the solid state require higher activation energies as compared to the same transformations in the gaseous or liquid state. In the first case the transformations occur at much higher surface potentials that those corresponding to the gaseous or liquid states. Three stages were found for two active centers, – A and B –, im200

Mechanochemistry of Polymer Fracture

plied in a reaction in a solid body: 1) macrodiffusion, when the particles A (or B) are uniformly distributed within the reacting volume, by a process that implies the concentration gradient; 2) microdiffusion, when the concentration gradient disappears and the overall rate is determined by the particle A and B collision frequency, under the assumption that both particles are uniformly distributed in volume. In this stage, the pair (A + B) is formed; and 3) the kinetic stage, when the process rate is determined by the chemical reaction rate, which occurs in the pair (A + B). Speaking about the polymer fracture mechanism, the most representative step is the mechanocracking one, having mechanoradicals formation as the final result. Under the action of high intensity mechanical forces or under the action of less intense stressing, both of them acting for long periods, the reiteration of the above-mentioned mechanocracking steps leads to the essential modification of some fundamental characteristics of the polymer as well as of its average polymerization degree and polydispersity index. Molecular scissions accumulation determines the decay of the average polymerization degree, until so low values that the polymer looses its functional properties,the process which was defined as mechanochemical destruction.

3.3.3. Chained mec hanism of macr omolecular cchain hain splitting mechanism macromolecular At the molecular level, the mechanochemical transformations evolve in the sense of polymer average molecular weight decay, process that has defined as linear mechanochemical destruction. In the case of certain polymers, especially an in inert medium, the macromolecule splitting in mechanoradicals is followed by their reaction with the adjacent chains, the net result being the network formation. This is a destructive-recombinatory process, for which the ratio between the destruction primary step rate and the subsequent one, which determines the crosslinking, is related to the polymer chemical nature and its physical state and the environmental medium nature (inert, presence of reticulation agents, etc.). Either the process locally occurs either at the level of fracture surfaces or within the whole solid body. In both cases, the mechanodegradation processes are based on a chain mechanism of bonds splitting which may be of the homolytic or heterolytic type, depending on the nature of the chemical bonds. In most cases, the covalent chemical bonds are homolytical split, giving rise to the 201

Macromolecular Mechanochemistry

free radicals and following the all elementary steps of the chained mechanism, i.e. initiation, propagation, chain transfer, and interruption or active centers stabilization, respectively.

3.3.3.1. Initiation Mechanocracking initiation is favored by certain structural particularities of the chains. Thus, frequently the scission place and therefore the type of mechanoradicals, possible to appear, can be foreseen. The following features worth to be mentioned: 1) the tertiary carbon atom existence weaknesses the neighboring bond; 2) the conjugation effect manifestation reduces the strength of the αbond to the double bond; and 3) presence of heteroatoms on the main chain favors the splitting of the C-heteroatom bonds. Generally, a segment belonging to a carbocatenary polymer under the action of mechanical energy generates two mechanoradicals: CH2

CH R

CH2

CH R

CH2

CH

M.E.

CH2

CH

CH2

R

R

M.E. - mechanical energy

•

CH R

(I)

(I)

+

•

CH2

CH R

(II)

( II )

As it is seen the radicals I and II are not identical ones; they differ from each other by the delocalization degree of the free electron. Since the fracturation process statistically occurs, the polymerization degrees of the two radicals are different and consequently the radicals’ motility and lifetime are different too. The place of chain splitting is related, in a great measure, to the chain flexibility. In the case of the macromolecules belonging to the rigid polymers, the mechanocracking occurs approximately to the chain’s middle, in this way being generated two roughly identical particles, which have a close reactivity. On the contrary, in the elastomer case, any chemical bond can be split with the same probability and thus the active particles can greatly differ from each by their dimensions and reactivity. Systematic study of the mechanoradicals formed by carbo- and heterocatenary polymers mechanocracking allows the classification in the formulation of the specific reaction mechanisms of the most important polymer classes. Thus, polyethylene subjected to vibratory milling, under helium atmosphere at 77 K, presents an ESR spectrum characterized by six components STS of the hyperfine structure, with ∆H ≈ 23 e. This 202

Mechanochemistry of Polymer Fracture

corresponds to the mechanoradical – CH 2 – CH 2 ., which appeared by macromolecule splitting, Figure 3.14. Heating of the mechanocracking products results in the modification of the ESR signals, as a result of the formation of secondary radicals by the reaction of the mechanoradicals with the chains from their proximity. At 135 K the spectrum becomes broader and new lines appear and at 150 K the spectrum becomes completely different from the initial one. The subsequent increase of the temperature is finalized by radicals gradual disappearance; at 270 K the signal intensity is minimal (d) and the spectrum becomes identical one to those corresponding to the alylic radicals (e), recorded in the same conditions. The presence of these radicals proves the presence of double bonds that arose by the disproportionation reaction, similar to thermal destruction of these polymers [58]. Mechanochemically processed poly(vinyl alcohol), either as powders or frozen solutions in H 2 O or D 2 O, under the inert atmosphere at the temperature of liquid nitrogen, gives the ESR spectra depicted in Figure 3.15, which are similar with those obtained during irradiation in the same conditions. Two types of macroradicals have

Figure 3.14. ESR Spectra of the free radicals formed by mechanochemical destruction of polyethylene at different temperatures: a) 77 K; b) 135 K; c) 160 K; d) 270 K; e) ESR spectrum of allyl radicals (d ≅ e) [58]. 203

Macromolecular Mechanochemistry

been recorded, namely: – CH 2 – (OH)HC . and . CH 2 – CH(OH) –; in addition, the radicals R – CH 2 . do not appear in ESR spectra. The spectra shape is not affected by the solvent nature (H 2 O or D 2 O). During heating of a frozen solution the signal intensity gradually decays, until its complete disappearance [58, 59]. Whenever tertiary carbon atoms exists along the main chain, mechanocracking is accelerated and the mechanodegradation rate of such polymers is strongly increased. Thus, in the case of poly(methyl methacrylate): CH2

CH2

CH C

O

OCH3

CH2

CH C

O

OCH3

CH C

CH2 O

•

CH C

OCH3

+ O

OCH3

•

CH2

CH2

CH C

O

OCH3

CH C

O

OCH3

which is an vitreous polymer, the rate of chains scission is high. It was proved that the mechanodegradation efficiency of PMMA is greater than of PVA or PVC. The conjugation effect manifested along the polymer chains labilises the α-methylene bonds, as in the case of polyisoprene:

Figure 3.15. ESR spectra of the free radicals formed by mechanochemical destruction of poly(vinyl alcohol), 1, polyformaldehyde, 2, poly(propylene oxide), 3, and poly(ethylene oxide), 4: 1a) PAV; 1b) idem heated at 295 K; 1c) 2% aqueous solution of PAV; 1d) overlapping of previous ESR spectra; 2a) polyformaldehyde in vacuum; 2b) idem heated at 200 K; 2c) idem in the oxygen presence; 3a) poly(propylene oxide); 3b) idem heated at 270 K; 4a) poly(ethylene oxide); 4b) idem heated at 200 K. 204

Mechanochemistry of Polymer Fracture

CH3 CH2

C

CH3

CH3 CH

CH2

CH2

C

CH

CH2

CH2

•

•

CH

CH2

CH2

CH

CH2

CH2

C

M.E. CH3 CH2

C

CH3

CH3 CH

CH2

CH2

C

CH

CH2 + CH2

C

It is considered that on the mechanocracking stage the following resonance structures might appear: CH 3

CH 3 CH 2

•

CH

C

CH 2

CH 2

C•

CH

CH 2

and CH 3

CH 3 CH 2

C

•

CH

CH 2

CH 2

•

CH

C

CH 2

In the case of this polymer R.J. Ceresa also assumed a heterolytic mechanism: CH3 CH2

C

CH3

CH3 CH

CH2

CH2

C

CH

CH2

CH2

C

CH

CH2

CH2

CH

CH2

CH2

M.E. CH3 CH2

C

CH3 CH

CH2

CH2

C

(

CH

-

)

+ CH2 + CH2 ••

CH3 C

Similar mechanoradicals are generated for butadiene-based elastomers during mechanocracking. Apart from them, the natural rubber is characterized by a more intense degradation process, due to the presence on its main chain both of the tertiary carbon atoms and conjugated double bonds. The influence of the chain rigidity has been investigated on a series of copolymers poly(butadiene-co-acrylonitrile) and poly (butadiene-co-styrene). It was proved that the copolymers containing much more rigid units the mechanodegradation is more intense. Thus, the rubbers of SKB–18, SKN–26, and SKN–40 type, respectively, have been studied and the mechanodegradation efficiency was followed by the dissolution capacity of the degradation products. This one increased in the following order [116]: 205

Macromolecular Mechanochemistry

SKN – 18 < SKN – 26 < SKN – 40 By comparing the mechanodegradation efficiency of all these elastomers it can be concluded that the highest one characterizes the poly(isoprene) rubber. It is clear that it is impossible to make a generalization of mechanodegradation efficiency and the mechanism must be particularly investigated for each class of polymers. In the case of vulcanized rubbers the mechanocracking process takes preferentially place to the C–S x bonds, resulting mechanoradicals with R–Sx⋅ type structure (x > 1) and in a lesser extend radicals of R ⋅ type. The last ones in the presence of oxygen give rise to peroxides, which are stable at the temperatures below to polymer’s vitreous temperature. Consumption rate of these radicals respects the following order: ROO . > R . > R – S ⋅x The following mechanoradicals have been evidenced during poly(formaldehyde) mechanocracking:  − O −; − O − C ( OH ) − . −O − CH.2 ; − CH 2 − O. ; − O − CH

Similar ESR spectra present poly(ethylene oxide) and poly (propylene oxide). In the above-mentioned cases, a part of founded oxygen belongs from peroxidized radicals. In the solid solutions of the oxygen containing polymers on the main chain, the secondary reactions occur with difficulty and subsequent the chain scission leads to the following radicals − O − CH 2 . or by radical transfer  −O− . giving rise to the structure − O − CH 2 − CH If mechanocracking occurs to the –O–CH 2 –bond, the ESR spectra would present particles such as –OCH 2 CH 2 . or –CH 2 O . . Their absence proves the splitting of the C–C bonds. The characteristics of the ESR spectra of some polymers containing oxygen on the main chain are collected in Table 3.7. It can be noted that poly(ethylene oxide) and poly(propylene oxide) as compared to poly(vinyl alcohol) give a series of macroradicals such as R–CH 2 . and –C–CH–C – representing more stable particles as –O–CH 2 . and –O–CH–O – due to the unpaired electron delocalization at the –C–O–bond; this implies the electron density decay on the carbon atom. Similar studies were performed on cellulose, starch, albumin, 206

Mechanochemistry of Polymer Fracture Table 3.7. ESR spectra parameters of the species formed during mechanocracking of some oxygen containing polymers

Polymer

Number of STS components

Intensities ratio

∆Hl

Poly(vinyl alcohol)

3

1:2:1

23

Maximal temperature for radicals stability (K) 350

Radicals ascribed structure •

CH2

C

CH2

OH •

CH2

CH OH

Poly(vinyl alcohol), solutions in: H 2O D 2O

3 4

1:2:1 1:3:3:1

23 22

Polyformaldehyde

2

1:1

15

•

CH2

CH OH

•

CH2

170

CH OH

Poly(ethylene oxide), solid solution in: H 2O CH3COOH Poly(propylene oxide)

3 3

1:2:1 1:2:1

15 15

5

1:4:6:4:1

17

O

•

•

OH

O

CH

O

CH

O

CH2 +

•

350

O

CH

CH2 O

or •

O

C•

O

CH

230 200 200

CH3 O

•

CH2

CH2 O

or •

CH3

carboxymethylcellulose, and triethylcellulose being identified the corresponding mechanoradicals. The formed radicals as well as the allylic ones are able to react with oxygen, by peroxidation: R•

+

ROO•

O2

In the case of glycozidic bonds scission, free radicals with unpaired electron to the oxygen atom should appear. Their presence has not identified on ESR spectra even if the increase of aldehyde groups number during mechanical solicitation was chemically proved. Most likely, the mechanoradicals take part in very fast reactions altering their structure. The ligno-cellulose complex generates inactive radicals due to the presence of conjugated double bonds from lignin macromolecules that induce a stabilization effect of the free radicals. Lignin and its complex with cellulose can be regarded as a protection substance, playing the role of stopping the propagation of radicalic chained reactions. 207

Macromolecular Mechanochemistry

ESR investigations performed on the mechanochemical destruction products of polyamides, natural silk, polyoxamides, under inert atmosphere and at 77 K, evidenced the existence of the follow ; − NH − CH  ; − CO − CH  , which are ing radicals [117] −CH 2 − CH 2 2 2 identical to those obtained under the action of radiant energy. Mechano-chemical destroyed albumins give the next radicals:  CH ; − CO − CH  CH ; − NH − CH  ; − CO − CH  − NH − CH 3 3 2 2. The chromatographic methods used to the analysis of the aqueous media indicated the presence of the corresponding monomers, which constitutes a supplementary argument in the favor of –C–C– bonds fracture on the polymers main chain. Table 3.8 presents the most important types of macroradicals that appear during mechanocracking of some common polymers. On the other hand, the mechanoradicals implied in the mechanodegradation mechanisms have indirectly been investigated using chemical reactions using either radicalic acceptors or grafting and block copolymerization reactions. In Table 3.9 some of typical polymer – radicalic acceptor reactions are presented too.

b g

b g

3.3.3.2. Propagation The second elementary step of the mecanodegradation is the propagation of the mechanocracking chain. For the simplest case, those of the fracture of a single polymer, under inert medium, the sense of propagation process is governed by the stressed chain capacity to react with the mechano-radicals, thus entering in the chain-transfer reactions. •

CH2 CH

CH2

R macromolecule

CH R

+

CH2

CH

R

•

CH2

CH

CH R

CH

+

CH2

R

CH2 R

•

CH2

mechanoradical

CH R

CH2

C R

+

CH2

CH2 R

When the polymer is characterized by stable chains with respect to the existent mechanoradicals, the chained mechanism does not develop, the mechanoradicals being stabilized by recombination or disproportionation reactions. The simultaneous destruction of two or more polymers, even in inert media, represent a much more complicated case, implying additional block copolymerization, grafting, and crosslinking reaction. The occurrence probability of any the above-mentioned reactions depends on the stressed polymers structure, on intermediary frag208

Mechanochemistry of Polymer Fracture Table 3.8. Chemical structure of the mechano-radicals obtained by destruction of some usual polymers Polymer

Radicals’ structure

Polyethylene Polytetrafluoroethylene

•

•

•

•

•

C6H5

X NH

CH2

C6H5 •

•

CH2 + CH2

CH2

Poly(ethylene oxide), Poly(ethylene sulfone) Proteins

CF2

CH2 + CH

CH

Aliphatic polyamides

CH2

CF2 + CF2

CF2

Polystyrene

•

CH2 + CH2

CH2

•

•

CH2 + CH2 •

CH ;

CO

CH3

NH X •

CH;

CO (X = O, S) NH

•

CH2 ;

CO

•

CH2

CH3

ments capacity to interact each to another and/or with the virgin chains. This case belongs mostly to mechanochemical synthesis (see Chapter 3.8.). Chain growing reaction is influenced by the presence of the chain transfer reagents, whenever these substances have the ability to react with the mechanoradicals. The solvents, for instance, can be implied in the radical mechanism as transfer reagents, interacting with the existent mechanoradicals and generating new radicals, as is illustrated below: R• +

AB solvent

RA

+

B•

If the radical B . is enough active it will interact with the neighboring macromolecular chain, usually abstracting a hydrogen atom and implicitly transferring its electronic nesaturation. Thus, a ramification and/or reticulation center is generated modifying in this way the structure of the polymer that suffers the mechanocracking. Contrary, when the radical B . is characterized by a low activity the solvent contributes to the chained mechanism interruption: R• +

B•

RB

The propagation can also occur by mean of oxygen atoms, by peroxidation reactions:

209

Macromolecular Mechanochemistry Table 3.9. Some of typical polymer-acceptor reactions during polymers mechanocracking [116]

Polymer

Acceptor

Duration (h)

Medium

0.5

-

0.5

air

-

-

0.5 0.5 0.5 0.5 0.5

nitrogen air nitrogen nitrogen nitrogen

3.72/1.75 3.72/1.56 3.72/1.84 3.72/2.58 3.72/2.76

80/22 M 80/15 M 80/47 M 80/55 M 80/51 M

20% gel -

0.5 0.5 0.5 0.5 5.0

nitrogen air nitrogen air air

4.19/3.64 4.19/1.81 4.19/3.60 4.19/2.00 5.0/0.12

90/86 M 90/23 M 90/76 M 90/25 M -

-

5.0 0.5 0.5 0.5

air nitrogen air air

5.0/0.14 -

98/72 M -

Carboxylation Plasticization

1.0

nitrogen

-

-

Gel formation

0.5 70

air nitrogen

16.8/2.7 -

63/33 M -

70

nitrogen

-

-

-

oxygen

-

-

Oxygen

70

air

-

-

Oxygen

135

air

-

-

Oxygen

until 2000

air

-

-

-

until 2000

nitrogen

-

-

Starch

Oxygen

until 2000

nitrogen

-

-

Casein

Oxygen

50

air

-

-

Gelatin

Oxygen

70

air

-

-

Chemical fixation Chemical fixation Mechanodegradation Mechanodegradation Mechanodegradation Decrease of polydispersity Mechanodegradation Mechanodegradation Mechanodegradation Mechanodegradation

Collagen

Oxygen

70

nitrogen

-

-

Keratin

Oxygen

70

air

-

-

Natural rubber Oxygen ( 1.55 mm Hg) Atmospheric oxygen Thiophenol 1,6-Hexane-dithiol Benzyl mercaptan Naphthoquinone Naphthoquinone Hydroquinone Phenol Poly(butadiene 2,2’-Azobisiso–co-styrene) butyronitrile rubber Benzoyl peroxide Nitrile rubber Benzoquinone Maleic anhydride Pentachlorothiophenol Polychloroprene Polyethylene Kaptox Polystyrene Carbon tetrachloride Poly(methyl Carbon methacrylate) tetrachloride Oxygen Poly(vinyl chloride) Polyacrylonitrile Cellulose

210

Some characteristics of Other changes mechano-degradation products Plasticity [η] 4.19/1.30 90/22 M Plasticization

Mechanodegradation Mechanodegradation

Mechanochemistry of Polymer Fracture

HR OO •

HR • + O2 mechanoradical HR + HROO • macromolecule

HR OOH + R • mechanohydroperoxide HR •

HR OOH or HR OOH

•

+

HR O •

OOH •

+

OH

In the case of the double bond presence on the main chain: •

R OO • +

CH

CH

CH

CH

O OR

when the ramification and crosslinking reactions take place. Extremely active HOO . and HO . radicals lead to subsequent reactions of oxidation. The peroxidated radicals are much more reactive as compared to those they have formed; this finding was proved on the case of elastomers supposed to the cold mastication [118]: CH3

CH3 CH •

CH

C

CH2

CH

+ O2

CH

C

CH2

OO •

The formed peroxidic mechanoradicals react faster than the alylic radicals with some radical acceptors such as α-naphtol: O

OH CH2

CH

C

•

CH3

CH3 •

CH2

CH2 +

C

CH

CH3 +

O

OH CH2

C

•

CH3

CH3 CH

CH2

OO •

CH2

+

C

CH

CH2

OOH

+

or in the presence of other acceptors such as arylthiols: ROO

•

+

C6H5

SH

ROOH +

C6H5

S•

In these conditions the macromolecular chain is interrupted but the kinetic one should continue due to the formed radicals from the 211

Macromolecular Mechanochemistry

chain transfer reagent [119]. Mechanical processing of the reticulated rubbers, under the conditions of two rolls mixing, allows the obtainment of three types of radicals: mechanoradicals R . and R–Sx. that appear from the main chain and transversal crossbridges splitting, respectively, and peroxidated macroradicals ROO . . The study of their reactivity, using different radical acceptors such as trichlorophenol, ionolane, disulphides of di(tert-buthyl phenol) or di(isooctyl phenol) or stable radicals, such as RNO . and 2,2,6,6tetramethyl-4-oxypiperidole proved that: 1) ROO . reacts at 80 K with trichlorothiophenol (structure I) but not with ionolane (structure II) by splitting of the hydrogen atom from –SH or –OH groups with the formation of hydroperoxide radicals and thiolic and phenoxy radicals, respectively; Alkyl

Cl SH

Cl

Alkyl

SH

Cl

Alkyl

(I)

( II )

2) R . reacts at 150–200 K with trichlorothiophenol but not with ionolane; and 3) R–S .x under the similar conditions of temperature does not react with any of the above-mentioned acceptors; its stability was explained by the formation of a stable bond with the following structure: R

Sx-1

S

The two-roll mixing, at room temperature, of the peroxidated vulcanized elastomers has as result the increase of the mechanodegradation efficiency. At the temperature above the elastomer vitreous temperature the radicals R–S .x reacts with the elastomer double bonds giving rise to the crosslinked structures. CH3

CH3

•

CH2

CH

C

CH2

+

R

•

CH2

Sx

C Sx

•

C Sx

CH2

R CH3 CH3 CH2

CH3

CH3 CH2

CH

CH

•

CH2

+

CH2

C

CH

CH2

CH2

C Sx

R

212

CH R

C CH2

CH

CH2

Mechanochemistry of Polymer Fracture

Another way of chain destruction propagation is the so-called ‘initiated destruction’: R • + R1

R2

R

R1 + R2•

Starting from the idea that all the macromolecular chain bonds presents the same probability of new radicals formation, R .2 , which differ each to other by their dimensions [120] and expressing the rate of this reaction:

ν = k R R1 − R2 it can be concluded that the term R << R1 − R2

(3.37)

since the majority

of macromolecules do not suffer the mechanocracking process. If the interruption rate as expressed as:

ν′ = k ′ R ⋅

2

(3.38)

it is clear that ν′<<ν, therefore the “initiated destruction” reaction rate plays an important role in the mechanodegradation propagation and explains the appearance of the low molecular weight compounds, such as monomers, dimers, etc., which result in this process. 3.3.3.3. Interruption. Stabilization of destruction active fragments Under the conditions of mechanical solicitation of a polymer, in the absence of side reactions, the accumulation of mechanoradicals takes place, until a certain value of the average molecular weight is attained, which is specific one to the each stressed polymer and is called ‘destruction limit’. At the interruption of mechanical stress application the mechanoradicals will disappear by disproportionation and recombination reactions: R1

R2

R1• + R2• R1 + R2

(a saturated macromolecule and a unsaturated one)

If the mechanocracking process occurs in the presence of stable radicals, DPPH or NO, the macroradicals will be intercepted before reaching the ‘destruction limit’. In the case of polystyrene, the stage of destruction fragments 213

Macromolecular Mechanochemistry

stabilization during vibratory milling, in the presence of nitrogen oxide, NO, has been investigated by H. Grohn and K.Bischoff [121], and later by R.E. Eckert [122]. H C

H •

CH2 +

CH2

C

CH

•

CH3 +

CH2

C

The two radicals are stabilized by resonance with the electrons of the aromatic ring. Nitrogen oxide present in system may react with radicals as it follows: H

H

C • + NO

C

C

NO

C

H

H

C

•

C

H

H

NO

ON + NO

NO

The nitrozo derivative has been evidenced by Eckert using IR spectroscopy and by applying the technique of total attenuated reflexion in the case of vibratory milling processed polystyrene and poly(methyl methacrylate). The author also demonstrates that the of nitric groups formation during poly(methyl methacrylate) mechanodegradation is also possible. In this case the following radicals appear: CH3 C C

CH3

•

C O

C

OCH3

O•

OCH3

(1)

(2) 214

Mechanochemistry of Polymer Fracture

For sterical reasons, radical (2) easier reacts with nitrogen oxide. CH3

CH3

C C OCH3

+ O•

NO

C

CH3 •

+ ON

O

C

C•

C

OCH3

OCH3

NO2

3.3.3.4. Types of homolytical mechanodegradation mechanism of some usual polymers Polyamides The intensive mechanical processing of polyamides by vibratory milling is decisively influenced by several factors, such as: particles size, temperature, mechanical regime, medium nature, etc. It was found that in the humidity presence or absence plays a main part in this case, since it determines the mechanism of the mechanodegradation process [83,123–131]. Thus, aliphatic polyamides, nylons 6 and 6,6, have been supposed to mechanical processing by vibratory milling both in absolute dry media or moistened ones. The mechanodegradation products have been characterized at different periods of time, by determination of average molecular weight (by viscosimetry) as well as by end functional groups measurement. The comparison of the obtained data in the two cases evidenced a series of particularities, such as: 1. Mechanodegradation takes place both in dry an wet medium, since the viscosimetric molecular weight always decays during processing (in moistened medium the decay is more evident); 2. Chains splitting occurs homolytically to the C–C bonds and not to the C-heteroatom bonds (energetically lower) as it should be expected; 3. The number of final functional groups, amino and carboxylic ones, not only do not increase during milling but even diminished in dry medium, until their disappearance after 95 h of processing; 4. In wet atmosphere the sense of their variation is the same as in dry medium, i.e. the number of functional groups diminishes until a minimal value that corresponds to the maximal duration of processing, Table 3.10; and 5. Recording of the IR spectra of the processed polymers in dry and wet states evidenced the increase of the peak corresponding to the –CO–NH– groups (Figure 3.16). 215

Macromolecular Mechanochemistry Table 3.10. Variation of the number of end-functional groups in the final products of polyamide-6 mechanodegradation by vibratory milling [83]

Medium Absolute dried

Wet

Milling duration 0 24 48 72 96 0 24 48 72 96

[η] 1.0624 0.8568 0.7696 0.6581 0.5114 1.0624 0.5005 0.3020 0.2322

Nr. of eq. of Nr. of eq. of –NH2 in 106 g –COOH in 106 of polymer g of polymer 161.54 83.61 51.55 46.80 0 161.59 110.00 100.14 95.53

16.18 16.18 -

Average molecular weight [η ] = kM α M = 200,000 a+b 11,422 8,087 6,807 5,295 3,553 11,422 3,412 1,526 987

11,250 11,250 -

Figure 3.16. IR spectrum of the polyamide – 6 after 48 hr of milling: 1) absolute dried medium; 2) wet medium; 3) blank sample [83].

Correlation of the above-mentioned results evidenced that the mechanodegradation is not the only process that occurs in system. In the presence of water it seem that a compensatory process, which assures the presence of the amino functional group until the end of milling, namely – the mechano-activated hydrolysis – accompanies the main process of degradation. The consumption of the end-functional groups sometime until their complete disappearance and the intensification of the IR absorption peaks, corresponding to the amido groups, is a supplementary argument in the favor of the concomitant occurrence of a polycondensation process, which is also mechano-activated. Based on these experimental results the reaction mechanism consists in the following events: 1. Mechanodegradation, by homolytical splitting of the C–C bonds:

216

Mechanochemistry of Polymer Fracture

H2N

CH2 CH2 CONH CH2

CO2H

M.E. H2N

•

CH2

•

CH2 CONH CH2

CO2H

2. Mechanochemically activated hydrolysis, by scission of the Cheteroatom bond; CO

NH

M.E. + humidity (H2O)

CO2H +

H2N

3. Mechanochemical polycondensation: H2N

CH2 CH2 CONH

CH2

CO2H

•

+ H2N

polyamide macromolecule

CH2

macroradical

M.E. H2N

CH2 CH2 CONH

•

CH2

CO

HN

CH2 + H2O

The above reactions may also occur between the functional groups of the stable fragments of destruction. It can be noted that the clarification of the polyamide mechanical degradation mechanism was of first importance since it constituted the basement of the new polymers synthesis by mechanochemical polycondensation. It was proved that introducing in the reaction system of suitable agents of condensation, wearing functional groups able to react with the polyamides destruction fragments, the mechanochemical polycondensation may proceed, leading to new macromolecular compounds with special properties [127, 130]. Linear polyesters. Poly(ethylene terephthalate) Poly(ethylene terephthalate), PET, is a linear polymer that cumulates on its macromolecular chain different structural characteristics, such as: –C–C– bonds, ester groups, –CO–O–, endfunctional groups (–OH and –COOH) that are able to be mechanochemically activated and depending on the nature of the reaction medium to release multiple transformations. Thus, poly(ethylene terephthalate) mechanical solicitation, by vibratory milling in inert atmosphere, determines its mechanodegradation. The generated active particles are sensitive to the radical acceptors and able to initiate the grafting of vinyl 217

Macromolecular Mechanochemistry Table 3.11. The influence of moisture on the decrease of molecular weight [131] Milling time

Molecular weight viscosimetric

Molecular weight calculated from end groups

Dried

0 12 18 24 48

35,200* 33,450 31,700 28,630 24,590

35,200 33,060 30,700 28,100 23,100

Humidified (12 g polyethylene terephthalate + 1 ml H2O)

0 12

35,200 30,900

35,200 29,200

18 24 48

27,210 24,080 21,404

26,100 23,580 20,300

The state of polymer

*Drying of polymer at 255 °C does not affect mol. wt. of polymer (melting point 265 °C)

monomers whenever they are present in the reaction medium. The mechanocracking process occurs to the ester groups. This fact was experimentally proved by: 1. the good agreement between viscosimetric molecular weight and the number of end-functional groups, Table 3.11; and 2. the appearance in the IR spectra of the stressed samples in the presence of nitrogen oxide as radicalic acceptor of the peaks at 1600 and 1630 cm –1 , corresponding to the –ONO group. The splitting of the –C–C– bonds is not excluded but it should be considered as limited [131]. The same conclusion was drown by the analysis of the results concerning the influence of moisture. Both in absolute dry medium and in the presence of humidity during mechanical stressing the new functional groups gradually appear, their number increasing in time. This finding constitutes an argument that sustains the splitting of the

CO

O

CH2

bonds. The great number of the end-func-

tional groups, which were recorded in wet medium proves, as in the case of polyamides mechanodegradation, the occurrence of the competitive mechanochemically activated hydrolysis [131]. The most important reaction that occur during PET mechanodegradation are illustrated on the following page: The presence of free radicals has been evidenced by grafting reactions with different monomers, Table 3.12, and the proposed mechanism being the following one: 218

Mechanochemistry of Polymer Fracture (a) The homolytic mechano-chemical destruction In absolutely dry inert medium:

O

(CH2)2 O

O

(CH2)2 O

C

C

O

O

C

C

O

O

O (CH2)2 O

O•

•

+

C

C

O

O

CH2 CH2 O

(CH2)2 O

O

C

C

O

O

(CH2)2 O

O

In wet medium:

O

(CH2)2 O

C

C

O

O

O (CH2)2 O

mechano-chemically activated hydrolysis

O

(CH2)2 O

+ H

C

C

O

O

C

C

O

O

OH

O (CH2)2 O H

+

The breaking of the

O

O

(CH2)2 O

(CH2)2 O

C

C

O

O

C

C

O

O

O

O

CH2 CH2 O

•

CH2

(CH2)2 O

O

+

HO

C

C

C

O

O

C

C

O

O

•

(CH2)2 O

links

C

CH2 O

O

(CH2)2 O

O

C

C

O

O

O

(CH2)2 O

The stabilization of radicalic fragments occurs by disproportionation reaction, having as result the formation of new functional groups – COOH and CH 2 =CH -:

219

Macromolecular Mechanochemistry (b) Mechano-chemical grafting Initiation:

O (CH2)2 O

C

C

O

O

O • + n CH2

CH

O (CH2)2 OC

COO

CH2 CH

O

R

R

•

CH2 CH n-1

R

growing macroradical

R= Chain transfer:

O

(CH2)2 OC

COO

•

CH2 CH

O

R

Cl C N OCOCH3

CH2 CH

+

R

n-1

H +

O (CH2)2 O

C

C

O

O

O (CH2)2 OC

O

COO

CH2 CH

CH2 CH

O

R

O

C

C

O

O

O

(CH2)2 O

CH2 CH2 + R

n-1

•

+

O (CH2)2 O

C

C

O

O

C

C

O

O

O

CH2 CH

O

C

C

O

O

C

C

O

O

O

(CH2)2 O

O

(CH2)2 O

Grafting:

O (CH2)2 O

O

CH2 CH •

O

+ monomer or growing macroradical O (CH2)2 O

C

C

O

O

O

CH2 CH

O

CH2 CH

C

C

O

O •

CH2 CH R

R

(CH2)2 O

O

CH2 CH p

R

Table 3.12. The mechanochemical grafting on poly(ethylene terephthalate) with vinyl monomers [131]

Monomer

State of monomer

Milling time

Chemically linked polymer

12 18 24

7.40 9.45 13.30

13.04 16.66 23.45

1.94 2.99

(h) Vinyl chloride gas

Homopolymer

Functional groups chemically connected by grafting (-Cl, -CN, -OCOCH3, respectively)

(%)

Acrylonitrile

liquid

12 24 36 48

1.61 3.79 6.20 7.72

3.18 11.33 22.30 28.70

2.92 2.87 1.20 0.60

Vinyl acetate

liquid

12 18 24

2.73 5.10 10.50

2.11 3.89 8.35

0.82 1.46 6.77

220

Mechanochemistry of Polymer Fracture

O

O

O

CH2 O C

C

O

O(CH2)2 O C

C

•

•

O +

H2C

disproportionation O

O

O(CH2)2 O C

C

OH + H2C

O

O

CH2 O C

C

As in the case of polyamides, the functional groups – COOH are continuously formed by mechanodestruction and these ones can activate polycondensation reactions: O

O

O(CH2)2 O C

C OH + H2N

(CH2)n NH2

vibratory milling O

O

O(CH2)2 O C

C

HN

(CH2)n NH2 + H2O

Subsequently will result sequences where amide structural units alternate with ester ones. O

O

O(CH2)2 O C

C

O

O

O(CH2)2 O C

C

O HN

HN

O

(CH2)n NH2 + HO C

(CH2)n NH

C O

O

O

C

C O

(CH2)2O

(CH2)2O

+

H2O

Mechanism of increase of elastomer plasticity during two-roll milling processing The increase of elastomers plasticity by their processing by two-roll mixing, in order to achieve good homogenization of different additives is based on the macromolecular chains splitting, under the action of mechanical energy. Therefore, this process is essentially of mechanochemical nature, having a radicalic character. 221

Macromolecular Mechanochemistry

The direct measurement of the free radicals by ESR technique was not possible since above the elastomer’s glassy temperature the radicals disappear by recombination and disproportionation reactions. However, the radicalic character of this process was evidenced using stable radicals, whose concentration varies during mechanical processing. Whenever the mastication occurs in the air presence, at the temperature above 80 o C, the formed macroradicals enter in oxidation reactions that cause the apparition of the carbonyl aldehyde or even carboxyl groups on the macromolecular chains. These groups have been identified by IR spectroscopy. The reaction mechanism implies: a) formation of a secondary radical, which is energetically more favored than the primary one, by the reaction of the primary radical with a neighboring chain: CH3

CH3 •

CH2 C CH CH2 + mechanoradical

CH2

C CH CH2 macromolecule

M.E. CH3 CH2

b)

CH3

C

CH

CH C CH CH2 • secondary macroradical

CH3 +

the reaction of secondary radicals with oxygen: CH3 CH •

C

CH3 CH

CH2

+ O2

CH

C

CH

CH2

OO • peroxide macroradical CH3 CH

C

CH3 CH

CH2

+

CH2

CH

CH2

+

CH •

C

CH

CH2

CH

CH2

OO• CH3 CH

C

CH3 C

OOH hydroperoxide

regenerated macroradical

Being labile species, the macrohydroperoxide suffers a dehydration reaction:

222

Mechanochemistry of Polymer Fracture

CH3 CH

C

CH3 CH

- H2O

CH2

C

OO H

C

CH

CH2

O

If the hydroperoxide group – OOH is attached to a terminal carbon atom the dehydratation reaction result is the formation of an aldehyde group. On the advanced stages of mechanodegradation may appear strongly oxidated macromolecular sequences. Thus a –OOH group can be located in an adjacent position with respect to the carbonyl group:

CH3

CH3 CH2 C

CH CH

C C

CH CH2

OOH O

CH3 CH2 C

H

O +

CH C O

CH3 C C

CH CH2

HO

The oxidated labile chain is split generating two oxidated fragments, which contain carbonyl and carboxyl end-groups, respectively. In this manner, the formation of oxidated groups O C

O ;

C H

O ;

C HO

during two-roll mixing elastomers’

processing, at the temperatures around of 40 o C is explained. Same crosslinkings can also arise due to the following reaction: ROO ROO • +

CH

CH

CH

•

CH

At lower temperatures (T = 15 o C), when the mechanodegradation dominates, the main role of oxygen molecules is to peroxidate the 223

Macromolecular Mechanochemistry

mechanoradicals and to prevent the reticulation. In the case of ethylene-propylene-based rubbers, EPDM, the mechanism of plasticity increase by cold mastication has been suggested by K. Baranwal [132]. The author investigated a large range of temperature (T = 68–480 o F) and evidenced three distinct zones of process evolution, namely: 1) T = 68–150 o F – low-temperature zone, when the shearing force concentrated on the main chain is maximal and determines important decay of viscosity; 2) T = 150–315 o F – the polymers become soft, the system elastically responds, the force developed in the polymer is low and mechanodegradation is unimportant; 3) T > 315 o F – the shear force diminishes but thermal oxidation becomes important and the overall degradation increases. Depending on the processing temperature, two typical reaction mechanisms have been suggested:

A. Cold mastication Under an inert atmosphere (nitrogen), the primary act is mechanodegradation, but the subsequent evolution has as result the crosslinking process:

M.E. R mastication

R

•

R

+

•

2R

mechanoradicals

C

C

C

C•

macromolecular chain

C

R

+

R

macroradical

C

•

C

C•

In the presence of oxygen: 224

R

Mechanochemistry of Polymer Fracture

•

R

ROO •

+ O2

ROO • +

•

ROOH

R'H

+ R'

In the presence of radical acceptors: •

R

+ R''A

•

RAR''

B. Hot mastication [133] R

R CH2

CH2

C•

+ O2

CH2

CH2

C OO • R

R 2

CH2

2

CH2

C

CH2

CH2

C

+ O2

O•

OO •

The alcoxy radical formed by scission leads to a cetone group, as follows: R CH2

R CH2

C

CH2

+

C

•

CH2

O

O•

The new generated radical rapidly reacts with oxygen by a peroxidation process that is interrupted by the following reactions [134]: 2

CH2

OO

•

CH3 CH2

C O-O.

CH2

OH +

CH3

CH3 CH2

CHO

CH2

C H

CH3

C

CH2 +

O

O

•

C H

There are some cases when the mechanoradicals may suffer electronic transformations leading to ionic particles. Thus, poly(dimethyl siloxane), as a solution in benzene, exposed to the ultrasound field generates radicals that are subsequently 225

Macromolecular Mechanochemistry

transformed in macro-anions and macro-cations:

CH3 O

O

Si

CH3

CH3 homolytical scission

Si

CH3

•

+

•

Si

CH3 CH3 mechano-radicals

O

Si •

Si +

+ e-

CH3 macrocation CH3

CH3 O

Si

O

CH3

CH3

O

Si

CH3

CH3 O

O

CH3

•

+

e-

O

Si

•-• O

CH3 macroanion

CH3

|

|

|

|

− + Particles − Si ⋅ and − Si O have been evidenced by their reaction

with labeled methanol, proving that they are able to fix it.

3.3.3.5. Heterolytical mechanism Whenever on the main chains or certain networks ionic bonds exist, the mechanodegradation initiation by mechano-ions is possible, too. The most typical example is that of inorganic crystalline substances, which are not the object of this book. In the case of polymers the most investigated cases are presented below [135]: R

COO

Me OCO R' O

R

In the case of polysilicates:

226

+

COO Me +

-

OCO

R'

Mechanochemistry of Polymer Fracture

O

O O

Si

O

Me +

-

O

Si

O

O

O

and polyaluminates O

O Al+

-

O

Al O

O

The corresponding degredation compounds of these macro-ionical structures posses a very high reactivity. For instance, polysilicate milling yielded products that quickly react with the cement. 3.4. KINETICS In contrast to the high number of experimental data concerning the fracture and the mechanodegradation mechanism, only few kinetic studies are known at this moment. The difficulty of deriving some general valuable equations is related to the numerous factors that influence the process, such as: macroradical side reactions, the oxygen and of some impurities presence (playing role of inhibitor or radical-acceptor) and of different low molecular weight substances, for instance acting as plastificant or simply as impurities. In addition, a very special role is played by the polymer supramolecular structure that determines the reactions taking place at the molecular level. The type and resistance of the intermolecular bonds, the degree of ordering and crystallinity are frequently decisive factors in polymer mechanodegradation. For these reasons, the most rigorous kinetic results have been obtained in the case of polymer degradation in diluted solutions, where the magnitude of the above-mentioned factors is strongly diminished [136–146]. Based on a study of polymer mechanodegradation by ultrasonic irradiation, D.W. Ovenall derived a series of kinetic equations with a high degree of generalization [136]. Considering that 227

dBi is the dt

Macromolecular Mechanochemistry

macromolecule splitting rate and taking the polymerization degree equal to P I , the considered equation is the following:

b

g

dBi / dt = k Pi − Pe / ni

for

Pi > Pe

(3.39)

and

dBi / dt = 0

Pi ≤ Pe

for

(3.40)

where: n i – number of macromolecules with the polymerization degree equal to P i . The integration of above equations, at boundary conditions, leads to the following expression:

LM N

OP LM Q N

OP F Q H

4 P0 4 P0 1 3 Be = -1 - exp - kPt e 3 Pe 3 Pe 2 2 n0

I K

(3.41)

where: B e – number of chemical bonds split in the polymer after removing the mechanical stress; n 0 – the initial number of macromolecules; P 0 and P e – initial and final polymerization degree; t – duration of mechanical stress application. On the other side, Jellinek proposed the equation [148–151]:

b

g

dBi = k Pi − 1 ni dt

(3.42)

Under the conditions of the ultrasound field, the author accepts that the active force acting on the macromolecular chain is a function of chain length. By integration: B = n0

LMF 2 P I − 1OP − L 2 P + k b P − P gt Oexpb− kP t g PQ MNGH P JK PQ MN P 0 e

0

0

e

e

e

(3.43)

The equations derived by Ovenall and Jellinek have been verified by Minoura and coworkers [152, 153] for the high speed stirring of poly(ethylene oxide) solutions, Figure 3.17. The equation describing polymers mechanodegradation by ultrasonic irradiation was proved to be also valid for the kinetic description of polymer solution 228

Mechanochemistry of Polymer Fracture

Figure 3.17. High-speed stirring of a poly(ethylene oxide) solution: numbers of bonds broken per molecule versus time: ( ___ ) experimental; (J) from Jellinek’s equation; (O) from Ovenall’s equation [152].

destruction by freezing [143]. Another relation that express the dependence between the mechanodegradation rate and the average molecular weight, to the power m + 1, was proposed:

dM = kM m+1 dt

(3.44)

By integration equation (3.44) becomes:

ln M = −

FG 1 IJ ln t + ln M H mK

(3.45)

1

where: M 1 – value of M at t = 1. This equation was applied both to the capillary flow and the degradation by ultrasound. The degradation rate can also be calculated using the relation:  1   dM    M   dt

  1   M1  m  = kM = −      m M 

m

(3.46)

In this case, the molecular weight decay in unit time is only a function of the initial molecular weight, as is seen in Figure 3.18. 229

Macromolecular Mechanochemistry

Figure 3.18. Polyisobutylene in a mineral oil–kerosene solution: rate of degradation as a function of molecular weight [139]. M pc is the pseudocritical molecular weight.

Harrington and Zimm [140] have calculated the reaction rate varying the number of split bonds in the time unit, under the conditions of the mechanodegradation process, from the value of the initial average molecular weight M 0 to the chains with average molecular weight M. In the given equation, x represents the number of bonds that are available for splitting, in the volume unit, until to the destruction limit M e .

dB / dt = kx

(3.47)

For intensive mechanodegradation, it was found that:

g FG H

b

d 1/ M 1 1 =k − dt Me M

IJ K

(3.48)

and in the case of moderate degradation, when M >> M e :

b

g

d 1/ M =k (3.49) dt The mechanodegradation rate can be also expressed as a function of the probability of the stressed bonds to attain the activation energy required for splitting. This probability is regarded as the sum of thermal and mechanical energy distributions. When the thermal Me

230

Mechanochemistry of Polymer Fracture

degradation is insignificant the corresponding term is neglected. By analogy with the thermal activation kinetic, Bestul proposed the following equation [147]:

b

k = B exp − ∆E / a ⋅ j

g

(3.50)

where: ∆E – activation mechanical energy; j – rate of shear energy application; a – factor corresponding to T, which reflects the temporary stocked amount of energy in the chemical bonds. The graphic representation of log k v.s. 1/j is a strength line and its slope is equal to ∆E/a. The use of partial derivatives of the split macromolecules at a given moment to the initial ones, with respect to the time, allows to define the ‘degradation index’, ∆I. In the double logarithmic representation of ∆I v.s. time the all data lead to the same type of dependence; above this domain the curve bends toward the time axis. By shifting the curves parallel to the time axis, a master curve results, as Figure 3.19 illustrates. The shift factor α, which is independent of M 0 and MWD, provides a simple measure for expressing the effect of the experimental conditions on the degradation rate. When the strength line slope is lower than unity (0.03) the degradation rate decreases in a certain measure in time. On the other hand, if ∆i > 1 a deviation from linearity is recorded. A new index, ∆i + , was defined in order to take into account the limit mo-

Figure 3.19. Mechanochemistry of polystyrene solutions: degradation index DI as a function of the product of time t by the shift factor α. The symbols represent different polymers and conditions [155]. 231

Macromolecular Mechanochemistry

lecular weight, M e . The slope of line ∆i + vs. t, was found to be equal to 0.85 that is very close to the value found using ∆i. From the expression for ∆i + a value for M e equal to 30000 was calculated. The mechanodegradation rate of some polymers in solution, under the conditions of high speed stirring, has been also described by the following empirical relation [144]:

b

dPt / dt = k Pt − Pe

g

2

(3.51)

The above relation was verified for many experimental data. Since a second order equation with respect to P e was obtained, Goto and Fujiwara considered that the chain splitting concerns the length of adjacent macromolecules. The same equation was also applied to describe the mastication of poly(methyl methacrylate) [154]. Apart from this case, the mastication process of poly(vinyl chloride) is described by a first order equation. Bruce and Greenwood established a relation of degradation rate corresponding to a zero order kinetic [155]:

w k0 =

FG 1 - 1 IJ HP P K t

0

M0 t

M0 t

(3.52)

where: M 0 – molecular weight of the structural unit, w – polymer weight. For the first order equation, the authors proposed the following relationship:

k1 =

F 1I FG 1 - 1 IJ H tK H P P K t

(3.53)

0

where: P t and P 0 are the polymerization degrees at the time t and zero, respectively. In the both cases, it can be observed that the value of degradation rate constant is proportional not to P but to P –1 , which, on its turn, represents a linear function of time. If the mechanodegradation process is followed by viscosimetry, the rate constant is obtained by the representation of [η] –1 vs. time. The application of this relation 232

Mechanochemistry of Polymer Fracture

for describing polystyrene or cellulose degradation does not indicate the rate decay in time. However, R.J. Ceresa and W.F. Watson have empirically found a linear representation for a series of masticated polymers vs. t –2/3 . In the case of poly(methyl methacrylate) mastication the strength line is obtained when the time is taken at the –4/3 power [158]. Based on the model of polystyrene solutions in toluene degradation by ultrasounds, the equation of degradation rate, in terms of the number of split bonds, was established [159]:

b g

N xt = N xo exp − kt

(3.54)

where: N x 0 and N xt – number of macromolecules to the initial moment and to the time t, respectively. Equation (3.54) proved its validity both in the case of poly(ε-caprolactone) in 40% aqueous solutions of H 2 SO 4 exposed to ultrasound [160] and aqueous solutions of poly(vinyl alcohol) [161]. Not only the degradation period but also the polymerization degree and the concentration of polymer solution play a major role in the kinetic of mechanodegradation, Figure 3.20. In the case of the polymers processed in the fluid-viscous state, peculiar rate equations have been proposed. Thus, polystyrene mechanodegradation, under extrusion conditions, is caused by the profile of the melt flow rates in the transverse section of the capillary [163–168]. R.S. Porter and coworkers suggested that the rate gradient appears from the capillary center towards its wall and the longest macromolecules still coiled and unorientated in the flow direction suffer a high stress that is finalized by their splitting in macroradicals. In this case, the temperature and oxygen presence are favoring factors of mechanodegradation, too [163, 166]. From kinetic point of view, the mechanodegradation process is governed by a second order reaction and the rate equation is the following one:

b

dP = k Pt − Pe dt

g

2

(3.55)

where: P t and P e are the polymerization degrees at the moment t and at the limit of destruction, respectively. During polyethylene [169] and polypropylene or polyethylenepolypropylene blends [170] capillary extrusion the split bonds ac233

Macromolecular Mechanochemistry

Figure 3.20. Three-dimensional diagram showing the kinetics of polymers ultrasonic degradation [162].

cumulation kinetics is described by the equation:

wi 1 dn = ( k 4 − k3 ) dt k5 Mn

(3.56)

where: w i – constant rate of chemical bond splitting at temperature T and stress τ; Mn – numeric average molecular weight. Schott and Koghan observed that in the graphical representation in logarithmic coordinates of the apparent viscosity η/η 0 vs. number of passes through the extruder, straight lines are obtained for any investigated temperature. Considering that the dwell time is proportional to n/Q (where Q is the volumetric flow rate; n – number of passes through the extruder) the authors found the following expression [171, 172]: (3.57) η = η0 ⋅ 10− kn / Q Equation (3.57) allows the calculation of the relative effect of force and temperature on the mechanodegradation processes.. Pohl and coworkers established the dependence between the number of split bonds and the residence time in capillary. They found that the bond splitting rate is related to the shearing rate γ 234

Mechanochemistry of Polymer Fracture

and temperature [173, 174]:

c

t = k exp 11000 / RT g 1/ 3

h

(3.58)

For the mechanodegradation of the rubbery-state polymers, F. Bueche developed a theory that assumes the existence of some coils between the macromolecules, Figure 3.21. These coils generate tensions in the proximity of the half-distance between two knots of coiled chains [173]. The splitting rate is in this case:

b

g

Pdt = k exp − E − F0δ / KT dt

(3.59)

where: P – probability, independent of time, of splitting of the central bond; k – rate constant; F 0 – stress to the chain central bonds; K – Boltzman’s constant. Since F 0 depends on the molecular weight, the degradation rate will strongly be influenced by its value. Empirical equations describing the degradation rate in the case of mastication of several polymers, such as polyethylene [175], poly(methyl methacrylate) [154], butadiene–styrene rubbers [176, 177], polychloroprene [157] and EPDM rubber [133], have been proposed. For treating the kinetic aspects related to the degradation of solid state polymers N.K. Baramboim introduced the notion of ‘the

Figure 3.21. (a) Shear stress on an entangled molecule during cold mastication and (b) stress analysis on an entangled molecule. 235

Macromolecular Mechanochemistry

destruction limit’. It is known that the most important characteristic of polymers affected by mechanodegradation is the average molecular weight. By prolongation of the mechanical processing period it decreases until a minimal value, below which irrespective of solicitation duration (theoretically until t = ∞) or intensity this one does not change. Destruction limit was noted by M ∞ and for its estimation the following relation has been proposed:

M∞ =

E1m E2

(3.60)

where: M ∞ – the lowest molecular weight of destruction fragments which does not change when the degradation process is prolonged; E 1 – activation energy of chemical bond splitting on the main chain; m – molecular weight of the polymer structural unit; and E 2 – activation energy required for intermolecular bond splitting [178]. Theoretical calculation of M ∞ is hardly to be done due to the impossibility of evaluation in any moment of the micro- and macroheterogeneities from the polymer body as well as the mechanical force distribution on the chemical bonds. Generally the shape of force distribution curve is not known. It should be admitted that the mechanodegradation is described by an exponential law; consequently, the bonds fraction that is characterized by the deformation

d

i

energy, E def , is proportional to the value of exp − Edef / ∆E def . On the other side, since the tensions act periodically, the energy redistribution is made in a time period 1/A, which depends both on solicitation frequency and the relaxation time that is characteristic to any stressed material. Whenever the kinetics of mechanochemical process depends on the mechanical energy redistribution between the chemical bonds (A, s –1 ), the probability of deformation energy accumulation E *def on the chemical bonds must be high enough to initiate the mechanocracking process. Under these conditions it may be written that [55,56,179– 181]:

e

j

* / ατ r w k = A exp − Edef

(3.61)

where: k – the mechanocracking rate constant; A – the stress redistribution rate, s –1 ; E *def – the probability of mechanical energy accumulation on the chemical bonds; α – coefficient that is close to the mechanodegradation rate constant k<α<1; τ – stress relaxation 236

Mechanochemistry of Polymer Fracture

time; and w – the power used in the system. Clearly, equation (3.61) is an Arrhenius-type equation but the the terms have a different meaning. Thus, the exponential factor ατ r w is closed by the tension relaxation rate (10 2 –10 3 s –1 ). Temperature is replaced by the intensity of mechanical energy. This means that the shape of the tension distribution function is changed and the shape of the curve describing equation (3.61) is changed as well. The aforementioned equation is also valuable for cyclic actions exerted under stationary regimes, when the mechanical power transmitted to the stressed material is maintained constant. After any individual cycle of loading a part of mechanical energy is absorbed by the material and after a certain number of cycles the system is shows the average deformation degree of material, which corresponds to the average level of absorbed energy E def . The energy absorption rate is directly proportional to the transmitted power and the dissipated powder is proportional to the average value of deformation ∆E def . For a stationary regime we have

1 ∆E def τr

(3.62)

∆Edef = ατ r w

(3.63)

αw = or

The meaning of the parameters was given for equation (3.61). The dependency of mechanochemical rate constant induced by the intensity of absorbed mechanical energy in material into a variable field of forces has been determined for some typical cases: ultrasonic irradiation, vibratory milling and some dynamical conditions of vulcanized material testing [55, 56, 180, 181]. In the first two cases the intensity varies in a very large range (w is modified 20 times), therefore in a greater measure as the temperature, which is changed by 2–3 times, Table 3.13. It can be observed that the preexponential factor has small values (10 1 –10 4 s –2 ). However, the values α and τ r are unknown and consequently E *def representing the minimum deformation required for the initiation of the chemical reaction cannot be determined. In order to estimate the value of τ r , one can suppose that α ≈ 10 –2 that is in accordance with the de* struction yield and Edef varies from 10 4 to 10 5 cal . mol –1 . For instance, in the case of poly(methyl methacrylate), the values of τ r and 1/A are close each to other in magnitude. 237

Macromolecular Mechanochemistry Table 3.13 Values of constants A and E *def /ατ γ for some polymeric materials [56] Material

Conditions of determination

Poly(methyl methacrylate) Vibratory milling Polystyrene Ultrasonic irradiation Vulcanized natural rubber Dynamical tests

* Edef

/ ατ r = 700

and τ r =

A, s -1

* ατ r E def

10 -4 3-5 10 -2

700 3700 -

104 − 105 700 ⋅ 10

−2

= 103 − 104 s –2

The results confirm that the destruction rate is limited by the elastic energy redistribution rate or, in other words, it depends on the material properties. Analysis of equation (3.61) leads to a series of useful conclusions. Thus, in a field of variable mechanical forces the efficiency of mechanochemical process increases with the increasing of the applied stress. The most favorable conditions appear for the maximal concentration of mechanical energy on the unit of stressed volume and time unit. At low intensities the characteristic effects related to residual stress accumulation can not be manifested. In addition, the mechanochemical processes that occurs in a variable field of forces are sensibly influenced by the elastic vibration frequency. As Figure 3.22 shows, if the process is stopped for a period, the mechanochemical rate strongly decays. For a solid body is compulsory for the solicitation frequency to coincide with the inferior limit of the spectrum of mechanical losses frequencies [182]. In the case of mechanochemical reactions occurring in gaseous media is important as the frequency to correspond to the average period of energy transfer (for instance the phenomena of sound propagation in gases) [183]. The dependence of the mechanochemical rate on temperature does not clearly appear in equation (3.61) but the constants contained in this equation are related to the relaxation times and depend on temperature. In the case of polymers this dependence is in the highest extent manifested in the vicinity of T g . Therefore, around this transition temperature changes in the dependence of reaction rate on temperature are expected. This result has not been observed during solicitation in a constant field of forces. Concomitant measurement of the mechanochemical destruction rate by vibratory milling and the propagation rate of the ultrasound 238

Mechanochemistry of Polymer Fracture

Figure 3.22. Mechanochemical destruction of poly(methyl methacrylate) by vibratory milling [56]: 1) continuous regime; 2) periodic regime (5 min pause). N – number of broken bonds. Temperature, 100 K.

waves, in the case of polystyrene and poly(vinyl acetate) in the temperature range from 223 to 303 K, confirms once again the assumption that the mechanochemical reaction rate occurring into a variable field of forces as well as the rate constant dependence on temperature are strongly related to the physico–mechanical properties of material. It is clear that the limiting stage of the mechanochemical process is that of the elastic energy redistribution [184]. The rate of the mechnochemical process depends on many external parameters, such as: uniform distribution of mechanical energy, time of tensions relaxation, capacity of mechanical energy absorption by the particles with different dimensions, and when the rate determinant step is the chemical reaction in kinetic equation must be included the chemical bonds resistance and their vibration frequency. Macromolecular chains splitting into shorter fragments implies the chemical bonds scission and the apparition of the active particles (macroradicals or macroions) that are able to initiate specific reactions, for instance the grafting of some monomers, if these ones are present in system. Usually, the quantitative measurement of some effects is used for determination of the reaction rate. Thus, the kinetic curves are drown taking as criterion the variation in time of the number of split chemical bonds or of formed active particles, for instance macroradicals (determined by calculation, ESR spectroscopy or specific chemical reactions). Alternatively, one can follow the variation of specific surface in time, kinetic of some reactions initiated by active particles, or kinetic of the accumulation of low molecular 239

Macromolecular Mechanochemistry

weight compounds, the rate of their formation being a measure of the mechanochemical reaction. In the most usual situation the variation of the average molecular weight in time, from the initial value M0 until to destruction limit M ∞ is followed. In order to avoid the difficulties related to the calculation of M ∞ using equation (3.60), Baramboim developed a graphical method that is based on the processing of experimental curves as is seen in Figure 3.23 [178]. M ∞ is a function of polymer chemical structure, temperature, mechanical vibration regime, and the nature of the environmental medium. For a given polymer M ∞ is constant only for a given set of processing conditions:

b

M ∞ = f S , T , M , Em

g

where: M ∞ –destruction limit; S–polymer structure; T–temperature; M–nature of the reaction medium; E m–adsorbed mechanical energy. The value of E m is calculated as follows:

γ I − k p ∆ Em = 0 therefore:

Figure 3.23. Scheme for graphical determination of M ∞ [178]. 240

(3.64)

Mechanochemistry of Polymer Fracture

∆E m =

γI kp

(3.65)

where: γ – the adimensional coefficient that determines the energy absorption; I – intensity of the mechanical energy, J . mol –1 s –1 ; k p – tension relaxation rate constant. The mechanical energy is non-uniformly distributed in volume and the function of tensions distribution on the chemical bonds in unknown especially due to the supramolecular organization of the polymer and of tensions concentration mainly on the “linking” bonds. If it is accepted that the bond fraction with higher energy than E m required for their scission is proportional to exp(E m /∆E m ) the destruction rate constant k can be expressed as:

b

k = A exp Em / ∆E m

g

(3.66)

where: A – coefficient that takes into account the mechanical energy redistribution in system. In the case of poly(methyl methacrylate) destruction it was found that

 700  k PMMA = 4 . 10 –5 exp  − .  I  It can be noted that the value of A is close as order of magnitude to the tensions relaxation rate constant. Clearly, the founded value is valuable only for the considered function of tensions distribution. Since the mechanodegradation occurs from the initial molecular weight until to the destruction limit M ∞ , in any moment of the process appears chain fragments having dimensions of M t – M ∞ ( M t – value of the average molecular weight at the moment t). Considering that the rate of mechanodegradation, which represents the number of splitting steps in unit of time, is proportional to the mechanocracking probability at the respective moment, and, on its turn, this probability is proportional to the number of possible elementary steps of fracture until to the destruction limit, it my be written:

ν=k

FG M − M IJ H M K ∞

t

∞

on the other hand: 241

(3.67)

Macromolecular Mechanochemistry

−d

FG M − M IJ H M K ∞

t

∞ (3.68) dt equalizing the two expressions and separating the variables, is obtained:

ν=

d

FG M − M IJ H M K = −kdt ∞

t

∞

Mt − M∞ M∞

(3.69)

by integration equation ( 3.69 ) becomes:

ln

Mt − M∞ = kt + C M∞

(3.70)

The value of the integration constant, C, is obtained for boundary conditions, at t = 0 when M t = M 0 , therefore:

M0 − M∞ M∞

(3.71)

Mt − M∞ M − M∞ − ln 0 = −kt M∞ M∞

(3.72)

C = ln and

ln or

ln

Mt − M∞ = − kt M0 − M∞

(3.73)

and finally

Mt − M∞ = e − kt M0 − M∞

(3.74)

Equation (3.74) allows determination of the average molecular 242

Mechanochemistry of Polymer Fracture

weight in any moment of the mechanodegradation:

c

h

M t = M 0 − M ∞ e − kt + M ∞ Noting

cM

0

(3.75)

h

− M ∞ = A the relation (3.75) becomes: M t = Ae − kt + M ∞

(3.76)

As is seen in Figure 3.24, equation (3.76) is in good accordance with the experimental data [185–187]. Equation (3.76) describes a first order kinetic of a chemical reaction under the statement that the concentrations were replaced with values of chains length. It is very important that the equation describes the whole process, including the boundary states, which are defined by M 0 and M ∞ . Thus, to the initial moment of the destruction, t = 0, M t = M 0 , and to t = ∞ at the end of the process, M t = M ∞ . Starting from the equation (3.76) and expressing the time in small intervals ∆t n (where n = 0, 1, 2, 3,…..n) is obtained:

c

h

M ∆tn = M 0 − M ∞ e − k∆tn + M ∞ and

e

(3.77)

j

∆M ∆tn = M ∆tn − M ∆t n +1 = M 0 − M ∞ 1 − e − k∆t e − k∆tn

b g

(3.78)

therefore:

Figure 3.24. Overlapping of the experimental (full lines) and calculated (dotted lines) values of molecular weight: 1) poly(vinyl alcohol); 2) polystyrene [187]. 243

Macromolecular Mechanochemistry

M∞ =

FH

M ∆tn ⋅ M ∆t n + 2 − M ∆t n +1

b g

b

I gK

2

M ∆tn + M ∆t n + 2 − 2 M ∆t n +1

b g

b g

(3.79)

Analyzing equation (3.79) it can be concluded that for the calculation of M ∞ it is enough to know three values of M ∆tn . The rate of mechanodegradation can also be expressed by the number of macroradicals formed by chain splitting at a given moment, t, on the weight unit (expressed in grams). If the total number of chain splitting steps, starting from the moment t and until to the end of destruction is ( M t / M ∞ − 1 ) and any fracture step leads two macroradicals, then the mechanodegradation rate is given by the expression:

v=k

FG M − 1IJ ⋅ 2 N HM K

m Mt

t

∞

(3.80)

where m – is the quantity of the processed polymer; N – Avogadro’s number. Rearranging the above equation and taking m = 1 g, the following equation is obtained:

 1 1  v = 2kN  −   M∞ Mt 

(3.81)

or replacing M t with the expression from equation (3.76):

v=

2 kN Ae − kt ⋅ − kt M ∞ Ae + M ∞

(3.82)

Clearly, the higher M t and lower M ∞ the most intense mechanodegradation occurs; at M t = M ∞ the process is stopped. The total number of macroradicals that may appear during polymer mechanocracking from M0 to M ∞ is:

Z = 2mN

FG 1 HM

∞

−

1 M0

IJ K

(3.83)

Considering now a constant rate dependency of the mechanochemical reaction by the polymerization degree k = f(P) [185]:

dn = dt

∞

∑ k Z nZ

(3.84)

1

where: n – the total number of macromolecules in the volume unit; 244

Mechanochemistry of Polymer Fracture

k Z – the rate constant of the macromolecules having Z structural units; n Z – the number of macromolecules having Z structural units. It can also be written:

d ln

P0 Pt

(3.85) = kZ dt where: P 0 and P t are polymerization degrees at the initial and final moment of mechanodegradation. The concrete shape of function k = f(Z) is unknown and varies in function of mechanocracking conditions. Consequently, it is supposed that value of k is not affected by Z. Under these conditions:

Pt = P0e − kt

(3.86)

for k Z = k 1 Z

Pt =

P0 1 + P0 k1t

(3.87)

and for k Z = k 2 Z 2

Pt =

P0

e j

1 + 2β P02 k 2 t

(3.88)

where β – polymer polydispersity. W. Deters and H. Grohn have considered that the mechanocracking rate is described by a zero order equation and the following relation was used [186]:

dX P = k ; X = kt + 1; Pt = 0 (3.89) dt kt + 1 where X – the number of split bonds. For k = 1/t µ (t µ corresponds to P t = P 0/2) is obtained: Pt =

P0 t +1 tµ

(3.90)

Equation (3.90) has been verified on the cellulose acetate supposed to degradation by vibratory milling, when a linear dependence P t vs. 1/(t/t µ + 1) was found. To correctly describe the results ob245

Macromolecular Mechanochemistry

tained for cellulose acetate, the following equation was suggested as being suitable:

P0 − P∞ = kt + 1 Pt − P∞

(3.91)

P0 + P∞ t (3.92) +1 k N.K. Baramboim proposed the use of the destruction degree for the characterization of the mechanodegradation process on its different stages: Pt =

ϕ1 =

M0 − Mt M0 − M∞

(3.93)

As equation (3.93) shows, the destruction degree is defined as the ratio of the difference between the initial molecular weight, M0 , and the molecular weight at the given moment t, M t , to the difference between the initial and limit molecular weight, M ∞ , under the destruction conditions. Expressing M t with the mean of equation (3.76) it results that ϕ1 = 1 − e − kt and M t can be expressed as M t = M 0 − ϕ1 A . If the destruction degree is expressed by the relative number of split bonds in the moment t:

ϕ2 =

n1 n0

(3.94)

where

n0 =

M0 − M∞ A = M∞ M∞

and nt =

M0 − Mt Mt

(3.95)

the following expression is obtained:

ϕ2 =

cM cM

h − M hM

0

− Mt M∞

0

∞

therefore ϕ 2 = ϕ1

t

M∞ Mt

(3.96)

In this case M t can also be expressed by the terms n 0 and ϕ 1 :

246

Mechanochemistry of Polymer Fracture

e

M t = M ∞ 1 − n0e − kt or

b

j

M t = M ∞ 1 + n0 1 − ϕ1

(3.97)

g

(3.98)

The graphical representation of the curves ϕ 1 = f(t) and ϕ 2 = f(t) for three polymers, i.e. poly(methyl methacrylate), polystyrene and poly(vinyl acetate), Figure 3.25 shows that ϕ 2 describes the final stages of the mechanocracking process more accurately than ϕ 1 . Since both ϕ 1 and ϕ 2 contain the value of the initial molecular weight M0 these expressions are not convenient for the polymer comparison, which strongly differ from this point of view. Baramboim proposed another expression ϕ 3 = M ∞ / M t which more adequately responds to this requirement. Irrespective of the initial value of M0 , this parameter varies from zero to unit in the moment of reaching the destruction limit. Consequently, it allows for description and comparison of different types of polymers during the mechanodegradation process. If the values of ϕ 1 , ϕ 2 , and ϕ 3 are compared for a concrete case, polystyrene degradation for instance, for each M ∞ = 700 and M t = 30000, the dependence of the destruction degrees ϕ 1 and ϕ 2 by M0 and the independent character of ϕ 3 are clearly observed in Table 3.14. The expression used for calculation of destruction limit was α = S/n (where S – the number of the split macromolecules at

Figure 3.25. Comparative values of the destruction degrees expressed by ϕ 1 (full lines) and ϕ 2 (dotted lines) for different polymers: 1) and 4) poly(methyl methacrylate); 2) and 5) polystyrene; 3 and 6) poly(vinyl acetate) [187]. 247

Macromolecular Mechanochemistry

the moment t; and n – total number of macromolecules) [188] or (n – n 0 )/n 0 (where n and n 0 – the number of bonds initially and at a given moment of the mechanodegradation process). The last relation was used to describe elastomer mastication by W.F. Watson and coworkers [118]. The same behavior is also observed in Figure 3.26. Destruction rate, expressed as dM/dτ vs. τ, has also been used for the characterization of the mechanodestruction of some polymers by utrasonic treatment in homogeneous media. For instance, for the case of poly(vinylchloride) dissolved in cyclohexanone (1% solutions), at room temperature, the destruction curves are presented in Figure 3.27 [123]. The destruction degree ϕ 3 and the number of split bonds were calculated and their variation in time is depicted in Figure 3.28 [123]. The number of split bonds was calculated using the viscosity data, according to Hess, Steurer and From, from the relation [189]: (3.99) Z = Zm ⋅ N where: Z – total number of split bonds; Z m – number of split bonds on each macromolecule; and N – number of macromolecules.

Zm =

η0 ηt

−1

(3.100)

[η 0 ] – initial intrinsic viscosity; [η t ] – intrinsic viscosity at the Table 3.14. The influence of moisture on the decrease of molecular weight [131] The state of polymer

Milling time

Molecular weight viscosimetric

Molecular weight calculated from end groups

Dried

0 12 18 24 48

35,200* 33,450 31,700 28,630 24,590

35,200 33,060 30,700 28,100 23,100

Humidified (12 g polyethylene terephthalate + 1 ml H2O)

0 12

35,200 30,900

35,200 29,200

18 24 48

27,210 24,080 21,404

26,100 23,580 20,300

248

Mechanochemistry of Polymer Fracture

Figure 3.26. Comparative modification of the destruction degree expressed by ϕ 1 (full lines), ϕ 2 (dotted lines), and ϕ 3 (interrupted lines) for different values of M ∞ [187]: 1) and 3) 10,000; 4 – 6) 20,000; 7 – 9) 30,000.

Figure 3.27. Variation of the average molecular weight (1) mechanodegradation rate (2) with duration of ultrasonic treatment [123].

and

Figure 3.28. Variation of the destruction degree, ϕ (1) and number of broken bonds, Z, (2) with the duration of ultrasonic treatment [123]. 249

Macromolecular Mechanochemistry

moment t of mechanodegradation.

m (3.101) M where: N L – Loschmitd’s number; m – polymer amount, expressed in grams; M – average polymer molecular weight. The factor A = M τ − M ∞ / M ∞ was used for kinetic evaluation of mechanodegradation by vibratory milling at different periods of time (Table 3.15) and reaction media (inert, air, nitrogen oxide) of some cellulose materials, (Table 3.16). Graphical representation of the equation (3.74) in coordinates ln M t − M ∞ / M 0 − M ∞ vs. t leads to a straight line that characterizes the mechanodegradation evolution. This criterion has been used by Popa, Oprea, and Riess for characterization the polybutadiene solutions (0.5% in toluene) degradation under the conditions of high speed stirring or ultrasonation. The study was carried out at 29 °C in nitrogen atmosphere and to a stirring rate of 2000 rot/min [190, 191]. From the line slope, Figure 3.29, the value of the mechanodegradation rate constant equal to 3.72 .10 –4 s –1 was found. Under similar conditions but under ultrasonic irradiation, a very close value k = 3.33 . 10 –4 s –1 was obtained [192]. The value of k depends on the parameters of the destruction process. Thus, k =4.75 . 10 –4 s –1 in the presence of atmospheric oxygen or k = 3.48 . 10 –4 s –1 in nitrogen. Other important factors are temperature, Figure 3.30, solvent nature, Figure 3.31, solution concentration, Figure 3.32, and stirring rate, Figure 3.33, respectively [191]. The kinetic of polymer networks mechanodegradation can be followed by correlating of the crosslinking degree to some physical properties. Thus, the polyurethane elastomer based on 4,4’–dibenzyl diisocyanate presents a very good correlation of the crosslinking degree with the swelling kinetic, Figure 3.34. The maximal swelling degree α m = (m – m 0)100/m 0 (where: m and m 0 – polymer weight in swollen state, at equilibrium, and initial state, respectively) and especially its variation ∆α m = α m final⋅100/α m initial have been correlated to the mechanochemical process parameters i.e. number of cryolitic cycles, N c , in air and nitrogene, Figure 3.35 a and b, cooling rate, Figure 3.36, and the temperature difference, ∆T, between the frozen and unfrozen state, Figure 3.37. As Table 3.17 shows, for N c = 120 the reticulation degree in inert atmosphere and air were directly correlated [193]. N = NL ⋅

c

c

h

h

250

Mechanochemistry of Polymer Fracture Table 3.15. Behavior of different types of cellulose during vibratory milling [130] Type of cellulose

Milling time (h)

Mτ − M∞ Average molecular A= weight M∞

Cotton cellulose

0 1.5 4 6 8 10

391 716 221 778 105 786 42 930 25 596 24 462

15.01 8.06 3.73 0.75 0.043 0.000

Reed cellulose

0 1.5 4 6 8 10 16 20 24

125 712 111 132 64 152 52 974 45 684 41 044 24 948 23 812 22 032

4.70 4.04 1.91 1.40 1.07 0.86 0.13 0.08 0.00

Poplar down cellulose

0 1.5 4 6 8 10

83 636 50 544 31 752 20 574 12 636 10 106

7.27 4.00 2.14 1.03 0.25 0.00

Regenerated cellulose (Viscose)

0 1.5 4 6 8 10

62 856 42 606 33 372 31 428 28 026 25 272

1.48 0.68 0.31 0.24 0.10 0.00

Figure 3.29. Time dependence of ln M t − M ∞ / M 0 − M ∞ during high-speed stirring degradation of a polybutadiene solution, PBut, (c = 0.5% solution in toluene; T = 29 °C; nitrogen atmosphere; and v = 20 400 rpm) [190]. 251

Macromolecular Mechanochemistry Table 3.16. The influence of the reaction medium on the molecular weight and factor A [130] Medium

Duration (h)

Mw

A=

Mτ − M∞ M∞

Nitrogen

0 1.5 4 6 8 10 24

125 712 111 132 64 152 52 974 45 684 41 044 22 032

4.70 4.04 1.91 1.40 1.07 0.86 0.00

Air

0 1.5 4 6 8 10 24

125 712 59 616 40 824 34 020 27 054 22 842 16 200

6.76 2.68 1.52 1.09 0.67 0.41 0.00

Nitrogen oxide

0 1.5 4 6 8 10 17

125 712 15 211 8 100 7 452 4 698 3 402 3 400

35.9 5.32 1.38 1.19 0.38 0.002 0.000

Figure 3.30. Variation of the PBut average molecular weight with time at different temperatures: 1) 29 °C; 2) 5.5 °C; 3) –18 °C; 4) – 40 °C (c = 1% solution in toluene and v = 20, 400 rpm) [190]. 252

Mechanochemistry of Polymer Fracture

Figure 3.31. The effect of stirring time on the average molecular weight of PBut in the presence of different solvents. 1) tetrahydrofuran, THF; 2) toluene; 3) ethylbenzene, EB; 4) cyclohexane Ch. Degradation conditions: T = 18 °C; inert atmosphere; v = 20, 400 rpm; and c = 1% [190].

Figure 3.32. The effect of polymer concentration on the variation of PBut molecular weight for different degradation periods: 1) 10 min; 2) 30 min; 3) 60 min. Degradation conditions: T = 29 °C; inert atmosphere; v = 20, 400 rpm; solvent – toluene [190].

5. FACTORS THAT INFLUENCE THE MECHANODEGRADATION PROCESS The factors that affect mechanocracking, mechanodegradation, and fracture efficiency can be classified in two main groups, namely: 253

Macromolecular Mechanochemistry

Figure 3.33. The effect of stirring speed on the PBut molecular weight for different reaction periods: 1) 10 min; 2) 30 min; 3) 60 min; 4) 30 min with inhibitor; 5) 60 min with inhibitor. Degradation conditions: concentration 1% in toluene; T = 29 °C; inert atmosphere [190].

Figure 3.34. Kinetic of polyurethane elastomer swelling (9% solution in phenol/ water mixture) in function of crosslinking degree, ν c : 1) 159.74; 2) 172.07; 3) 185.2; 4) 214.59. All values x10 –6 mole/cm 3 ) [193].

254

Mechanochemistry of Polymer Fracture

Figure 3.35. The influence of cryolitic cycles, N c , on the maximal swelling degree (v = 28 K/min; ∆T = 130 °C; 1 – 5 as in Figure 3.34): (a) in air; (b) in inert atmosphere (nitrogen).

Figure 3.36. Variation of α m during cryolisis with cooling rate (N c = 120; ∆T = 130 °C; 1 – 5 as in Figure 3.34) [193].

Figure 3.37. Variation of α m during cryolisis with ∆T (the difference between the highest and lowest temperature of cryolitic cycle) (N c = 120; v = 28 °C/min; 1 – 5 as in Figure 3.34) [193]. 255

Macromolecular Mechanochemistry Table 3.17. The increase of maximal swelling degree (α m ) after N e = 120, in air and inert medium (nitrogen) [193] νe

∆αmair – ∆αmnitrogen

∆αm

( 10–6 mol/cm3 )

Air (%)

Nitrogen (%)

159.74 172.04 185.12 203.67 214.59

11.11 21.34 29.74 44.84 89.03

5.72 9.36 14.22 13.26 51.61

5.39 11.98 15.52 34.58 37.42

structural or intrinsic factors, such as chemical structure of the macromolecular chain, initial average molecular weight, M0 , chains conformation, packing degree, ratio of crystalline and amorphous phases, morphology; and external factors, i.e. temperature, medium nature, mechanical regime, etc. 3.5.1. Structural factors Polymer’s structure, including all its organisation levels, represents the most complex factor having the widest sphere of influence and being decisive in the achievement of the mechanocracking and fracture processes. If the supramolecular–morphological structure only indirectly acts in the above-mentioned processes, the molecular one represents just the level at which these processes take place, preestablishing the succession of changes at the superior levels. 3.5.1.1. Macromolecular chain characteristics Chemical structure The existence of the weak bonds, able to determine intra- and intercatenary interactions, macromolecular chains geometry (i.e. linear, branched, and crosslinked), chains rigidity are factors that governs the efficiency, kinetic, and mechanism of mechanocracking [113,116,194]. If we compare the mechanodegradation of the following polymers/poly(methyl methacrylate), polystyrene, different sorts of poly(vinyl chloride), polyacrylonitrile, and polyethylene, the first polymer suffers the most advanced degradation, (Figure 3.38, curve 4). Instead, polyacrylonitrile, containing many –CN groups, the strongly polar ones that develop intercatenary hydrogen bonds that will improve its higher mechanical resistance, is only little affected (curve 1 in Figure 3.38). The rate and destruction degree of the 256

Mechanochemistry of Polymer Fracture

aforementioned polymers lie in the following series [194]: PMMA > PS > PVC > PAN > PE Alongside molecular weight decay, expressed by the decrease of intrinsic viscosity, in the case of some polymers, the activation of side reactions also occur. Thus, in the case of poly(vinyl chloride) and polyacrylonitrile the destruction products modify the initial polymer colour, they acquiring a yellowish nuance due to the intraand intermolecularly elimination of acid (HCl and HCN, respectively). The influence of the polymer chemical structure on the limit and rate of mechanodegradation is illustrated in Table 3.18 [116]. The relative high rate of poly(methyl methacrylate) chain splitting as compared to those of polystyrene is related to the presence, in the first case, of the tertiary carbon atoms along the main chain. These atoms labillise the C–C bonds from its vicinity favouring their splitting. This observation was also confirmed by the thermal destruction data that, in the case of PMMA, proved a lower activation energy, only 25 Kcal/mol, then those required for polystyrene destruction of about 34 Kcal/mol. Their packing density, which increases from the first to the last term of series, also justifies the resistance to mechano-destruction

Figure 3.38. Influence of polymer chemical nature on the vibratory milling mechano-chemical process in inert medium at 18 ± 2 °C: 1) polyacrylonitrile; 2) poly(vinyl chloride); 3) polystyrene; 4) poly(methyl methacrylate) [194]. 257

Macromolecular Mechanochemistry Table 3.18. Influence of the polymer chemical structure on the destruction limit and rate constant [116] Polymer

Poly(vinyl acetate)

Structural unit CH2

CH

11 000

Destruction rate constant k 0.0468

10 000

-

9 000

0.1200

7 000

0.0945

4 000

0.0237

Destruction limit M∞

OCOCH3

Cellulose triacetate

C6H7O2(OCOCH3)3 CH2

Poly(methyl methacrylate)

CH C

O OCH3

Polystyrene

CH2

CH C6H5

Poly(vinyl alcohol)

CH2

CH OH

of the polymers in the above-mentioned series. The flexibility, a fundamental property of the macromolecules, plays an important role in mechanodegradation. For the same molecular weight, M 0, the polymers have different behaviour during mechanodegradation, (Figure 3.39). For instance, poly(vinyl acetate) is characterised by the highest chains flexibility. At the temperature close to the environment temperature this polymer flows. Therefore, in the conditions of vibratory milling it will elastically take over the mechanical energy. This explains the highest value of limit molecular weight, M ∞ = 11,000 and the lowest value of the mechanochemical constant. Poly(alcohol vinyl) contains hydroxylic groups, _ OH, polar one, able to develop interacting hydrogen bonds that increase its rigidity and put it as the second therm of the series. Mechanodegradation of poly(methyl methacrylate) and polystyrene, both the brittle materials, is governed by their pronounced rigidity. The influence of polymer rigidity on the mechanodegradation process was systematically studied on poly(butadiene-coacrylonitryle) copolymers. Changing the monomers ratio the chains flexibility can be easily controlled. In the series SKN-18, SKN-26, SKN-30, and SKN-40, respectively, it was found that the more intense mechanodegradation occurs to those copolymers characterised by a high content of –CN groups. Thus, the elastomer SKN-26 is more rigid and easier degradable than SKN-18. On the other side, the mechanical processing of the same copoly258

Mechanochemistry of Polymer Fracture

Figure 3.39. Kinetic curves of different polymers mechanodegradation calculated for the same value of M 0 : 1) poly(vinyl acetate); 2) poly(vinyl alcohol); 3) poly(methyl methacrylate); 4) polystyrene [116].

mers evidenced different features. The effect of mechanochemical reactions was followed by changes of elasticity and DEFO hardness, under the conditions of two rolls mixing of the selected polymers. Figure 3.40 shows the variation of DEFO hardness during the mechanical processing. Curves 1 (SKN-18) and 2 (SKN-26) contain a slightly decreasing part, which correspond to a duration of about 100 min, passing after that by a minimum, to increase for longer processing periods. The increasing part corresponds to a crosslinking process. In the case of SKN-40 (curve 3 in Figure 3. 40) the curve slope continuously increases which denotes that only the first step is common, i.e. chain mechanocracking which is directly followed by reticulation. The data concerning the solubility of these elastomers are in good agreement plasticity variation. As a function of their solubility, the SKN copolymers are placed in the following order: SKN-18 > SKN-26 > SKN-40 (94%) (68%) (29%) Nevertheless, even if the natural rubber does not contain any rigid units, its mechanodegradation is more pronounced than of any other synthetic elastomer. It seems that its structural particularities, i.e. the presence of the tertiary carbon atom and the conjugation effect 259

Macromolecular Mechanochemistry

Figure 3.40. Modification of DEFO hardness in time in function of elastomer ’s rigidity: 1) SKN-18; 2) SKN-26; 3) SKN-40 [116].

along of macromolecular chain influence the mechanodegradation process to a greater extent than the elastic/rigid balance of the poly(butadiene-co-styrene) copolymers. It is clear that a general valuable rule of mechanodegradation in mechanochemistry can not be formulated and any polymer must be individually studied. All the above mentioned results have been obtained on linear polymers. The crosslinked structures were investigated in a lesser extend. Some studies concerning the insoluble tridimensionally resins, which were processed by vibratory milling, proved that the scission preferentially occurs to the crossbridges. As result of mechanodegradation some fragment are detached from the network and on the initial stages partial soluble products are obtained. Prolonging the solicitation period, linear structures with specific properties are accumulated [195–202]. If the phenolformaldehyde or glyptalic resins are subjected to the mechanodegradation process fragments of network, with dimensions varying in a very large range, as is seen in Figures 3.41–3.43 are obtained [199,200]. In other cases, the macroradicals formed during mechanodegradation or the functional groups, which appear by their stabilisation, react in the direction of new crosslinked structures formation that differ from the initial ones [203–206]. The behaviour of a cast polyurethane elastomer based on 4,4’dibenzyl diisocyanate was studied on a dynamic fatigue apparatus 260

Mechanochemistry of Polymer Fracture

that allows the control of stress frequency, amplitude and deformation. The degree of reticulation was expressed by the value M c (molecular weight of the segment between two adjacent crosslinking points). In Table 3.19 gives the values of the number of stress cycles to fracture, N F , as the function of samples crosslinking degree

Figure 3.41. Variation of different functional groups content of gliphthalic resin by vibratory milling [ 116 ]: 1) hydroxylic groups; 2) esteric groups; 3) carboxylic groups.

Figure 3.42. Variation of dissolution (in alkaline solutions) and swelling rates of a phenolformaldehyde resin with the particle size (dispersion degree) (milling time, 20 hrs) [116]: 1) solubility in 10% NaOH aqueous solution; 2) swelling in 10% NaOH aqueous solution.

Figure 3.43. Some characteristics of a phenolformaldehyde resins after 20 hr of vibratory milling [116]: 1) free phenol content; 2) methylic groups content; 3) bromine number. 261

Macromolecular Mechanochemistry

and solicitation amplitude, γ, for a constant frequency (ν = 4 Hz). It is clear that N F reflects the polyurethane resistance under dynamical conditions of solicitation decays with the increase of the cross-linking degree. In the case of considered polyurethane, by increasing the number of alophanate crossbridges a relative dislodgement of the macromolecular chains takes place. The cohesion energy, whose value is given by the number of hydrogen bonds and van der Waals-type interactions, diminishes for sterical reasons and consequently the resistance under dynamical conditions decays, too. At the same time, with the increase of applied stress the number of cycles to fracture decreases for all samples, irrespective of their reticulation degree [207, 208].

Initial molecular weight, M 0 The initial average molecular weight, M0 , is the factor of primary importance in polymer mechanochemistry, because: 1) molecular chain is the structural level at which the primary step of the mechanocracking process occurs, by the scission of chemical bonds and it preestablishes the reaction mechanism by the nature of the generated active centres; 2) since M0 is directly related to the polymer’s structural characteristics, the variation of the molecular weight represents the kinetic criterion for the evaluation of the mechano-chemical destruction. The clearest evidence of the influence of M0 on mechanodestruction was found in the case of degradation of polymers in diluted solutions when the macromolecules are free of any physical interactions. There are a lot of studies on this subject [137, 139, 145, 146, 209–215]. R.S. Porter and J.F. Johnson, studying the behaviour of polyisobutene solutions under conditions of flowing between two Table 3.19. Variation of the number of cycles to fracture (N F ) with the degree of crosslinking and unitary effort for casting polyurethane (ν = 4 Hz) [207,208] Mc, g/mol → σ, MPa ↓ 0.810 0.820 0.850 0.905 1.000 1.100 1.200

7700 30.856 23820 20510 10250 9520 7410 6340

7134

6613

23250 19510 16790 9310 8920 6830 5700

262

22200 18250 14340 8770 7930 6240 4910

6000 20400 13830 9710 8120 7410 6590 4150

5690 16810 12850 9070 7510 7200 5010 3810

Mechanochemistry of Polymer Fracture

concentric cylinders, have found a clear dependence between M0 and the shear force, as is seen in Figure 3.44. The effect of mechanodegradation increases with the increase of M0 , as is illustrated in Figure 3.45 that refers to the shearing of poly(α-methylstyrene) in toluene, under the conditions of capillary flowing. The authors have also verified these results on polystyrene extrusion, Table 3.20 [214]. Many other experimental data leading to the same conclusions have been obtained by ultrasonation of many polymer solutions [148–151, 216–229]. The influence of M0 on the kinetic of polymer mechanodegradation was also studied on solid state polymers. In order to eliminate the indirect influences, induced by the polymer chemical structure, cellulose materials from different sources of cotton cellulose, poplar down cellulose, and regenerated cellulose were used. These materials were processed by vibratory milling under a nitrogen atmosphere at the environment medium temperature (T = 18±2 °C), [131, 230]. The destruction degree is in agreement with the initial molecular weight of the materials. The only exception is given by poplar down cellulose, which even having a much lower M0 suffered a mechanodegradation with the same intensity as cotton cellulose, the first term in series, Table 3.21 and Figure 3.46. Its particular behaviour was related to the differences in the supramolecular-morphological structure. The two types of

Figure 3.44. Shear of polyisobutylene of three different M in in cetane, 9.6–9.8 vol.%, stress in dyn/cm 2 , temperature, K [211]: (l ) 25 °C; (m , o , ∆) 40 °C; (n ) 80 °C. 263

Macromolecular Mechanochemistry

Figure 3.45. Constant rate of degradation K for poly(α-methylstyrene) of different viscosity average molecular weights in toluene during capillary flow [146]. Table 3.20. Mechano-chemistry of polystyrene degradation within the capillary reservoir during extrusion of different polystyrenes of M w /M n > 1.1

a b

Original a

After extrusionb

234 670 1800

230 570 690

Mw reduction ( % ) 2 14 60

Weight-average molecular weight ×10-3. From Whitlock and Porter [ 214 ]. Temperature 202 ± 2 °C; shear stress at the capillary wall 2.5 ± 0.1 × 106 dyn/cm2.

cellulose are degraded with approximately same rate by different reasons. Thus, the cotton cellulose is characterised by the highest value of M0 , a greater packing density of the chains, by the highest degree of crystallinity and consequently by the highest mechanical resistance. Apart from this, the poplar down cellulose has the low molecular weight and degree of crystallinity and therefore low mechanical resistance. From morphological point of view, the cotton cellulose is characterised by longer and more resistant fibres as those of poplar down cellulose. Consequently, the poplar down cellulose is converted in the first hours of vibratory milling into a highly disperse powder, the cotton cellulose passes into a mixture consisting of two fractions after 10 hours of mechanodegradation. In this case, the first fraction consisted of a highly dispersed powder for which the fracture process has been finalised and the molecular level of the destruction limit was attained. The second fraction still retains the fibrous character having a 264

Mechanochemistry of Polymer Fracture Table 3.21. Influence of M 0 on the mechanochemical destruction limit and rate of some cellulosic material processed by vibratory milling (T = 18 ± 2 °C, inert atmosphere, nitrogen) [131]

Type of cellulose

Cotton cellulose Reed cellulose Poplar down cellulose Viscose

Initial average molecular weight M0

Destruction limit M∞

Destruction rate k ( h-1 )

Order of reaction n

391 716 125 000 83 632 62 856

24 462* 22 032 10 106 25 275

0.5024 0.3470 0.5250 0.1590

1.1 1.0 1.0 1.1

* For the highly-disperse fraction

Figure 3.46. Variation of destruction rate with mechanodegradation duration [131]: 1) cotton cellulose; 2) poplar down cellulose.

molecular weight M = 322,398 that is relatively close to M 0 . It is clearly that the mechanocraking process is controlled by the mechano-dispersation process. The influence of M0 on mechanodegradation was also studied in the conditions of mastication by two rolls mixing of poly(vinyl alcohol). Once again, in order to avoid any influence of the superior levels of structural organisation, the polymer was fractionated in three fractions with different molecular weights. The results, in terms of limiting viscosity, are presented in Table 3.22. PVA 1 fraction with the highest limiting viscosity, η lim = 60, and, 265

Macromolecular Mechanochemistry Table 3.22. Influence of M 0 on the mechanochemical destruction limit of poly(vinyl alcohol) processed by mastication [158] Type of poly(vinyl alcohol)

Mastication duration ( min )

Limit viscosity

PAV1

0 5 10 20 30 45 60 100 180

60 23 48 41 37 34 32 27 27

PAV2

0 11 15 30 36 60 100 200

34 32 30 29 28 27 26 26

PAV3

0 10 15 25 160

28 26 27 27 26

consequently, having the highest M0 was proved to be gradually degrading with time. The destruction limit is attained after 180 min of mastication. PAV 2 , η lim = 34, shows a narrower range of variation which corresponds to slower degradation. PAV 3 , η lim = 28, practically does not suffer any degradation. Its chains have practically the critical length below which chemical bond splitting does not occur. Chains conformation The influence of chains conformation on mechanodegradation was demonstrated by the comparative investigation of two polymers with a similar structure that differ from each other only by chains conformation. N.K. Baramboim selected two proteins, gelatine and casein. The first one has a stretched and asymmetrical conformation while the second one is characterised by an approximately spherical symmetry. The proteins were subjected to vibratory milling. He found completely different kinetic curves for the destruction of the two proteins. Gelatine was intensely degraded and the viscosity of its destruction products sharply decreased with time. In the case of casein, the above effect is not 266

Mechanochemistry of Polymer Fracture

observed and a slight increase of viscosity was recorded. Gelatine with its stretched and strongly asymmetric macromolecules was split in smaller fragments with lower asymmetry and, therefore, its viscosity diminishes. The globular conformation of the casein is characterised by a smaller asymmetry and, consequently, viscosity is low in the initial stages of degradation. Under the action of mechanical forces, the globular formations are broken, changing to more asymmetric conformations. Asymmetry increases in time and this fact explains the observed increase of viscosity, Figure 3.47 [113]. The assumption that mechanocracking occurred in the case of casein was proved by the titration method, which clearly evidenced the change of the number of end functional groups [231]. All the literature in this field shows that mechanodegradation is a selective process with respect to M0 , the scission of the longer macromolecular chains being stimulated first. In addition, the chains shorter than the ‘critical length’, which depends on the type of polymer, are not affected by the action of mechanical energy. 3.5.1.2. Characteristics of the supramolecular–morphological structure Among the first reports concerning the influence of the supramolecular structure, particularly the effect of crystallinity on mechanodegradation, are those published by W. Deters. He carried out vibratory milling trials on cellulose triacetate samples and plotted the kinetic curves in the number of split bonds vs. time coordinates. For the all investigated samples the milling time was

Figure 3.47. Change of intrinsic viscosity of polymers solutions during mechanodegradation [113]: 1) gelatin; 2) casein. 267

Macromolecular Mechanochemistry

70 h, the maximum number of split bonds was obtained after 30 h of processing. Above this period, the number of split bonds was not affected by mechanical stress. This finding was explained by the increased rigidity of polymer at the beginning of mechanodegradation due to high crystallinity. The material was gradually amorphised, as confirmed by X-ray diffraction [232, 233]. Conclusive results regarding both the crystallinty and polymer morphology influence on the mechanodestruction process have been obtained on a series of cellulose materials, native and artificial ones, processed by vibratory milling. Figure 3.48 shows typical curves recorded for cotton cellulose, reed cellulose, viscose and carboxymethyl cellulose sodium salt subjected to mechanodegradation. Some kinetic data depicting their mechanodegradation were already presented in Tables 3.15 and 3.21. Hereinafter, the packing density, crystalline/amorphous ratio, and morphology (fibrous character) are correlated to the mechanodestruction parameters. The maximum packing density characterises the stable state of equilibrium towards which all polymers tends. Consequently, the structural changes that occur under the action of mechanical energy must be explained considering not only the modification of the crystalline/amorphous ratio but also the modification of the molecular packing degree which determines the number of macromolecular chains passing in unit time through an elementary stressed volume. In the case of a polymer with a high packing density of its chains, i.e. the case of cotton cellulose in the considered series, mechanical energy is concentrated in a higher number of chain fragments included in fault areas causing their splitting. Due to its higher crystallinity, the material has the highest rigidity which favours athermal mechanodegradation is favoured. Consequently, the rate and degree of destruction are the highest, Tables 3.15, 3.21, 3.23 and Figures 3.49 and 3.50. The same judgement explains the position in the series of the reed cellulose, viscose and sodium salt of carboxymethyl cellulose that are arranged in the order depicted in Figure 3.48. This order is also determined by the value of initial molecular weights (curves 2, 4, and 5 in Figure 3.48). Poplar down cellulose constitutes an exception from this rule, as Table 3.23 shows, this one being degraded faster even than cotton cellulose. The explanation of this behaviour was given in the part dealing with the effect of M0 on mechanodegradation. These results were confirmed using the X-ray diffraction method, 268

Mechanochemistry of Polymer Fracture

Figure 3.48. Influence of milling time on the destruction effect: 1) cotton cellulose; 2) reed cellulose; 3) poplar down cellulose; 4) regenerated cellulose, Viscose-type; 5) sodium salt of carboxymethyl cellulose [230].

Table 3.24 and Figure 3.51. X-ray diffraction patterns obtained for the investigated cellulosic materials show for the virgin samples the presence of paratropical surfaces (002), (101), and (101) . In all cases, the last two disappear after vibratory milling. Figure 3.51 presents cotton cellulose amorphisation during processing. Amorphisation is a common feature of all the investigated celluloses. Comparative analysis of X-ray indices evidenced the decay of the crystalline phase; in the case of cotton cellulose, reed cellulose

Figure 3.49. Dependence of number of broken bonds with the duration of vibratory milling in the case of cellulose acetate [233]: (a) number of broken bonds per gram of polymer; (b) from total amount of processed polymer. Filling ratio: 1) 0.29%; 2) 0.44%; 3) 0.59%. 269

Macromolecular Mechanochemistry Table 3.23. The influence of cellulose nature on the decrease of polymerisation degree and reaction rate (Number of split bonds/sec) [131] Cellulose type

Milling time (h)

[η ]

DP

Number of split bonds Z.10-18

Destruction rate Z/s.10-15

Cotton cellulose

initial 1.5 4 6 8 10

1.0181 0.6520 0.3351 0.1490 0.0937 0.0901

2 418 1 369 653 265 158 151

3.8 29.1 212 274 613

0.703 2.02 9.81 19.9 17.0

Reed cellulose

initial 1.5 4 6 8 10 16 20 24

0.3920 0.3503 0.2140 0.1798 0.1574 0.1304 0.0929 0.0876 0.0828

776 686 396 327 282 228 154 147 136

1.6 19.5 34.2 49.0 81.4 191 218 254

0.30 1.35 1.58 1.70 2.26 3.36 2.98 2.93

Poplar down cellulose

initial 1.5 4 6 8 10

0.3000 0.1727 0.1138 0.0768 0.0496 0.0401

578 312 196 127 78 63

22 77.6 212 600 963

4.07 5.38 9.81 20.8 26.7

Regenerated cellulose (Viscose)

initial 1.5 4 6 8 10

0.2060 0.1478 0.1184 0.1126 0.1016 0.0924

380 263 206 194 173 156

13.6 33.2 39.4 54.0 73.8

2.51 2.30 1.88 1.87 2.05

Figure 3.50. Variation of the destruction degree, , with the type of cellulose [131]: 1) cotton cellulose; 2) poplar down cellulose; 3) reed cellulose. 270

Mechanochemistry of Polymer Fracture

and viscose the crystallinity diminishes from 20% to 10% and in the case of poplar down cellulose from 15% to 10%. The change of the crystalline/amorphous ratio is sustained by IR spectroscopy data [234]. After mechanical milling, the absorption bands 1430, 1340, and 1320 cm –1 diminish and that from 900 cm –1 , which is defined in the literature as the ‘amorphous band’, intensifies Fibre length and macromolecule dimensions play an essential role in the evolution of mechanodegradation. The effects occurring on the molecular and morphological levels are interconnected with each to other. This is why when describing the behaviour of these materials during stressing, the influence of M0 must be explained in correlation with their morphological features. The influence of granular morphology on mechanodegradation has been studied on polyamide and poly(vinyl chloride) – suspension. Polyamide particles were subjected to vibratory milling and PVC granules were exposed to the action of ultrasound waves, respectively. In the case of polyamide-6 the behaviour during vibratory mill-

Figure 3.51. Roëntgenograms of cotton cellulose [131]: (a) unmilled; (b) 4 hr milled; (c) 8 hr milled. 271

Macromolecular Mechanochemistry Table 3.24. X-ray diffraction characteristics of cellulose samples [230] Factor of Distance longitudinal between Crystallinity Order Amorphous direction MesoNo. Cellulose type lattice index index fraction along of morphisme plans I0 Icr [%] (002) plane 2d fx Cotton cellulose 1 non-milled 34.45 0.233 0.419 0.453 0.220 0.447 22.50 15.80 4 hrs of milling 2 20.40 0.165 - 0.141 0.298 0.133 0.702 8 hrs of milling 20.00 0.133 - 0.141 0.227 0.094 0.773 3 4

5 6 7

8 9 10

11

12 13

Reed cellulose non-milled

4 hrs of milling 8 hrs of milling 24 hrs of milling

Regenerated cellulose (Viscose type) non-milled 4 hrs of milling 8 hrs of milling

Poplar down cellulose non-milled

4 hrs of milling 8 hrs of milling

34.30 22.50 15.40 20.70 20.30 20.30

20.90 20.20 20.00

34 22.20 15.20 20.90 20.60

0.222

- 0.105

0.427

0.205

0.573

0.220 0.204 0.145

- 0.142 - 0.127 - 0.1305

0.314 0.285 0.263

0.088 0.081 0.118

0.686 0.715 0.737

0.223 0.155 0.147

0.356 - 0.138 - 0.140

0.408 0.245 0.240

0.185 0.090 0.093

0.592 0.755 0.760

0.143

- 0.127

0.202

0.077

0.798

0.125 0.113

- 0.1215 - 0.132

0.174 0.172

0.031 0.059

0.826 0.828

ing of a virgin sample was compared with the corresponding behaviour of two particle fractions with a narrower size distribution, obtained by sieving the virgin sample. The most intense mechanodegradation was shown by the finest fraction (φ = 50 – 90 µm). For all three samples, the highest destruction rate is attained in the first stages of the process, after a milling period of about 48 h, Figure 3.52, [235]. Poly(vinyl chloride) – suspension, PVC – S, was subjected to the effect of ultrasound, in heterogeneous systems (dispersion in water) for ultrasonic treatment periods ranging from 0 to 120 hrs. Meaningful results have been obtained concerning the influence of 272

Mechanochemistry of Polymer Fracture

the particle size of the initial powder on mechanodegradation and mechanodispersion processes, Figure 3.53. After about 90 hrs of ultrasonic irradiation a minimal value of M ∞ is obtained for all samples fractioned by sieving from the virgin powder. The relative position of the curves describing the behaviour of the fractions with different particles size, curves 2, 3, and 4 in Figure 3.53, as compared to the original sample (curve 1 in Figure 3.53) leads to the following order of mechanodegradation efficiency [236, 237]. PVC-S φ

= 200

> PVC-S virgin > PVC-S φ

= 80

> PVC-S φ

= 40

The most intense mechanodegradation was recorded for the fraction with the particle size higher than 200 µm; these particles have the highest porosity and, therefore, the lowest mechanical resistance, Table 3.25. The finest fraction, characterised by the highest packing degree of granules is placed on the last place on the scale of mechanodegradation efficiency. This shows that mechanochemical destruction is controlled by the morphology of the stressed polymer. The fraction consisting of large and porous particles shows not only the most intense mechanodispersion but also higher degradation. The small granules, φ = 40 mm, formed by longer chains and having a denser packing, are less affected under the conditions of the same mechanical regime. The two destructive processes show optimum efficiency at different times, namely – mechanodegradation after 90 hrs, Figure 3.52, and mechanodispersion after 60 hrs, curve 2 in Figure 3.54. Above this limit, in the range from 90 to 120 hrs, the particle size distribution widens and the maxi-

Figure 3.52. Influence of the particle size on the destruction process [235]: 1) unsieved; 2) φ = 0.40 – 0.63 mm; 3) φ = 0.05 – 0.09 mm. 273

Macromolecular Mechanochemistry

Figure 3.53. Kinetic curves of ultrasonic mechanodegradation of PVC-S, aqueous dispersion, in function of particles diameter [236]: 1) unsieved PVC-S; 2) φ = 200 µm; 3) φ = 80 µm; 4) φ = 40 µm.

mum is displaced to higher values (curves 3 and 4 in Figure 3.54). Ultrasonic treatment for long periods, above 60 hrs, favours particle agglomeration giving rise to particles with diameters up to 80 µm. Analysis of the IR spectra proved the concomitant modification of some functional groups. The results show the large decrease of the absorption intensity corresponding to the –C–Cl bonds at 750 cm –1 and 1500 cm –1 after a treatment period of about 30 hrs. The same modifications were found in the conditions of vibratory milling of the PVC-S powders dispersed in methanol. In the presence of atmospheric oxygen, new absorption bands Table 3.25. The influence of the initial particles size of PVC-S, processed by vibratory milling, on the some polymer characteristics [234] Sample PVC-S, K = 70 Fraction [ µm ] 250 200 160 125 80 60 40 a

Gravimetric fraction [%] -

[η]

M ⋅ 10−4

1.05

5.497

5.5 11.0 21.3 30.1 22.2 9.73 0.17

1.02 1.06 1.06 1.07 1.08 1.08 1.11

4.947 5.259 5.259 5.337 5.517 5.417 5.658

Unsettled 0.425

Density Settled 0.540

Bulk 1.341

(DOP)a, [ °C ] 100…114

0.267 0.367 0.381 0.425 0.445 0.526 -

0.850 0.450 0.460 0.512 0.539 0.621 -

1.337 1.369 1.365 1.355 1.440 1.330 1.3235

90…107 92…107 100…110 103…112 104…118

– Temperature of plasticizer (dioctyl terephthalate) sorption

274

Mechanochemistry of Polymer Fracture

Figure 3.54. Influence of the initial particle size on the particle size distribution of ultrasonically treated polymer [237]: 1) witness, 120 hr treated; 2) φ = 80 µm, 20 hr treated; 3) φ = 80 µm, 90 hr treated; 4) φ = 80 µm, 120 hr treated; 5) φ = 40 µm, 120 hr treated [237].

appeared, at 1700 and 1720 cm –1 . These bands are not characteristic of the initial polymer and correspond to the carbonyl groups formed by oxidation of the destruction fragments. The vibratory milling of the polymer in the presence of atmospheric oxygen and DPPH (diphenylpycril hydrazine) leads to formation of products containing both the absorption bands characteristic for carbonyl groups and the bands from 1630–1700 cm –1 related to the chemical bonding of DPPH to the destruction fragments. Mechanodispersion, regarded as the process of grain fracturing, is correlated to mechanodegradation, which in turn is activated by the mechanocracking process. Thus, free radicals appear on the new generated surfaces and, after their stabilisation, also new functional groups form. Consequently, the reactivity of fresh surfaces increases as evidenced, for instance, by intensification of sorption processes (solvation with water molecules and plasticizer sorption) as well as by acceleration of some reactions in the heterogeneous system (to the new generated surfaces). Mechanodispersion is not only the process of new surface generation but it also increases the free energy in the system. It has been again proved that mechanodispersion involves not only a physical process but also a chemical reaction, because the free 275

Macromolecular Mechanochemistry

energy variation determines the displacement of chemical and phase equilibria. The presence in the solid polymer of an excess of free energy leads to the formation of thermodynamically unstable states, with the highest values of thermal effect ∆H and entropy ∆S corresponding to the highest excess of free energy. At any moment of the process, an equilibrium is established between the number of split macromolecules defining the decrease of molecular weight and the corresponding specific surface which is an evaluation criterion of mechanodispersion. The interdependence of these effects brought about by mechanical energy is clearly made evident for the 80 µm diameter fraction subjected to ultrasonic treatment for different periods of time, Fig. 3.55. Considering the particles size dispersion and the different structure of the small and large PVS-S particles, one can conclude that both mechanodispersion and mechanodegradation preferentially occur in the last ones, as is evidenced by changes of particle size distribution curves, Figure 3.54. The direct correlation of mechanodegradation intensity with the particle size is illustrated in Figure 3.56. Modification of the particle size by dispersion occurs by three steps. The first one is characterised by continuous decrease of the particle size. The second one corresponds to particles agglomeration, up to certain specific values, for instance 80 µm in the case of PVC–S under the effect of ultrasound. The last step reflects the establishment of an equilibrium; when this equilibrium is established, the particle size no longer varies with time. Corresponding to these steps the superficial tension of system is changed, too. Both mechanodispersion and mechanodegradation are characterised by limiting values which are specific to each of the two processes and influenced by the same factors: polymer structure, nature of environment, and temperature. Usually, the limit of mechanodispersion is reached before the limit of mechanodegradation. Thus, firstly the particle size decrease up to an equilibrium value, which depends on the working conditions and after that the dispersion process no longer occurs, but the mechanodegradation process proceeds, having as its main result the decrease of the molecular weight to the limiting value. The dispersion degree is the most important parameter that characterises the value of the destruction limit, and mechanodegradation is the primary cause of fracture and, therefore, of new 276

Mechanochemistry of Polymer Fracture

surface generation [236, 237–242] in polymers. 3.5.2. Temperature Temperature is an essential factor in the activation of chemical reactions because molecular agitation is of primary importance for

Figure 3.55. Specific surface area variation, S, with molecular weight for different durations of ultrasonic treatment (0, 60, 90, 120 h) of PVC-S with φ = 80 µm as aqueous dispersion.

Figure 3.56. Variation of mechanodegradation rate constant with particle size: 1) PVC-S ultrasonically treated as an aqueous dispersion in the presence of a surfactant (sodium mersolate, 0.1%); 2) idem, without surfactant.

their occurrence. In polymer mechanochemistry, its implication is very important. The dependence of mechanochemical destruction on temperature was studied for the first time by K. Hess and coworkers [242, 243]. They conducted vibratory milling trials on cellulose and polystyrene, in the temperature range from 0 to 277

Macromolecular Mechanochemistry

90 °C. In these conditions, the authors established a negligible influence of temperature, concluding that mechanodegradation is characterised by almost zero activation energy. Subsequently, after the discovery of aggregation and physical states of polymers, whose delimitation depends on temperature only, the results obtained by K. Hess were correctly explained. In the investigated temperature range (0–90 °C), both cellulose and polystyrene are in the solid state (semicrystalline and amorphous state, respectively) when the macromolecules are rigid and chains splitting is the result of mechanical energy action in athermal conditions. Mechanodegradation is implicitly related to the modification of polymer mechanical properties. These changes are realised by specific mechanisms, depending on the crystalline or amorphous state of polymers. In the last case, depending on temperature, the polymer may be in the vitreous, rubbery, or fluid-viscous state, respectively. It is obvious that the influence of temperature on the mechanochemical reactions must be investigated in correlation with the physical states of polymers [113, 244]. As a criterion to estimate the influence of temperature on the  d (η) 

mechanochemical reactions, the temperature coefficient   dT  dt  was introduced and used as an instrument of delimitation of thermal degradation by the mechanochemical one, whenever the both factors jointly affect the process [131–133, 158, 194, 209, 230, 245–263]. A minimal effect of temperature was found in the case of gelatine, poly(vinyl alcohol), poly(vinyl chloride), poly(methyl methacrylate), and polyamide-6, processed by vibratory milling in the vitreous state. The temperature coefficient was zero in all cases. The influence of this parameter becomes important only when the temperature attains values corresponding to the moment when the processed material suffers thermal destruction. Thus, poly(methyl methacrylate) is in the vitreous state below 170 °C. Working in the temperature range from – 10 to 220 °C. H. Grohn and co-workers completely characterised the behaviour of this polymer during vibratory milling. The transformations endured by the polymer, followed by viscosimetric measurements, in the temperature range from –10 to 170 °C were ascribed to mechanochemical destruction. In the temperature range from –10 to 40 °C, the influence of temperature was insignificant. The decay of [η] is related to the mechanical factor, expressed by milling time 278

Mechanochemistry of Polymer Fracture

(curves 1–4 in Figure 3.57). Above 40 °C up to the vitreous temperature a slight decrease of the degradation rate takes place. In this temperature range, the chain flexibility increases and the shock forces are more elastically absorbed by the polymer chains, but the temperature is still too low in order to influence the destruction process. Above T g the temperature is high enough to enable thermal destruction. Anyhow, its activation energy is diminished by the concomitant action of mechanical energy, as is seen in Figure 3.57 (curves 5 and 6). Evaluation of the degree of destruction is in good agreement with the results from Figure 3.57. For the same amount of mechanical energy, evaluated by milling time, the highest degradation corresponds to the lowest temperature (T = 80 °C), curve 1 in Figure 3.58. Above T g the degree of destruction is governed by the competitive action of the thermal and mechanical factors. In this case, maximum degradation corresponds to the maximum temperature of processing (curves 4 and 5 in Figure 3.58) that proves the decisive role of the thermal effect. W.F. Watson and co-workers studied the influence of temperature on the cold mastication of natural rubber. Clearly, mastication efficiency passes through a minimum at 115 °C. Curve A in Figure 3.59 describes mechanical degradation [249] and curve B is the result of thermal-oxidative degradation. In the temperature range below 115 °C, the temperature coefficient is negative and increases in absolute value. Above this limit, the polymer passes into ytje flowing state and the temperature coefficient becomes positive. In can be mentioned that in the absence of oxygen no degradation was

Figure 3.57. Variation of mechanochemical destruction degree with temperature [194]: 1) 2 hr; 2) 4 hr; 3) 6 hr; 4) 12 hr; 5) thermal destruction, 3 hr; 6) thermal destruction, 12 hr. 279

Macromolecular Mechanochemistry

Figure 3.58. Comparative illustration of thermal and mechanochemical degradation (variation of the intrinsic viscosity in time at different temperatures) [194]: 1) 80 °C; 2) 120 °C; 3) 140 °C; 4) 180 °C; 5) 220 °C.

Figure 3.59. Efficiency of natural rubber mastication at different temperatures [249].

recorde at temperatures up to 140 °C [249, 264]. Mastication in an inert medium (nitrogen) in the presence of some radical acceptors with different reactivity allowed separation of the two involved mechanisms. Figure 3.60 illustrates the negative coefficient and the absence of thermal energy contribution to the establishment of the degradation minimum. N.K. Baramboim repeated the experiments, working on a synthetic elastomer, poly(isobutylene), in the presence of oxygen and 280

Mechanochemistry of Polymer Fracture

Figure 3.60. Influence of temperature on efficiency of rubber mastication in a sizeB Banbury malaxor under nitrogen with 0.0925 mg/1000 g radical acceptors of different reactivity: (l ) thiophenol; (o ) benzoquinone; (m ) azobenzene [249].

obtained similar results. Experiments were conducted in a wide temperature range (T = 20–140 °C) and T = –100 °C, which practically corresponds to all physical states, each of them being characterised by specific values of intra- and intercatenary interactions, by a proper mechanism of deformation, and by a typical relaxation spectrum. As Figure 3.61 shows, the minimum of destruction was obtained for the temperature of 140 °C [265]. The mechanism of mechanodegradation implies the random splitting of chains and, in the presence of oxygen, the peroxidation reactions of free radicals, leading to peroxidated species ROO .. The thermal oxidation mechanism and its decisive role during elastomer mastication was first explained by Kuzminskii and co-workers [266–269]. Because the ROO . radicals formed by reaction of oxygen with shear-generated radicals are sources of hydroperoxides, oxidative degradation may be expected to increase the extent of shearinitiated breakdown [132, 257, 259, 264, 270, 271]. As Figure 3.62 shows, degradation during hot mastication is more rapid than in static oxidative ageing at the same temperature. The behaviour of EPDM elastomers follows the same rules. Variation of [η] with temperature is described by a curve having 281

Macromolecular Mechanochemistry

Figure 3.61. Variation of molecular weight during two-roll milling of polyisobutylene at different temperatures: 1) 140 °C; 2) 100 °C; 3) 80 °C; 4) 60 °C; 5) 20 °C; 6) below –100 °C [265]. Figure 3.62 (right). Degradation of natural rubber (1) at 140 °C in films and on mastication at (2) 46 and (3) 105 rpm rotor speeds [264].

three distinct temperature ranges: 1) T = 20–65 °C, where intrinsic viscosity increases with the increase of temperatue; 2) T = 65–155 °C, in this relatively wide temperature range the viscosity only slightly varies; and 3) 155–250 °C which corresponds to a rapid decrease of viscosity with increasing temperature, Figure 3.63. The interpretation of these results from the point of view of Bueche’s theory [278] leads to the conclusion that the probability of splitting a chemical bond just at the midle of the chain is inversely proportional to the temperature and the stress at the central bonds (F 0 ) is proportional to the viscosity and shear rate. The increase of temperature determines the decrease of melt viscosity but influences density to a lesser extent. Deformation of some melted polymers, under injection or extrusion conditions, leads to a combined process of mechanodegradation and thermal-oxidative destruction. A series of results concerning polystyrene destruction are available in the literature [163– 165, 272, 273]. Evaluation of the number of split bonds and of the energy required for their splitting at different temperatures shows that polystyrene has maximum stability at about 180 °C. Below this temperature, even in the presence of oxygen, mechanodegradation prevails. Above 180 °C, thermal-oxidative degradation becomes more 282

Mechanochemistry of Polymer Fracture

Figure 3.63. Roll milling of EPDM: change in viscosity with mastication temperature [133].

important but it is still favoured by the action of mechanical forces. The shear energy, mostly dissipated as heat, combines the effects of fortuitous forces (like thermal vibrations) with the oriented (mechanical) forces to accomplish polystyrene degradation at 180 °C. Point-by-point determination of M w and MDW shows that the highest degradation progressively occurs in the radial direction from the axis to the apparatus wall where both the shear forces and oxygen action are more intense [273, 274]. In the same temperature range but under static conditions, neither viscosity nor molecular weight decrease were recorded. When the temperature is increased, overall degradation increases [274]. The concomitant action of the thermal and mechanical factors has also been evidenced in the conditions of polyethylene injection or extrusion [171, 173, 174, 274–276]. In this case, the melt index was measured and it was found that in the lower temperature range its value decreases. This behaviour was explained by macroradicals recombination to crosslinked structures [276]. Another example of degradation and reticulation has been reported in the case of injection moulding of poly(vinyl chloride) [277]. The effect of temperature on the rheological behaviour of poly (ethylene terephthalate) melts was also investigated. It was found that an increase of the shear rate in a certain temperature range leads to a decrease of the of flow activation energy, Figure 3.64. 283

Macromolecular Mechanochemistry

Figure 3.64. Activation energy of shear flow with shear rate in the temperature range from 270 to 300 °C [281].

Figure 3.65. Influence of the extrusion temperature on the intrinsic viscosity of extruded polymer [279].

This result was also obtained in the case of polyethylene [164, 279–283]. At low shear rates tending to zero, the PET activation energy was about 16–17 kcal/mol. The decrease of flow activation energy with the increase of shear rate follows a non-linear law. This behaviour indicates a change of the flow mechanism as a result of structural modification of the melt. The first argument in the favour of this statement is the viscosity decrease with increasing temperature, Figure 3.65. PET extrusion, using a rheometer, in the following conditions: L capillary = 60 mm; D = 1 mm; angle of entrance = 90°; and extrusion rate = 45 s –1 , was investigated at 270, 280, 290, 300, and 310 °C, respectively. The experiments were carried out in an inert and absolutely dry medium. The temperature dependence of shear 284

Mechanochemistry of Polymer Fracture

Figure 3.66. Influence of temperature on shear stress at capillary wall [279].

stress is depicted in Figure 3.66 [279, 281]. In the investigated temperature range, the shear stress to the capillary wall decreases, the recorded variation being a non-uniform one. Thus, in the temperature range from 270 to 290 °C the decay is 0.1 . 10 6 dyn/cm 2 and in the range from 290 to 310 °C it is practically twice this value. As already mentioned, the nonlinear variation of the stress to the capillary wall as a function of temperature and, in particular, the modification of the rheological behaviour is explained by changes in the polymer structure. The correlation of the obtained results regarding the viscosity variation (Figure 3.65) and the number of the end-functional groups, –COOH, (Figure 3.67), evidences the decrease of the values of the two characteristics in the whole investigated temperature range. One can also admit the existence of two distinct temperature zones. The first one, corresponding to low temperatures, 270–290 °C, where degradation must be ascribed to mechanochemical destruction, and the zone of high temperatures, 290– 310 °C, where overall degradation is intensified due to the contribution of the thermal factor. The thermal degradation is accompanied by the formation of low-molecular weight compounds which act as lubricants of the molten polymer, decreasing the shear stress, Figure 3.66. The decrease of the flow activation energy of an poly(ethyleneco-vinyl acetate) copolymer, EVA, stressed in a rheometer, is illustrated in Figure 3.68. The minimum of degradation, expressed by the minimum value of the flow activation energy, 16.97 kJ/mol, was obtained in the temperature range from 100 to 110 °C. The maxi285

Macromolecular Mechanochemistry

Figure 3.67. Influence of extrusion temperature on the content of carboxylic groups of extruded PET [279].

mum stability to shear force for some polymers is presented in Table 3.26. A major impediment in obtaining rigorous results in this field is related to the attainment of isothermal conditions in poor thermalconductive materials as the polymers are, especially in the fluidviscous state when temperature is high enough[163, 284–288]. Some experiments carried out with high accuracy, for instance in the case of polystyrene extrusion, proved that the differences between the target temperatures and the real (measured) ones are higher in the range of low temperatures, Figure 3.69. In addition, large temperature gradients appear across the capillary radius [284]. Increasing the temperature to the reactions wall results not only in the variation of the value of maximum but also in a decrease of the average polymer temperature, passing to a minimum after which it increases again tending to the wall temperature, Figure 3.70. During EPDM rubber extrusion it was found that in the polymer melt ∆T increases as a function of the temperature of the capillary wall and shear rate, Figure 3.71. There are considerable differences between the properties of the products of mechano- and thermal degradation, respectively, both for different experiments, Figure 3.72 and even for the same experiment, Figure 3.67, [116, 279, 287]. In the case of polymer degradation in solution, all the results obtained, irrespective of the type of stress applied, i.e. ultrasound 286

Mechanochemistry of Polymer Fracture

Figure 3.68. Rheogram of ethylene-vinyl acetate copolymer, EVA, showing the variation of temperature, torque, and total torque with time. Table 3.26. Maximum shear stability of polymers [284]

Polymers

Temperature

Poly(isobutylene) Natural rubber Polystyrene EPDM Poly(vinyl chloride) Poly(1,4-cis-butadiene) Polyisoprene Poly(methyl methacrylate) a

140 115 180 ~ 160 ~ 195 > 100 100a 140

In the absence of stabilisers

waves, high speed stirring, flowing through very narrow orifices, frozen–unfrozen cycles, converge to the same result – maximal mechanodegradation to the minimal temperature. Different correlations between the mechanodegradation efficiency, polymer characteristics and temperature have been established. PVC solutions in cyclohexane showed the maximal decay of viscosity and molecular weight with time at the temperatures ranging from 0 to 90 °C, Figure 3.73 a and b. Thus, the direct correlation of M vs. t for different durations of ultrasonic treatment 3 and 5 hrs respectively, is presented in Figure 3.74a. As is seen, the 287

Macromolecular Mechanochemistry

Figure 3.69. Temperature profiles for power-low fluid during capillary extrusion at different capillary wall temperatures [285].

Figure 3.70. Average degradation rate Ψ over capillary cross section versus wall temperature for polystyrene; n is the (power law) flow behavior index [285].

temperature plays the controlling role in the evaluation of the mechanochemical character of degradation by ultrasonic irradiation. Starting from Arhenius’s equation, where constant k was calculated using Baramboin’s relation (3.75), in the following form

288

Mechanochemistry of Polymer Fracture

Figure 3.71. Temperature increase as a function of capillary wall temperature and shear rate during EPDM extrusion [287]: 1) 100 ºC; 2) 120 ºC; 3) 140 ºC; 4) 190 ºC.

Figure 3.72. Changes of the acid properties of gelatin as a function of the conditions of mechanodegradation [116]: 1) air, 50 °C; 2) air, 0 °C; 3) air, –10 °C; 4) nitrogen, –10 °C.

1 M −M∞ k = ln τ τ M0 − M ∞

and 289

(3.102)

Macromolecular Mechanochemistry

(3.103) ln k = ln k 0 − Ea / RT from graphical representation of equation (3.103) it was found that E a = 1.805 Kcal/mol and k 0 = 0.0187. The almost negligible value of E a proves the controlling role of mechanodegradation in this process. Figure 3.74 b shows the increase of destruction gradient ϕ 3 in the conditions of molecular weight decay, in the same temperature range. The effect of ultrasound on ternary copolymer poly(acrylo-nitrile-co-vinyl acetate-co- α -methylstyrene) solutions in dimethyl formamide led to the results similar to those obtained in the case of PVC. In addition, as Figure 3.75 shows, the maximal mechanodegradation is attained for the lowest polymer concentration [289]. The factor M t / M 0 was used to characterise the behaviour of polybutadiene solutions in toluene under a variable field of forces. The temperature range was extended in the zone of negative values (T ≈ –30 to 30 °C). The comparative results, under the conditions of ultrahigh stirring speed and ultrasonic irradiation, are pre-

Figure 3.73. Kinetic curves of the mechanodegradation of PVC solutions expressed as the variation of M (a) and intrinsic viscosity [η] (b) at different temperatures [123]: 1) 5 °C; 2) 20 °C; 3) 60 °C; 4) 90 °C.

Figure 3.74. Variation of the average molecular weight and destruction degree with temperature [123]: (a) average molecular weight; (b) destruction degree. 290

Mechanochemistry of Polymer Fracture

Figure 3.75. Influence of temperature on the intrinsic viscosity: 1) c = 13.75%; 2) 9.0%; 3) 4.25% (t = 3 hrs) [289].

Figure 3.76. Kinetic curves of polybutadiene (solutions in toluene) mechanodegradation at different temperatures: 1) 30 °C; 2) 5 °C; 3) –18 °C; 4) –30 °C; (a) high-speed stirring (v = 20 400 rpm; c = 1%, nitrogen atmosphere, curve 4 at –40 °C [190] and ultrasonic treatment (c = 0.5%) (b) [191].

sented in Figure 3.76. The most intense degradation occurred under the action of ultrasound waves, Figure 3.76 b, the process being favoured in diluted solutions [190, 191]. In their study concerning the influence of temperature in the range from 30 to 80 °C, Goodman and Bestul presented in double logarithmic coordinates k vs 1/j from equation (3.50), where: k is the reaction rate constant; j – the average value of the shear energy per gram of polymer. At the highest temperatures, the recorded pairs are distributed on strength lines as a function of temperature, Figure 3.77. For a given value of j the reaction rate constant decreases with increasing temperature. The most pronounced effect characterises the highest value of j. The slope 291

Macromolecular Mechanochemistry

Figure 3.77. Solution shearing of polyisobutylene: ( l ) 30 °C; (∆) 40 °C; ( o ) 50 °C; ( ¡ ) 60 °C; ( F ) 80 °C. Rate constant dependence upon 1/J, where J is the average rate of shear energy input per gram of polymer in the McKee consistometer [147].

of these lines is equal to E/a, where E – activation energy; and a – the ratio between the energy introduced in system and those temporary stocked in chemical bonds, as potential energy. The calculation of the required energy for chemical bonds splitting at different temperatures led to the results collected in Table 3.27. The calculated increase of the energy required for chemical bonds splitting with the increase of temperature corresponds to a negative coefficient of temperature for degradation, which suppose a mechanochemical mechanism. 3.5.3. Reaction medium 3.5.3.1. Inert media The nature of the reaction medium influences the type and mechanism of the mechanochemical reaction as well as the nature of the final products. In order to make a clear delimitation of the mechanochemical reactions and secondary effects, mechanodegradation processes are usually carried out in inert gaseous and absolutely dried media. The widely used gases are nitrogen and argon, carefully purified to remove oxygen traces. In an inert and absolute dry medium, chemical bonds splitting and subsequent reactions up to their stabilisation depend, at a given temperature, mainly on the applied mechanical regime. In the inert media, the rigid polymers (crystalline or vitreous) as solutions or melts, with the macromolecules freed by physical interactions, are degraded by splitting of the chemical bonds from 292

Mechanochemistry of Polymer Fracture Table 3.27. Variation of activation energy, E a , with temperature [147]

Temperature, °C

Ea, kcal/mol

30-50 60 80

325 400 480

the main chain. This reaction is accompanied by molecular weight decay to the limit value, in other words, linear mechanochemical destruction occurs. However, the nature of inert gas may still influence the mechanochemical reactions efficiency whenever these ones depend on electronic flux rate, which either accompany the polymers fracture processes, or, for instance, which are released under the conditions of vibratory milling, due to the collision of the milling bodies with the vessel walls. It is generally known that the kinetic energy released by vibratory milling is at least partially used for the excitation of superficial layers of the building material of the apparatus inducing the elimination of electronic fluxes whose velocity and efficiency depend on both the amount of released kinetic energy and the nature of the gaseous medium, within which the mechanochemical reaction is developed [290–297]. Influence of the nature of the inert gaseous medium on the mechanochemical efficiency has been verified on the example of solid-state polymerisation of acrylamide by vibratory milling [297] and of styrene copolymerisation with different monomers [294]. Variation of the conversion degree with reaction time has been investigated in three chemically inert gaseous media, namely nitrogen, argon, and carbon dioxide, having molecules with variable dimensions. The obtained experimental results were compared to those acquired in high vacuum (10 –4 mm Hg). It was found that with the decrease of the gas molecules dimensions, the inhibiting effect of the mechanoemission flux decreases and leads to a higher conversion degree. The highest values of the conversion degree were obtained in vacuum (Figure 3.78 curve 1) [297]. Similar results were obtained in the case of using monomers in the liquid state, for instance, a mixture of styrene and isoprene [284]. The order of disposition of the conversion vs. time curves is the same as in the case of acrylamide polymerisation, the 293

Macromolecular Mechanochemistry

Figure 3.78. Conversion – time curves of the mechanochemical polymerization of acrylamide (a) and styrene/isoprene system (b) in different gaseous media: 1) vacuum; 2) nitrogen; 3) argon; 4) carbon dioxide.

differences being only quantitative, Figure 3.78b [294]. One can notice that in all cases the conversion vs. time curves pass through a maximum, whose position depends on the nature of the reacting system. In the case of acrylamide polymerisation, the maximum is located at 100 hrs of milling and in those of styreneisoprene polymerisation at 95 hrs. The shape of curves suggests the occurrence of two processes, namely: mechanochemical polymerization, up to the maximum, and mechanodegradation, respectively. In the case of highly elastic polymers, for instance natural rubber processed by cold mastication in an inert atmosphere even if macroradicals are generated but the process does not evolve to linear mechanodegradation because the primary active particles 294

Mechanochemistry of Polymer Fracture

Figure 3.79. Influence of inert liquids on the mechanodegradation as expressed by intrinsic viscosity (a): 1) dioxane; 2) acetone; 3) argon and the number of split bonds, Z, (curves 1, 2) and number of formed radicals, R, (curves 3, 4), respectively, (b): 1 and 3) acetone; 2 and 4) dioxane [83, 126].

react, by transfer, with neighbouring chains, generating crosslinking centres. This finding was experimentally demonstrated by the increase of the insoluble fraction in acetone with mastication time [298]. Poly(isobutene) processed in the rubbery state, in an inert medium, do not suffer major changes of M 0 , even if the macroradicals generation is practically inevitable. It is most likely that in this case the mechanical energy is mainly consumed for exceeding ing the cohesion energy and only in a little measure for bond splitting [299]. Mechanodegradation reactions of polymers dispersed in inert liquids, which do not swell, dissolve, or chemically react with the polymer [83,126,131,236,237] were also studied in inert gaseous atmospheres. Thus, aliphatic polyamides, nylon 6 and nylon 6,6, were subjected to vibratory milling in non-polar liquids, dioxane and acetone. The results were compared with those obtained in the absence of solvents and in the same gaseous atmosphere, for instance, argon. It was found that on all structural levels the mechanochemical reactions took place with a diminished efficiency as compared to those in the gaseous medium, Figure 3.79. A mechanodispersion process occured on the supramolecular-morphological level and was accompanied by an increase of the content of the amorphous phase, Figure 3.80. 295

Macromolecular Mechanochemistry

Figure 3.80. Influence of inert liquid media on the amorphisation of polyamide6: (a) milling period, 48 hr – 1) witness; 2) milled in argon; 3) acetone; 4) dioxane; (b) milling period, 96 h – 1) dioxane; 2) acetone [126].

Mechanodegradation of poly(ethylene terephthalate) dispersions in aliphatic hydrocarbons (hexane and heptane, respectively) led practically to the same results [131]. In all investigated cases, mechanodegradation efficiency depends on the nature and quantity of solvent but is reduced by its presence. In inert liquid media, mechanical energy is partially dissipated in the solvent and only a part of it is used for the mechanodegradation process. The moistened new generated surfaces formed by mechanodispersion are less reactive and this fact explains the quantitative differences in the obtained destruction degrees. 3.5.3.2. Radical acceptors Radical acceptors have been used for the identification of the mechanodegradation processes, demonstration of the reaction mechanisms, and even for changing some polymer properties [123,130,190,191,230,235,298,300–307]. In an inert atmosphere, natural rubber mechanodegradation can not be evidenced in the absence of radical acceptors. It was 296

Mechanochemistry of Polymer Fracture

Figure 3.81. Change of stress relaxation during the processing into a Brabender plastograph (F 0 – initial force and F – force at time t) in air (a) and nitrogen (b): 1) 80 °C; 2) 100 °C; 3) 120 °C [299].

proved that oxygen plays a major role in this process [298]. Thus, if oxygen is present in the system as traces, 0.05% in argon, it does not affect the reticulation mechanism. By increasing its concentration, but still remaining in the range of low values of about 1%, the inverse effect is obtained, i.e. the molecular weight decay and the occurrence of linear mechanodegradation [116]. However, the presence of a limited amount of oxygen in the reaction medium is required in order to ensure mechanochemical destruction. The action of oxygen can be influenced by the co-existence of other radical acceptors. The mastication of poly(1,4-cis-butadiene) in a Brabender plastograph also evidenced the most intense mechanodegradation effect in the presence of air in comparison with dry nitrogen (Figure 3.81 a and b). The increase of temperature strongly intensifies degradation (curves 2 and 3 as compared to curve 1 Figure 3.81 a). In an inert atmosphere, Figure 3.81 b, the relaxation force is practically constant at 80 °C (just where mechanodegradation 297

Macromolecular Mechanochemistry

Figure 3.82. Destruction curves of poly(cis-butadiene) in Brabender plastograph: 1) vacuum; 2) vacuum + phenylhydrazine (0.5p/100p elastomer); 3) air; 4) air + phenylhydrazine [299].

should occur) and only slightly increases by increasing the temperature to 100 °C (curve 2) and 120 °C, respectively, in fact as the effect of temperature. Under vacuum, curve 1 in Figure3.82, and in the same medium but in the presence of phenylhydrazine, curve 2 in Figure 3.82, only a weak effect of mechanodegradation was recorded. Instead, under the effect of oxygen, curve 3 in Figure 3.82, is more ‘intense’ than of phenylhydrazine. However, the coupling of the two acceptors determines a cumulative effect, curve 4 in Figure 3.82 [299]. In the range of high temperatures, oxygen induces thermooxidative effects and for this reason many other radical acceptors, some of them labelled, have been used, in the investigation of elastomers mechanodegradation, Table 3.28 and 3.29 [298]. A peculiar behaviour was found in the presence of benzo-quinone; this compound may change mechanodegradation as a function of its concentration and temperature. Thus, in the range of low temperatures, 55°C, and in an inert atmosphere, the increase of the benzoquinone concentration determines a progressive increase of mechanodegradation. Above 1.5%, it determines a decay of plasticity, expressed by a decrease of Money viscosity. With increase of the benzoquinone concentration to 5% the plasticity decreases practically to zero. The concentration of 1.5% should be considered as optimal one, from the point of view of mechanodegradation effects. Above this limit, benzoquinone favours reticulation effects; the material becomes brittle and can not be processed. In the 298

Mechanochemistry of Polymer Fracture Table 3.28. Plasticizing of rubber by mastication in nitrogen and air for thirty minutes

Compound

a

Oxygen (150 mm Hg) Oxygen (150 mm Hg) Thiophenol Thiophenol (0.455 m) Hexamethylene dimercaptan (0.0667 M) Benzyl mercaptan (0.0807 M) Mercaptobenzthiazole Dibenzthiazole disulfide (0.0223M) Diphenyl disulfide Benzoquinone Naphthaquinone Hydroquinone

Compound

Phenol o-Nitrophenol 2,4-Dinitrophenol Pyrigallol α-Naphthol β-Naphtol 2,2-Diphenyl-1-picryl-1-hydrazyl (2.5 x 10 –2 M) Diphenylguanidine (0.0474 M) Hydrazobenzene Azobenzene Trinitrobenzene m-Dinitrobenzene Iodine Stearic acid Benzoic acid o-Nitroaniline p-Nitroaniline 2,4-Dinitroaniline Sulfur (1 g/100 g) a b

In nitrogen at 55 °C Mooney Intrinsic Plasticizing viscosity viscosity efficiency

In air at 55 °C Mooney Intrinsic viscosity viscosity

In air at 100 °C Mooney viscosity

95 73 22 19 22 19 47

4.19 3.72 1.80 1.50 1.75 1.53 2.81

1.82 1.78 1.54 1.78 0.56

22 19 15 20

1.80 1.50 1.56 1.80

14 10 -

Rubber batch No. 1 2 1 2 2 2 2

55 57 56 69 36 51 56

2.58 2.86 2.77 3.34 2.20 2.76 3.64

0.38 0.46 0.36 0.14 1.06 0.46 0.05

20 15 19 23 10 23

1.82 1.59 1.71 1.82 1.94 1.81

5 6 34 34 44

2 1 2 2 1 2 1

In nitrogen at 55 °C Mooney Intrinsic Plasticizing viscosity viscosity efficiency

In air at 55 °C Mooney Intrinsic viscosity viscosity

76 43 38 63 57 71 55

3.60 2.68 2.39 3.30 3.23 3.74 2.94

0.15 0.79 0.98 0.35 0.25 0.11 0.38

25 20 23 27 21 25 -

2.90 1.90 2.02 2.66 2.02 2.16 -

59 38 53 43 56 45 65 70 61 73 72 75

3.01 2.41 2.94 2.89 2.98 3.76 3.50 3.82 3.40 3.53

0.31 0.98 0.43 0.65 0.48 0.60 0.20 0.12 0.27 0.08 0.09 0.16

15 24 22 81 37 21 18 19 21 18 27 25

1.50 1.79 1.82 4.34 2.40 1.73 1.73 2.00 1.97 2.00 1.96

In air at 100 °C Mooney viscosity 19 30 31 43 23 23 40 17 59 23 1 9 9 15 18 26 21 (100 g in Nitrogen)

Rubber batch No.b 1 1 1 1 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1

Concentration of the added compounds 0.0925 mole/1000 g rubber. Initial Mooney of U.S.F. rubber: batch 1, 90 ± 3; batch 2, 80 ± 3

range of high temperatures, 140 °C, and in the presence of air, a typical thermal-oxidative process takes place, curve 2 in Figure 3.83. As Figure 3.84 shows (curves 1 and 2), at 55 °C mechanodegradation efficiency increases and the benzoquinone effect is insignificant in comparison with the effect of oxygen. At 140 °C mechanoactivated thermal-oxidative processes occur and benzoquinone plays an inhibiting role, Figure 3.84, curves 4 and 5. 299

Table 3.29. Mastication of rubber in nitrogen and air for thirty minutes [298] In nitrogen at 55 °C

In air at 55 °C

Compounda

300

Chloranil Maleic anhydride m-Aminophenol p-Aminophenol Benzidine Aniline p-Toluidine Trimethylene dimercapran p-Nitrophenol m-Nitrophenol Trinitrophenol m-Nitroaniline n-Butyramide Azoisobutyronitrile Benzoyl peroxide Cobalt naphthenate (0.0057 mole Co) Oxalic acid o,o’-Dibenzamidodiphenyl disulfide a b

200 120 118 100 102 96 77 98 91 82 28 90 83 80 47 69 33

ηin

% Gel

0.92 1.76 3.30 6.14 3.40 4.00 3.70 2.17 3.80 5.57 2.53 3.76 5.60 5.46 3.66 2.66 4.00 2.98

80 75 45 37 50 0 0 73 11 1 0 15 0 0 0 9 0 0

ηM 77 26 64 96 96 100 27 30 21 22 50 22 80 80 15 22 85

Concentration of the added compounds 0.0925 mole/1000 g rubber. Initial Mooney of U.S.F. rubber: batch 1, 90 ± 3; batch 2, 80 ± 3

ηin 1.08 2.46 2.48 5.20 4.30 5.75 2.10 2.30 2.22 2.10 4.84 2.10 5.33 5.55 4.86 1.44 2.14 5.07

81 0 45 0 82 0 0 0 0 0 4 0 0 0 0 1 0 0

204 88 114 103 98 84 91 107 99 85 94 102 81 114 75 75 79

In air at 140 °C ηM 77 25 80 60 80 24 24 20 17 31 54 17 17 5 5 25 5

Rubber batch No.b 1 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2

Macromolecular Mechanochemistry

ηM

In nitrogen at 140 °C % Gel ηM

Mechanochemistry of Polymer Fracture

Figure 3.83. Influence of benzoquinone concentration on the mastication efficiency of USF rubber (Mooney viscosity, 80 ± 3): 1) nitrogen, 55 °C; 2) air, 140 °C [ 298 ].

Figure 3.84. Rate of rubber plasticizing (Mooney viscosity, 80 ± 3): 1) air, 55 °C; 2) air + 1g benzoquinone/100g rubber, 55 °C; 3) nitrogen + 1g benzoquinone/ 100g rubber, 55 °C; 4) air, 140 °C; 5) air + 1g benzoquinone/100g rubber, 140 °C [298]. 301

Macromolecular Mechanochemistry

Figure 3.85. Influence of mastication agents on the DEFO hardness of smoked sheets natural rubber (0.3% agents, 130 °C): 1) control; 2) peptone 22; 3) renazit IV.

Figure 3.86. Variation of efficiency factor with temperature during mastication of natural rubber: 1) control; 2) renazit IV; 3) peptone 22; 4) peptone 65.

302

Mechanochemistry of Polymer Fracture

Figure 3.87. Energy consumption for the mastication of 100 kg smoked sheets rubber into a Banbury masticator: 1) control; 2) peptone 22; 3) renazit IV (0.2%).

The above-mentioned results have important industrial implications. Thus, it was proved that the use of some chemical reagents, the so-called ‘mastication’ agents, reduces energy consumption during rubber mastication. DEFO hardness is used as a criterion of mechanodegradation evolution, and the decrease of this parameter was measured as a function of mastication time. The collected data have been represented in semilogarithmic co-ordinates and the slope of the obtained strength lines was used to calculate the mastication constant, Figure 3.85. Finally, the use of the mastication constant allowed the determination of the efficiency factor as: DH 0 − DH t where: ∆H 0 and DH 0

∆H t – DEFO hardness in the initial and at mastication moment t, respectively. The efficiency factor is strongly influenced by temperature and the nature of the mastication reagent, Figure 3.86. Its optimal value is attained after a specific period of mastication that assures the homogenisation of rubber with the mastication reagent. The decrease of energy consumption in the presence of mastication reagents is illustrated in Figure 3.87. The elucidation of the mechanodegradation mechanism of some rigid, crystalline or amorphous polymers, processed by vibratory milling implied also the use of a large number of radical acceptors. 303

Macromolecular Mechanochemistry

Figure 3.88. Influence of the gaseous radical acceptors on the mechanodegradation of polystyrene (a) and carboxymethyl cellulose (b) by vibratory milling: 1) argon; 2) oxygen; 3) nitrogen oxide (NO). Table 3.30. The influence of radical acceptors on the destruction limit and rate for some polymers, processed by vibratory milling (T = 18 ± 2 °C) [131] Polymer Poly(ethylene terephthalate)

Reed cellulose

Nitrogen Air NO

18 460 16 500

k ( h-1 ) 0.053 0.054

Nitrogen Air NO

22 032 16 200 3 400

0.159 0.219 0.437

Medium

M∞

References [ 191 ]

[ 230 ]

Atmospheric oxygen and nitrogen oxides have been used extensively. In the case of elastomers, oxygen was always found to be the most efficient reagent, and the most efficient compound during in vibratory milling polystyrene, polyamides, poly(ethylene therephtalate), cellulose and its derivatives was nitrogen oxide, Figure 3.88. The influence of the type of gaseous atmosphere on the limit and rate of destruction in the case of some usual polymers processed by vibratory milling at the environmental medium temperature and in different gaseous media is presented in Table 3.30 [191, 230]. 304

Mechanochemistry of Polymer Fracture

Figure 3.89. Variation of intrinsic viscosity with milling time in different gaseous media: 1) vacuum; 2) nitrogen; 3) vinyl chloride; 4) air [306].

Figure 3.90. Variation of chlorine percentage content and of intrinsic viscosity with milling duration [306]. 305

Macromolecular Mechanochemistry

Both in the case of PET and cellulose, the kinetic parameters M ∞ and k are clearly influenced by the nature of the reaction medium, the most intense mechanodegradation being recorded in NO atmosphere. Vibratory milling of a thermoplastic linear elastomer of polyurethane type (Etane–5705, B.F. Goodridge) was carried out in vacuum and in a series of gaseous media, such as nitrogen, vinyl chloride and air, Figure 3.89. Air was found to be the most reactive from the investigated reagents (curve 4 in Figure 3.89). The viscosity decay due to the reaction of mechanoradicals with vinyl

Figure 3.91. ESR spectra of mechanoradicals of six methacrylic vinyl polymers mechanically degraded for 10 min.

chloride and subsequent evolution of the grafting process of the gaseous monomer on the polyurethane support is illustrated in curve 3 of this Figure. On one side, the intrinsic viscosity decay due to the main chain splitting in shorter fragments and, on other side, due to the increase of the new product symmetry by fixation of PVC ramification on the two sides of the main chain. As is seen in Figure 3.90, viscosity decay is well correlated with the amount chlorine of chemically bonded by grafting [207, 306]. 306

Mechanochemistry of Polymer Fracture

Figure 3.92. Progressive changes in mechanoradical concentration in the course of vibratory milling: 1) PMMA; 2) PMAAm [307].

The formation of mechanoradicals in the absence of oxygen and their reactivity with oxygen at room temperature has been investigated for a series of methacrylic vinyl polymers (Figure 3.91). All electron spin resonance spectra, ESR, of the formed mechanoradicals were essentially similar and are clearly assigned to the respective end-chain radical. The ESR kinetics of mechanoradical formation in the case of poly(methyl methacrylate) (PMMA) and poly(methacrylamide) (PMAAm) exhibit an interesting contrast. The progressive change of the radicals concentration in PMMA, as a function of milling time, gradually decreases after Table 3.31. Radical concentration obtained from double integration of spectra a [307] Polymer

Mechanoradical

Peroxy radical from mechanoradical

PMMA

7.3

2.09 (4.18)b 0.47 0.80 1.54 0.04 4.62 (13.2)b

PMMA Eudragit L100 c-PMMA PHEMA PMAAm a b

1.2 3.0 6.0 0.5 15.5

× 1018 spin number/g. Includes the remaining mechanoradical.

307

Peroxy radical formed in air 0.1 0.2 0.4 0.1 0.01 0.02 (0.36)b

Macromolecular Mechanochemistry

reaching the maximum value (curve 1 in Figure 3.92), while in the case of PMAAm (curve 2 in Figure 3.92) it shows a parabolic increase. This discrepancy bas been explained by the strong stabilisation of PMAAm mechanoradicals, especially by intermolecular and intramolecular hydrogen bonds among the amide groups. In reaction with oxygen, both PMMA and PMAAm mechano-radicals do not give rise a single peroxy radical, but rather a mixture of mechanoand peroxy radicals even after exposure in air, while the mechanoradicals of other polymers are rapidly converted to the corresponding peroxy radicals. Such a difference was observed in experiments dealing with the mechanical fracture of these polymers under aerobic conditions. The radicals concentration (spin number/ g) corresponding to each investigated polymer are summarised in Table 3.31 [307]. Oxygen and nitrogen oxide (NO) have also been used for characterisation of mechanodegradation reactions of some polymers in solutions [123,190,191]. The influence of diamines, as radical acceptors, was studied both in the case of heterocatenary and homocatenary polymers [308–314]. A systematically investigated polymer was poly(vinyl chloride), which was processed by vibratory milling, two-rolls mixing, ultrasonic irradiation and cryolysis, especially in the presence of aromatic diamines (o-, m-, and p-phenylenediamine and benzidine). In all cases, the change of polymer molecular weight and chemical bonding of diamine to the destruction fragments was proved [308–314]. Vibratory milling and cryolysis were carried out in inert medium (nitrogen) at room temperature (18 ± 2 °C) and in the range from –60 to 30 °C for cryolysis; in addition, the two rollmixing of PVC was performed at 170 °C, in the air atmosphere. In the first two cases, the processing times were in the range of several hours and for the two-roll mixing process the mixing time was of several tens of minutes, Figure 3.93. Vibratory milling, curve 1, and cryolysis, curve 2, leads to typical mechanodegradation curves, characterised by a molecular weight decay. The two-roll mixing process occurs under mechano-thermo-oxidative conditions and, therefore, the curve corresponding to the molecular weight variation, curve 3, differs by curves 1 and 2. Thus, the first part of this curve describes a typical process of mechanodegradation, passing through a minimum, and, finally, an increasing part related to the crosslinking process is recorded. The graphical representation of the molecular weight variation 308

Mechanochemistry of Polymer Fracture

Figure 3.93. Influence of the mechanical processing conditions on the molecular weight of PVC modified with benzidine [308]: 1) vibratory milling; 2) freezing; 3) roll milling.

with the diamine concentration clearly evidences the co-existence of the two destruction processes, Figure 3.94. In all cases, the molecular weight passes through a minimum, located at about 0.5% for benzidine and 1% for other diamines, and after that increases with the increasing of the transfer reagent concentration. An inexplicable increase of the molecular weight was recorded in the case of p-phenylenediamine, curve 3 in Figure 3.94. The produced polymer is characterised by limited solubility in cyclohexanone. The influence of aromatic diamine on mechanodegradation during vibratory milling and cryolysis and the correlation of viscosimetric data to the amount of chemically bonded diamine are presented in Table 3.32. The bonding of diamine structural units on the macromolecular chains affects the polymer properties. The best results were obtained in the presence of benzidine, which determines an increase of about 140% in tensile strength as compared with the virgin polymer. In addition, for diamine concentrations higher than 3% in PVC it was posisble to reduced to 1% the amount of the thermal stabiliser, i.e. a lead-based compound. In other words, the bonded diamine acts as a thermal stabiliser, Figure 3.95. Temperature and processing time exert a lesser influence on the tensile strength values. The best results were obtained at 170– 180 °C and 15 min of milling, respectively. The collected data were processed using simulation software and 309

Macromolecular Mechanochemistry

Figure 3.94. Variation of molecular weight with diamine concentration [309]: 1) PVC + benzidine; 2) PVC + m-phenylenediamine; 3) PVC + p-phenylenediamine.

Figure 3.95. Variation of tensile strength with diamine concentration [309]: 1) PVC + benzidine; 2) PVC + p-phenylenediamine; 3) PVC + m-phenylenediamine.

it was found that benzidine is the best reinforcing reagent from all the investigated diamines. The optimum milling conditions, found by simulation, lead to a value of tensile strength of 760 kgf/cm 2 and the experimentally verified value of 775 kgf/cm 2 was achieved, Fig310

Mechanochemistry of Polymer Fracture Table 3.32. Influence of the mechanical work duration on the reaction effectiveness for the system PVC – S + diamine [309] Sample PVC – S + benzidine ( 10 g ) (2g) (soluble fraction)

PVC – S + p-phenilendiamine ( 10 g ) (1g) (soluble fraction) PVC – S + benzidine (1%) (2g)

Duration and type of the mechanical work vibratory milling hours 0 24 72 96 0 24 72 96 cryolysis, number of cycles 0 20 60

M ⋅ 10−3

Amount of chemically bound chlorine diamine

54.97 26.00 20.00 18.00

0 4.6 4.8 5.46

55.07 43.46 39.83

54.97 9.00 8.25 6.35

0 1.78 5.39 5.40

55.07 42.35 46.35 29.20

54.97 51.80 50.24

0 4.33 6.30

-

ure 3.96 [312]. It is worth noting that the effect of ultrasound on the poly (acrylonitrile-co-vinyl acetate-co-α-methylstyrene), 92% acrylonitrile, solutions in dimethylformamide, in the presence of diamines determines a similar behaviour, but at low temperatures, 50 °C, Figure3.97, [310]. 3.5.3.3. Organic liquids compatible with the stressed polymer Organic liquids compatible with polymers induce different effects depending on the chemical nature of both components, which determines the type of their reciprocal interactions. Mechanically stressed swollen or plasticized systems, as well as highly concentrated solutions suffer mechanocracking and fracture processesed with an efficiency determined by the nature of the applied stress. If the shock forces, for instance those generated by vibratory milling, have a small effect, due to the elastic response of the system, under the action of mixing, stirring, shearing forces, and of hydraulic shock waves, generated by ultrasonic treatment or by electrical discharges in liquids support both mechanodegradation and fracture processes are favoured. These processes follow the general laws of the viscoelastic state, quite similar to liquid– viscous systems. The main difference between the two systems is related to the fact that, in the last case, high viscosity is reached 311

Macromolecular Mechanochemistry

Figure 3.96. Tensile strength, σ r , as a function of stabiliser and diamine concentration [312].

Figure 3.97. Variation of intrinsic viscosity of the copolymer with solution concentration in the presence of benzidine (1) and (2) o-phenylenediamine (T = 50 °C, t =3 hr) [310].

due to high temperature and, in the first case, it is mainly related to the presence of the liquid component. Many polymers, such as: polystyrene, poly(methyl methacrylate), poly(vinyl alcohol), poly(vinyl chloride), poly(vinylidene chloride), poly(acrylamide), polyethylene, cellulose and its derivatives, (ethyl, benzyl- and acetyl cellulose), plasticized with organic solvents show mechanodegradation process, whose efficiency depends on 312

Mechanochemistry of Polymer Fracture

the initial average molecular weight, M0 , temperature, mechanical regime, and the nature of liquid present in the reaction medium [315, 316]. In this case, the mechanodestruction particularities are strongly related to the viscoelastic state attained by the polymer. As Figures 3.98 and 3.99 show, this state may be modified either by the nature and amount of organic liquid or by temperature. Generally, decreasing the temperature and the polymer/liquid ratio determines the increase of the mechanodestruction rate and decrease of M0 , because both the mentioned factors modify the intensity of shear forces. Figure 3.100 offers a comparative representation of the mechanodegradation of the polymers in diluted solutions processed by high speed stirring, forced to flow by narrow orifices or by capillaries, under the action of ultrasound waves, as well as of the concentrated solutions or plasticized systems, when the poymer concentration is high. In diluted solutions, the macromolecular coils are displaced practically independently of each other in the solvent and under the action of shear forces the chains tend to orient in the direction of these forces, and above a given stress some chemical bonds homolyticaly split, giving rise to mechanoradicals, Figure 3.100 a. In the case of swollen or plasticized systems, the macromolecules have a ball-like shape and still retain the inter- and intracatenary secondary bonds. Their packing density and the type of polymer/solvent interactions depend on the quality of organic liquid (good or poor solvent). The viscoelastic state, by its particularities, is much more closer to the fluid–viscous state (melts), characteristic of polymer melts, attained under the action of temperature than those of diluted solutions. In the fluid–viscous state, subjected to shear forces, the macromolecular coils are broken up and the stressed macromolecules are parts of them, being stressed and oriented in the direction of forces and undergoing scission when the forces reach critical values, Figure 3.100 b. The use of liquids capable of weakening certain chemical bonds of the main chain determines their bonding to the end of destruction fragments. Water is a highly reactive reagent. Being present in system, even in small amounts, water is able of releasing the mechano-activated hydrolysis. Water also determines the specific behaviour of the polymer depending on its chemical nature or on the position of structural faults. The mechanodegradation of many hetero-catenary polymers, such as: polyamides, poly(ethylene 313

Macromolecular Mechanochemistry

Figure 3.98. Influence of solvent nature on the polystyrene mechanodegradation: 1) toluene; 2) dichloroethane; 3) methyl ethyl ketone; 4) acetone; 5) benzene; 6) butyl acetate; 7) carbon tetrachloride; 8) petrol ether [316].

Figure 3.99. Influence of temperature and of solvent on the mechanodegradation of poly(methyl methacrylate): 1) 30 pph benzene, 35 °C; 2) 30 pph benzene, 12 °C; 3) 30 pph benzene, 12 °C [316]. 314

Mechanochemistry of Polymer Fracture

Figure 3.100. The shape of and mechanodegradation of macromolecules in solution [316]: 1) diluted solutions; 2) swelled/plasticized systems.

tereph-thalate), cellulose and its derivatives, has been investigated from this point of view. Some results and particularities of their mechanodegradation were given in the Chapter 3.3.3.4, entitled ‘Reaction mechanism’ [83, 124–131, 230]. A series of synthetic fibres and polymers from which the fibres were produced have been investigated under the conditions of vibratory milling or cryolysis, with the results being in accordance with those already mentioned [317–323]. The stressing of polyamides 6 and 6,6 by vibratory milling, in the presence of methanol, is accompanied by chains splitting and chemical bonding of alcohol to the destruction fragments. As is seen in Figure 3.101, the number of bonded methoxy groups increases concomitantly with the decrease of polymer viscosity [126]. Some liquids can cumulate many of the above-mentioned functions. Thus, it was proved that carbon tetrachloride, in proportions up to 3% with respect to the polymer, during mechanochemical processing of polystyrene and poly(methyl methacrylate) acts as a 315

Macromolecular Mechanochemistry

Figure 3.101. Vibratory milling of polyamide-6 dispersed the methanol in dried inert atmosphere at 18 ± 2 °C [126]: 1) variation of [η]; 2) variation of number of methoxy groups.

plasticizer, radical acceptor, and chain transfer reagent, Figure 3.102, [113]. The linear polyurethane elastomer, type Estane, was subjected to vibratory milling in different active liquid media with respect to the polymer, such as: isoprene, acrylonitrile, benzidine (solution in ethanol absolute). The obtained results were compared to those obtained in the presence of absolute ethyl alcohol that is inert with respect to polyurethane. The most intense mechanodegradation was obtained in the presence of benzidine (curve 4 in Figure 3.103). Curves 2 and 3 describe the viscosity decay in the presence of isoprene (curve 2) and acrylonitrile (curve 3), where the mechanoradicals initiate the polymerisation of the respective monomers. In the case of acrylonitrile, the chemical bonding of monomer structural units on the polyurethane macromolecular chain is graphically represented in Figure 3.104 (curve 2). It can be seen that the variation of intrinsic viscosity [η] with time is described by a typical exponential curve (curve 1 in Figure 3.104), whilst the one describing the variation of chemically bonded nitrogen passes through a maximum. The grafting reaction occurred at a high rate up to 50 hrs of stressing when the maximum was reached. Above this period, the content of chemically bonded nitrogen starts to decay up to 120 hrs of processing and then remains constant to the 316

Mechanochemistry of Polymer Fracture

Figure 3.102. Vibratory milling of polystyrene and poly(methyl methacrylate) in the presence of carbon tetrachloride [ 113 ]: 1) PS + 0.3% CCl 4 ; 2) PS; 3) PMMA +0.3% CCl 4 ; 4) PMMA.

end of processing, 192 hrs, respectively. This behaviour was explained by grafted polymer mechanodegradation; the results are in good agreement with the variation of intrinsic viscosity with time, curve 1 in Figure 3.104. It is possible, as in the range of long periods of processing the cyano groups, –CN, to form acrylonitrile to induce some cyclization reactions; this kind of nitrogen is not identified by the Kjeldahl method, used for nitrogen identification. Anyhow, cyclization must by intracatenary one, because the products keep their solubility until the end of process and the curve [η] vs. time decreases continuously in the whole investigated range [207,306]. In addition, the chemical reactivity of some labile substances (benzoyl peroxide and AIBN) was verified in the process of vibratory milling. Their influence has been studied using, as a reaction medium, a liquid monomer, styrene, which also acts as solvent for the two compounds. The criterion of the chemical reactivity of initiators was monomer conversion into the polymer. Styrene solutions of the two initiators were subjected to vibratory milling at the environmental medium temperature (18 ± 2 °C), in an inert atmosphere of purified nitrogen. The conversion vs. time curves, Figure 3.105, show an apparently strange behaviour. The highest polymer yields, i.e. about 70%, are obtained in the inert atmosphere, curve 317

Macromolecular Mechanochemistry

Figure 3.103. Variation of intrinsic viscosity with milling duration in various liquid media [207, 306]: 1) absolute alcohol; 2) isoprene; 3) acrylonitrile; 4) benzidine.

Figure 3.104. Variation of nitrogen percentage content and of the intrinsic viscosity with milling duration [207, 306].

1 in Figure 3.105, to decrease in the presence of initiators, in the order: benzoyl peroxide (curve 2) and AIBN (curve 3), respectively. The obtained results clearly prove that the mechanochemical decomposition of initiators took place, because the conversion degree is modified by their presence. However, this effect extends to very long processing periods 318

Mechanochemistry of Polymer Fracture

Figure 3.105. Mechanochemical decomposition of some initiators during styrene mechanochemical polymerization by vibratory milling [324]: 1) without initiator; 2) benzoyl peroxide; 3) AIBN.

when styrene polymerization is already taking place under the direct action of mechanical energy [324]. At the moment of their formation, the radicals produced from initiators already find the mechanochemically formed polystyrene macroradicals. The recombination reaction of the two types of radicals, i.e., PS . and I, is favoured because it requires no activation energy, while initiation polymerization requires much more energy for double bonds splitting (Table 3.33). Before initiator decomposition in free radicals, the source of initiation of styrene polymerization initiation consists of electronic fluxes of mechanoemission as well as the formation of mechanoexcited states by monomer sorption to the apparatus walls. The elements from the composition of the metallic wall of the reaction vessel and of milling bodies, especially, Fe 3+ , were found in the final products. Their presence confers a permanent magnetic moment to the mechanochemically synthesised polystyrene, as it was demonstrated by ESR spectroscopy, Figure 3.106 and Table 3.34. Using Mössbauer spectroscopy, it was proved that iron is present in the final product, being included both as Fe 3+ and magnetic powder, Figure 3.107 and Table 3.35 [324]. It is clear that mechanochemical initiation occurs by specific mechanisms and leads to polymers with special properties.

319

Macromolecular Mechanochemistry Table 3.33. The values of activation energy for mechanochemical polymerization of styrene [324] Sample

Duration (h)

Activation energy ( kcal/mol )

Order of reaction

Polystyrene + Benzoyl peroxide

24

- 0.107.104 - 0.752.104 - 0.307.104

0.22.10 0.00 0.00

Polystyrene + Benzoyl peroxide

48

- 0.556.104 - 1.881.105 - 0.344.104

0.17.10 0.00 0.00

Polystyrene + Benzoyl peroxide

72

- 0.125.105 - 0.946.104 - 0.277.105

0.17.10 0.00 0.00

Polystyrene + Benzoyl peroxide

96

- 0.792.104 - 0.944.104 - 0.269.104

0.12.10 0.00 0.00

Polystyrene + Benzoyl peroxide

120

- 0.638.104

0.00

Polystyrene + Benzidine

120

- 0.106.104 - 0.633.104

0.00 0.00

Table 3.34. Characteristics of ESR spectra of mechanochemically synthesised polystyrene

Sample No.

H

g

1 2 3

816.32 3 116.30 3.367.22

8.33 2.18 2.02

3.5.4. Mechanical regime Mechanodegradation occurs with maximum efficiency if there is optimal correspondence between the nature of stressing (the type of applied force, the form within which the mechanical energy is supplied to the system) and the structural particularities of the polymer related to the aggregation and physical states of the polymer in the stressing moment. Practically, in all cases the main mechanochemical reaction is accompanied by a series of secondary effects, which are directly implied in the process complicating it, Table 3.36. General parameters of mechanical regime are the following: du320

Mechanochemistry of Polymer Fracture

Figure 3.106. ESR spectrum of mechanochemically synthesised polystyrene [324].

Figure 3.107. Mössbauer spectrum of mechanochemically synthesised polystyrene [324]. Table 3.35. Characteristics of Mössbauer spectra [324] Iron’s hyperfine vicinities

I II III iron magnetic powder

V1 ( mm/s ) - 0.527 - 0.275

V1 ( mm/s ) 0.471 0.051

Position δ ( mm/s ) - 0.028 - 0.112

∆EQ 0.998 0.326

ε (%) 1.1 0.8 Traces

δ - isometric shift; ∆EQ – 4 – polar splitting; ε - Mössbauer effect

ration of its application, which is a measure of the accumulated mechanical energy in the system, the frequency and amplitude of vibration, geometry and building material of the apparatus. Combination, into an optimum set, of these parameters is made as a func321

Macromolecular Mechanochemistry Table 3.36. Types of forces and polymers mechanically stressed in different aggregation and physical states Type of stressing

The response of stressed material

Frequency

Types of stressed polymers

Uniaxial deformation

The macromolecules displacement and stretching as well as of crystalline planes, accompanied by fracture

Low

Two rolls mixing, mastication, extrusion through small orifices (splitting, shearing, mixing, stirring gradients)

Fluxes of material with high speed gradient

Low high

and Elastomers; polymers in visco-elastic state (melts, high concentrate polymers solutions, swollen polymers, plasticized polymers)

Heating, static electricity, mechanoemission, luminescence, high energy radiations

Grinding, milling, all types of dispersing under the shock waves action

Propagation of shock waves in solid bodies, the generation and growth of faults, cracks, and cleavage planes

Mostly high Solid state polymers, crystalline and amorphous, chemical networks; solid solutions

Heating, static electricity, mechanoemission, electrical discharges, luminescence

Irradiation, ultrasounds waves, spinning of polymer melts and solution

Polymer’s compressions and dilatations, fluxes with high speed gradients

High

Swelling and Non-uniform stressing of Low osmotic pressure polymer chains, macromolecular coils over-stressing due to nonuniform absorption of solvent; volume changes, stressing of polymer chains under the action of osmotic forces

Crystalline polymers as fibres or thin films

Accompanying phenomena Static electricity, irradiation, mechanoemission

Polymer melts; polymers in Cavity bubbles, heating, fluid-viscous state surface electrons; (concentrate solutions) electronic discharges in cavity bubbles Linear or crosslinked polymers in swollen state

Polymer-solvent interactions that modifies the bonding energy

Discrete change of the specific volume, stressing of the chain fragments located to the border of regions with different packing densities

Low

Crystalline polymers, Polymer-solvent polymers as solid solutions interactions that modifies the bonding energy

Displacement of material fluxes Electro-hydraulic effect in solutions and dispersions

High

Linear polymers in Heating, electric solution, linear or discharges crosslinked polymers as dispersions

Overpressures

Displacement of material fluxes

Low

Linear polymers in solution Heating, static electricity

Fracture’s shock waves

Shock wave propagation through High solid body

Phase transitions (crystallisationmelting, frozenunfrozen during cryolysis)

Solid state bodies

Heating, all types of irradiation

tion of the proposed aim. Whenever the aim is to prove the destructive phenomena, the parameters that allow an intensive mecharegime are used. This permits a rigorous and reproducible measurement of the changes taking place in the polymer. The apparatus itself responds to the followed objectives when it is especially designed for the concrete proposed aim; this is because standard equipment is usually less capable of adapting to the concrete problem. Thus, the results constitute strong arguments for 322

Mechanochemistry of Polymer Fracture

establishing the mechanodegradation and fracture regularities, which control the mechanochemical process in the conditions of a given mechanical regime. On the other hand, the results should be collected into a database, very useful for designing and operating industrial equipment for polymer processing. On the industrial scale, the parameters of mechanical regime must be harmonised with the temperature and medium conditions, in order to minimise the degradation and to obtain the optimum characteristics of the material for the given aim. These results are helpful in the elaboration of adequate procedures for the processing conditions on the industrial scale. Only when the set of physical and chemical transformations, taking place in specific conditions of mechanical, thermal and medium regime is known it is possible to produce materials with optimal characteristics. For the exploitation stage of polymeric materials, the combination of the mechanical regime parameters into an optimal set can also be realised taking into account the same principle as in the case of processing.

3.6. Modification of the structure-properties relationship by polymer degradation and fracture 3.6.1. Modification of the relation between molecular structure and physico-chemical properties of polymers Variation of the molecular weight constitutes the most direct structural response of the polymers under the action of mechanical forces. Irrespective of the nature and fault position where the stress is concentrated, the induced stress is distributed both on the intra- and intercatenary bonds. During mechanodegradation, the most stressed chemical bonds are first split down and the molecular weight decreases. The time dependence of M is described by an exponential function, Figure 3.108; this holds valuable for all the investigated polymers. The destruction rate is always the highest in the first moments of the process and gradually decreases to destruction limit M ∞ that is constant only in those conditions for which it was determined. Thus, vibratory milling of cellulose and its derivatives, Tables 3.15 and 3.16 [130], of poly(ethylene terephthalate), Table 3.30 [191], in the presence of radical acceptors, especially NO, resulted in lower values of M ∞ than those determined in similar conditions but in the inert medium. 323

Macromolecular Mechanochemistry

Figure 3.108. Destruction limit of cellulose triacetate [351] (a) as a function of filling ratio, η,: 1) 0.59%; 2) 0.44%; 3) 0.29% and of spruce fir cellulose (b) dried in: 1) air; 2) vacuum; 3) by azeotropic distillation of humidity.

The change of destruction limit values can also occur by modification of the mechanical regime parameters. Conclusive data have been obtained from the first studies in polymers mechanochemistry, concerning mechanochemical destruction, by vibratory milling of starch [325–350]. Using a very high filling ratio of the milling vessel, 18%, L.H. Lampitt achieved after 4000 hrs of milling a decrease of the polymerisation degree from 200 anhydro-glucozidic units to 41. At this value of the polymerisation degree the polymer becomes soluble in cold water [344,345]. C.H. Boissain reduced the filling ratio much more, to 0.3%, and obtained similar results, but only after 168 hrs [342]. H. Grohn and S. Augustat [328] stressed starch in even harder conditions by combining the effects of the filling ratio with those of the nature of building material of milling bodies and vessel walls. Figure 3.109 shows that the starch was depolymerized to 32 (curve 1) and 19 (curve 2) anhydroglucozidic units, respectively. Another characteristic of the destruction limit is related to the fact that it defines the dimensions of the macromolecular chain fragments. No examples of total depolymerization of the polymers to the corresponding monomers are available. Polyoxymethylene, for instance, constantly eliminates formic aldehyde during the entire period of degradation by vibratory milling. The percentage of released aldehyde to the destruction limit is about 50 [56]. The destruction limit is the result of a mechanochemical process of radicalic degradation whose rate depends on polymer nature, temperature, reaction medium, and mechanical regime [350, 352]. The amount of the released monomer is determined by the ratio of 324

Mechanochemistry of Polymer Fracture

depolymerization and mechano-radicals disappearance rates. As a result of mechanodispersion at –78 °C, poly(methyl methacrylate) released at 20 °C (after the stabilisation of radicalic species) 0.6×10 5 molecules of monomer/cm 3 s, which is ten times greater than the disappearance rate of the corresponding macroradicals. At –36 °C about 10±3 monomer molecules are formed for any two macroradicals that appear by chain scission. Temperature plays a controlling role in this process. Thus, at 25 °C and 45 min of processing the molecular weight of PMMA decreases from 5×10 6 to 3.3×10 3 g/mole without releasing any detectable amount of monomer. For the same mechanical conditions but at –85 °C, the final molecular weight was 5.5×10 4 and about 10% of liquid monomer was formed as the degradation product, Figure 3.110a. The formation of peroxy radicals in the presence of oxygen was also evidenced. These radicals react with methylene groups, giving rise to hydroperoxy end groups and alylic radicals, which subsequently undergo the depolymerization reaction [350]. Mechanodispersion of polypropylene at 80 K and 195 K, respectively, is accompanied by the evolution of other volatile compounds than its own monomer, such as methane, ethane and propane that is formed in the highest quantities. Propylene and higher hydrocarbons were found only as traces, Figure 3.110b, [353]. Polymethacrylamide mechanical degradation produces at 20 °C both oligomers and a monomer, a process accompanied by small

Figure 3.109. Destruction limit in the case of starch vibratory milling [329]: 1) porcelain vessel and balls, η = 1.25%; 2) stainless steel vessel and balls, η = 1.25%. 325

Macromolecular Mechanochemistry

Figure 3.110. Formation of volatile compounds during mechano-dispersion [350, 353]: a) mass spectrum of degradation volatile compounds of poly(methyl methacrylate) mechanodispersed at –85 °C; b) chromatogram of volatile substance obtained by polypropylene mechanodispersion: 1) methane; 2) ethane; 3) propane; 4) propylene; 5) C 4 +.

changes of the average molecular weight [353]. Vibratory milling of the polymers with pendant functional groups is accompanied by the release of small molecules, such as water, in the case of poly(vinyl alcohol), HCl, in the case of poly(vinyl chloride) and poly(vinylidene chloride), and acetic acid in the case of cellulose triacetate degradation [231, 354, 355]. The presence of these compounds in the degradation products was established by chemical analysis and IR spectroscopy. The reaction can be either intramolecular, generating double bonds, or intermolecular, stimulating the crosslinking or cyclization, which can take place irrespective of the elimination mechanism [355]. Hydrochloric acid release was clearly proved in the case of PVC, which when subjected to vibratory milling gradually looses chlorine with accompanying changes of colour due to the accumulation of double bonds, Table 3.37 [354]. The mechanodegraded PVC, by vibratory milling, both in solid Table 3.37. The change of poly(vinyl chloride) chemical structure by vibratory milling in inert atmosphere (nitrogen) and temperature of 18 ± 2 °C Vibratory milling duration ( hr )

Content of chlorine (%)

Colour of final product

0 2 4 6 8

71.8 70.0 61.5 49.0 41.5

white yellowish intense yellow brown brown dark

326

Mechanochemistry of Polymer Fracture

state and as methanolic dispersions, suffers intense structural changes, which consist not only of a decrease of the molecular weight but also a decrease of the chlorine content. The same polymer, mechanochemically processed in the presence of radical acceptors (DPPH, atmospheric oxygen, and diamines), is characterised by appearance of new functional groups [123, 236, 308–314, 356, 357]. The most evident changes were found during vibratory milling of absolutely dry solid polymers and under the effect of ultrasound action on polymer solutions. Presence of radical acceptors (oxygen, nitrogen oxides, diamines, etc) favours the mechanodegradation and chemical modification of PVC. IR spectroscopy proves the modification of all characteristic peaks, Table 3.38. Intra- and intercatenary dehydrocyanuration was also identified during poly(acrylonitrile) degradation by vibratory milling. The HCN released by the intramolecular reaction was collected from the gaseous atmosphere of the reaction vessel in an argon stream, cooled, and reacted with AgNO 3 to give a precipitate, which by analysis was proved to be AgCN. Its intermolecular elimination led to the formation of imido and azomethine groups, belonging to crosslinked or cyclic structures [355]. CH2 CH CH2

CH2 CH CH2 C

CH2 CH CH2 CN (I)

;

;

N

HC C

CH2 CH CH2

CH2 CH2

CH2

CH

NH

N

CH

CH

C

C N

N

( III )

CN ( II )

It is unanimously accepted that mechanical energy is partially converted to thermal energy during mechanochemical processing of polymers, locally the temperature can be very high, and this factwas regarded as a reason for the decrease of low-molecular weight compounds [352]. The mechanochemical processing of some materials with a complex chemical structure, such as wood, lignocellulose, and based on proteins or nucleic acid ones usually determines the change of the components ratio. Thus, mechanical destruction of wood resulted in plasticizing of lignine and, consequently, the modification of the hydrophilic characteristics and viscoelastic properties of wooden fibres. The elasticity and plasticity of wood increase as a result of 327

Macromolecular Mechanochemistry Table 3.38. The change of absorption peaks intensity in the IR range of PVC samples processed by vibratory milling Variation of bands surface with respect to initial surface

Mechanodegradation type

Variant

Initial

-

Ultrasonic irradiation

2

Vibratory milling

Total γ C − Cl duration ( min ) -

90 ( 60 sol. + 30 precip.) Suspensio 30 n in methanol

Initial

-

-

Ultrasonic irradiation

2

60

γ CH 2

γ CH

δ CH − CH schelet al

δ CH

δ CH

δ CH

δ CH

7.094 10.98 25.30 2 5 14.97 3.899 20.98 6 1

11.029 16.98 8.805 6.280 3.059 1 9.279 4.705 15.59 15.01 9.961 4 8

18.23 23.15 11.28 5 7 1

30.360 11.79 8.466 1.545 0.881 8

9.372 11.26 4.107 8 11.78 5.935 8.578 9

22.587 9.299 4.422 13.05 12.94 5 ? 2.656 17.29 7.498 3.670 11.55 5 ?

splitting of the secondary bonds and depolymerization results in an increase in the number of the end functional groups, –OH, and therefore of hydrophic nature. The partial release of some constituents, especially pentozes, also occurs [358]. As early as in 1936, H. Staudinger and co-workers found that after 12–14 hrs of milling, in the dry or wet state, wood is converted in a proportion of 35–50% to a soluble fraction, in the Schweitzer reactive that was called cellulose [359]. H. Grohn proved that the flour of pinewood subjected to methylation or acetalisation reactions gives soluble products. These products were used by authors to establish the quantitative ratio between the most important constituents of wood, Table 3.39 [360]. They underlined the modification of lignine and polyuronic acids structure under the action of mechanical energy. F.F. Brauns [361] developed a mechanochemical method of lignine separation from wooden materials, which was subsequently applied by many other teams as it is or associated with other biochemical methods [362–367]. It results that the most important consequences of mechanodegradation and fracture on the molecular level are the following ones: the decrease of the average molecular weight up to a limiting value, M ∞ , the formation of new functional groups, and the change of the polar/non-polar ratio of the macromolecules. Usually, polymer solubility increases with the decrease of the polymerization degree and the increase of polarity of the mechanodegradation products. Mechanochemical modifications 328

Mechanochemistry of Polymer Fracture Table 3.39. Chemical composition of beech wood [360] Constituent Cellulose Pentose Lignin

Fractional content (%)

Content of – OCH3 groups (%)

45.5 24.3 22.7

45.6 38.7 15.0

occurring in the polymer structure are sometimes so important that the processed polymers become soluble in new solvents in which the initial polymer does not dissolved. Thus, gelatine is soluble in water only at temperatures above 40 °C, but its destruction products, obtained by vibratory milling, are soluble in cold water and, furthermore, they are soluble up to 10% in ethyl alcohol and acetone [196]. As Figure 3.111 shows, technical cellulose processed by vibratory milling increases its solubility up to 90% [368]. Vibratory milling of pine cellulose and halocellulose resulted in the separation of methyl glocuronoxilane, ramnaose, arabinose, galactose, xilane, glucozouronic acids, and all low molecular weight compounds soluble in water [369]. Mechanochemically processed PVC not only increases its solubility in acetone but it becomes partially soluble in ethyl alcohol and benzene [116]. In polymer fibres based on polyamide 6, poly(ethylene terephthalate), and poly(acrylo-nitrile), vibratory-milling mechanodegradation modifies the average polymerization degree, the number of end functional groups, and even the chain structure, as it was described in Chap-

Figure 3.111. Change of solubility of technical grade sulphite cellulose with the decay of polymerisation degree by vibratory milling [368]. 329

Macromolecular Mechanochemistry

ter 3.3.3, ‘Mechanism of mechanochemical destruction’, where partial polymer dissolution in unusual solvents was explained, Table 3.40. For instance, the partial dissolution of poly(acrylonitrile) in nonpolar solvents may be explained only by the occurrence of secondary reactions that implies the reaction of strongly polar cyano groups, –CN, either by cyclization or HCN elimination reactions. When crosslinking reactions occur during mechanochemical processing, as in the case of two-roll mixing mastication of poly(butadiene-co-acrylonitril) rubber, the polymer solubility in specific solvents decreases, Figure 3.112. The rubbers of SKN-type can be arranged in the following order of their solubility decay [370]: SKN – 40 < SKN – 26 < SKN 16 The mechanodegradation of polyelectrolytes and, generally, of heterocatenary polymers, which increase the number of dissociating functional groups by mechanodegradation, determines the modification of their biochemical properties. Proteins as well as aliphatic polyamides, like polyamide 6 and polyamide 6,6, or polyesters, such as poly(ethylene terephthalate), mechanically dispersed by vibratory milling, are converted to the final products with an increased number of acidic and amino end groups. In the case of proteins, in the presence of atmospheric oxygen, dominantly acidic groups were obtained, with the appearance of amino groups being inhibited.

Figure 3.112. Change of solubility of poly(butadiene-co-acrylonitrile) copolymer by two-roll milling [370]: 1) SKN-18; 2) SKN-26; 3) SKN-40. 330

Mechanochemistry of Polymer Fracture Table 3.40. Modification synthetic fibres solubility by vibratory milling, 5 minutes in air Solvent

Acetone Ethyl acetate Benzene Dichloroethane Ethyl alcohol Water NaOH, 0.1 N HCl, 0.1 N

Polyamide 6 Initial

Without cooling

0 2.1 0 2.0 0 0 7.8 7.8

8.0 1.7 1.6 3.1 4.8 6.5 22.2 26.5

Poly(ethylene terephtalate)

With cooling

7.9 3.7 2.0 3.0 5.9 6.8 28.2 28.5

Initial

7.0 6.5 0.6 5.0 0 0 21.0 5.0

Poly(acrylonitrile)

Without cooling

With cooling

Initial

7.2 6.8 3.4 4.9 5.0 5.2 30.5 5.1

9.0 7.5 3.5 9.2 5.2 4.8 32.5 7.2

6.0 1.9 0 5.4 0 0 13.9 5.8

Without With cooling cooling

9.1 7.0 8.6 5.7 9.8 3.3 30.8 7.1

12.3 12.9 11.6 13.7 11.4 12.8 32.2 7.7

Figure 3.113. Curves of potentiometric titration of natural silk (full lines) and of casein (dotted lines) [370]: 1, 2) initial samples; 3, 4) mechanochemically degraded samples.

These effects were evidenced by potentiometric titration of the solutions obtained by vibratory milling of natural silk (fibroin), casein, collagen, or cheratin, Figures 3.113 and 3.114. It was found that the isoelectrical point of protein was also changed by mechanodegradation [116]. The flowing of some polymer solutions through narrow orifices is accompanied by the modification of the electrophysical properties of the polymers. By passing from the stationary state to the dynamical ones, many properties of dissolute macromolecules are changed. Thus, in the dynamic field, the values of the dielectric constant depend on the specific positions that are occupied by the polymer chains in the solution. As Figure 3.115 shows, under the action of the electrical field the macromolecule is moved in the di331

Macromolecular Mechanochemistry

Figure 3.114. Curves of potentiometric titration of collagen (full lines) and of keratin (dotted lines) [370]: 1, 2) initial samples; 3, 4) mechanochemically degraded samples.

Figure 3.115. Orientation of macromolecules in the dynamic field of forces [378].

rection which depends on polarity. The dynamic field will tend to orient the suspended particle in the flow direction. If this field is perpendicular to the electrical field, i.e. acting as in Figure 3.115 in the direction x, the dipole orientation is inverse an attraction force acts between them, with the effect of the two fields being additive [370–378]. In these conditions, the macromolecules are under the influence 332

Mechanochemistry of Polymer Fracture

of: 1) electrical field; 2) mechanical field; and 3) Brownian thermal movements. Apart from the static conditions, where the macromolecules are randomly moved in all directions, in dynamical field they are oriented in the flow direction. In addition, rotation takes place with different angular rates, determined by their shape and dimension [374]. P. Wendisch studied the modification of the dielectric constant of cellulose nitrate solutions in a dynamic field [378]. It was considered that the particles with kinetic independence are not simple macromolecular coils but agglomerates of macromolecular coils. These deviate from the spherical shape, tending to an elliptical one. Their rotation rate depends on the position of the two axes with respect to the flow direction. When the major axis hypothetically coincides with the direction of action of the dynamic field, the rotation rate is lower and it is higher when the axis is perpendicular to the flow direction. The electrical properties of the polymer solutions are governed by the possibilities of polarisation and orientation, and the reasons for changes of the dielectric constant must be found in these two effects as well as in the changes occurring at the level of the macromolecular structure. For mathematical treatment it is assumed that the shape of the macromolecules is that of an ellipsoid of rotation, possessing a permanent dipole along its major axis. The momentum that acts on the particle is composed of two components, the first one is related to the electrical field and the second one to the flow [375]. Assuming that the speed gradient, G, is constant in a variable electrical field, E = E 0 cos ωt, and assuming also the perpendicular orientation of the two fields, the following relation is obtained for the electrical moment, µ :

LM MM N

FG IJ H K

µ 2 E 0 eiωt µE0 µ= + KT 3KT 1 + iω 2D

2

FG H

cG f1 + 2 KT

OP IJ f P K P Q 2

2

(3.104)

where: µ is the dipole moment of macromolecules; K – Boltzmann’s constant; T – temperature; D – diffusion coefficient; c – constant that depends on solution viscosity; f 1 and f 2 – functions depending on the ellipsoid axis ratio. The most important effects produced under the influence of 333

Macromolecular Mechanochemistry

shear forces are the following ones: 1) temporary orientation of the particles; 2) particle deformation, accompanied by dipole moment modification; 3) viscosity decay that can induce the detachment of molecular fascicles and an increase of orientation capacity with respect to the two fields. Macromolecule orientation in the dynamic field of forces causes a change of the polarisation ratio in the electric field, which in turn leads to a change of the dielectric constant whose value is strongly affected by both the values of the rate gradient, Figure 3.116, and temperature, Figure 3.117, [378]. Modification of the biochemical properties of some natural polymers was found to be also connected with structural changes induced by mechanodegradation. Special attention was paid to investigating the influence of fermentative hydrolysis of the polymers subjected to mechanodegradation. Thus, crosslinked collagen, used for the fabrication of footwear, achieves a good stability with time under the action of specific ferments. However, during the wearing period a part of crossbridges are broken and the material becomes sensitive, especially in the wet state, to the action of ferments and finally starts to rot [379]. A similar behaviour was

Figure 3.116. Dependence of dielectric constant by rate gradient [378]: 1) c = 5%, T = 20 °C; 2) c = 3%, T = 20 °C; 3) c = 1%, T = 20 °C; 4) c = 5%, T = 40 °C; 5) c = 3%, T = 20 °C; 6) c = 1%, T = 40 °C. Figure 3.117. Variation of dielectric constant with temperature at different rate gradients [378]: 1) 588 s –1 ; 2) 410 s –1 ; 1) 261 s –1 ; 1) 134 s –1. Solution concentration, 5%. 334

Mechanochemistry of Polymer Fracture

observed in the case of mechanochemical processing of starch. In particular, amylopectin is split by γ-amylase and, in addition, the acceleration of hydrolysis was observed. The amount of simple sugars increases by about 10% due to the scission of C 1 – C 6 bonds which, under normal conditions, are resistant to the action of ferments. The ferments itself increase their biocatalytical activity under the action of mechanical forces. Thus, the intensification of pepsin and tripsin action in collagen decomposition was proved, as the effect of activation by vibratory milling. The activation of these ferments is manifested from the first stages of the process. Subsequently, the cyclisation of peptide chains occur and fermentative activity is stopped [379]. The activity of ferments also changes under the action of ultrasound. In this case, the nature of reaction medium is a very important co-factor. It was found that the catalytic activity of tripsin decays in the presence of oxygen with 75–85%, while in the presence of hydrogen it is unchanged [380–383].Thus, in the presence of both oxygen and hydrogen diastaze activity is inhibited by ultrasound [384]. Hialuronidose in relation to the solution concentration and ultrasound velocity looses its biocatalytic activity by the oxidation of certain functional groups. These effects are irreversible. Reduction reagents, such as cistein or ascorbic acid added to the reaction medium, are able to protect the ferment by inactivation [385]. Oxidases, for instance, are more sensitive than reductases or amylase whilst catalase is not inactivated even in heavy conditions [385]. A pronounced stability characterises invertase from yeast. It was assumed that the decrease, by ultrasonation, of the content of polymanone, from proteohydrocarbonate complex of invertase reduces the ferment stability due to the oxidative reactions [386]. The activity of proteolitic ferments, pepsin and tripsine, decreases under the action of ultrasound due to the splitting of cyclical amide residues. These transformations have been studied using spectral methods, Figure 3.118, and, as Figure 3.119 shows, are affected by the nature of the reaction medium [387]. The scission of sulphur bridges was also confirmed by polarography, Figure 3.120 [388]. The oxidation of aromatic aminoacid residues was also demonstrated in the case of ribonuclease, but the enzyme does not loose its biocatalytic function [389]. Under the action of ultrasound, some low-molecular weight compounds are released, such as peptides and aminoacids. In UV spectroscopy, this corresponds to the for335

Macromolecular Mechanochemistry

Figure 3.118. Dependence of optical density of pepsin aqueous solutions, saturated with oxygen, by the duration of ultrasonic treatment [380]: 1) initial; 2) ultrasonically treated 5 min; 3) ultrasonically treated 30 min; 4) ultrasonically treated 60 min. Ferment concentration, 0.2%.

Figure 3.119. Dependence of optical density of pepsin aqueous solutions by the nature of dissolved gaseous substance during ultrasonic treatment [380]: 1) helium; 2) hydrogen; 3) argon; 4) air; 5) before of ultrasonic treatment. Ferment concentration, 0.2%, ultrasonic treatment duration, 30 min.

mation of two absorption peaks, located at 280 and 250–260 nm, which disappear after dialysis. As is seen in Figure 3.121, after dialysis the absorption spectrum of the mechanodegraded protein is 336

Mechanochemistry of Polymer Fracture

Figure 3.120. Polarograms of ultrasonically treated tripsine in the presence of different gaseous substances [380]: 1) control; 2) hydrogen; 3) oxygen; 4) argon.

Figure 3.121. Spectrometric curves of ribonuclease aqueous solutions (0.2%) ultrasonically treated at different values of pH [380]: 1) witness; 2) ultrasonic treatment at pH = 9; 3) ultrasonic treatment at pH = 7; ultrasonic treatment at 4) pH = 4.65.

practically similar with those corresponding to the initial protein [380]. As already mentioned, protein degradation to the low-molecular weight compounds takes place both in the presence of atmospheric oxygen and hydrogen, in the first case the destruction effect being more pronounced. In the presence of hydrogen a part of lowmolecular weight compounds can be separated by dialysis and others enters into reciprocal interactions, generating higher segments; in this way an increase of the molecular weight of about 40% was 337

Macromolecular Mechanochemistry Table 3.41. Variation of ribonuclease molecular weight with ultrasonic irradiation duration in the presence of hydrogen Ferment Ribonuclease

Ultrasonic irradiation period ( min )

Ferment molecular weight ( g/mole )

Modification of molecular weight (%)

0 30 60 120

17,300 24,000 19,000 17,000

0 45 12 0

achieved, Table 3.41. The splitting of small fragments, corresponding to some aminoacids such as valine, serine, and alanine, and their removal from the protein extremity do not imply ferment inactivation. However, the splitting of higher fragments such as asparoyl-alanil-serine-valine tetrapeptide from the same chain extremity leads to the loss of ferment activity [380]. Important conclusions were drawn by comparing the behaviour of nucleic acids during ultrasonic treatment. In the case of deoxyribonucleic acid, ADN, by changing the temperature and pH the splitting of hydrogen bonds take place, which causes the lost of double helix conformation as well as of chain flexibility. In this way ADN is denatured passing into a compact-coiled structure and keeping the initial value of the molecular weight. During ultrasonic treatment, small fragments of ADN are released which keep their native shape due to the preservation of hydrogen bonds. A criterion of the evaluation of hydrogen bond density in ADN was represented by the molecular coefficient of extinction ε(P) for the UV range of the spectrum. In the presence of hydrogen bonds, the extinction coefficient shows a broad maximum of absorption between 2580 and 2630 Å. It was found that the extinction molar coefficient remained constant throughout the whole period of treatment, Table 3.42, but the viscosity and, therefore, the molecular weight decreased, Table 3.43. Under the investigated conditions, the destruction limit corresponds to a molecular weight of about Table 3.42. Molar extinction coefficients of deoxyribonucleic acid after ultrasonic treatment [380] Raw material used for deoxyribonucleic acid extraction Lamb timus Herring soft roe Wheat seeds

ε(P)250

Solution pH Initial Final

Initial

Final

5.62 6.06 5.90

7 700 7 500 7 300

7 800 7 620 7 400

338

5.00 5.50 5.46

Mechanochemistry of Polymer Fracture Table 3.43. Molar characteristics of deoxyribonucleic acid, 0.2 M NaCl after ultrasonic irradiation [380] Ultrasound treatment time (min) 0 1 5 20 60

Molecular weight

Sedimentation rate S0w20

7 400 000 3 400 000 700 000 450 000 300 000

22.0 12.2 9.0 7.75 6.9

Intrinsic viscosity [η] 69.0 37.3 5.35 3.12 1.77

Figure 3.122. Localisation of the isolated centres of interruption [387].

300 000 g/mole. As Figure 3.122 shows, the fragmentation of ADN chains occur by isolate interruption in different points of the double helix. It was calculated that for initial M 0 = 5 ⋅ 106 until about 500 of such interruptions might appear. It seems that bonds splitting takes place at the same points of the two filaments. The most important feature of nucleic acids destruction under the action of ultrasound in an inert medium (nitrogen) is related to the appearance of fragments keeping the native structure, i.e. the hydrogen bonds, of the initial polymer. However, these fragments have high enough molecular weight, M ∞ , to be able to conserve the biological functions [380, 388].

339

Macromolecular Mechanochemistry

3.6.2. Modification of the relation between supramolecular-morphological structure and polymer properties 3.6.2.1. Modification of the polydispersity–properties relationship The change of polymer polydispersity by mechanodegradation is the first problem that must be approached in relation to the supramolecular level. Molecular inhomogeneity is typical for technical polymers and is very small in the case of the natural ones. The data concerning the influence of M0 on mechanodegradation proved in fact the selective character of this process. In the polydisperse systems, under the action of mechanical energy, the macromolecules with the highest molecular weight are preferentially broken. The short fragments are continuousl accumulated due to the splitting of the higher ones. Theoretically, the system must be monodisperse to the destruction limit. In reality, only a severe narrowing of the molecular weight distribution is recorded and, consequently, the destruction limit still remains an average value, M ∞ . The direction of polydispersity variation during the mechanodegradation process is important from both the theoretical and practical point of view. Currently, the mechanodegradation processes are evaluated by measuring the average molecular weight, very often expressed as viscosimetric or numeric average molecular weight. Alternatively, the measurement of the rate of free radicals generation might be used. The above-mentioned methods are not always sufficient to define the reaction mechanism and the final properties of the stressed polymer. The concrete and complete settlement of this problem requires knowing the change of the whole range of molecular weight variation. There are cases, such as those of polymer processing by mastication, two-roll mixing, compression, injection, extrusion, etc, when the shear rates vary in a very wide range, starting from 1 s –1 to the values higher than 10 –3 s –1 . This fact has as its result the release of some competitive reactions, for instance, mechanodegradation and mechanoreticulation. In such cases, the changes that occur in the chain length distribution allow a clear delimitation of the possible reactions and the separation of the unexpected transformations by the selective ones [389, 390]. In addition, the exploitation properties of polymers depend strongly on the molecular weight distribution. It is well known that in order to achieve superior mechanical properties, a narrow distribution of the molecular weight is required [391]. 340

Mechanochemistry of Polymer Fracture

The systematic investigation of polymer mechanodegradation justified the assumption that this process does not take place randomly. The splitting occurs in the macromolecules that are able to concentrate the applied stress having the length greater than a minimal value which was defined as ‘the critical’ length [216, 392, 393]. The preferential splitting of the longer macromolecular chains resulted from theoretical treatment by F. Bueche [278] and was confirmed by the experimental results of D.J. Angier, W.L. Chambers and W.F. Watson [394], D.J. Harmon and H.L. Jacobs [395, 396] and K. Baranwal and co-workers [132]. The study of MWD modification caused by mechanochemical reactions is ideally carried out on ‘chemically pure’ polymers, characterised by high values of molecular weight, regular chemical structure and nonpolar linear chains which do not have the reticulation ability and are in the amorphous state. For this purpose, the most convenient method of mechanochemical degradation is by far the shearing of homogeneous polymer solutions (flowing through a capillary, high speed stirring, laminated flow, ultrasonic irradiation, etc) using diluted solutions. In the literature, there are many systematic studies, accurately realised, which allow the formulation of some conclusions concerning the polydispersity modification as well as the correlation of the obtained data with the mechanism of the mechanochemical reaction [216, 278, 389–393, 397–399]. A.M. Kotliar applied the Monte-Carlo simulation and calculated the changes of MDW for the polymers with a Schultz–Zimm distribution of the molecular weight. The author considered both the chains splitting case and the chain splitting followed by cross-linking [400–404]. He concluded that irrespective of the initial width of MWD, finally M w / M n → 2 , Figure 3.123 [404]. This result is in accordance with other ones published on this topic [405]. G. Gooberman assumed that the dimensions of the mechanochemical destruction fragments are determined by the force distribution along the macromolecular chain. This one depends on the chain orientation with respect to the direction of force action and the chemical bond that will be split is just that one for which the energy concentration is maximal and overtakes the bonding energy [216]. If it is admitted that mechanical vibration propagates from the chain end toward its centre, the force that subsequently stresses the chemical bond increases to attain the maximum on the first bond located in the plane, perpendicular to the direction of force action, containing the weight-centre of the chain. The value of this maximum depends on the number of 341

Macromolecular Mechanochemistry

Figure 3.123. Effect of scissions per molecule on MWD for three initial MWDs [404].

structural units between the chain extremity and the bond that will be split. After this point, the mechanical force decreases following a pseudo-sinusoidal variation with maximal and minimal values. However, the values of the maxima are always lower than the developed force in the proximity of the weight centre of the chain and, consequently, lower than the force required for chemical bond splitting. F. Bueche also demonstrated the sinusoidal propagation of mechanical vibration [279]. Working on elastomer mastication, the author considered that a macromolecular chain, from a viscous matrix, subjected to the force action is stretched alongside of its axis O–O′, with contraction in the direction I–I′, Figure 3.124. Consequently, the chain accomplishes molecular rotation with the frequency equal to half of the shear force. Because any rotation involves stretching and contraction, the net result is the sinusoidal oscillation. However, having the coiled shape, the macromolecules are not free to effectuate these rotations under the force action. According to this model, the maximal stress is attained to the central bonds from both sides of the chain. Its value is related to the viscosity and shear rate, and is obtained as a function of chain length (molecular weight). For the most general case, Bueche derived the following expression for the ratio between the number of split chains to the q-th bonds from the centre, and the number of scissions to the central bond [278]:

342

Mechanochemistry of Polymer Fracture

Figure 3.124. (a) Shear stress on coiled molecule and (b) stress analysis on coiled molecule.

{b

ge

exp − F0δ / KT / 4q 2 / n 2

j}

(3.105)

where: F – the force acting on the bond; δ – distance through which the bond will be stretched before splitting; n – number of bonds per chain. When F 0 δ/KT = 20 (usually it takes values from 10 to 20) ten bonds are split at the middle of each chain that breaks one third of the way out from the splitting centre. This theory predicts that the splitting rate is a sensitively varying function of the molecular weight, being high for the high molecular weight and greatly reduced for the low ones. Due to its applicability, Bueche’s theory was extended to the polymer solutions and melts mechanodegradation [278]. A comparative study of several fractions of natural rubber, which was processed either by different mechanochemical methods (high speed stirring, mastication, vibratory milling) or by X-ray irradiation proved the arbitrary nature of degradation in the last case and high selectivity of mechanodegradation, Figure 3.125. Using the model of high-speed stirring, it was demonstrated that the mechanochemical reaction occurs at a bond located close to the middle of macromolecular chain, Figure 3.126, [406]. Some high values of M w obtained by fractionation were explained by the occurrence of crosslinking reactions [407]. In order to prove that fracture occurs in the proximity of the macromolecule centre, Glinn and van der Hoff developed a math343

Macromolecular Mechanochemistry

Figure 3.125. Change of MWD by mechanodegradation and under the action of X-rays [406]: 1) witness polymer; 2) degraded by high-speed stirring; 3) degraded by mastication; 4) degraded under the action of X-rays.

Figure 3.126. MWD variation with progress of mechanodegradation by high-speed stirring at 30–50 °C [406]: 1) 120 min; 2) 25 min; 3) 12 min; 4) reference sample.

ematical model. The authors followed the polydispersity variation with time during mechanodegradation of polystyrene solutions under the action of ultrasound at different concentrations. They used samples with initially narrow, broad, and bimodal MWD. The MWD measurements were performed using the GPC technique. It was concluded that the changes do not depend on the experimental con344

Mechanochemistry of Polymer Fracture

ditions, i.e. M0 , concentration, temperature, ultrasound intensity, and degradation rate, which is affected just by the above-mentioned factors. The obtained data are described by a Gaussian curve, centred on the middle bonds of the macromolecules. The end of reactions was followed using a radical acceptor, DPPH [408–410]. Stressing in a Couette viscometer of aqueous solutions of polyacrylamide evidenced that the final molecular distribution is strongly influenced by shear intensity, Figure 3.127a. At high shear forces a peak appeared, corresponding to very low molecular weights, Figure 3.127b [411]. The area corresponding to this peak is about 1/ 3 of the whole area. In the case of PVC and thermoplastic butadiene–styrene rubber, the broad distribution was associated with the presence of some fractions with high molecular weight, most likely generated by reticulation [277, 412, 413]. Accepting that in the given conditions mechanodegradation occurs until to the destruction limit, M ∞ , and that the scission takes preferentially place in the middle of the chain, the obtained molecular weights, from different fractions, cover the range delimited by M ∞ / 2 and M ∞ [140, 277, 278, 393, 414, 415].

PLEASE SEND ORIGINAL OF THIS FIGURE WE DO NOT HAVE IT

Figure 3.127. (a) Degradation of polyacrylamide at 0.7% aqueous solution at 20 °C, effect of shear on MWD [411]: Run 28, 2.15×10 –4 s –1 , 3.24×10 4 dyn/cm 2 ; Run 32, 11.5×10 –4 s –1 , 5.75×10 4 dyn/cm 2 and (b) polyacrylamide bimodal degradation products shown by GPS. 345

Macromolecular Mechanochemistry

Figure 3.128. Changes during processing of high-density polyethylene. MWD curves as a function of degree of mixing: 0) base resin; 1) extrudate 1; 2) extrudate 2; 3) extrudate 3 [416].

The crosslinking effect was also evidenced studying the modification of the MWD curve in the case of high density polyethylene on a Brabender plastograph, Figure 3.128. R.S. Porter and J.F. Johnson and co-workers studied the modification of MWD on polymer solutions and melts under shearing conditions [163, 164, 211, 214, 252, 272, 273, 389, 390, 397]. Thus, solutions of polymers with narrow or broad distributions, especially polyisobutene, and polystyrene, which were subjected to degradation under the shear forces or ultrasound action, and polymer melts forced to flow by capillaries, were investigated. Whether by thermal degradation these polymers give rise to important quantities of monomer, in the case of mechanodegradation the monomer does not appear even as traces. As already mentioned, mechanodegradation occurs with a negative coefficient of temperature and, by elution chromatography and GPC, it was found that the obtained curves are independent of the initial ones. The results were differently interpreted for diluted solutions and for concentrated ones or melts, respectively. In the first case, it was accepted that the individual macromolecules do not have the capacity of storing the shear energy on the individual bonds and, consequently, these ones are not split but only deformed. The deformation mechanisms depends on the time scale, temperature, and probability of sliding and coiling of macromolecules. In the case of concentrated solutions and melts the concentration of mechanical energy occurs with higher efficiency at the level of intra- and intercatenary ‘network’ of coils. In this case, the affected bonds are located in the centre of the chain, in the 346

Mechanochemistry of Polymer Fracture

proximity of coils coupling, or at the middle of the distance between two adjacent coils. Under the conditions of intensive shearing, a second peak was found, corresponding to low values of MDW. The results obtained in the case of polyizobutene solutions in two different solvents are presented in Figure 3.129 [389]. For high-molecular weight polyisobutene it was found that for any stage of the mechanodegradation process the polymolecularity index M w / M n remains constant and corresponds to random splitting of the chains, Figures 3.130 and 3.131. In the case of solid-state polymer mechanodegradation, by vibratory milling, the majority of authors found distributions that justify the selective character of this process [231, 329, 418]. For instance, cellulose triacetate fractionation is described by the curves in Figure 3.132, those for gelatine and poly(vinyl alcohol) are presented in Figure 3.133. The molecular inhomogeneity, which is characteristic of polymers and the modification of MDW, in conditions of mechanical stress applied to their solutions and melts, has a peculiar practical importance. The polymers in the rubbery state at normal temperature do not suffer any degradation. This behaviour arises just from the definition of the viscoelastic state, i.e. the modality of chains

Figure 3.129. Mechanochemistry of polyisobutylene solutions [389]: (a) original polymer; (b) sheared in 1,2,4-trichlorobenzene; (c) sheared in n-hexadecane. GPC shows bimodal distribution produced in two different solvents. 347

Macromolecular Mechanochemistry

Figure 3.130. Ultrasonic irradiation of a concentrated polyisobutylene solution [417]: initial M w /M n = 2. Relative changes of M w and M n are compared with theoretical behaviour for random scission of a most probable MWD.

Figure 3.131. Relative changes in weight and number average molecular weights for random scission of polymers with a Schultz–Zimm molecular weight distribution at six values for initial heterogeneity [417].

displacement as independent kinetic units. Under the action of shear forces, the modification of the flowing or rheological properties is recorded. Frequently, in the case of viscosity determination with capillary viscometers a viscosity decrease, accompanied by an increase of shear force, was found. A non-linear relation was established between the shear force and the shear rate. Based 348

Mechanochemistry of Polymer Fracture

Figure 3.132. Modification of cellulose triacetate MWD in time by vibratory milling [329]: 1) original polymer; 2) 14 hr; 3) 25 hr; 4) 75 h.

Figure 3.133. Integral curves of MWD for gelatine supposed to vibratory milling (full lines) and poly(vinyl alcohol) (dotted lines) [116]: 1, 2) original polymers; 3, 4) degraded polymers.

on this relation, polymer melts and polymer solutions are defined as non-Newtonian liquids [419–429]. Starting from relatively low shear rates of about 100 s –1 , a series of specific effects, such as macromolecule orientation and deformation in the direction of forces, were observed. Both of them are directly dependent on both chain flexibility and changes of intermolecular interactions. Viscosity decreases with an increase of the rate gradient. It was proved, on the example of cellulose nitrate solutions, that the deviation from the Newtonian flow is mainly caused by the modification of intermolecular interactions and not by the orientation and deformation effects [430]. By continuing to increase the shear rate the viscosity decays, reaching values even 10 000 times lower as compared with the initial one [431]. The dilution of polymer solutions does not eliminate this effect since the orientation and deformation effects are not influenced by concen349

Macromolecular Mechanochemistry

tration [432]. Two are the causes that explain the viscosity decay, namely: 1) macromolecules release by reciprocal interactions; and 2) splitting of the longer chains from the polydisperse polymers. As shown in Figure 3.134, the macromolecules with higher molecular weight suffer the most intense degradation. The results refer to anionically synthesised polyisoprene with M w = 450,000 . Using destructive methods, this polymer was separated into fractions with different molecular weights, which were subjected to shearing in a Ostwald–Fenske viscometer, working in the range of shear rate from 1 000 to 10 000 s –1 [428]. In the case of polymer melts, the shear-force and rate affect, in the first place, and the the average molecular weight and MWD, both of them controlling the rheological properties. The effect of polydispersity on the rate and destruction limit is illustrated in Figure 3.135. The fraction with the widest dispersity induces the highest number of scissions, curve 1 in Figure 3.135. In all cases, the narrowest polydispersity corresponds to the destruction limit. Over a wide range the three curves are close to each other and sometime overlap. For an initial narrow polydispersity the number of split bonds with time is insignificant (curve 3 in Figure 3.135). As expected, mechanodegradation occurred with the highest velocity for the polymers with a wide molecular weight distribution (curves 1 and 2 in Figure 3.135), [401]. 3.6.2.2. Modification of the relation supramolecular-morphological structure – properties

Figure 1.134. Variation of intrinsic viscosity with shear rate for polyisoprene with various molecular weights [401]: 1) 2.80.106; 2) 2.35.106; 1) 1.80.106. 350

Mechanochemistry of Polymer Fracture

Figure 3.135. Influence of polydispersity on the number of broken bonds by mechanodegradation [401]: 1) polyisoprene; 2) polybutadiene, 93% cis-form; 3) polybutadiene, 40% cis-form.

The investigation of the transformations that occur on the supramolecular–morphological level during mechanical stressing led to relevant results in the case of highly oriented, crystalline, and with a rigorously determined morphology. Since fracture is local, the crystalline level may be considered as optimal one for illustrating the phenomena that occur on this level during the mechanocracking process. Thus, the linear and crystalline polyethylene, subjected to the effect of fluctuating shock forces at the temperature of liquid nitrogen, and characterised by TEM method, offer direct images concerning the relation between the transformations to the level of crystalline lamellae and the relief of the new generated surfaces, Figure 3.136 [432]. It can be seen that, under the given conditions, fracture is brittle and propagates alongside the crystallographic surfaces. Mechanical loading of some individual microdomains results in their plastic sliding and the displacement of lamellar crystals. Consequently, longer fibrilar formations appear and, on their level, one can see small spheres or irregular nodes connected together by short threads. Similar changes at the supramolecular structure level have also been observed during PE thermal degradation at a temperature in close to the melting point [418], or during its dissolution [434]. The microrelief, depicted in Figure 3.137, illustrates the initial stage of the deformation process of the lamellar crystals 351

Macromolecular Mechanochemistry

Figure 3.136. Electron micrographs of the lamellar–stratified structure of polyethylene [432]: (a) initial polyethylene, ×16,500; (b) fractured polyethylene, ×30,000.

from superficial layers. The thick fibrilar formations represent, in fact, lamellar crystals ‘crushed’ under the action of shock forces. This prepares the next stage of their fracture in spherical formations. When fracture is the only transformation that occurs in the system, the microrelief of the formed surfaces consists only of spherical elements, representing fragments of oriented ‘fibrils’, oriented in the normal direction to the surface, Figure 3.138. The crystalline character of the microrelief is maintained whether the trajectory of crack propagation coincides or at least passes in the proximity of the crystallographic plane of the lamellar stratified elements. If this condition is fulfilled, the crystal displacement is energetically favoured and its propagation occurs by cleavage. The microcracks appear before breaking of the surrounding material in its viscous state and which continues to be plastically deformed for a period. Some local overheating appears along with the transformations occurring under the action of mechanical energy in the conditions of brittle fracture and contributes to the modification of the supramolecular structure and fracture microrelief [433]. The change of the supramolecular structure from globular to fibrillar one was observed in the case of two-roll processing of PVC [434]. Poly(vinyl chloride)-emulsion, PVC-E, was subjected to mechanical stress, using either the usually applied technique on the industrial scale or it was stretched in a single direction by removing the PVC sheet after a half of roll rotation and its reintroduction several times, keeping the orientation. Using electron microscopy, the gradual destruction of globules and their transformation in fibrils was proved. The above mentioned phenomenon is influenced by the applied mixing technique, the transformation being more evident when the second mixing method was applied. As Figure 352

Mechanochemistry of Polymer Fracture

Figure 3.137. Electron fractography of the deformed superficial layer of a polyethylene sample evidencing "globular" formations of the fracture surface relief [432]. Figure 3.138. (right) Electron fractography showing the traces of displacement during the apparition of fibrous formations and element of viscous fracture at polyethylene fracture, ×22,500 [432].

3.139 shows, the mixing duration and temperature plays an important role in this transformation. Using X-ray diffraction technique, the anisotropic character of the obtained microfibrils was evidenced. Such kind of changes can also occur in other types of mechanical stressing, such us extrusion, casting, and moulding [434]. When the mechanical forces are not high enough to cause final fracture of the crystalline lattice, some deformation can be induced to modify the distance between the crystalline planes. Thus, polyamide 6 was compressed at a pressure of 5600, 10000, and 22000 atm, respectively. After removing the pressure, the relaxation process was accompanied by significant changes in the polymer fine structure [435–437]. The presence of crystalline and amorphous zones, with different degrees of chain orientation, determines the anisotropy of mechanical properties, for instance of compression coefficients. For this reason, the increase of pressure is followed by non-uniform relaxation of the tension. As shown in Figure 3.140, the distances between the crystalline planes, retained in shape both by hydrogen bonds (020) and van der Waals interactions (200) 353

Macromolecular Mechanochemistry

decrease [437]. The same effect is achieved by increase of the applied stress. As expected, a temperature increase from 20 to 190 °C has no significant effect on the distance between the crys-

Figure 3.139. Change of globular structure into fibrilar formations during roll milling of PVC-E: 1) fracture of a particle; 2) fragment from a roll milled PVC film at 100 °C, 0.5 min; 3) idem, 2 min; 4) idem, 105 °C, 5 min; 5, 6) idem with 2 but subsequent masticated at 110 °C, 10 min; 7–12) roll-milled films in accordance with technique 2 at 120 °C; 13) using technique 2 as in (4), 5 min; 14, 15) fragments close by film surface (parallel chipping with surface plane) [434]. 354

Mechanochemistry of Polymer Fracture

Figure 3.140. Polyamide-6 roëngenogram after compressing [437]: 1) p = 22 000 kgf/cm 2 , t = 60 min, T = 230 o C; 2) p = 5,600 kgf/cm 2 , t = 60 min, T = 20 o C. Cooling 1.5 K/min.

talline planes. Polymer compression at 230 °C and 260 °C determines the decrease of the distance between the planes (200) and the detachement of the planes retained by hydrogen bonds (020), Figure 3.141. X-ray diffraction patterns show additional crystallisation in the amorphous zones, mainly in the plane of weaker van der Waals bonds. The breaking of hydrogen bonds must be correlated with irreversible deformation which affects the periodicity of the crystalline lattice and finally destroys the crystalline element [438]. When the stress reach critical values, the loss of lattice stability occurs, followed by its internal reorganisation and accompanied by some effects of orientation. A sliding effect appears along the plane (020), favouring stress relaxation in this direction and bending of the plane (200). Subsequently, the stress action on the crystalline planes increases, causing high deformation in the plane (020) that determine the faults appearance and fracture initiation [438]. In intensive mechanodegradation conditions, for instance in vibratory milling, the more rigid crystalline entities are destroyed and the amorphous/crystalline ratio increases. This effect was found for many semicrystalline polymers, such as aliphatic polyamides [83], and different types of cellulose and their derivatives [130, 232, 439]. Cellulose amorphisation is achieved due to the cancellation of a 355

Macromolecular Mechanochemistry

Figure 3.141. Change of distances between the crystalline planes (200) and (020) with temperature [441]: 1) p = 5600 kgf/cm 2 , t = 60 min; 2) p = 22000 kgf/cm 2 , t = 60 min, after removing of pressure; 3) p = 5600 kgf/cm 2 keeping the sample 30 days at 20 °C; 4) p = 22000 kgf/cm 2 keeping the sample 30 days at 20 °C.

great number of hydrogen bonds. Consequently, the corresponding number of hydroxy bonds is released and they contribute to the increase of material's hydrophylic nature, Figure 3.142, [439]. The X-ray diffraction data indicate that after milling all the cellulosic materials are completely amorphous. It was found that after holding them in water for 30 min at 20°C, a recrystallisation process occurs. If the initial samples were characterised by a typical X-ray

Figure 3.142. Water absorption by the celluloses processed by vibratory milling [439]: 1) sulphite cellulose; 2) bisulphite cellulose; 3) kraft cellulose (1–3 dried medium); 4) sulphite cellulose; 5) kraft cellulose (4, 5 wet medium). 356

Mechanochemistry of Polymer Fracture

diffraction pattern as the cellulose of type I, after this treatment the recordings correspond to the type II cellulose [440]. The same phenomenon was found by N.K. Baramboin in the case of cheratin samples, processed by vibratory milling [113]. Changes occurring under the action of mechanical energy at the molecular and supramolecular level (crystalline and amorphous) are also reflected on the morphological level, having as the main effect the appearance of new surfaces. The changes are more pronounced for rigid polymers, both for highly crystalline or amorphous ones. In the case of fibrous materials these changes can be even visualised. For instance, the fibrous character disappears as a result of vibratory milling, being gradually replaced with that of highly dispersed powders [116, 131, 230]. In the case of rigid polymers, mechanodispersion occurs up to the geometrical limit of the produced particles, usually in the range from 1 to 3 µm. Below this limit, the dispersion degree remains practically unchanged, but the molecular weight continues to decrease until the destruction limit is reached. Mechanodispersion is affected by the same factors as those affecting mechanodegradation, i.e. polymer chemical structure, its physical and aggregation state, mechanical regime, temperature, nature of the reaction medium, etc. The variation of the specific surface area is a suitable criterion for the quantitative characterisation of this process. It was found that for a processing period of 100 hrs, in air, the specific surface area of silk fibres increases from 0.15 to 1.57 m 2 /g and for the collagen fibres from 0.59 to 1.96 m 2 /g. The difference found between changes of the specific surface area of the two processed polymers are related to the molecular packing degree. In the case of polystyrene and quartz, after vibratory milling, in argon, at –196 °C the final specific surface was equal to 3 m 2 /g and 7 m 2 /g, respectively. Under the conditions of vibratory milling, a peculiar behaviour was found for a series of highly-orientated polymers, such as polyamides, poly(acrylonitrile) and poly(ethylene terephthalate). In all cases the specific surface area changed due to milling. Its direction of variation and final values strongly depend on temperature. During vibratory milling, the largest part of energy is converted to heat and locally it can exceed by 1000 times the target temperature. It was established that without cooling the process is affected by temperature even in its first moments. In the case of poly(ethylene terephthalate) in the first stages of processing, a 357

Macromolecular Mechanochemistry

slightly increase of the specific surface area was observed; the maximum is attained after 60 s, after that the curve which describes the variation of specific surface area in time shows a descending part. In the first moments, before the appearance of local overheating, fibres fracture leading to the observed increase of the specific surface area. When the maximum is reached, overheating becomes more and more intense, and locally the temperature can be higher than the polymer meting point, causing particle agglomeration and a continuous decrease of the specific surface area. In the case of polyamide, the specific surface area remains at approximately constant values until about 120 s of processing and after that continuously decreases, Figure 3.143 (curves 1 and 2). Mechanodispersion at low temperatures, –60 °C, determines an increase of chain rigidity and, in all cases, the increase of the specific surface area was achieved (curves 4 and 5 in Figure 3.143). The most intense variation was recorded in the case of polyacrylonitrile. The mentioned differences between polyamide and PET behaviour have been explained by different numbers of structural micro- and macrofaults of the two polymers [88]. Changes of the granular structure and the characteristics of the powders of vitreous polymers have been investigated on the

Figure 3.143. Change of specific surface area during mechano-dispersion process for different fibrous polymers [88]: 1) polyamide, without cooling; 2) poly(ethylene terephthalate), without cooling; 3) polyacrylonitrile; 4) polyamide, with cooling; 5) poly(ethylene terephthalate), with cooling; 6) polyacrylonitrile, with cooling. 358

Mechanochemistry of Polymer Fracture

PVC-S model. As obtained by synthesis, PVC-S powders are characterised by a broad particle size distribution and this fact determines the non-uniformity of the most important polymer properties [273]. The mechanodispersion carried out under mild conditions, i.e. by vibratory milling and ultrasound treatment of aqueous dispersions of PVC-S, was found to be an efficient way for reducing the particle size and increasing the size distribution uniformity and, therefore, improving the tensile properties. The aqueous dispersions of PVC-S were subjected to the action of ultrasounds waves for periods ranging from 1 to 120 hrs. It was found that the optimum duration, which corresponds to the narrowest particle size distribution, is about 60 hrs (curve 4 in Figure 3.144). At longer times, especially in the range from 90 to 120 hrs, the particle size distribution increases and the curves maximum is shifted toward higher values (curves 5 and 6 in Figure 3.144). The initial PVC powder (curve 1 in Figure3.143) remained most polydisperse, in spite of particle reagglomeration. Similar results were obtained in the case of mechanodispersion by vibratory milling. In accordance with the changes of the particle size distribution, changes of the surface and volume properties such as: porosity, specific surface area, plasticizer absorption, apparent density, etc. were observed. Changes in the physical structure of PVC-S under

Figure 3.144. Influence of ultrasonic irradiation duration of PVC-S aqueous solutions on the particle size distribution [237]: 1) initial particles; 2) 30 hr; 3) 40 hr; 4) 60 hr; 5) 90 hr; 6) 120 hr. 359

Macromolecular Mechanochemistry

Figure 3.145. Correlation between mechanodispersion, mechanodegradation and some superficial and volume properties of PVC-S [357] in a dried inert medium (a) and as methanolic solutions (b): 1) M ; 2) D n ; 3) porosity; 4) specific surface area; 5) plasticizer sorption (W).

the conditions of controlled mechanodegradation resulted from vibratory milling and ultrasonic treatment. In the case of vibratory milling, the experiments were carried out in a dry inert atmosphere, purified nitrogen as well as in methanolic dispersions with other conditions being similar. Comparative results are presented in Figure 3.145 a and b. In an inert medium, the porosity practically remains constant but in the presence of methanol a sharp increase of this property occurs after 15 min of milling. Porosity gradually increases passing through a maximum and after that slightly decreases with increasing milling time. In the first stage with increasing branch, the liquid exerts a pressure on the particle microcavities, Figure 3.146, and on the intergranular spaces, Figure 3.147, with the last ones being irreversibly expanded. On the decreasing branch, corresponding to high processing times, the dispersion effect prevails, mainly occurring to the particles that are delimited by intergranularly spaces, characterised by lesser dense packing degree (Figure 3.147). The data concerning the plasticizer absorption are in good agreement with the above mentioned results, i.e. porosity’s small variation for the milled powders in an inert atmosphere (curve 5 in Figure 3.145 a) and much more pronounced in the presence of methanol (curve 5 in Figure 3. 145 b). In addition, the variation of the specific surface area, ∆S%, is in good accordance with the above mentioned results (curve 4 Figure 3.145 a and b), [387]. Changes of the specific surface area were studied in the conditions of mechanodispersion and mechanodegradation of two sorts of PVC, namely OLTVIL–10 and Diamond–450. The samples, as 360

Mechanochemistry of Polymer Fracture

Figure 3.146. SEM micrograph of a PVC-S granule, ×1000 [442]. Figure 3.147. (right) Agglomerate of primary granules of PVC-S [442]: 1) microcavity within primary granule; 2) intergranular space with dense package; 3) intergranular space with sparse package; 4) primary granule.

aqueous dispersions, were subjected to the action of ultrasound. As shown in Figure 3.148 (curves 1 and 2), the variation of the particle number is the same for the unit surface. In the case of OLTVIT–70, at least 50% of them are small ones, having approximately the same dimensions which correspond to the recorded maximum at 0.01 m 2 (curve 1 in Figure 3.148). Diamond–450 powders are characterised by a broader distribution and the maximum was attained at a lower value of the particle number, curve 1 in Figure 3.148. Under the action of ultrasound, the changes of the same nature were found for the two investigated powders (curves 3 and 4 in Figure 3.148), i.e. the fraction of particles with the smaller specific surface area takes place in the proximity of the observed maximum. Thus, in the case of OLTVIT–70 the specific surface decreases from 0.01–0.04 mm 2 to 0.008–0.02 mm 2 . For Diamond450 the maximum that defines the smallest particles is attained in the vicinity of 60% and the specific surface decreases from 0.01– 0.03 mm 2 to 0.01–0.004 mm 2 . The dispersion phenomenon was also confirmed using optical microscopy. As Figure 3.149 shows, under an inert atmosphere, in the first hours of processing the agglomeration of particles (Figure 3.149 b and c) occurs and only in a small measure the dispersion tendency is observed (Figure 3.149 c). The same behaviour was observed in the presence of methanol, Figure 3.150 a and b, where this behaviour was more clearly evidenced in the case powders with a higher particle size (Diamond-450). In the liquid medium, dispersion is faster that in the gaseous one, since in the first case the 361

Macromolecular Mechanochemistry

Figure 3.148. Differential curves of particles specific surface distribution of two types of PVC-S (OLTVIL-70 and Diamond-450, respectively) [357]: 1) untreated OLTVIL-70; 2) untreated Diamond-450; 3) aqueous suspension of OLTVIL-70 ultrasound irradiated for 1 hr; 4) aqueous suspension of Diamond-450 ultrasound irradiated for 3 hr.

Figure 3.149. Influence of mechanodispersion by vibratory milling of PVC-S (OLTVIL-70) on polymer morphology [357]: (a) initial particles; (b) milled for 15 min in dried inert medium; (c) milled 1 h in dried inert atmosphere.

small particles prevails from the first hours of milling, as seen in Figure 3.150 b. Microscopic examination of some samples, stressed by vibratory milling and ultrasonic treatment, and moistened with a plasticizer (dioctylphtalate) showed important changes in the morphology of the granules. Once again, for both OLTVIT-70 and Diamond-450 the changes were similar, i.e. the modification of granulites or of their aggregates surface, which is protected by a pericellular membrane of the suspension stabiliser. When the samples are maintained in a plasticizer for a long time, for instance 1 hrs, their swelling occurs. In the investigated conditions, the samples ultrasonated as dispersions are only slightly affected by ultrasound, irrespective of the nature of liquid (water or methanol) or 362

Mechanochemistry of Polymer Fracture

Figure 3.150. Influence of mechano-dispersion by vibratory milling of PVC-S (OLTVIL-70) as dispersion in methanol on polymer morphology [357]: (a) 15 min in dried inert atmosphere; (b) 1 h as dispersion in methanol under inert atmosphere.

ultrasonation time [357]. In conclusion, a careful control of the mechanodispersion of the polymer particles allows the modification of the surface and volume properties of the stressed polymer. These characteristics can be modified in such a way as to improve some polymer properties, like plasticizer absorption. Mechanical destruction by vibratory milling in a dry medium is always more intense that the one occurring in liquid media and the particles from the powders obtained by concomitant mechanodispersion have a reagglomeration tendency, due to the pronounced electrostatic effects In liquid media, in both cases, the molecular weight decay is diminished in the presence of the liquid, mainly due to the dispersion of mechanical energy. In these conditions, the liquid continuously moistens the new generated surfaces, preventing, in a certain measure, particle agglomeration. The mechanism of particle fracture is practically similar to that in the dry medium but is a little more complicated, due to the presence of the solvent. Comparing the two methods of mechanodispersion, i.e. vibratory milling and ultrasonation, used for polymer dispersion in liquid media, it was established that in the first case the pericellular membrane was completely destroyed and the dispersing effect was higher as compared with the second case when the membrane was only slightly affected. By dissolution of PVC-S in a suitable liquid, the protective pericellular membrane disappears. If ultrasonic treatment is applied together with the addition of a non-solvent, the size of precipitated PVC particles is tuned by the action of mechanical energy. The ‘granulites’ have a smaller average particle size and the size distribution is more uniform than those obtained by mechanodegradation of the witness PVC-S particles. As a result of me363

Macromolecular Mechanochemistry

chanical processing of the powders in the dry state or even as dispersions in liquid media, their superficial morphology of granulites and of granulitic agglomerates is strongly modified. Apart from them, during ultrasonation, particle agglomeration in liquid media is accompanied by important changes of internal morphology. The relation between the effect of mechanodegradation, reflected in the particle size distribution, Figure 3.144, and the changes of the internal and external morphology of the polymer particles can be investigated by the swelling method. Unfractionated PVC-S was chosen for studying the influence of the ultrasonation period on the swelling kinetics. A considerable increase of the swelling degree and rate with the treatment period was found (curves 2 and 3 in Figure 3.151). The changes induced on the morphological level are reflected in the modification of mechanical properties. Thus, it was proved that the real tensile strength of PVC-S is lower than that theoretically predicted, due to the existence of faults, which are distributed to the all hierarchical levels [27, 443–461]. During polymer processing and exploitation, the absorbed mechanical energy is concentrated on the faults or inhomogenities that are statistically distributed on the molecular, supramolecular– morphological, or compositional level; this fact affects material durability and its mechanical resistance. On the other side, it is clear that the amelioration of some faults, on the structural or compositional level, represents a way of increasing the material durability. In the case of PVC-S powders, the particle size distribution, Figure 3.152, was correlated with some surface and volume properties and, subsequently, with tensile strength, which was taken as

Figure 3.151. Variation of PVC-S swelling degree with ultrasonic irradiation duration [236]: 1) witness; 20 hr; 40 hr. 364

Mechanochemistry of Polymer Fracture Table 3.44. Variation of PVC-S physico-mechanical characteristics with particles size homogeneity PVC-S

Tensile strength, σr ( kgf/cm2 )

Strain, ε (%)

183.66 186.92 193.24

509 498 504

Virgin (broad size distribution) Fraction with φ = 100 µm Fraction with φ < 45 µm

Table 3.45. Effect of average particle size on some physical characteristics of PVC-S Temperature Density Fractions b −1 distribution Apparent Bulka of plasticizer M × 10 Sample [η] sorption Settled Unsettled ( °C ) (%) ( g/cm3) PVC-S, K = 70 unsieved Fractions: 250 µm 200 µm 160 µm 125 µm 80 µm 40 µm < 40 µm

5.5 11.0 21.3 30.1 22.2 9.37 0.17

1.05

5.497

0.425

0.540

1.341

100…114

1.02 1.06 1.06 1.07 1.08 1.08 1.11

4.947 5.259 5.259 5.337 5.417 5.417 5.658

0.267 0.367 0.381 0.425 0.445 0.526 -

0.350 0.450 0.460 0.512 0.539 0.621 -

1.377 1.369 1.365 1.355 1.344 1.330 1.323

90…107 92…107 100…110 103…112 104…113

a

– Pycnometric method in a mixture carbon tetrachloride – toluene; b – Dioctyl phthalate.

an evaluation criterion of the polymer mechanical properties, (Tables 3.44 and 3.45) [310]. The influence of the particle size distribution on the tensile strength was established by measuring the tensile strength for two PVC-S fractions with φ = 100 µm and φ ≤ 45 µm, respectively, which were separated by sieving from the initial powder. It was found that the original PVC-S is characterised by the lowest tensile strength, the highest value being recorded for the finest fraction (Table 3.44). The tensile strength is not affected by the particle size distribution. The same results were found after particle ultrasonation. However, the tensile strength of the samples subjected to the action of ultrasound at different periods of time decreases more rapidly for the virgin PVC-S (curve 1 in Figure 3.153), followed by the sample having the average particle size of 100 µm (curve 3 in Figure 3.153), and the fraction with the smallest particle size (curve 2 in Figure 3.153), which showed the highest 365

Macromolecular Mechanochemistry

Figure 3.152. Variation of PVC-S particle size distribution with ultrasonic irradiation duration [310]: 1) original particles; 2) 3 hrs; 3) 6 hrs; 4) 20 hrs.

stability [340]. The variation of the tensile strength with the ultrasonation time allowed the determination of the optimum time, corresponding to the narrowest particle size distribution, and, consequently, the mechanical properties are improved, Figure 3.154. The virgin PVC-S powders were also subjected to the action of ultrasound, as aqueous dispersions, and in order to prevent particle agglomeration, for long processing periods, a surfactant was introduced into the reaction medium (0.1% wt/wt sodium mersolate). At the end of the process, the homogeneous fractions with the average particle size of 80 and 40 µm were separated by sieving each investigated period. The tensile strength was determined for all samples and its variation with irradiation time was graphically represented. The shape of the resultant curves is the same in all cases. Firstly there is a decreasing branch, AB, after that the minimal value of tensile strength is attained in B, and on the BC segment the resistance increases. The portion CD corresponds to a relatively constant value of σ r , and, finally, on the DE branch the tensile strength decays again. In the first moments of ultrasonation the tensile strength decay is more pronounced for the PVC samples with a broad particle size distribution. In all cases, in the time 366

Mechanochemistry of Polymer Fracture

Figure 3.153. Experimental curves showing the dependence of tensile strength by ultrasonic treatment duration [310]: 1) unsieved PVC-S; 2) fraction with φ = 45 µm; 3) fraction with φ = 80 µm.

Figure 3.154. Variation of tensile strength with ultrasonic irradiation duration [310]: 1) unsieved PVC-S in the presence of 1% sodium mersolate; 2) fraction with φ = 80 µm sieved from ultrasonically treated polymer; and 3) fraction with φ = 80 µm sieved from ultrasonically treated polymer.

range of 10 to 20 hrs the tensile strength sharply increases, due to structure homogenisation on both the granular and molecular level. By virtue of the selective character of mechanodegradation, the macromolecules with the highest molecular weight are continuously broken and, in this way, the polydispersity index decreases. The molecular and dimensional uniformity are the two causes that determine the increase of σ r on the BC segment. The CD portion of the curves is related to granular uniformity which, in accordance to the data concerning the particle size distributions (Figure 3.152) 367

Macromolecular Mechanochemistry

attain its optimal values in this range of processing time, i.e. about 60 hrs of treatment. Fragment DE describes the tensile strength decrease caused by breaking up of the granular structure, as the swelling curves show (curve 1 in Figure 3.151) passing through a maximum after 100 hrs of processing. In the conditions of two-roll mixing where mechanical energy and temperature influence the destructive process, the behaviour of PVC-S is different. The most important factors that influence this process are the following ones: temperature, duration, and reactants ratio (PVC/diamine). In all the investigated cases, a significant increase of tensile strength was achieved, Table 3.46. Mathematical processing of the obtained results allowed the optimisation of the processing conditions in order to obtain the maximum mechanical properties. This set of parameters is given below: Benzidine concentration, (%) 4.2 Temperature, (°C) 170 Time, (min) 15 In the above-mentioned conditions σ r increased by 133.5% in relation to the original PVC. In this case, the nature of the reaction medium is the factor that favours the increase of tensile strength. It was established that in the presence of aromatic diamines the variation of σ r has a specific evolution which essentially depends on diamine concentration, Table 3.46. The influence of two-roll mixing conditions on the tensile strength of PVC-S [308–312] Increase of tensile strength, σr ( % ) for samples with: Processing Parameter Benzidine m-Phenylenep-Phenylenevalue conditions diamine diamine 1% 5% Duration (min) (T = 170 °C; diamine, 1%) Temperature ( °C ) (t = 5 min; diamine, 1%) Diamine concentration ( % ) (T = 170 °C; t = 5 min)

5 10 15 20 30 150 160 170 180 190 1 2 2 4 5

108 112 119 118 112

145 155 152 130 -

108 117 114 106 -

104 116 117 -

103.5 105 108 111 108.5

105 106.5 108 107.5 105

103 103.5 104 103.5 102

108 117 125 138 145

108 112 118 123 -

104 111 116 121 -

368

Mechanochemistry of Polymer Fracture

Figure 3.155, mastication time, Figure 3.156, and temperature, Table 3.46. As Figure 3.155 shows, the tensile strength linearly increases with the increase of diamine concentration. Its dependence on the mixing time is described by a curve that passes through a maximum (Figure 3.156). The presence of the maximum of tensile strength was explained by polymer reticulation with the structural units of diamine. The descending branch was related to polymer mechanodegradation occurring in the range of high processing times

Figure 3.155. Dependence of polymer molecular weight by diamine concentration [301]: (a) 1) PVC-S + benzidine; 2) PVC-S + m-phenylenediamine; (b) PVC-S + p-phenylene-diamine.

Figure 3.156. Variation of average molecular weight with roll-milling duration [ 301 ]: (a) PVC-S + p-phenylenediamine; (b) 1) PVC-S + benzidine; 2) PVC-S + m-phenylenediamine. 369

Macromolecular Mechanochemistry

[311]. In all cases, with the increase of diamine concentration and mixing time up to a specific value of these parameters, the molecular weight decreases, and macromolecule destruction takes place. After that the maximum of destruction is attained, the molecular weight increases, due to the occurrence of crosslinking process, Figures 3.157, and 3.158 [301]. During elastomer stressing, mechanical energy also determines macromolecule fracture, having as the result the generation of new surfaces. Due to the adhesive properties of the polymers in the rubbery state, elastomer fracture is not accompanied by particle dispersion and, therefore, by the increase of the specific surface area. The new generated surfaces have been evidenced by introducing into the system in a controlled manner compounds able of protecting the new surfaces. For instance, the use of talc allows an increase of the rubber specific surface area by dispersion. An intense fracture process occurs when the elastomers are processed below their vitreous temperature. In this case fracture follows the laws of solid bodies and is accompanied by dispersion [462–465]. Below T g , the elastomers containing ingredients (black carbon, chalk, etc) suffer brittle fracture. This fact affects the mechanical properties, especially the adhesive ones, which considerably decrease. In the case of elastomer–chalk mixtures, fracture surfaces characterisation by electron microscopy, below T g , revealed a blurred relief; well delimited surfaces are obtained in the case of elastomer-black coal mixtures when fracture occurred at a temperature of about 20 °C below elastomer’s T g . In the case of butadiene-co-styrene rubber, concomitantly with the decrease of temperature, at the values ranging from –10 to – 20 °C, the mobility of chain segments, which is related to the displacement of aromatic rings, also changes. Consequently, in this temperature range, the rate of fracture rapidly decreases. Electron microscopy was used to characterise the changes occurring to the fracture surface in a wide range of temperature, – 60 to 60 °C, including both the highly elastic and vitreous state of poly(butadiene-co-styrene) copolymer. In this range, temperature strongly influences the nature of fracture microsurfaces. This effect is manifested on the whole surface in both the vitreous and rubbery temperature ranges. In the highly elastic temperature domain ≈40 °C, the surface microrelief is relatively smooth showing by small excrescences and cavities with diameters of up to 0.5 µm. Between them, thin ‘micro370

Mechanochemistry of Polymer Fracture

stems’ of about 30 µm can be seen. They have an irregularly shape and their dimensions are several times larger than the dimensions of black carbon particles (Figure 3.159 a). Figure 3.159 b presents an irregular fracture surface which is less rough than that presented in Figure 3.159 a, with a lower density of excrescences and cavities that alternate with zones of high concentration in short and thickened elements (micro-stems). Figure 3.159 c illustrates a rougher relief, consisting of formations with a longitudinal length of about 1–3 µm and a transverse dimension of 0.5– 1 µm. These formations arose by ‘micro-stems’ packing in those domains where their concentration is high. The three images reflect: a) the initial stage of fracture; b) the central portion of the microsurface; and

Figure 3.157. Effect of dimine concentration on the tensile strength [311]: 1) PVCS + m-phenylenediamine; 2) PVC-S + p-phenylenediamine; 3) PVC-S + benzidine.

Figure 3.158. Influence of the mastication time on the tensile strength [311]: 1) initial PVC-S; 2) PVC-S + benzidine; 3) PVC-S + p-phenylenediamine; 4) PVC-S + m-phenylene-diamine. 371

Macromolecular Mechanochemistry

c) defines the limits of the rough area, at the boundary of the fracture surface. The decrease of temperature, with temperature still remaining in the rubbery range, leads to a decrease of the dimensions of the domains with the rough relief (Figure 3.159a and b) and broadening of more intricate microrelief (Figure 3.159c). The dimensions of the structural elements of this microrelief increase outside the resolution limits of the electron microscope used.

Figure 3.159. Electron micrographs of the fracture surface of the samples based on rubber SKS-85 and black carbon DG-100 at 40 °C, ×17500 [465]: (a) initial stage of fracture; (b) median zone of surface; (c) final stage of fracture. 372

Mechanochemistry of Polymer Fracture

In the temperature range (20–30 °C), the fragments of the rough relief, presented on the stages a, b, and c in Figure 3.159, practically disappear. In this case, the final stage of fracture is characterised by a relatively smooth microrelief as in Figure 3.159c, and individual bundles can be seen. These bundles are related to the secondary fracture and have dimensions varying from 0.2 to 0.4 µm, Figure 3.160a. This image illustrates the initial stage of fracture in this temperature range. In the final stage, i.e. 10–0 °C, the microrelief is constituted by excrescences and circular cavities, with large sizes of the order of several microns, Figure 3.160b. In the vitreous range, below T g , a new type of microrelief appears, consisting of larger excrescences, separated from each other by distances of 1–2 µm, as Figure 3.161a shows. These formations, whose dimensions are several times higher than those of black carbon particles, represent marks of secondary fracture which was initiated in the proximity of the black carbon particles. This type of randomly distributed elements can also be observed between the excrescences, accentuating in this way the irregular shape of the surface, Figure 3.161b. The distance between excrescences is in this case about 0.5–2 µm. From the structural point of view, these formations are analogous to those presented in Figure 3.160a. However, in some places, especially at their borders, these formations resemble a sworm of ‘micro-stems’, Figure 3.161a. The rough character is more evident, due to the clearly delimited relief of the excrescences as well as the higher number of traces belonging to the black carbon particles. These traces are randomly distributed on the surface, the domains where the traces are highly concentrated alternates with

Figure 3.160. Electron micrographs of the replicas of fracture surfaces of the samples based on rubber SKS-85 and black carbon DG-100 at 20 °C, ×15 000 [465]. 373

Macromolecular Mechanochemistry

Figure 3.161. Electron micrographs of the replicas of fracture surfaces of the samples based on rubber SKS-85 and black carbon DG-100 at different temperatures, below the vitreous temperature, ×15000 [465]: (a) +10 °C; (b) –10 °C; (c) –60 °C.

domains penurious of such traces. Generally, the microrelief resembles long ridges 1–2 µm from each, Figure 3.161c. The space between ridges also contains excrescences and cavities, whose dimensions are an order of magnitude larger than the average diameter of the black coal particles. Even if the distance between excrescences and ridges is approximately the same, their structure is different, Figure 3.161 a and b. Individual traces of black carbon and even particles can easily be seen at the base of the ridges, and above them there are small traces of secondary fracture with only a slightly expressed relief. The ridge itself consists from one or more layers of high traces density, disposed in a straight manner which corresponds to a clearly expressed relief, Figure 3.161 b. Some higher structural formations were identified sometimes on the ridge and resulted from the coalescence of small domains of secondary fracture. As in the case of rigid polymers, mechanical processing, for instance by two-roll mixing, evolves up to the molecular level by the 374

Mechanochemistry of Polymer Fracture

mechanocracking effect whose net result on the macroscopic level is the fracture, accompanied by the formation of new surfaces. The elastomer properties that are directly affected by these transformations are the elasticity and DEFO hardness. The time dependence of the above-mentioned properties is described by exponential curves, which indicate the reaching of the destruction limit, for a given set of the experimental conditions. The curve shape is totally similar to that of the curves describing the time dependence of the average molecular weight. From this reason, these properties are frequently taken as a criterion for the evaluation of mechanodegradation efficiency during cold mastication. In this case, the destruction limit was noted by ∆H ∞ and represents the value of DEFO hardness that remains constant irrespective of prolongation of the mastication period, Figure 3.162. However, it varies with the type of apparatus, the distance between the rolls, roll speed and friction coefficient, and the amount of processed material. The time dependence of DEFO hardness is described by the following equation [301]:

b

g

− d∆H = m ∆H − ∆H∞ (3.106) dt By solving the above equation, an exponential function is obtained:

b

g b g

∆Ht = ∆H0 − ∆H∞ exp −mt + ∆H∞

(3.107)

Figure 3.162. Variation of DEFO hardness with mastication duration. 375

Macromolecular Mechanochemistry

where m is the mastication constant which depends on both the polymer nature and mastication conditions. For the concrete mastication conditions and knowing ∆H ∞ , ∆ Η t , and t, the value of m may be experimentally determined. In this case:

m=

2.303 ∆Ht2 − ∆Ht∞ lg t 2 − t1 ∆Ht1 − ∆Ht∞

(3.108)

Knowing m and ∆H ∞ it is possible to determine the values of DEFO hardness at any moment of mastication. The mastication constant, m, is a characteristic parameter of the mastication process and is strongly influenced by the polymer nature and mastication conditions. As Table 3.47 shows, its value can also be affected by the presence of some additives in the elastomer matrix. The variation of DEFO hardness with time is used for drawing the mastication diagram (Figure 3.163). This diagram is used for the estimation of mechanodegradation at a given moment of processing or, conversely, for determining the optimal period of mastication of certain sorts of elastomers, characterised by a specific value of DEFO hardness. In the last case, knowing the initial value of the DEFO hardness of rubber, which was not subjected to mastication, from the corresponding point we draw a perpendicular line to the abscissa and the optimal period of mastication is read [301]. Polymer fracture in the fluid–viscous state occurs by a specific mechanism, related to the particularities of this physical state, that implies the initiation, development and propagation of the mechanical shock waves. Due to the short relaxation times and high deformation rates, the developed stresses, alongside the flow direction, overtake the polymer resistance, generating a wave that propagates Table 3.47. The additives influence on mechanodegradation efficiency, expressed by DEFO hardness variation Mastication → Duration (min ) ↓ 0 5 10 15 20 25

Without additives: m = 0.067 ∆H ∆H experimental calculated 3 250 2 580 2 000 1 500 1 080 810

2 430 1 870 1 460 1 440 910

376

With additives: m = 0.150 ∆H ∆H experimental calculated 3 250 1 730 1 000 680 500 400

1 800 1 025 680 540 460

Mechanochemistry of Polymer Fracture

Figure 3.163. Mastication diagram.

circularly, its displacement overlapping the flow direction. The final deformation has a sinusoidal shape. Depending on the mechanical factor intensity and geometry of the space through which the polymer melt flows, the mechanodegradation controls either the polymer molecular level or its supramolecular structure. Thus, on reaching the critical shear tension the supramolecular structure changes. This implies the rearrangement of the position of macromolecules position or even the ‘fracture’ of the melt [466–468]. The presence of free radicals was observed in the case of an extruded polymer where clear evidence of fracture in the melt is present [469,470]. The obtained effects are influenced by temperature and oxygen presence. The break accompanied by the generation of new surfaces takes place when stressing melted polymers. The rapid decrease of surface energy, tending practically to zero, is characteristic of the molten media. Another special feature is the decrease of flow resistance to the values close to zero, which approximately correspond to the flowing conditions [471]: σ < KT

(3.109)

or

σ < σ* ≈

KT Sm

(3.110)

where σ is the specific surface energy, which is characteristic of the surface developed in the stressed body at its interface with surrounding medium. 377

Macromolecular Mechanochemistry

Sm ≈ δ 2m

(3.111)

where S m is the average surface of a square, with the length equal to δ m , included in the fault structure; K is Boltzman’s constant; T is temperature in Kelvin degrees. Equation (3.110) shows that the mechanical work required for solid body fracture can be deduced from thermal energy, calculating the entropy of an isothermal system of dispersion. The necessary condition is σ < σ*, the difference between the two values increases with increasing temperature. Thus, at usual temperatures (T ≅ 300 K) and admitting that δ m ≅ 10 –6 cm it was found that σ* ≈ 0.01 erg/cm 2 . When σ > σ* the mechanical work necessary for the generation of new surfaces requires, along with thermal energy, a contribution of elastic energy: βPmVm ≈ ρδ m − KT

(3.112)

where: P m – tensile strength ; V m – average value of the block between two faults; β – a dimensional factor, including the value of relative deformation. It was proved that for stresses causing material stretching β > 0 and in those cases when the material is compressed β < 0; V m = δ 3m ; S m = δ 2m, and therefore:

βPmδ m ≈ σ − σ*

(3.113)

Relation (3.113) illustrates the importance of the molecularsurface phenomena in liquid media, which are related to the movement of the interfacial layers, representing diffusional phenomena or chemical reactions. 3.7. PHYSICAL PHENOMENA THAT ACCOMPANY POLYMER MECHANODEGRADATION AND FRACTURE Dielectric material dispersion brought the first data concerning the accumulation on their new generated surfaces of electrical charges, a process followed by the emission of electron fluxes or of releasing of electrical discharges in gases. It was found that polymer particle detachment from some supports is accompanied by high-energy electron emission [472]. The new generated 378

Mechanochemistry of Polymer Fracture

surfaces of polymer films maintain their capacity of emitting electrons for a prolonged period of time [473]. In this state, these films become chemically active and are able to initiate some chemical reactions, such as grafting or block copolymerization [474–476]. Generally, the destruction of adhesive contact releases the manifestation of electrical properties to the new generated surfaces. If it is accepted that in the contact zone the adhesive bonds form by interactions of the donor–acceptor type, just at the fracture moment a double electrical layer is expected to appear [477]. At the moment of adhesive contact destruction the donor groups are positively charged and acceptor ones become negatively charged, respectively. It was established that the destruction of the adhesive bonds from solid bodies represents the elementary step of the mechanochemical processes that usually occur at the fracture surfaces when a suitable reactant exists in contact with the new surface. It was established that the destruction of adhesive layers is a common feature of some inorganic or organic materials, such as quartz, mica and polymers. Electronic mechanoemission may cause subsequent transformations. This phenomenon is mainly manifested in vacuum, but it also can appear in atmospheric conditions, in the presence of some liquids or gaseous reactants. The first cracks appear in vacuum. Due to the high gradient of the potential, the conditions for electronic emission are fulfilled and the formed flux subsequently interacts with the molecules of gas or liquid which penetrates into the crack. Consequently, the formation of radicals is stimulated and they will enter in chemical reactions with the components of the environmental medium as well as with the new generated surfaces. In this way, the polymerization of some monomers and grafted copolymerization were successfully achieved. On the other side, some volatile compounds were formed. Their presence increases the pressure in the reaction vessel. The characterisation of volatiles was performed by mass spectroscopy. The following sequence of physical and chemical processes should be taken into account: 1) electrification of surfaces freshly formed by the splitting of adhesive bonds followed by the appearance of a double-charged layer or chemical bond splitting in solid bodies, especially in the case of polymers; 2) emission of mechanoelectrons; 3) generation of free macroradicals by the interaction of the primary layer and gaseous or liquid media; and 4) separation of the volatile compounds as the effect of the radicalic side reaction 379

Macromolecular Mechanochemistry

[477, 478]. A direct correlation was found between the intensity of mechanoemission and the nature of the surface [479–489]. Thus, the results obtained for a series of polyesters are collected in Table 3.48 [116]. The following series of diacid efficiency is obtained on the basis of mechanoemission intensity: m-phthalate < o-phthalate < maleate The high energy of emitted electrons of about 10 5 eV was explained by their acceleration in the strong electrical field of faults and cracks which appear during mechanical stress application. During solid body fracture, the luminescence effect was evidenced concomitantly with electronic emission [478]. This effect was proved using both impressions on photographic paper, placed in the medium where degradation occurs, and some specific photoelectronic devices, Figure 3.164 [116]. Chemical bonds splitting at the moment of crack generation determines the migration of the new appeared surfaces. In this way, differences of the potential appear and are accompanied by a luminescence phenomenon [477]. Other causes of photon elimination are the following ones: free radical recombination, especially of peroxy radicals; and F-centres recombination typically at temperatures below –120 °C. The duration and intensity of luminescence are strongly related to the polymer nature and the conditions of mechanical regime [58, 490–501]. In the case of radicals recombination, the kinetics of this reaction can be described by the following equation: d ROO ⋅ 2 = k ROO ⋅ dt

b

k = − k 0exp − E / RT

(3.113)

g

(3.114)

Table 3.48. Correlation between the intensity of mechanoemission and the chemical nature of polymer surface [116] Polyester type

In condition of dispersion fracture imp/s imp/s.m2 103 102 101

Glycerine + maleate Glycerine + terephthalate (p-phthalate) Glycerine + o-phthalate Glycerine + m-phthalate (isophthalate)

380

5.107 1.107 1.106 2.105

Mechanochemistry of Polymer Fracture

Under the assumption that the intensity of luminescence, I, is directly proportional to the macroradicals recombination rate (Eq. 3.116) and that the temperature gradient is constant (Eq. 3117): I≈

d ROO ⋅ dt

(3.115)

dT =β (3.116) dt During the disappearance of peroxy radicals and under the conditions of temperature increase, the luminescence intensity is changed according to the relation: I≅

k 0exp − E / RTb t g

R| S|k exp − E / RTb g βRE Tb g + T 0

2 t

t

1 ROO ⋅

2 0

U| V| W

(3.117)

The curves describing the temperature dependence of luminescence show a maximum for which it can be written:

Figure 3.164. Variation of illumination intensity under throwing conditions up to +10 °C of poly(methyl methacrylate) dispersed in air at –78 °C [116]. 381

Macromolecular Mechanochemistry

E βE + ln = ln k 0 ROO ⋅ 2 RTmax RTmax

(3.118)

The position of T max depends on the values of kinetic constants, E and k 0, temperature gradient and the initial concentration of peroxy radicals, [ROO⋅] 0 . Mechanoluminescence is also influenced by discharges in gases. Its intensity and spectral composition depend both on the polymer nature and the type of gas, Figure 3.165. The luminescence spectrum is located in the range of long wavelengths, i.e. infrared region, while the one cprresponding to charge recombination occurs in the blue–green range, and in the case of electrical discharges in gases the wavelengths are even shorter, Table 3.49, [116]. Thermal radiation [502–504], radiowaves [489, 505–507], X-rays [489], and acoustic emission [507, 508] have been also identified during mechanodegradation. In the case of dynamically stressed crystalline polymers, the splitting of chemical bonds was proved using IR spectroscopy, which allowed to follow both the manner of stress distribution on the chemical bonds and the identification of functional groups that appear as a result of the stabilisation of free radicals [509–511]. Thus, valuable data, concerning the accumulation of double bonds, hydroxyl and carboxyl groups, have been obtained studying polypropylene behaviour. During dynamic stressing of polyamide 6 in the conditions of increasing temperature, the scission of chemical bonds was confirmed by the accumulation of carboxylic end groups. Systematic investigations of the thermal effect, in the case of crystalline polymers, such as: poly(ethylene terephthalate), polyamide 6, and polypropylene, subjected to dynamical stretching were Table 3.49. Correlation between the polymers chemical structure and the spectrum range of luminescence that accompanies their fracture [116] IF/I0a

Polymer Poly(ethylene terephthalate) Poly(tetrafluoroethylene) Polyethylene Polystyrene a

300 – 480 nm

460 – 654 nm

0.6 – 1.00 0.6 – 1.00 0.6 – 0.90 0.6 – 0.95

0.03 – 0.15 0.10 – 0.35 0.04 – 0.10 0.03 – 0.06

) IF – intensity using filter and I0 – intensity without filter.

382

Mechanochemistry of Polymer Fracture

Figure 3.165. Dependence of illumination intensity by the pressure of different gases during poly(ethylene terephthalate) mechanodispersion [116].

Figure 3.166. IR signal obtained by polymer tensile stressing [514].

performed recording IR radiation [514, 515]. The shape of IR signal obtained is approximately the same in all cases, Figure 3.166. In this Figure, time τ 1 was correlated with the appearance of the exothermal effect in the ‘incandescent’ zone that is located close to the top of the main crack, being a measure of its growth rate (~400 m/s). τ 1 represents the required time for cooling this area after the formation of the fracture surface. For instance, in the case of poly(ethylene terephthalate) the quantity of developed energy varies in the range from 2·10 –3 to 5·10 –3 cal/mm 2 . Acoustic emission is also a consequence of microcrack and magistral crack formation. It arises due to an energy difference between the mechanoactivated state and that of equilibrium, attained after mechanodegradation. This difference is dissipated in polymer as acoustic energy [82, 507, 508]. This effect was used for establishing the maximum stress and tensile strain which can be supported by a polymer without suffering irreversible modifications of its structure that could modify its properties. Thus, when monofilaments based on 383

Macromolecular Mechanochemistry

poly(acrylonitrile-co-styrene-co-vinyl acetate-co-a-methylstyrene) were subjected to dynamical tensile stress, sharp sounds were emitted that are perceptible even by the human ear. A special device was designed for accurate recording of these sounds [508]. The essential component of the device is the acoustic probe. It collects the vibrations released in monofilament fascicles by acoustic emission and converts them into electric impulses. As Figure 3.167 shows, these impulses can be recorded simultaneously with stress– strain curves. In principle, the point on the rheological curve corresponding to the maximal number of impulses of the acoustic diagram identifies the stress and deformation values at which the microcracks start growing. These values represent about 80–90% from those corresponding to macroscopic fracture. The same copolymer under shearing also releases fluxes of photons recorded on photographic paper, Figure 3.168 [58]. Polymer fracture as well as the destruction of the contact area between different polymers is accompanied by discharges in gases which can generate variable magnetic fields which, in turn, cause irradiation in the range of radiowaves, characterised by frequencies varying from 20 to 30 kHz, Figure 3.169 [505, 506]. All phenomena of different flux emission, i.e. photons, electrons, ions, and molecules, during or after polymer fracture, and splitting

Figure 3.167. Acoustic diagram correlation with the rheological curve of a polymer [508]. 384

Mechanochemistry of Polymer Fracture

Figure 3.168. Chemoluminescence produced by stressing of AN-AcV-aMSt copolymer film [515].

of adhesive bonds are included in the term ‘fractoemission’. Their importance is related to the possibility of studying the failure mechanisms of the most important materials, such as polymers, ceramics, and composites. In composite materials, fracture take usually place at the interface of two components and it is difficult to establish the right moment and place where different elementary steps are initiated. Thus, in composite materials with a semitransparent matrix it was possible to record the released photons at the interface of the two components. The photons pass through the matrix and can be recorded with an adequate detector. Most likely, the elimination of photon fluxes coincides with the unloading stage of glass fibres and breaking of some bonds [516–523]. If a stronger bond is produced between fibres and the matrix (by gluing, for instance), photon emission strongly decays and this reflects the absence of internal fracture. Reinforcing some polymeric matrices with black carbon fibres that were previously treated with silicon oil, allowed electron microscopic detection of failure. In the absence of silicon oil the adhesive bonds between black carbon and matrix are very strong and,

Figure 3.169. Oscillograms obtained by debonding of a rubber film from a PET surface with a speed of 10 –3 m/s [116]: 1) radio signal; 2) luminescence. 385

Macromolecular Mechanochemistry

consequently, photon emission does not occur. Interesting results concerning the correlation between the photon or electron fluxes and applied stress were obtained using a device with special geometry, Figure 3.170. The behaviour of the epoxy resin, i.e. DEVON TM -5 Min Epoxy and Ciba-Geigy Araldine-502 was investigated using different chemical reagents and stretching times. Both resins are transparent and allow visible photons to reach the photomultiplier tube which was placed in the vicinity of the vacuum-zone resin. The glass fibres were replaced with cylindrical stainless steel rods with variable length and diameter (diameter of 2.5 mm and length varying between 5 mm in 5 Min Epoxy to 50 mm in Ciba-Geigy Araldine, Figure 3.171. For experimental details see Ref. [523]. A good correlation was found between photon and electron emission and the sequence of events that occur during failure and fracture at the interface of the metallic rod and the epoxy matrix.

Figure 3.170. (a) phE; (b) EE; and (c) applied force in pullout of a box-nail out of epoxy resin [524]. 386

Mechanochemistry of Polymer Fracture

Figure 3.171. Experimental arrangement for the debonding and pullout tests. The length and diameter of the stainless steel rods varied. Most of the tests were done with one PMT positioned to view through the epoxy most of the debonding region [524].

Figure 3.172. Photon and electron emission accompanying interfacial failure of a long stainless steel rod in epoxy an a slow time scale: (a) phE; (b) EE [523].

Analysis of electron and photon emission that accompanies slow and fast fractures led to the results presented in Figures 3.172 and 3.173, respectively. In the first case, the identification of electromagnetic waves of radiofrequency as a fracture accompanying phenomenon was possible. Analysis of Figure 3.172 suggested that 387

Macromolecular Mechanochemistry

the events occurring along the stainless steel rod embedded in the epoxy matrix follow the next sequence: 1) crack appearance by splitting of the interfacial metal–epoxy bonds, in the rod extremity but below the free surface; 2) crack propagation alongside the metal–epoxy interface; 3) pull out of the stainless steel rod accompanied by the generation of numerous cracks to the free surface and concomitantly by electron emission (typical times of rod detachment and movement were about 15 µm; and 4) for the longest rods detachment should not occur before crack propagation towards the central part of the rod (in the case of short rods, the detachment is the first effect observed). At the end of bonds scission and cracks generation, the applied effort decays to zero. Pushing back the rod causes the stress to increase to 400 N for every ‘stick-slip’ attempt. The stick-slip movement is related to the local instability existing between the contact surfaces. The technique of interpherometry proved that this movement is accomplished by the collective deformation of many semi-microscopical regions along the metal–resin interface [525]. Geometrically, the contact regions caused by ruggedness, are illustrated in Figure 3.174a. During the displacement of the metallic rod extremity, asperities are deformed and, therefore, the applied stress must increase. Locally, the shear stress increases, due to microscopic bonding between the two surfaces, Figure 3.174 b. Some roughness slip and detachment cause catastrophic failure along the entire rod. When the rod is repositioned in a new alignment, the asperities favour its repositioning before the stress decreases to zero and a new cycle starts. During these detachments, especially for fast displacements, a new excited surface appears, which presents local charges and, consequently, photon emission. High charge density and the presence of a gaseous medium are suitable conditions for microdischarges and explosions of light usually occur. These findings have been confirmed by scanning electron microscopy, SEM, [532]. The ‘stickslip’ movement is accompanied by a high consumption of energy. Important acoustic emission was recorded at each slip, which was ascribed to the ‘catching’ part of the cycle when the rod displacement is finished. The investigation by SEM of the epoxy resin surface after fracture and stick-slip cycles showed a large number of microcracks, perpendicularly oriented to the movement direction. This means that along with roughness deformation, an additional mechanism of energy dissipation occurred, namely matrix fracture. 388

Mechanochemistry of Polymer Fracture

Figure 3.173. Photon and electron emission accompanying interfacial failure of stainless steel rod in epoxy at fast time scale. (a) phE detected by PMT A located near the free surface; (b) phE detected by PMT B viewing the lower portion (tip region) of the metal rod; (c) EE [523].

Figure 3.174. Schematic of a stick-slip mechanism and the local shear stress versus deformation in the vicinity of an asperity [523]. 389

Macromolecular Mechanochemistry

Figure 3.175. Load vs. elongation during the frictional pullout of the stainless steel rod from the epoxy after the debonding has occurred: (a) low friction sample; (b) high friction sample. Both exhibit extended regions of stick slip [523].

Many other details of fractoemission that accompanies the stickslip motion have been obtained by measuring photon emission and radiosignal on a faster time scale, Figure 3.176. The arrows from Figure 3.176 a and b mark the stress failure. This effect was associated with strong emission of photons and radiofrequency waves. Figure 3.176 c and d depicts the area of this explosion. On their entirety, all these results reflect the complexity of the failure and fracture processes which occur by chemical reactions, accompanied by phenomena of mechanoemission of photons, electrons, radio effects, and important increases of temperature and pressure. Conventionally, the reactions that occur during polymer failure and fracture are defined as mechanochemical reactions, because the stress applied to the material constitutes the driving force that releases these reactions. However, in a certain measure all other kinds of emitted energy can influence the chemical reactions. 3.8. MECHANOCHEMICAL REACTIONS AT FRACTURE SURFACES 3.8.1. Mechanochemical synthesis Mechanically stressed solids, crystalline or amorphous–crystalline materials increase their free energy, due to the concentration of 390

Mechanochemistry of Polymer Fracture

Figure 3.176. The correlation between radio wave and photon emission on a fast time scale: (a) phE; (b) RE. Expansion of (c) photon emission about spike and (d) RE signals to show details [523].

mechanical/elastic energy that is adsorbed by structural faults, especially of the dislocation type [525]. When sufficiently high gradients of the chemical potential are locally accumulated, the mechanochemical phenomena acquire quantitative characteristics which increase the reaction rate several times. These reactions are accompanied by important caloric, electrical (discharges in gases, electron emission), light (photon emission) and acoustic phenomena as well as the emission of high-energy radiation (X-rays),[314, 525]. Under the conditions of cleavage and crumbling of supramolecular formations, the mechanical energy is mainly consumed for the scission of chemical bonds. This process tha isfollowed by the formation of free mechanoradicals, and of interionic bonds, which is accompanied by the separation of the contrary sign charges. By cancelling of the intermolecular bonds, or after stabilisation of the free macroradicals, new functional groups appear. In this way, strongly activated surphaces result, which are continuously renewed, able to constitute the support of many chemical reactions. Radical and ionic species, free radicals, and all other active centres formed in mechanodegradation and fracture processes, Table 3.7, are able to initiate reactions of homo- and copolymerisation as well as grafting and bloccopolymerisation. The new appeared end functional groups can also participate to some 391

Macromolecular Mechanochemistry

mechanochemical polycondensation reactions. The intracatenary functional groups just released from intercatenary physical interactions, so-called ‘active macromolecules’ cause that the macromolecular chains, to which these groups belong, have the character of macromolecular ligands, allowing reactions of mechanochemical complexation. 3.8.1.1. Mechanochemical polymerisation

Mechanochemical polymerisation, starting from low molecular weight compounds (monomers) was only relatively recent investigated. This because it was unanimously accepted the idea that mechanical energy can be adsorbed, and consequently it can activate the chemical reactions, either by high-dimension molecules, over a certain critical length [278], or by the mater in condensed state. The first signals concerning to mechanochemical synthesis are based either on the use of crystalline monomers or of the ‘mechano-initiators’, which are crystalline inorganic substances [526–541] or of the mechano-radicals obtained by macromolecules mechano-cracking [542–543]. 3.8.1.1.1. Mechanochemical polymerisation of crystalline monomers

Crystalline monomer polymerisation is important from both theoretical and practical viewpoints. This kind of polymerisation follows a peculiar mechanism which involves a mechanochemical component and usually leads to stereoregulated polymers with superior properties. The majority of monomers containing unsaturated bonds or strained rings polymerise in the crystalline phase. This type of polymerisation has a number of major advantages, namely: it occurs at high speed, at low or even subzero temperatures; allows the polymerisation of certain monomers that do not polymerise in other physical states; allows the polymerisation of some substances which can not polymerise by any other way; it leads frequently to stereoregulated polymers without using special catalysts. In order to initiate the polymerisation reaction, in the first place it is efficient to use high-energy radiation which due to its penetrability assures uniform initiation in the whole crystalline body. Photochemical initiation is also possible but only in the presence of radical or ionic initiators. G. Adler and co-workers proved that the interruption of the strict order from the crystalline structure decisively influences the 392

Mechanochemistry of Polymer Fracture

it is efficient to use high-energy radiation which due to its penetrability assures uniform initiation in the whole crystalline body. Photochemical initiation is also possible but only in the presence of radical or ionic initiators. G. Adler and co-workers proved that the interruption of the strict order from the crystalline structure decisively influences thepropagation rate during polymerisation. Using polarised light microscopy, they observed that in the case of some acrylamidebased monomers, such as: acrylamide, N,N’-methylene-bisacrylamide, N-tert-butylacrylamide, polymerisation takes place just to the edge of crystalline irregularities [544]. This effect is explained by the fact that during the reaction the network volume decreases, stresses appear in the volume and subsequent propagation is inhibited. However, in the fault zones, the resultant stresses are sufficiently high to destroy the monomer network, allowing polymerisation to occur. Formation of a new phase, corresponding to the formed polymer, influences both the propagation rate and conversion degree. Some monomers, such as acrylamide and tributylvinylphosphonium bromide, are totally converted into a polymer but, in most cases, polymerisation occurs to a limiting degree of conversion. Participation of the newly formed polymer in chain propagation explains these results, Table 3.50 [545]. In the case of acrylamide, which polymerises at the monomer– polymer separation limit, the reaction product favours the attainment of 100% conversion [546]. Furthermore, its adding in small proportions (0.1–1%) during polymerisation of another monomer, i.e. N-vinyl succinimide, determines the acceleration of the reaction proportionally to the amount of the polymer introduced. It seems that the polymer macromolecules, more mobile, generate new faults in the monomer crystalline structure, favouring, in this way, the increase of the polymerisation rate. Table 3.50 Influence of monomer nature on the conversion degree [546] Monomer Conversion degree ( % )

Acrylamide Tributylvinylphosphonium bromide Trioxane Acetaldehyde β -Propiolactone Dicetene 3,3-Bis(chloromethyl)oxycyclobutane Acrylonitrile *

100 100 50 50 15–17 17 17

*T = –140°C

393

Macromolecular Mechanochemistry

Formation of the new phase in the reaction system, that of the generated polymer, exerts stresses on the monomer crystalline lattice, determining the mechanical splitting of chemical bonds and consequently the formation of new active centres, usually radicalic ones, which accelerates polymerisation by a mechanochemical mechanism. C.H. Bamford presented the second experimental proof in the favour of the mechanochemical hypothesis concerning the polymerisation in the solid phase [547]. Thus, in the first step he exposed grounded crystals of acrylic or methacrylic acid to pressure in the range from 1 to 5 atm, applied perpendicularly to the axis of crystalline lattice. Subsequently, the monomers were irradiated with UV light. It was noted that polymerisation proceeded, without the addition of any initiator, just in the region where the crystals were broken up by grinding. It was proved that the mechanical activation may contribute not only to the increase of the propagation rate but also to the initiation of polymerisation. The above mentioned results have been confirmed by other researchers [548,549]. In order to demonstrate the ability of mechanical energy to activate exclusively the polymerisation of certain solid monomers, some model experiments have been carried out by applying highintensity shock waves capable of inducing very rapid processes in their crystalline structure. Thus, methacrylamide and trioxane, in the shape of tablets obtained by compression, were exposed to the action of a shockwave, characterised by a pressure at its front of about ~1.5–3·10 4 atm. The shockwave was generated by a trotylhexogene explosion in a close space, the initial temperature being below 50 o C. After explosion, the temperature was quickly decreased to room temperature. In this way, the contribution of thermal energy to polymerisation was excluded. However, in the above-mentioned conditions, polymerisation took place, Table 3.51 [550]. The capacity of shockwave energy to induce polymerisation processes has been proved in many experiments [551–553]. In other experiments, V.A. Kargin carried out vibrational milling of the ionic crystalline lattice of sodium acrylate. In principle, the author accepts that in an ideal crystal the number of anion and cation centres must be equal. However, the real crystalline lattice contains structural faults and consequently during mechanical dispersion by vibrational milling the charges are only partial compensated. For instance, when a negative ion is missing from the crystal node, it becomes an attraction centre for the neighbouring 394

Mechanochemistry of Polymer Fracture Table 3.51 Polymers synthesised under the action of shock waves [550] Initial substance

Melting point of initial substance ( °C )

Conversion degree

+ 62 + 84 110 - 10 + 80 + 120

5-6 60 10.7 2 traces 3–4

Trioxane Acrylamide Potassium acrylate Methacrylamide Salicylaldehyde Stilbene Diphenyl-1,3-butadiene

Observations

(%)

T = - 78°C non polymerise unsoluble polymer

electrons, playing thus the role of an acceptor. In the case of sodium acrylate, the electronic gap from the crystal lattice will attract with the highest probability an electron from the carboxylic group –COO – located in its proximity. Consequently, a radical will arise by the following reaction: -

CH

2

-

(e ) CH2

CH

COO

CH

-

(-e )

CH

2

CH COO • Radic al

-CH

••

COO Na+

•

2

CH

COO Na+ Anion-radical

Both particles are able to initiate the polymerisation. Under identical conditions, V.A. Kargin tested without success the polymerisation of some monomers characterised by non-ionic lattices, such as acrylamide and methacrylamide. Based on these results, the author attributes the essential role to the ionic character of the monomer crystalline lattice [554]. Subsequenty, studies of acryl- and methacrylamide polymerisation, by vibratory milling, were restarted in Romania [293,297, 555]. The experiments were performed at room temperature (18±2 o C), in an inert atmosphere (purified nitrogen) at a filling ratio of 0.5%. The experimental results were plotted as conversion degree versus time. As seen in Figure 3.177, the polymerisation period develops slowly for a long period of time [533]. In the first 24 hrs the rate polymerisation is low, the reaction rate increases after 48 hrs and accelerates in the range from 72 to 192 hrs. The conversion–time 395

Macromolecular Mechanochemistry

Figure 3.177. Influence of grinding time on conversion: (1) acrylamide; (2) methacrylamide.

Figure 3.178. Influence of grinding duration on the conversion degree (1) and molecular weight (2).

curves corresponding to this range show a maximum for both investigated polymers and the conversion degree then decreases. The shape of the curves is characteristic of the initiated mechanochemical polymerisation and it has to be connected with the simultaneous development of the mechanical degradation of the polymer. On the increasing part of the curves, the polymerisation rate is higher than the degradation rate and the situation is reversed after 96 hrs of milling. As Figure 3.178 shows, M w varies with the duration according to a curve with the shape similar to the one which describes the conversion–time function (2 by comparison with 1). When the macroradicals reach a critical length, they are able to concentrate on their chains the mechanical energy undergoing a homolytical scission leading to the formation of low molecular compounds which can be removed during purification. Because in the case of polyacrylamide (PAA) the low molecular fraction was similar to the monomer units, the authors conclude that the mechanodegradation process takes place at the chain ends. 396

Mechanochemistry of Polymer Fracture

It was found that the two monomers are characterised by different reactivity in this type of polymerisation. This behaviour was related to the specific electronic structure of monomers. +δ

-δ

CH 2

C C

+δ CH 2

H O (-M)

-δ C

CH 3 O (-M)

C NH2

NH 2 ( -I ) Methacrylamide

( -I ) Acrylamide

In the case of methacrylamide the effect of attraction of the double bond electrons is partially compensated by the methyl group, which induces the effect of electronic repulsion (+I). As result, the polarity of double bonds decays and, consequently, monomer reactivity decays too. This fact explains the obtained lower degrees of conversion. In order to establish the nature of the active centres involved in mechanochemical polymerisation, the experiments were performed in the presence of some radical acceptors (such as phenol and hydroquinone) in amounts of about 1.0% versus the monomer. The influence of the radical acceptor is quite strong as is seen in Figure 3.179; one should mention here the stronger influence hydroquinone (curve 3), as compared with phenol (curve 2). Thus, in the absence of inhibitors, with the other parameters unchanged, the maximum degree of conversion attained is 42.0%, while in the presence of phenol it decreases to 12.25% and to 2.25%, respectively, in the presence of hydroquinone. Both the conversion degree and average molecular weight M w are strongly influenced by the filling ratio and temperature. The plotting of the conversion degree–time curves emphasised first of all the importance of the mechanical parameter, i.e. filling ratio which is in the inverse ratio with the monomer transformation degree into polymer. The filling ratio is defined as α = a/p × 100, where a is the amount of the monomer (in g), p is the weight of the grinding bodies (in g). The smallest filling ratio used (0.5%) ensures the maximum conversion degree (about 60%). As is illustrated in Figure 3.180, the maximum conversion degree, in the studied working conditions, is achieved after about 144 hrs, irrespective of α. The influence of the filling ratio must be related to the free volume of the reaction flask, which ensures statistical displacement 397

Macromolecular Mechanochemistry

Figure 3.179. Influence of some inhibitors on mechanochemical polymerisation of acrylamide: (1) without initiators; (2) phenol; (3) hydroquinone.

Figure 3.180. The curves of the time–conversion degree for the mechanochemical polymerisation of acrylamide in the presence of the sphere shape-like used grinding bodies. The diameters of the spheres (Φ) are: 1) 3 mm; 2) 6 mm; 3) 9 mm; 4) 12 mm; 5) 15 mm (Inert medium, α = 0.5%; T = 18±2°C).

after a rigorously determined trajectory of the grinding bodies. If the reaction flask volume is kept constant and small quantities of the grinding bodies (large filling ratios) are used then the free volume available for movement of the bodies will be large. The movement of spheres takes place according to the trajectories characterised by higher amplitudes (higher velocities); on the other hand, the number of collisions with the vessel wall is smaller. Therefore, the effective overall kinetic energy in the polymerisation activity is mainly dependent on the statistical number of collisions and the shock intensity (when the size of the grinding bodies is taken into account), Figure 3.181. 398

Mechanochemistry of Polymer Fracture

Figure 3.181. The conversion degree-time curves as a function of the filling ratio (α): 1) α = 0.5 ; 2) α = 1.0; 3) α = 1.5; 4) α = 2.0; (Inert medium, T = 18±2°C, Φ = 15 mm).

When large quantities of grinding bodies are used (α is small) the collision frequency increases and, in addition, friction intensifies, participating in the polymerisation reaction either directly (as a component of mechanical energy, together with the shock force), or by means of the equivalent caloric contribution resulted in their partial transformation. The effect of temperature on the polymerisation reaction was investigated for six different temperatures ranging from 30 to 80 o C. Milling was carried out for a short time (1–24 hrs), for the filling ratio of 0.5% and the diameter of the grinding bodies of 9 mm. The conversion degree increases with time for both cases (Fig 3.182; curves 1–6) resulting in higher values at t = 80 o C. The presence of polymer was observed after 3 hrs. The experimental results show a substantial decrease of the polymerisation induction period. The conversion degree obtained under the conditions shown in Figs 3.178 and 3.180 is insignificant when the duration is below 24 hrs (less 10%), while it increase to 80–90% at 65 o C and 80 o C, respectively. The relation T vs. M w is different in the usual method. Within the limits of the values of times and temperatures investigated, one can notice a progressive increase of the average molecular weight depending on the duration of the reaction and implicitly with the increase of heat supply. The results obtained are related to the increase of the entrance rate of the structural units into the chain thanks to the additional heat supply towards the system energy, on the one, hand and the polymer obtained for a shorter length of time 6–24 hrs) instead of 24–192 hrs at T = 18±2 o C, which does not undergo any important mechanochemical degradation, on the other hand. PAA obtained in this way is water-soluble. The amorphous char399

Macromolecular Mechanochemistry

Figure 3.182. The curves of the conversion degree–time for: 1) 30°C; 2) 40°C; 3) 50°C; 4) 65°C; 5) 75°C ; 6) 80°C (Inert medium, T = 18±2°C, Φ = 15 mm).

acter of the prepared compounds, proved by the X-ray method, shows that the reaction does not develop inside the crystal lattice but the polymer forms as a new phase on the surface of the mechanically destroyed crystalline monomer. Another mechanochemical polymerisation realised using monomers in the crystalline state and vibrational milling as activation manner was that of ε-caprolactam, a cyclic monomer [556]. The polymerisation of anhydrous ε-caprolactam led to rather low conversion (e.g. 3.1% for 56 hrs vibrational milling). Therefore, the influence of typical activators was studied (Table 3.52). The conversions obtained were strictly dependent on their nature, the best results being obtained with water. The development of the polymerisation process was followed by plotting the conversion–time curves (Fig. 183). The curves were compared with those obtained during acryl- and methacrylamide polymerisation, respectively, under similar conditions. The curves presented in Figure 3.183 show, for all cases, a maximum, whose position depends on the monomer nature and, for ε-caprolactam, on activator nature. ε-caprolactam shows a different behaviour in the presence or absence of Lewis acid. In the latter case, the conversion is significantly higher, namely 62.7% after 72 hrs (curve 5, Fig. 3.183) while in the presence of Lewis acid (AlCl 3 + H 2 O) the maximum conversion is 15% after 96 hrs, depending on the amount of the cocatalyst. 400

Mechanochemistry of Polymer Fracture Table 3.52 Mechanochemical polymerisation of ε-caprolactam in presence of different activators a [156] Factors of influence

MECHANICAL -duration ( t ) -building material of equipment -equipment wearing degree -vibrations amplitude ( A ) -diameter of grinding bodies (Φ) -filling ratio TEMPERATURE REACTION MEDIUM -inert -oxygen -radical acceptors -polar media

Reaction conditions

HOMOPOLYMERISATION Monomer Conv. Solub.

(%) (%) Polymerised in solid state Vibratory Acrylamide 43 H2O (100) milling ε-Caprolactam*) 37.7 m-crezol (45) η = 0.5% Methacrylamide 26 H2O (100) Polymerised in liquid state Φ = 9 mm 99.4 DMF (55) A = 4 mm Acrylonitrile Styrene 42.8 DMF (19.7) t = 96 h 28.7 Methanol T= 18±2°C Isoprene α-Methylstyrene 17.2 Ins. Methyl 12.17 Ins. methacrylate Vinyl acetate 12.13 Ins. Non-conventional monomers Benzonitrile 15.5 Ins. Acetonitrile 10.8 Ins. Cyclohexane 6.5 Ins. Pyridine 5.5 DMF (3.5) Benzene 5.1 DMF (2.0)

COPOLYMERISATION Comonomers Monomer Conv. ratio (%) Acrylonitrile - Styrene -α-Methyl styrene -Vinyl acetate

-Vinyl acetate - α-Methylstyrene -Styrene -Styrene

Isoprene Methyl methacrylate Maleic -Styrene anhydride

Solub. (DMF) (%)

1:1 1:3 1:1 3:1 1:1 1:2 1:5 2:1 5:1 3:1 1:3 1:1:2 2:1:1

45.5 34.9 48.0 89.5 47.00 33.99 20.21 56.05 92.58 87.16 6.10 19.25 47.60

73.5 33 20.14 2.08 10.00 Ins. Ins. 55**) -

1:1 1:1

20.50 11.57

-

1:1

89.70

-

Figure 3.183. Conversion–time curves for the polymerisation of monomers in solid state: 1) acrylamide ; 2) methacrylamide ; 3, 4) ε-caprolactam/AlCl 3 /H 2 O ; 5) ε-caprolactam/H 2 O.

This presence of maxima has to be correlated to the simultaneous presence and action of mechanochemical synthesis and mechanical degradation. As in the case of acrylamide mechanochemical synthesis, low-molecular-weight products, soluble in the extracting agent used for the purification of the polymer are formed. They are responsible for the observed decrease of conversion. In the case of ε-caprolactam, air does not influence the development of the polymerisation process and the chemical nature of the activators used to promote the reaction supports a typical ionic mechanism (hydrolytic in the presence of water, cationic in the 401

Macromolecular Mechanochemistry

presence of Lewis acid). ESR and Mössbauer spectral measurements evidenced the presence of chemically bonded metal in polymeric structures, the metal being supplied by the equipment walls. The complexation capacity of the monomer and polymer under vibrational dispersion conditions was also proved. The following cationic mechanism was proposed for the polymerisation of ε-caprolactam in the presence of Lewis acid:

Cl H

O

N

C

H +

MnCl2

complexing

O

N

C

Mn

C

N

O

H

Cl complex C1 Cl H N

O C

Mn

C O

O

N

dehy dro

N

C

chlorination

H

N

O

Cl

C

Mn

complex C2 O HCl + HN

O C

O

C

C

N H2

O

(+)

NH2

(+)

+ n HN

C

O

(+)

Polymer

HN

C

3.8.1.1.2. Mechanochemical polymerisation initiated by crystalline inorganic compounds A. Activation of inorganic surfaces Mechanical dispersion, by vibrational milling, of some crystalline inorganic combinations is accompanied by the formation of new surfaces that are characterised by high chemical reactivity. This is due to the destruction of crystalline lattice, under the action of shock forces, when intense electron fluxes of electrons, capable of initiating the polymerisation of unsaturated monomers, are released [525,544]. N.A. Plate and V.A. Kargin [26,529], H. Grohl [530], N.K. Baramboin and co-workers [531–534] have used, as mechano402

Mechanochemistry of Polymer Fracture

initiators, various inorganic substances such as metals (magnesium, iron, calcium, aluminium, chromium, bismuth, tin, etc.), non-metals (graphite, black carbon), oxides (SiO 2, TiO 2 , ZnO, Al 2 O 3 , BaO, Fe 2 O 3 ), and salts (NaCl, NaF, KCl, KBr, KI, LiF, CaF 2 , HgCl, HgI, ZnS, BaS, ZnSO 4 , CuSO 4 , CaCO 3 ), succeeding in initiating the polymerisation of a large number of unsaturated monomers, such as: styrene, α-methyl styrene, acrylonitrile, acrylic acid, methyl methacrylate, acrylamide, methacrylamide, maleic anhydride, etc.). The chemical reactivity of inorganic surfaces is directly connected to their chemical structure. Thus, these surfaces show a different capacity for fixing the monomers by chemisorption or by chemical bonds. The presence of macroradicals, ions, and electrons on the inorganic surfaces determines monomer polymerisation. It can be noticed that styrene polymerisation, on the surface of some crystalline salts, such as sulphur and sulphates, etc., occurs both in the presence of oxygen and an inert medium; on the surface of black carbon or graphite, under similar reaction conditions, polymerisation starts only in the absence of oxygen. Clearly, the reaction mechanisms in the case of crystalline ionic networks differ from those characterised by C–C bonds. The amount of formed polymer increases with the increase of the specific surface of the inorganic material. These results prove the involvement of the inorganic substrate in the reaction. Polystyrene and poly(methyl methacrylate) obtained in this way are usually characterised by low average-molecular-weight, M w =30 000, due to the large number of paramagnetic centres formed. Thus, using ESR spectroscopy, ~2·10 7 spins/g were determined. These results indicate a radicalic mechanism. However, the type of reaction mechanism depends on the chemical structure of the surface. In the same conditions, certain solid crystalline monomers, such as acrylamide and methacrylamide, have been polymerised with good results [528]. A large number of monomers could be polymerised to the new formed surfaces by mechanodispersion of aluminium silicate (SiO 2 91.4% + Al 2 O 3 4.1% + H 2 O). With increase of milling time the vapour pressure of the introduced organic substances decreases, proving their chemosorption at the inorganic surface, or even authentical reactions of polymerisation, Figure 3.184. The absorption characteristics of some organic substances with or without polar groups (carbonyl, imino) or double bonds are in good agreement with the specific surface of the inorganic substrate, Table 3.53. One can see a stronger absorption of the substances containing 403

Macromolecular Mechanochemistry

Figure 3.184. The variation of vapour pressure with vibrational milling time [558]: 1) (CH 3 )CHCOOCH 3 ; 2) H 2 C = C(CH 3 )COOCH 3 . Table 3.53 Adsorption characteristics of some organic compounds during vibrational milling of aluminium-silicate [558] Organic compound CH2=C(CH3)COOCH3 (CH3)2CHCOOCH3 CH2=CHCOOCH3 C6H5COOCH3 CH3COOCH=CH2 CH3COOC2H5 CH2=CH(CH2)4CH3 n-C7H16 (CH3)2CO n-C3H7NH2 (n-C3H7)2NH

Molecular surface area, S (Å)

N1.10-18 ( molecules/g )

N50. 10-18 ( molecules/g )

(N1 + N50).S ( m2/g )

34.3 36.1 30.8 32.1 31.2 32.5 41.4 42.5 16.9 29.0 40.7

3.0 2.1 3.1 2.7 2.7 2.7 1.6 1.3 3.3 4.1 2.8

4.9 1.2 4.6 1.2 1.0 1.0 0.57 0.57 1.2 2.5 1.6

2.7 1.2 2.4 1.2 1.2 1.2 0.91 0.80 1.2 1.9 1.8

a

a

a

– N1 and N50 represent the number of adsorbed molecules per gram of inorganic salt after 1 and 50 min, respectively, from the introduction of organic vapours

carbonyl, imino, or amide groups, as a consequence of hydrogen bonds type interactions with silanolic groups of inorganic substrate. The coexistence of carbonyl and double bonds strongly increases the absorption degree due to the release of polymerisation reactions. Mechanically dispersed alkaline or earth-alkaline halogens also allow styrene polymerisation. The electron microscopy data proved that polymer chains are initiated and grow only in the crystalline zones of the inorganic substrate giving rise to globular formations. Inorganic halogens used as a substrate are disposed in the following order, as a function of initiation efficiency: KCl (30 min) < LiF (60 min) < CaF 2 (60 min) Mechanoinitiated polymerisation in the presence of inorganic substances depends on a series of factors that influence both the maximum conversion degree for the given system and the reaction 404

Mechanochemistry of Polymer Fracture

mechanism and kinetics. In the first place, it is necessary to mention the chemical nature of the inorganic substance. Even for the same class of chemical combination, for instance alkaline halogens, as it was already discussed, the reactivity is different [538]. As Table 3.54 shows, equimolecular mixtures of styrene and maleic anhydride were used for initiating diverse inorganic combinations, such as: oxides, halogens, sulphides, etc. It appears that concomitantly with the decrease of bond dissociation energy, i.e., with the decrease of ionisation degree, the electron mechanoemission increases, and consequently, the capacity for the initiation of polymerisation lso increases. Indirectly, we can conclude that polymerisation initiation is caused by the electronic emission released by vibratory dispersion of inorganic crystals. However, this conclusion cannot be extended to all types of mechanoinitiators and, especially, to those having C-C bonds (black carbon, graphite). The monomer/mechanoinitiator ratio is also an important factor. As in the case of classic polymerisation, the initiator concentration varies in the range from 0.5 to 1%. Higher amounts of inorganic substance determine the increase of the reaction rate and the decrease of the average molecular weight of the formed polymer. The reaction time also constitutes another parameter that influences this type of mechanopolymerisation. The reaction system evolves in time and, therefore the conversion degree also increases with time, up to a maximum value, which is specific to each investigated system [528]. Degradation processes can occur above certain values of reaction time and lead to low-molecular-weight products. These compounds are removed in the polymer purification stage and the polymer yield diminishes. In the limits of the monomer phase state, the temperature does Table 3.54 Influence of the nature of the ‘mechanoinitiator ’ on the copolymerization yield [538] Bonds Intensity of Copolymerization “Mechano”Dissociation Ionisation energy degree of ionisation electronic yield initiator bonds in degree in emission molecule crystal (%) (%) ( imp/s ) ( kcal/mol ) (%) Barium oxide Barium sufide Mercury chloride Mercury iodide Zinc oxide Zinc sulfide

134±3 100±5 23±2 8.2±0.4 65±1 48±3

66 39 29 14 44 19

88 69 60 31 62.5 46

405

25 95 30 40 25 35

0.0013 3.9 0.006 0.80 0.90 1.10

Macromolecular Mechanochemistry

not influence polymerisation [530]. The formal calculation of activation energy for this type of polymerisation leads to values of 0.1–0.7 Kcal/mol, apart from polymerisation induced by high-energy radiation, which requires 3–10 Kcal/mol. In this way, the athermal character of mechanochemical processes is again verified. The reaction medium constitutes another controlling factor in synthesis. Thus, the oxygen present in the case of mechanodispersion of some substances having C–C bonds, black carbon or graphite nature, strongly delays polymerisation, but has no influence on the polymerisation that occurs on the surfaces of ionic networks, with electrovalent bonds. In spite, in the latter cases the moisture presence decreases the polymerisation rate. Thus, on calcium carbonate (CaCO 3) the styrene polymerisation easily occurs in the moisture absence, being strongly influenced by its presence [535]. Polymerisation of the same monomer on graphite occurs with the same speed in the moisture presence or absence. There are certain cases where water presence is required in order to initiate the polymerisation reactions. Thus, the milling, under vacuum, of NaCl followed by its contact with the monomer does not release any polymerisation reaction. In turn, the preliminary mixing of the mechanodispersion products with water vapours induces styrene polymerisation [540]. In the case of the use an aluminium silicate as initiator, the oxygen plays the role of inhibitor; in turn vapours of ethanol or benzene stimulate the polymerisation process [545]. Concluding, the medium nature and nature of inorganic surface are the most important factors that influence qualitatively the reaction mechanism. The activation of inorganic compounds decomposition by friction was observed a long time ago. In the last century it was proved that friction causes decomposition of several salts of silver or mercury [546,547] or many other combinations, such as: carbonates, oxalates, nitrates, halogens, and some complex salts [546,561]. Direct measurements by mass spectroscopy show that the average number of monolayers decomposed by cleavage of Pb, Mg, and Ca carbonates crystals represents 2, 0.37, and 0.009, respectively. The data concerning to the establish of equilibrium pressure, thermal dissociation, dissolution enthalpy, particles size, and specific surface, obtained after mechanical activation allow the calculation of ∆Z, ∆H, and ∆S, respectively. Mechanical activation determines the decrease of the values of these parameters. Thus, thermal decomposition at 625 o C gives the following changes: from 8.1 to 6.2 406

Mechanochemistry of Polymer Fracture

Kcal/mol for ∆Z; ∆H decreases from 33.2 to 14.8 kcal/mol; and ∆S from 28.0 to 9.6 u.e., respectively [562]. In similar way, the decomposition of iron, zinc, and magnesium carbonates takes place. In function of the mechanical treatment conditions different final products were obtained. Thus, under the conditions of mechanodispersion in air, iron carbonates passes in Fe 2 O 3 ; the same compound in the presence of moisture gives Fe(OH) 3. Carbonates milling under vacuum gives by decomposition higher amounts of CO 2 than in air [563]. Measurements performed on different powders show that grinding of diamagnetic substances causes paramagnetic centres to appear in surface layers (with a thickness of 20–30 µm) which, in turn, are conditioned by the formation of free radicals. Thus, quartz grinding in a wide temperature range causes free electrons to appear in concentrations of 10 14–10 15/g; the concentration of the active centres increases in proportion to the decrease of the particle size. Graphite milling results in the formation of new surfaces characterised by the presence of carbon atoms having two electronic states, namely singlet bivalent and tensioned quasi-acetylenic bonds; free radicals have been also identified, representing carbon atoms with split π and σ bonds [564]. Based on the above-mentioned properties, the inorganic surfaces are widely used for the activation of monomer polymerisation leading to homo- and block copolymers [561]. On the other side, as in the case of polymers mechanodispersion, the inorganic surfaces constituted supports for grafting and block copolymerisation. B. Initiation of polymerisation at the mechanically activated inorganic surfaces It was found that acryonitrile and methyl methacrylate easily polymerise by vibratory milling in the presence of some metals, such as: iron, aluminium, magnesium, at the temperatures ranging from –30 to 50 o C. Polymerisation takes place directly on the surface of grinding bodies and on reaction vessel walls and is accompanied by iron separation. By collision of the grinding bodies each to other or with apparatus walls, the shock energy is consumed for particles fracture and for excitation of the electrons located on the external layers of metal atoms. The excited electrons have the capacity to relatively easy split from the metal surface passing towards monomer molecules, which are retained by sorption, generating anion-radicals, according to the following reaction [565568]: 407

Macromolecular Mechanochemistry

CH2

CH

+ e

C

N

•• CH2

•

CH C

N

Anion-radical

When polymerisation was carried out in the presence of metallic magnesium, using ESR spectroscopy the following radical was identified: • Mg

CH2

CH C

N

based on this structure, two reaction mechanisms were proposed, namely: 1) ionic, according to this mechanism the macromolecules growth by successive introduction of monomer molecules between magnesium and methylene group: +δ Mg

-δ CH2

+δ Mg

•

CH C

-δ CH2

CH

N

C

CH2 N

•

CH C

N

CH

CH2

C

N

2) radicalic: (n + m) CH2 Mg

CH2

C

•

CH C

C H2 N

N

CH2

CH C

Mg N n+1

CH2

•

CH C

N m

Hydrolysis of the thus obtained macromolecular compound leads to the decrease of its molecular weight, which sustains the second mechanism [567, 568]. Monomers such as acrylonitrile, methyl methacrylate, styrene have been polymerised by vibratory milling, at environmental medium temperature, in the presence of some salts (barium sulphate, sodium chloride, silicon dioxide). These reactions implies a postpolymerisation effect, which is accelerated by oxygen presence:

408

Mechanochemistry of Polymer Fracture •

•

R + O2

ROO

O

•

ROO + (CH2O)3 ROO H •

OH + (CH2O)3

CH2

ROOH + • CH •

RO +

O

•

OH O

CH2

CH2

H2O + •CH O

O

O CH2

Concomitantly, on the same principle several reactions of copolymerisation have been performed. 3.8.1.1.3 Initiation of mechanochemical polymerisation and copoly-merisation in the absence of mechanoinitiators Subsequently, the polymerisation and copolymerisation of a large number of vinyl, acrylic, cyclic, dienic, and unconventional monomers were performeced without using the mechanoinitiators, Table 3.55 [294, 313, 314, 324, 569–576]. In all cases the conversion–time curves have the same shape, i.e. two branches, an ascending part and a descending branch, passing by a maximum, Figures 3.185 and 3.186. These results are in good agreement with those obtained to the mechanochemical polymerisation of the crystalline monomers, Figures 3.177 and 3.178. The magnitude and peak position depend on the monomer nature, mechanical regime (milling duration, dimensions of milling bodies, vibrations amplitude, etc.), temperature, and nature of reaction medium. All these results certify the two characteristics of the mechanochemical polymerisation: 1) the chemical reaction is permanently controlled by mechanodegradation, which starts after the chain length overtakes the critical dimensions, and 2) the molecular weight of the synthesised polymer is continuously adjusted by mechanochemical destruction. The highest polymer yield is obtained in the case of acrylonitrile polymerisation, when the transformation is practically total one, followed by styrene polymerisation. In this process essential is the influence of monomer chemical nature. Thus, in the case of acryonitrile the simultaneous presence of two chemical groups able to polymerise, i.e. vinyl and cyano groups, both of them participating to the monomer polymerisation, is very important. As is seen in Figures 3.187 and 3.188, the reaction is influenced by the presence 409

Macromolecular Mechanochemistry Table 3.55 Mechanochemical homo-copolymerisation [294,313,314,527-529,549552,569-576] Factors of influence

MECHANICAL -duration ( t ) -building material of equipment -equipment wearing degree -vibrations amplitude ( A ) -diameter of grinding bodies (Φ) -filling ratio TEMPERATURE REACTION MEDIUM -inert -oxygen -radical acceptors -polar media

Reaction conditions

HOMOPOLYMERISATION Monomer Conv. Solub.

(%) (%) Polymerised in solid state 43 H2O (100) Vibratory Acrylamide milling ε-Caprolactam*) 37.7 m-crezol (45) η = 0.5% Methacrylamide 26 H2O (100) Polymerised in liquid state Φ = 9 mm 99.4 DMF (55) A = 4 mm Acrylonitrile Styrene 42.8 DMF (19.7) t = 96 h 28.7 Methanol T= 18±2°C Isoprene α-Methylstyrene 17.2 Ins. Methyl 12.17 Ins. methacrylate Vinyl acetate 12.13 Ins. Non-conventional monomers Benzonitrile 15.5 Ins. Acetonitrile 10.8 Ins. Cyclohexane 6.5 Ins. Pyridine 5.5 DMF (3.5) Benzene 5.1 DMF (2.0)

COPOLYMERISATION Comonomers Monomer Conv. ratio (%) Acrylonitrile - Styrene -α-Methyl styrene -Vinyl acetate

-Vinyl acetate - α-Methylstyrene -Styrene -Styrene

Solub. (DMF) (%)

1:1 1:3 1:1 3:1 1:1 1:2 1:5 2:1 5:1 3:1 1:3 1:1:2 2:1:1

45.5 34.9 48.0 89.5 47.00 33.99 20.21 56.05 92.58 87.16 6.10 19.25 47.60

73.5 33 20.14 2.08 10.00 Ins. Ins. 55**) -

1:1 1:1

20.50 11.57

-

1:1

89.70

-

Isoprene Methyl methacrylate Maleic -Styrene anhydride

of oxygen traces and generally by the presence of radicalic acceptors [324]. The introduction of the radicalic initiators, such as benzoyl peroxide (POB) or AIBN paradoxically impedes the polymerisation process, Figure 3.189 [324]. Curve 1 describes the yield variation in polystyrene, in inert medium, when the highest values are obtained; in the presence of initiators POB (curve 2) and AIBN (curve 3) the obtained values are clearly lower. It is supposed that in the reaction medium the initiators are slowly decomposed in radicals according to the process evolution. The radicalic species belonging from initiators find the polymerisation already started, on the base of some preexistent active centres. In the first stages of mechanoactivation the shock energy obtained by vibratory milling is used at least partially for the excitation of the superficial layers of metallic lattice from apparatus walls and milling bodies. Consequently, two effects occur, namely: 1) electronic mechanoemission, as slower or faster fluxes, depending on the dimensions of the molecules that compose the atmosphere from reaction vessel [577, 578], and 2) sorption of liquid monomer to the mechanoexcited surfaces: Mechanoemission Me

Shock energy

(+)

Me

-e

Metal lattice Mechano-excited lattice (The wall of reaction apparatus)

410

Monomer sorption

Flux of electrons

Mechanochemistry of Polymer Fracture

Figure 3.185. Variation of conversion with milling time: 1) acrylonitrile; 2) styrene; 3) vinyl acetate; 4) acrylamide; 5) methyl methacrylate; 6) εcaprolactam, [313]. Figure 3.186. Variation of conversion with milling time during copolymerisation of: 1) acrylonitrile + vinyl acetate + α-methylstyrene; 2) acrylonitrile + styrene; 3) acrylonitrile + vinyl acetate; 4) acrylonitrile + α-methylstyrene; 5) styrene + isoprene; 6) vinyl acetate + styrene.

Figure 3.187. Influence of the gaseous atmosphere from the milling apparatus on polystyrene conversion: 1) nitrogen; 2) air; 3) nitrogen oxide.

In the case of the liquid monomers, the interaction with reaction apparatus walls plays a very important role. Their sorption to the mechanoexcited centres of the wall intensifies the scission process into metal lattice, process that inevitably occurs under the action of mechanical vibrations (by microcracks, which grow until to the 411

Macromolecular Mechanochemistry

Figure 3.188. Influence of nature of chain transfer reagent on the polystyrene conversion: 1) nitrogen; 2) benzidine; 3) phenol; 4) hydroquinone.

Figure 3.189. Influence of initiator nature on the polystyrene conversion: 1) without initiator; 2) POB; 3) AIBN.

catastrophic crack) and determines the detachment of very fine particles, usually colloidal ones, which passes in monomer mass. In these conditions the electronic transfer from the mechanoexcited walls to the monomer is assured: (+)

Me

(+) -

e +

CH2

CH C6H5

Mechano-excited lattice

Sorption

(-) ••

Me CH

•

C H2 C6H5

Primary center of polymerisation

412

Mechanochemistry of Polymer Fracture

The reactions carried out in the presence of radical acceptors (Figs. 3.187 and 3.188) proves that in the case of polymerisation, the radicalic end of the active centres is implied in chain growth, the metal being fixed to the monomer molecule, as illustrated below: (+) ( - ) ••

Me CH2

•

CH

(+) ( - )

+ n CH 2

C 6H 5

•

••

CH

Me CH2

CH

CH2

C 6H5

C6H5

CH C6H5

CH2 n-1

CH C6H5

The presence of metal in structural units of the polymer has been evidenced, by Mössbauer and ESR spectroscopy (Figs. 3.190 and 3.191), both in the case of styrene and acrylonitrile polymerisation. The following reactions occur in the presence of initiators: * I2

Mechanical energy •

I • + HC

2 * * I• (-)

CH2

HC

CH2

C6H5

C6H5

HC n-1

• •

C6H5 (-)

I

HC

CH2

HC

C6H5

C6H5

CH2

(+)

CH2 Me

HC

• •

(+)

CH Me

C6H5 n-1

* I2 : BPO, AIBN * * I• : Radic al from initiator

The activation energies, practically equals to zero, of the polymerisation reactions carried out in the presence of initiators, sustained the hypothesis of radicals recombination, Table 3.56. On the other side, the radical polymerisation of some crystalline monomers, such as acrylamide and methacrylamide is also accompanied, under the conditions of vibratory milling, by electronic fluxes of mechanoemission, but the data of ESR and Mössbauer analysis do not indicate the presence of chemically bonded metal [533]. Acrylonitrile shows a very interesting behaviour during the mechanochemical polymerisation. The fact is already known, that due to its structure acylonitrile shows a strong tendency towards polymerisation through the anionic mechanism, which allows easy activation of the polymerisation by electron donating mechanism. It is assumed that the electrons emitted by the metallic surface of the equipment plays the role of initiating agent, giving rise to the already illustrated anion-radical. Thus, the propagation step might be assumed to proceed both to 413

Macromolecular Mechanochemistry

Figure 3.190. Mössbauer spectra of the mechanochemically synthesised polymers: 1) reference spectrum of sodium nitroferricyanide; 2) poly (acrylonitrile); 3) polystyrene.

the radical and anionic centres. Indeed, the polymerisation in the presence of oxygen from air and of benzoyl peroxide, respectively, suggests the radical mechanism. Thus, carrying out the reaction according to the first variant, the maximum is attained at 120 hrs compared to 96 hrs under inert medium, which can be accounted for by the retarding action of oxygen. 414

Mechanochemistry of Polymer Fracture

Figure 3.191. ESR spectra of poly(acrylonitrile); 2) polystyrene.

mechanochemically

synthesised:

1)

Table 3.56 Styrene polymerisation by vibratory milling in the presence of initiators Sample Polymerisation time Activation energy Reaction (h) ( kcal/mol ) order Polystyrene + Benzoyl peroxide

24

- 0.107.10-4 - 0.752.10-4 - 0.307.10-4

0.22.10 0.00

Polystyrene + Benzoyl peroxide

48

- 0.556.10-4 - 1.881.10-5 - 0.334.10-4

0.17.10 0.00 0.00

Polystyrene + Benzoyl peroxide

72

- 0.125.10-5 - 0.946.10-4 - 0.277.10-5

0.17.10 0.00 0.00

Polystyrene + Benzoyl peroxide

96

- 0.792.10-4 - 0.994.10-4 - 0.269.10-4

0.12.10 0.00 0.00

Polystyrene + Benzoyl peroxide

120

- 0.638.10-4

0.00

Polystyrene + Benzidine

120

.

-4

- 0.106 10 - 0.633.10-4

0.00 0.00

In favour of a radical mechanism pleads also the synthesis carried out in the presence of phenol, known as an inhibiting agent for radicalic processes, where the conversion increases slowly in time. It is worthwhile to notice that a radicalic mechanism in this process seems to be not dominant, since the conversions obtained using radical agents are restricted to those obtained in inert medium. To test the probability of reactions proceeding through the anionic end active centre, syntheses were carried out in the presence of liquids of various polarities, at the same reaction duration (96 hrs). All tested liquids strongly hindered the polymerisation. For instance, in the presence of methanol, a liquid with dielectric constant ε = 415

Macromolecular Mechanochemistry

33.62; the conversion was diminished from 50% in inert medium with pure monomer, to approximately 8%. The influence of medium polarity on the polymerisation course was thus proved and based on the obtained data an anion-radical mechanism could be advanced. IR spectra of the polymer obtained show the presence of the – CN groups 2235 (cm -1 ) on the macromolecular chains and of the absorption bands located at 1380 and 1650 cm –1 , attributable to the –C=C– and –C=N– groups. The bands appearing at 2060 and 2180 cm –1 are due to the presence of the chemically bound metal existing in the polymer (as a general rule, they are attributed to inorganic azides). The results obtained indicate the participation of the –CN groups to the polymerisation process and the chemical binding of the metal to the polymer chain. It was established that mechanochemical processes are characterised by very low or even zero values of energy of thermal activation. This fact is related to the compensation of a great part of the energy of thermal activation by the added mechanical energy. Therefore, it becomes possible to perform some chemical reactions, which usually are impossible or require high temperatures (often higher than those of the thermal decomposition of the reagent) by vibratory milling. This is why in order to establish the possibility of cyano group polymerisation, some experiments were performed with aliphatic and aromatic nitriles (acetonitrile and benzonitrile). Polymers based on nitrils cannot be obtained under the conditions specific for the polymerisation of vinyl monomers, because the variation of the system free energy (∆G) is positive. On the other side, the aromatic compounds are characterised by a high stability, because ∆G is positive for the ring opening reaction is positive, due to the low resonance energy determining a positive variation of the enthalpy (∆H) which cannot be cancelled by the entropy variation (∆S > 0). If follows that the ceiling temperature for opening these rings has very high values for determining ∆G < 0, probably higher than those for thermal decomposition. Hence, the opening of rings becomes possible only by modification of the free energy of the system, which may be performed either by using catalysts or through activation of the reaction by other types of energy. Consequently, the investigation was focused on the possibility of breaking benzene and pyridine aromatic rings by vibratory milling and the results obtained are shown in Figure 3.192 [313]. In all these cases the polymer is formed on the milling balls or on the vessel walls as a dried powder (when the conversion is to416

Mechanochemistry of Polymer Fracture

Figure 3.192. Variation of conversion with milling time (N 2 , filling ratio η = 0.5%, T = 18±2°C): 1) pyridine (new balls); 2) benzene (new balls); 3) pyridine (old balls); 4) benzene (old balls).

tal) or is moistened with monomer (for low conversion values). Two fractions have separated from the reaction product: one soluble in specific solvents and another insoluble one. It is obvious that polymerisation initiation occurs on the surfaces of colloidal particles that become detached from the milling equipment under the action of impact and friction forces. The polymer is grafted on these very highly reactive particles. When the graft length reaches a certain value, the soluble fraction passes into the reaction medium as a result of splitting. The insoluble fraction represents, therefore, polymer grafted on the metal surfaces of the colloidal particles. In the case of mechanochemically initiated polymerisation of acetonitrile and benzonitrile, solid products were obtained which were considered to be polymers (yield at 96 hrs of grinding was 10.8% for acetonitrile and 15.5% for benzonitrile). On the other hand, the opening of cyano group triple bonds could be caused by the mechanochemical degradation of certain polymer sequences. It should also be mentioned that the reaction products showed a brown colour, which intensified by increasing grinding time. According to the experimental results discussed above the structure of poly(acrylonitrile) synthesised mechanochemically could be represented as :

417

Macromolecular Mechanochemistry CH

CH2

C

n

CN

N

C

p

N

CH2 CH

CH

CH2

with n > p, as evidenced by analytical data and polymer properties. As Table 3.57 shows, the data concerning IR, ERS, and Mossbauer confirm this structure [292,293]. Acetonitrile polymerisation is much less influenced by the oxygen, acting as radical acceptor. As in the case of acrylonitrile polymerisation, the polar liquids reduced conversion, while low constant dielectric liquids (cyclohexane) favoured it. As a consequence, the following a cationic mechanism through solvated electrons may be considered for acetonitrile polymerisation: M.E.

Me

*)

(+)

(-)

Me

e

Mechano-excited state

(+)

Me

e

lq.

( -)

**)

(+)

Me

e

( -)

(lq.)

Solvated electron

(+)

Me

-δ N

+

+δ C

( +)( - )

+ C

N

Me

CH3

CH3

Free carbocation M.E. lq.

**)

*)

- Mechanical energy ( vibratory milling ) - Hexane, methanol, acetonitrile (monomer), water

Table 3.57 Characteristic IR absorption bands and parameters calculated from ESR and Mossbauer spectra of poly(acrylonitrile) mechanochemically synthesised. Inert medium (N 2 ), old balls, filling ratio η = 0.5%, reaction time, t = 120 h, soluble fraction. IR Spectrum Wave length

Chemical bonds

(cm-1) 2900 2235

C

ESR Spectrum g Conc. of paramagnetic centres ( Gs ) ( spin/g ) H0

H

C

Position

Mössbauer Spectrum δ

∆Eq

ε

V1 ( m/s )

V1 ( m/s )

(mm/s)

I

- 0.449

0.531

0.007

1.012

II

- 0.429

- 0.131

0.028

0.298

0.39

-

-

traces

(%) 0.48

N

1606 (within the broad bands between 1600 and 1700 cm-1)

(in conjugated double bonds)

1445

CH2

3303 1.960 C

Hyperfine vecinities

9.25.1016

N

III

418

magnetic powder

Mechanochemistry of Polymer Fracture

Preliminary tests with both benzene and pyridine led to a mixture of fractions soluble as well as insoluble in methanol. The brown coloured products obtained from pyridine, and the yellowbrown ones obtained from benzene indicated profound modifications in the initial compounds during the vibratory milling. The amount of the product resulting in the reaction medium was found to depend on two factors, namely the duration of milling, and the equipment wearing degree (old or new balls). By following the variation of conversion in time for the equipment of a low and high wearing degree, respectively, the results presented in Figure 3.192 were obtained. For the range of time under study (0–192 hrs) the conversion curves for pyridine are of shape characteristic for the processes of mechanochemical synthesis (Fig. 3.192, curves 1, 3), showing maxima at durations of 92 hrs (1) and 144 hrs (3), respectively. This behaviour show that synthesis and mechanodegradation reactions compete during milling, the rate of the first prevailing until a certain product amount accumulates in the reaction medium. In the case of benzene the conversion-time dependence is described by a straight line, indicating that the equilibrium between the mechanosynthesis and mechanodestruction processes is not attained during the 192 hrs of milling. The mechanical degradation of the product resulting from benzene is less intensive, probably due to the >C=C< bonds, which are stronger than the –C–N= bonds existing in pyridine based products. The maximal conversion rates are higher than those of benzene at the same reaction time as a consequence of the lower stability of the heteroaromatic ring. The degree of wear of the milling balls also affects the process. With both compounds submitted to polymerisation, higher conversions are obtained with an equipment of a high wearing degree, as also evidenced in the polymerisation of some vinyl monomers. This is due to the fact that the number of the active centres (metallic ions, intensity of the electronic flux) is greater in the case of this equipment. As a consequence of the amount of the chemically bound metal in the structure of the reaction products, as well as of the crosslinking reactions proceeding during the milling. The solubility of the products is not complete and decreases with increasing time of reaction. Thus, for benzene-based products, the solubility in hot methanol is higher than in cold methanol. The solubility of both reaction products was found to decrease with increasing time of synthesis regardless the nature of the solvent (in the case of 419

Macromolecular Mechanochemistry

pyridine polymerisation, the products are also highly soluble in DMF). The decrease of solubility with increasing reaction time and equipment was attributed, in part, to the complexation of the growing molecules with the metalic atoms, as supported by ESR spectral analyses. The ESR spectrum of the DMF soluble fraction of a pyridine-based products is particularly suggestive (Figure 3.193). The first part of the signal appearing at low values of magnetic field (~ 600 gauss) corresponding to g ~ 10 is characteristic for the Fe 3+ ions in an intensive ligand field which partially screens the effect of the static magnetic field. The vicinity with an intensive ligand field proved that the obtained product is a complex. The second signal was ascribed to the superposition of two spectral components of different broadness (∆H = 495.87 gauss and 213.28 gauss, respectively) indicates, for g ≅ 2, formation of different coupling constants. Such values of the splitting factor (g) indicate, for organic polymers, the presence of some delocalized electrons in extended conjugated systems. Additional information on the structure of the soluble fractions was obtained from IR spectral measurements. Table 3.58 presents the main absorption bonds appearing in the spectra of the two products. It can be seen that the absorption band at 755 cm -1 corresponding to the deformation vibrations of the – C – H bonds in the aromatic ring are absent in both spectra. Based on this data it may be concluded that both aromatic rings split under vibratory milling conditions leading to linear structures of the polyacetylenic type. In the IR spectra of both types of reaction products an intense band, usually attributed to the oxidized structure, appeared at 3500 cm -1 . The IR spectra also revealed absorptions at 1720 cm -1 and 1108 cm -1 , attributed to >C = O groups in a-diketones and to etheric – C – O – groups, respectively. Since the syntheses were performed under inert atmosphere (N 2), the authors explained the presence of oxygen as based on some oxidation reactions of the double bonds occurring during the separation of the soluble fractions in methanol or DMF. This supposition was confirmed by liquid chromatography data. The authors proposed for the soluble fractions the linear structures, which contains double bonds in conjugated system such as (I) and (II): ( CH

CH )

( CH

I

CH

CH

CH II

420

CH

N)

Mechanochemistry of Polymer Fracture

Figure 3.193. ESR spectrum of the DMF-soluble fraction obtained from pyridinebased product (t = 144 h, old balls, h = 0.5%, T = 18±2°C), [ 536 ]. Table 3.58 Characteristic absorption bands of the products obtained from benezene and pyridine by mechanomechanical polymerisation

Assignment

Wave number ( cm-1 ) 3 500 broad 2 900 m 1 760 m 1 720 m 1 600 – 1 650 broad 1 291 m 1 144 m 1 108 w

–OH stretch (– OH or –OOH) –(CH2)x– (olefinic structure) –(CH2)x– (olefinic structure) >C=O stretch (α-diketones) >C=C< (polyenes) or >C=N–C< –C–H stretch (polyacetylenes) –C–O stretch (ether) –C–H stretch (polyacetylenes)

Such structures, being particularly sensitive to the atmospheric oxygen, lead under the action of high temperatures and light, to the structures (III) and IV) and to crosslinked structures of type (V). CH

CH CH

C

CH CH

CH

CH C

O

OH

III

IV CH

CH CH

C

CH

O CH

CH

C CH

CH V

421

CH

Macromolecular Mechanochemistry

On the other side, the reduced solubility of the products was explained by the crosslinking that should appear even during the vibratory milling, in the absence of oxygen, under the action of mechanical energy as a consequence of double bond splitting. The presence of metal in mechanochemically polymerised products conveys to them properties that differ from the properties of analogues synthesised by classical methods. Among these, very distinguishing is the thermal stability, which has a close connection with the quantity of chemically bonded metal. In the case of poly(acrylonitrile) up to about 200 ° C, the rate of weight loss was practically insignificant, while at 900°C, a considerable amount of residue (over 10%), representing organic structures stabilised by the metal, still remained. An increase in metal amount led to increase thermostability. The first decomposition stage shifts toward higher values and the calcination residue content increases. The existence of the metallic atoms as well as of the double bonds in the conjugated system of polyacrilonitrile or in the products of mechanical polymerisation, i.e. benzene, pyridine, aliphatic or aromatic nitriles) has suggested the possibility that the latter ones might posses semiconductor properties. The values of E a for the above-mentioned polymers, ranging from 1.12 to 2.5 eV, pointed out semiconductor properties, especially in the case of polyacrilonitrile synthesised at high milling durations and in the case of polyacetonitrile. 3.8.1.2. Mechanochemical block copolymerisation and grafting From the chronological point of view, mechanochemical block copolymerisation and grafting represent in fact the first direction of research developed in the field of mechanochemical synthesis In this case, the mechanoradicals generated by polymer chains splitting played a role of the initiator. The development in this direction of research has two distinct stages: 1) the use of the grafting-block copolymerisation reactions for the clarification of the mechanisms of the polymers mechanodegradation and fracture, and 2) their use for the obtaining of new structures with superior properties as compared to the initial polymers. A great amount of work has been devoted to the first mentioned objective, the main results being synthesised into a series of specialised books on grafting, including also the mechanochemical grafting [579–581] or other books or reviews dealing exclusively with the mechanochemical processes [85–91, 113–130, 158, 178, 179, 422

Mechanochemistry of Polymer Fracture

210, 211, 232, 235, 262, 263, 284, 298, 300, 316, 317, 325]. In the all cases, the mechanoradicals, obtained by the mechanical scission of the polymers macromolecular chains, have been used as initiator centres of the monomers polymerisation. Different types of mechanical stressings, such as/ vibratory milling, mastication and especially could mastication, extrusion, two rolls mixing, the mechanical energy released during the cryolitic freezing-thawing cycle, ultra high-speed stirring, ultrasonic irradiation, shock waves, produced during electrical discharges in liquids, on the swelled polymers, etc. Several data concerning the classes of polymers supposed to mechanocracking, in various conditions of mechanical stressing and in different media, leading to the mechanoradicals ale to initiate the grafting or block copolymerisation reactions, proved the other mechanoactivated reactions like hydrolytic or polycondensation ones and frequently reticulation can concomitantly occur, Table 3.59 [85–91, 126–128, 193, 207, 208, 230, 582–586]. Both natural and synthetic polymers, practically in the whole aggregation and physical states, such as melts or solutions have been mechanically stressed [585–659]. The investigations were focused on two directions, namely - in the systems: 1) polymer–polymer, and 2) polymer–monomer. The general mechanism of the mechanochemical block copolymerisation and grafting in the polymer-polymer system is concretely illustrated by low-density polyethylene grafting with ethyl cellulose on a Brabender masticator [603], and it can be schematically synthesised by the following elementary steps and ultimate reactions:

423

Table 3.59 Types of mechanoradicals obtained in different conditions of stressing and medium [85-91, 126-129, 193,207,208,230,583-586]

Solicitation type

Medium nature

Type of split bond

Type of primary radical

1

2

3

4

5

vibratory milling mastication

inert

Polyethylene

Poly(vinyl chloride)

424

vibratory milling ultrasonation (in solution and suspension) two roll mixing

C

CH2 CH 2

air inert air

-

radicalic acceptors - grafting - radicalic acceptors - grafting – block copolymerisation

•

C

CH2

C

•

CH 2 OO

CH2

•

CH Cl

C •

CH

Method of macroradical investigation 6

CH2 Cl

Stimulated mechanochemical reaction 7 mechano-degradation block copolymerisation mechano-degradation block copolymerisation grafting reticulation elimination of HCl

•

CH2

CH

OO

CH

Cl • CH2 OO

Cl

Poly(vinylidene chloride)

Poly(oxymethylene)

vibratory milling

inert

•

C

vibratory milling

inert air

C

C(Cl2 )

CH 2

•

C(Cl 2)

CH 2 •

CH 2

O •

O

CH 2

O

CH 2 OO

•

- grafting – block copolymerisation

•

-ESR -radicalic acceptors - grafting

mechano-degradation block copolymerisation grafting elimination of HCl mechano-degradation block copolymerisation grafting elimination of CH2O

Macromolecular Mechanochemistry

Polymer type

Table 3.59 (continued)

Poly(ε-caprolactam)

inert polar liquids

vibratory milling cryolisis

inert

C

C

C

OC OC

NH NH

H

CH2OH O H OH H

•

CH2 (CH 2)

N

O

air

H

O H

OH

H

425 Lignine

vibratory milling

inert air

C C

Table 3.59 (continued) 1 2 Poly(ethylene vibratory milling terephtalate) cryolisis

3 inert

OH

• OH H C OO H H O H CH2OH

___ C

4 C O O O CH2

-mechano-degradation -block and graft copolymerisation -polycondensation -hydrolissis -mechano-degradation -block and graft copolymerisation -mechano-chemical polycondensation -hydrolissis

OH H •C H H O H CH2OH

C O

OH

-radicalic acceptors - grafting

-radicalic acceptors - grafting

•

O

O

•

CH 2

5 C

•

C O

O O • O CH 2 CH 2 O C

•

C

O O • O CH 2 CH2 O

-ESR -radicalic acceptors -grafting

-mechano-degradation -block and graft copolymerisation -

6 -ESR -radicalic acceptors - grafting

7 -mechano-degradation -block and graft copolymerisation -mechano-chemical polycondensation and hydrolissis

Mechanochemistry of Polymer Fracture

Cellulose and derivatives

vibratory milling shearing in capillary

Macromolecular Mechanochemistry The mechanism of mechano-chemical grafting in the system POLYMER-P OLYMER

mixte R2 mechano- R1 + R2 recombinations • • R1 R2 cracking R1 + R 2 + chain transf er Polymers •

R1

*)

•

Block copolymers Grafted polymers Grafted networks

Example: CH2

•

CH2 + CH2

H OH CH2OC2 H5 H • O + • O OH H H CH O O OH H H O H CH2OH H OH

CH2OC2 H5 OH H H O O OH H H H O OH H O CH2OC2 H5 H OH

CH2OC2 H5 H O O H O OH H H

•

mechanodegradation

CH2 CH2 CH2 Polyethylene H

OH

CH2OC2 H5 O O H OH H H

OH

Ethyl cellulose

H O

CH2OC2 H5 O O• + H OH H H H

•

CH2

recombination

CH2

CH2OC2 H5 O O H OH H H H OH

H O

OH

CH2

CH2

Block copolymer

CH2

CH2

CH2

Polyethylene

2

•

R1H + R1 (or any other mechano-radical)

•

CH2

CH

CH2

•

CH2

+

CH2

CH

CH2

CH2

CH

CH2

CH2

CH

Crosslinked polyethylene CH2 CH2

CH2 CH2

CH CH

CH CH

CH2 CH2

CH2 CH •

•

R1 (or any other mechano-radical)

+

H

+ O

CH2

CH

CH2

CH2

CH

CH •

Grafting center

CH2OC2 H5 O O• H OH H H H

+ R1H

CH2

CH

CH2

CH

H5C2OH2C

OH

H

CH2 CH O

O H

O

H H

OH

Grafted and crosslinked polyethylene *)

- Mechano-thermal-oxidative effects are not illustrated

and for the monomer-polymer systemt the main steps are illustrated below:

426

Mechanochemistry of Polymer Fracture The mechanism of mechano-chemical grafting and block copolymerisation in the system POLYMER-MONOMER

I. GENERATION OF THE ACTIVE CENTRES I.1. Scission of the covalent bonds under the mechanical energy action R1

mechanodegradation

R2

R1• + R2• Mechanoradicals

Macromolecular chain

I.2. Subsequent reactions of the mechano-radicals with: - medium (frequently O2 from air) R1• (R2• ) + O2

•

R1OO (R2OO • ) Peroxide-type macroradicals

- neighbouring macromolecules (chain transfer) R1• (R2• ) +

R1

R1H (R2H)

R2

+

•

R1

R2

Ramification center • R1OO (R2OO • ) +

R2

R2

R1OOH (R2OOH)

+

•

R1

R2

Macrohydroperoxide •

R1OOH (R2OOH)

•

R1O • + (R2O • )

OH

- monomer R1• (R2• ) + M

R1M • (R2M • )

• R1OO • (R2OO ) + • •

R1O • (R2O , OH) + R1

•

R2

+

Initiation centers for Block copolymerisation

• • R1OO M (R2OOM )

M

•

•

• R1O M (R2OM , HOM )

M

M

R2

Initiation centers for grafting reactions

R2 M •

II. CHAINS GROWTH II.1. Block copolymerisation R1M • (R2M • ) + •

• R1Mn+1

nM •

R1OO M (R2OOM ) + •

•

• (R2Mn+1 ) •

R1OOMn+1

nM

•

• (R2OOMn+1 )

•

R1O M (R2OM , HOM ) + n M

R1OMn+1

•

Block copolymers •

(R2OMn+1, HOMn+1)

II.2. Grafting R1

R2 + p M

R1

R2

M •

( M )p-1 M •

M

III. CROSSLINKING •

2 R1 R1

•

R2 R2 + R1

R2 ( R1 M •

R1

R2 + R1 M •

R2 ) M

Tridimensional structures

( M )p-1 M •

R2 M

( M )p-1 M •

When polymers such as poly(ethylene terephthalate) or aliphatic polyamides, nylon 6 and nylon 6,6, are stressed by vibratory milling or cryolitic cycles in the presence of some vinyl monomers (vi427

Macromolecular Mechanochemistry

nyl chloride, vinyl acetate, and styrene) or acrylic monomers (acrylic acid, acrylonitrile), the mechanochemical mechanism should be particularised by the following elementary steps [125, 600, 605]: System POLYMER-MONOMER R1

R2 : polyester chain (polyamide)

R:

OC

CH3 ;

O C

C

Generation of the primary radicals OH

O N;

Cl;

VIBRATORY MILLING - inert medium, N2 - temperature, - 40 ÷ 18±2°C

R1

R2

mechanodegradation

R1• + R2•

Block copolymerisation initiation R1• + CH2 • (R2 )

CH

•

R1 CH2 (R2)

R

CH R

Chain growth through block copolymerisation R1

CH2

•

CH + n CH2

R CRYOLISSES Chain transfer - cryolisses cycle, 5 - 15 min - temperature, - 60°C R1• ; R2• + - cycles number, variable (max. 50) • R1 CH2 CH

CH

R1

R

CH2

CH

CH2

R n Block copolymer

•

CH R

•

R1

CH2

R2

R1H ; R2H R1 CH2

R

CH R2 + R1 CH2 Grafting center R

Grafting initiation R1

•

CH

R2

+ CH2

CH

R1

R

CH

R2 + n CH2

CH •

CH2 CH •

CH R

R

R2

CH2

Ramification growth R1

CH

R2

CH

R R2

CH2 CH

R n

CH2 CH •

R

Graft copolymer

In all investigated cases the interruption is accomplished by the recombination of different types of growing macroradicals. The researches in this field were focussed to obtain some polymers able to combine the properties of two ore more macromolecular compounds, thus turning the classical vinyl polymerisation monomers to a superior account. The mechano-chemical activation of these reactions constitutes an advantageous way as it allows the preparation of such products by employing, in most cases, the equipment currently used in the industrial processing of polymers. The studies concerning the grafting of some vinyl monomers by the mechanochemical method have developed in two directions: grafting on inorganic supports and on macromolecular compounds. The surfaces freshly formed during the mechanochemical dispersion of some inorganic compounds (kaolin, mica, volcanic tuff) initiate the vinyl monomers polymerisation, allowing the grafting of macromolecular compounds on them. Thus, a series of products of 428

Mechanochemistry of Polymer Fracture

methyl methacrylate, vinyl chloride, and acrylonitrile have been synthesised by grafting on the previously mentioned inorganic surphaces. Vibratory milling was used as activation method (LS-60 VEB Kefama Katzhutte Thuringen ball mills, at 18±2°C temperature, 0.5% filling ratio, and 1/1 inorganic support/monomer ratio [606]. The grafting degree increases with the milling time, attaining a maximum value at 72 hrs for all the cases studied, and decreases above this duration. This is a result of the mechanochemical destruction intensification, which accompanies the synthesis practically throughout its entire development; at the same time, it materialises in the reduction of the graft size as well as in the accumulation of homopolymer in the reaction medium, Figure 3.194 [ 606, 607 ]. The presence of oxygen and radical acceptors strongly decreases the reaction rate thus proving a radical-based mechanism. The synthesised products have been tested as filling materials for poly(vinyl chloride), at the same time studying the way in which the PVC mechanical properties are influenced. Thus, the samples obtained by two-roll mixing and pressing (170°C, 10 min; 170°C, 175 atm) have been analysed from the viewpoints of tensile and impact strength (Izod), and their characteristics are given in Table 3.60. One can notice, in all the cases mentioned, the superior physicomechanical characteristics of the samples containing polymers grafted on inorganic supports as filling compounds, in comparison with standard ones. The impact strength has particularly high values

Figure 3.194. Grafting degree variation as a function of grinding time: 1) PAN grafted on kaolin; 2) PAN grafted on mica; 3) PAN grafted on volcanic tuff [606].

429

Macromolecular Mechanochemistry Table 3.60 Physico-mechanical characteristics of PVC with and without filling materials (up to 10%) [606]

Sample

Tensile strength (kgf/cm2)

Standard sample PVC + kaolin PVC + PAN grafted on kaolin (72 h grindings) PVC + PMeM grafted on kaolin (72 h grindings) PVC + PVC grafted on kaolin (72 h grindings) PVC + volcanic tuff PVC + PAN grafted on volcanic tuff (72 h grindings) PVC + PMeM grafted on volcanic tuff (72 h grindings) PVC + PVC grafted on volcanic tuff (72 h grindings)

Izod impact E strength (kgf.cm/cm2)

624 531 587 610 566 552 570

5.39 5.21 9.69 * 6.04 * 8.74 * 2.48 * 9.72 *

605

5.60 *

685

8.86 *

when the grafted monomer is vinyl chloride alone, but it is even higher in the case of acrylonitrile. Therefore, the authors considered that the grafting products of both monomers on the two mineral supports could be successfully used as filling materials for PVC processing. The flow-state processing of the macromolecular compounds an classic equipment also takes place with the continuous formation of new surfaces with high reactivity and, consequently, with high chemical potential. Thus, the accomplishment of some grafting and block copolymerisation reactions in the polymer–monomer and polymer–polymer systems becomes possible. The systems studied and the total effects of the reaction on the polymer whose transformation has been investigated are shown in Table 3.61 [313]. Special results have been obtained when poly(vinyl chloride) was processed by two-roll mixing with various elastomers, such as polyurethane ones as well as nitrile rubber. The recombination in a single structure of the destruction fragments derived from the two polymers has sometimes resulted in improvement of the physicomechanical characteristics of the PVC (especially impact strength). The factors essentially influencing the modification of this property, justified by the bonding of the elastomers various amounts, have proved to be the following: the components ratio, the processing time, and the temperature. Analysing the results shown in Table 3.62 for the PVC-nitrile rubber system, one can notice that the most favourable processing conditions are as follows: 12.8% rubber (as 430

Mechanochemistry of Polymer Fracture Table 3.61 Influence of the processing conditions on PVC mechanical characteristics obtained by two-roll mixing with nitrile rubber [602] Parameters of Value of Mechanical propriety mechanical two-roll mixing Tensile Impact parameter strength strength

Elastomer concentration [(% given the PVC) T = 170°C, t = 14 min]

3.2 8.0 16.0

111 120 115.7

152 171 311

Duration (min) [T = 170°C, 8% rubber]

7 14 21

118 117 116

138 258 233

Temperature (°C) [t = 14 min, 8% rubber]

150 170 190

120 117 115

172 258 90

compared to PVC), T = 170°C, and t = 14 min. Similarly, the simultaneous two-roll mixing of PVC with polyurethane elastomers was influenced by the same parameters; however, in this case the elastomer concentration has a strongest effect. Taking into account the results depicted in Figure 3.195, the authors concluded that the processing temperature favours the increase of tensile strength, while a higher impact strength is obtained at high duration and low temperature. The variation of the tensile and impact strengths with the concentration of polyurethane elastomer is presented in Figure 3.196. Same block and graft copolymer formation, and not the one that Table 3.62 Polymer-polymer systems subjected to mechanical graft and block copolymerisation [313,599,600,603] Support polymer

Modifying agent

Type of mechanical Mechanochemical reaction stress

Polyethylene

Ethyl cellulose

Vibratory milling

Poly(ε-caprolactam)

Poly(vinyl chloride)

Nitrile rubber

Polyurethane elastomer

Vibratory milling

Two-roll mixing

Two-roll mixing

431

Effects of reactio

-

Grafting Block copolymerisation -

-

Crosslinking

-

Grafting Block copolymerisation -

-

Crosslinking

-

-

Grafting

-

-

Block copolymerisation

-

Crosslinking

-

Grafting

-

Block copolymerisation

-

Crosslinking

-

Insolubilisation Increase of melt viscosity index Improvement of wettability and of dielectric properties Insolubilisation Increase of melt viscosity index Improvement of wettability and of dielectric properties Increase of tensile and impact strength

-

Increase of tensile and impact strength

Macromolecular Mechanochemistry

Figure 3.195. Influence of the polyurethanic elastomer concentration on the mechanic properties of graft PVC. 1) σ r (190°C, 7 min); 2) σ r (150°C, 21 min); 3) a k (190°C, 7 min); 4) a k (150°C, 21 min) [602]. Figure 3.196. Variation of tensile strength (1) and impact strength (2) as a function of elastomer concentration [602].

occurs in some mixtures of those homopolymers subjected to processing, is demonstrated by the two discussed experiments. It was not possible to separate the elastomer out of the reaction products either by dissolving it in selective solvents or by precipitating it in a nonsolvent. At the some time, the fact that the turbidimetric titration curve presents only one level proved the existence of a single chemical compound. Introduction of segments or ramifications containing carboxylic groups onto the polymer-support chains, by mechanochemical grafting and block copolymerisation in the presence of acrylic acid, determined to increase of its hydrophilic properties, degree of swelling and solubility in water; the stability to the action of UV radiation increased, too. 3.8.1.3. Mechanochemical polycondensation The idea of this new type of mechanochemical synthesis has been suggested by a phenomenon noticed during the mechanochemical destruction of polyamides, when it has been found that besides the homolytical splitting of the macromolecular chains, some condensation reactions take place, implying the interaction of the polymer carboxyl and amino groups (proved by their drastic reduction concentration from the medium [83]. Some condensation achievement between the various functional groups belonging to the 432

Mechanochemistry of Polymer Fracture

destruction fragments, has also suggested the possibility of its development between the functional groups of a polymer and those of a judiciously selected micromolecular compound. Thus, it has become possible that by suitable selection of reaction partners, the condensation process should become dominant, allowing the obtaining of special-property products [85–90, 126–128, 193, 300, 317, 325, 660–663]. The aliphatic and aromatic diamines as well as the chlorides and dicarboxylic acids have been selected as micromolecular compounds, while the heterochain polymers from polyesters, polyamides, and polysaccharide classes (Table 3.63) have been used as macromolecular compounds. 3.8.1.3.1 Factors that affect mechanochemical polycondensation A. Chemical nature of polymers subjected to mechanodegradation Mechanodegradation of the heterochain polymers, particularly polyamides, poly(ethylene terephthalate) and cellulose, is accompanied by the variation of the final functional groups [83, 125, 126, 130, 131]. Based on this observation it was supposed that in the presence of some suitable agents the mechanochemical Table 3.63 Polymer disfunctional micromolecular compound system submitted to mechanochemical polycondensation [313] Polymer

Condensation agent

Mechanical activation technique

Poly(ε-caprolactam)

Sebacoyl chloride

Vibratory milling

Poly(ε-caprolactam) acid chloride

Ethylenediamine

Vibratory milling; cryolisis

Poly(ethylene terephtalate)

Ethylenediamine Hexamethylenediamine m-Phenylene diamine o-Phenylene diamine p-Phenylene diamine

Vibratory milling; cryolisis

Cellulose

Ethylenediamine

Vibratory milling; cryolisis

Poly(vinyl chloride)

Benzidine m-Phenylene diamine o-Phenylene diamine p-Phenylene diamine Urea

Two roll mixing

Poly(vinyl alcohol)

Ethylenediamine

Vibratory milling

Polyethylene

Ethylenediamine

Vibratory milling

433

Macromolecular Mechanochemistry

polycondensation should be activated. In order to establish the reaction possibilities of such systems, three types of polymers, namely – 1) heterochain polymers, having functional end groups whose number may increase by mechanodegradation (scission of the carbon-heteroatom bond); 2) carbochain polymers with side functional groups; and 3) carbochain polymers without any functional groups – have been selected as support. From the first group have been systematically studied: poly(εcaprolactam), poly(ethylene terephthalate), and cellulose; from the second group, poly(vinyl chloride) and poly(vinyl alcohol); and polyethylene from the third one. In the case of poly(ε-caprolactam), the sebacic acid dichloride has been chosen as condensation agent and aliphatic or aromatic diamines for all other investigated polymers. In all cases, the reaction evolution was followed by determining the amount of chemically bonded nitrogen. The reactions were carried out by vibratory milling, in inert atmosphere, and the condensation agent were used in liquid state at 18 °C. It was found that using acid dichloride, as coupling agent, the nitrogen content decreases while it increases in all other experiments due to the polymers’ reaction with diamine. Heterochain polymers, which in the presence of condensation agents suffers mechanocracking to the carbon-heteroatom bond, gain an increasing number of functional groups (or of active centres) and bind important amounts of condensation agent. Comparing the behaviour of cellulose with poly(vinyl alcohol), both polymers containing an increased number of –OH groups, it can be noticed the essential differences in the amount of bonded diamine. Thus, cellulose suffers mechanocracking to its glycosidic group, favouring the increase of the number of functional groups according to the increasing of mechanical stressing period and it attaches significant quantities of diamine. In turn, poly(vinyl alcohol), PVA, a carbochain polymer, binds in the same conditions only a small amount of diamine. As is seen in Table 3.64, this quantity is almost equal to those one fixed by polyethylene, polymer without any functional group [662]. It is clear that the reaction occurs with maximum efficiency whenever the polymer-support contains functional groups alongside of its backbone, which by mechanodegradation generates gradually in time an increasing number of active centres. New functional groups continuously built up as a result of the stabilisation of the above-mentioned active centres. 434

Mechanochemistry of Polymer Fracture

On the poly(ethylene terephthalate) model, which on destruction by vibratory milling at the room temperature (or lower) generates an increasing number of carboxylic groups, the reactions with a series of aromatic and aliphatic diamines have been achieved. From Figure 3.197 the correlation may be inferred between the chemical bonding of diamine (ethylenediamine) and the quantities characterising the mechanodestructive act promoting this synthesis, namely the increase of the chemically bonded nitrogen (curve 1) is in agreement with the increase of number of split bonds, hence the Table 3.64 Influence of the polymer nature on the mechanochemical polycondensation process [662] Polymer

Condensation agent

Milling duration (h)

Nitrogen content (%)

Poly(ethylene terephtalate)

Ethylenediamine

6 9 48 96

4.8 10.4 17.0 18.43

Poly(ε-caprolactam) Poly(ε-caprolactam)

Sebacoyl chloride

48

12.36 9.47

Cellulose Cellulose

Ethylenediamine Ethylenediamine

15 48

5.4 10.7

Poly(vinyl alcohol)

Ethylenediamine

48

1.5

Polyethylene

m-Phenylenediamine

48

1.9

destruction fragments formed under the same conditions but in the absence of diamine (curve 2), of the acidity index characterising the increasing number of carboxylic groups in the system (curve 3) which are correlated with the decrease in molecular weight (curve 4). The mechanochemical reaction between the destruction fragments of the support polymer and diamine used usually led two fractions, one soluble and the other insoluble, whose variation versus duration is described by Figure 3.198 (a and b). As is seen in this Figure and also in Figure 3.199 (a and b), the former fraction decreases quantitatively with increasing duration and the latter one increases but in both cases a limit of the conversion degree is attained. Determination of the kinetic characteristics, i.e. the constant of reaction rate (k) and reaction order (n) having the following values:

435

Macromolecular Mechanochemistry

Figure 3.197. Variation of the conversion degree and the amount of ethylene diamine chemically bound versus milling duration compared to the number of split bonds (Z), viscosimetric molecular weight and acid value (CA) (determined on a standard sample submitted to milling under the same conditions but in the absence of diamine): 1) amount of ethylene diamine chemically bound; 2) number of split bounds; 3) acid value; 4) molecular weight; 5) conversion degree into insoluble products; 6) conversion degree into soluble products [ 663 ].

Diamine k × 10 h –1 Ethylenediamine 0.63 Hexamethylenediamine 0.15

n 1.032 0.83

and proves that the thermal energy consumed in this process is very small, E = 4.69 kJ/mol [662]. B. Chemical nature of the condensation agent The effect of the chemical nature of the condensation agent has been demonstrated using reaction systems consisting by poly(ethylene terephthalate) as polymer support and aliphatic and aromatic diamines as condensation agents. The selection of the condensation agents was made in such way that the results obtained, concerning their structure, to contain useful informations about to the aliphatic or aromatic character of diamine, length of the hydrocarbonate chain, in the case of aliphatic ones, and the number of rings as well as the position of the amino group aromatic in ring, in the case of aromatic ones. Since, at room temperature the majority of diamines are solid substances, in order to enhance their accessibility to the polymer chains these substances have been used either in molten state or as solutions, Table 3.65. 436

Mechanochemistry of Polymer Fracture

Figure 3.198. Variation of the conversion degree of poly(ethylene terephthalate) in the polycondensation products, obtained from 10 g polymer and various amounts of ethylene dianime, EDA, (a) and hexamethylene diamine, HDA, (b): 1) 30 g ethylene diamine (HDA in curve b); 2) 20 g EDA(HDA in curve b); and 3) 10 g EDA (HDA in curve b). Solid line – soluble fraction, broken line – insoluble fraction.

C. Temperature It is well known that the temperature represent a decisive factor in the achievement of any chemical reactions, the sense of their occurrence being strongly influenced by this parameter. Each chemical reaction is characterised by its specific activation energy, which according to the formal kinetics can be calculated using Arrhenius’ equation. The effects produced by mechanical energy are particularly correlated with this factor, since the elastic energy and not the thermal one is essential for the mechanochemical processes initiation and progress. In this case, the caloric oscillations only modify the effects produced by the mechanical ones. Theoretically, the thermal activation energy should be equal to zero; however, since the mechanochemical processes can not occur outside of the action of medium temperature, it usually attains only small values. Mechanochemical reactions are significantly influenced by temperature only in the measure in which this one attains values that 437

Macromolecular Mechanochemistry

Figure 3.199. Variation of the content of chemically bonded EDA ethylenediamine (a) and hexamethylene diamine (b) in 10 g of poly(ethylene terephthalate) and: 1) 30 g diamine; 2) 20 g diamine; and 3) 10 g diamine, respectively. Table 3.65 Influence of the chemical structure of diamine on the amount of chemically bonded nitrogen during mechanochemical polycondensation a element of diamine

Aliphaticaromatic character Length of the hydrocarbonate chain for the aliphatic diamines

Type of diamine Ethylenediamine

NH2

p-Phenylenediamine Ethylenediamine

N H2

p-PhenyleneNumber of aromatic rings for diamine aromatic diamines Benzidine Number and relative position of the diamine groups in aromatic ring

Chemical structure

(CH2 )2

NH2

Aggregation Amount state of nitrogen bounded (%) solution 2.00

NH2

solution

3.75

NH2

(CH2 )2

NH2

liquid

16.50

NH2

(CH2 )6

NH2

solid melt

2.20 13.70

NH2

solution

3.75

solution

2.37

liquid

0.59

solution

1.67

solution

3.75

N H2

NH2

NH2

Aniline NH2

m-Phenylenediamine

NH2 NH2

p-Phenylenediamine

NH2

NH2

438

Mechanochemistry of Polymer Fracture

determines the change of the polymer physical state. In all the cases, low temperatures favour these reactions. However, according to the increase of temperature the effects released by the thermal energy compete with the mechanical ones and, in certain situations, can prevail. Mechanochemical polycondensation is a reaction that occurs in the presence of a polymer that suffers the mechanocracking process in the presence of a condensation agent. Even if for its achievement the polymer’s end functional groups must be essential, this process is apparently contradictory influenced by temperature. Let us take once again as example, poly(ethylene terephthalate) mechanochemical polycondensation with aliphatic or aromatic diamines. As this reaction to proceed the formation of a high number of carboxylic groups, by splitting of polymer’s macromolecular chains, is required. Since, this reaction is mechanically activated one, the number of molecular scissions and consequently of carboxylic groups will proportionally increase with the decrease of temperature and increase of chain rigidity. Subsequently, as the reaction of the functional groups with the condensation agent to occur, an increase of chains flexibility, which is possible by the increase of temperature, is required. These requirements are in contradiction only in the measure in which the polycondensation reaction is classically regarded, reducing its achievement only to the chemical interaction of the functional end-groups, accompanied by the elimination of low-molecular-weight compounds. Indeed, it was found that carrying the polycondensation within a large range of temperature (ranging from –30 to 75°C), the amount of chemically bonded diamine increases according to the increase of temperature. In order to clarify the essential features of the effect of temperature, the value of the thermal activation energy was determined, using the Arrhenius equation. From graphical representation of log k = f(1/T), using the initial reaction rates determined at different temperatures, a very low value, namely E a = 1.12 kcal/mol was found. The explicitly of the sense of mechanochemical reaction occurrence was possible by the evaluation of its efficiency. In this aim, apart to a series of mechanochemical reactions, carried out at durations varying from 1 to 48 hrs and temperatures varying from –30 to 75°C, control reactions have been performed, in the similar reaction conditions but in the absence of the mechanical energy. The efficiency of the mechanochemical reaction was calculated using the following relation ρ = (n–n 0 )/n 0 , where ρ is the efficiency of the 439

Macromolecular Mechanochemistry

mechanochemical reaction; n the content of chemically bonded nitrogen by vibratory milling (thermal + mechanochemical); n 0 – content of thermally bonded nitrogen, Table 3.66. As Table 3.66 shows, the efficiency of mechanochemical polycondensation decreases with the increase of temperature. Thus, for the maximal temperature used (75°C) the results concerning the amount of chemically bonded nitrogen by vibratory milling and thermally are very close each to other, i.e. 15.2 and 14%, respectively. Analogous to the mechanochemical destruction, whose efficiency, expressed by the number of split bonds (Z), increases concomitantly with the decrease of temperature (Figure 3.200, curve 1), the mechanochemical polycondensation evolves in the same sense. Thus, the amount of chemically bonded ethylenediamine is maximal to the minimal temperature (Figure 3.200, curve 2) [664]. The study of temperature influence also evidenced the formation by polycondensation of two distinct fractions: soluble one and insoluble, respectively. As Figure 3.201 shows, their quantitative ratio depends on both temperature and the chemical nature of the diamine [664]. In the given temperature range in which the polymer does not change its physical state, the mechanochemically synthesised polymers, by reactions having different efficiencies, are similar in the structure and properties. The increase of temperature above the investigated limit (75°C) on one side leads towards the change of the polymer physical state and on other side the frequent scissions of the macromolecular chains give rise to shorter and shorter chain fragments, which gradually become soluble in the condensation agent. In this way, the mechanochemical aminolysis plays a role more and more important. D. Nature of the reaction medium In order to establish the reaction mechanism of the mechanochemical polycondensation, the importance of the macro-radicals Table 3.66 Efficiency of mechanochemical polycondensation [664] Temperature Amount of the chemically Amount of the chemically Efficiency of the bounded nitrogen by bounded nitrogen by only mechano-chemical by thermal activation polycondensation mechano-chemical activation (%) (%) (°C) (ρ) -5 + 18 + 75

1.0 11.8 15.2

1.0 5.0 14.0

440

7.2 1.35 0.086

Mechanochemistry of Polymer Fracture

Figure 3.200. Variation of the amount of chemically bonded ethylenediamine (by mechanochemical polycondensation) versus temperature as compared to the number of split bonds by polymer support mechanodestruction: 1) number of split bonds; 2) amount of bonded ethylenediamine. Duration of vibratory milling was of 3 h for curve 1 and 9 h for curve 2 [664].

Figure 3.201. Influence of diamine chemical nature and of the duration and temperature on poly(ethylene terephtalate) mechanochemical polycondensation: 1) ethylenediamine (soluble, 18°C); 2) ethylenediamine (insoluble, 18°C); 3) hexamethylene diamine (soluble, –5°C); 4) hexamethylene diamine (insoluble, –5°C); 5) ethylenediamine (soluble,75°C); 6) ethylene-diamine (insoluble, 75°C).

that inevitably exist in the reaction medium was investigated, by studying the effect of radicalic acceptors. The existence of the polymer ’s free macro-radicals, in the presence of diamines was proved following the variation of the chemically bonded nitrogen and the chemical nature of certain radicalic acceptors. Depending 441

Macromolecular Mechanochemistry

on their chemical structure, the acceptors used in these experiments influence in different manner the mechanochemical polycondensation process, Figure 3.202. Thus, some of the acceptors added to behave as accelerators of the reaction with diamines (oxygen and nitrogen oxide, curves 2, 3, compared to curve 1 in argon) and others as retarders (curves 4, 5 obtained for different amounts of phenol). Table 3.67 lists the products capable of modifying in one sense of another the reaction of the destruction fragments with diamines. The results confirm the presence and significance of the radical centres in the reaction system of this type. On this basis and taking the fact into account that polyethylene alone is not able to get active functional groups by destruction reactions and considering the results obtained with the diamines, it was concluded that the latter may act as radicalic acceptors contributing in this way at least partially to the development of ‘mechanochemical polycondensation’. More detailed studies have been accomplished on poly(ethylene terephthalate) for which the conditions required to react either directly with the aliphatic and aromatic diamines or by means of acyl chlorides, e.g., sebacyl chloride, have been settled. Polyamides may be converted similarly by means not only of diamines but also of ethylene glycol, phenol, and diacids. The insoluble fractions obtained in this way are thermostable, resistant to chemical agents, exhibit features of organic semiconductors, being recommended for either direct use when substances with such properties are required or as intermediates in other reactions.

Figure 3.202. Variation of the nitrogen percentage with the milling time for products of mechanochemical polycondensation of poly(ethylene therephthalate) with ethylenediamine: 1) argon; 2) oxygen; 3) nitrogen oxide; 4) phenol (20 g); 5) phenol (30 g). Poly(ethylene terephthalate) to ethylenediamine ratio = 1 [664]. 442

Mechanochemistry of Polymer Fracture Table 3.67 Influence of the radical acceptor on the mechanical polycondensation reaction between poly(ethylene terephtalatae) and ethylenediamine a Component ratio

Poly(ethylene terephtalate : EthyleneDiamine 1 : 1 (gravimetric)

Acceptor nature

Acceptor structure

Dichlorothiophenol

SH Cl

Cl

β-naphtol Hydroquinone

(C10H7OH)

24 9

16.0 5.54

9 9

6.6 4.1

24

14.0

9 9 9

8.6 8.9 2.25

OH

HO

Dodecyl mercaptane 2-Mercaptobenzothiazole

Synthesis Content of time chemically bound nitrogen (h) (%) 9 6.7

CH3(CH11)SH N C

SH

S

Diphenyl picrylhydrazyl N N• NO2

O2N

NO2

Molecular oxygen Nitrogen oxide Phenol

O2 NO HO

a

– Temperature: 18°C; filling ratio: 0.4%.

For instance, the polymers of the polyester-polyamide type obtained from poly(ethylene terephthalate) with different diamines, especially aromatic ones, due to their end amino groups, can be converted by diazotization and coupling into coloured polymers, Table 3.68; if the coupling components contain in their turn diazotable primary amino groups the adjustment of the material nuance according to one’s desire becomes possible [663]. For the same reaction of poly(ethylene terephthalate) with diamines, but in order to keep polymer’s crystalline structure and its fibrous morphology, the crylolisis cycle frozen-unfrozen was chosen as mode of mechanical stressing. After diazotization and coupling, the sample obtained could be coloured, using the same coupling reagents. Thus, poly(ethylene terephthalate), which usually is coloured by the colorant or pigment particles dispersion in polymer bulk, on this way may be chemically coloured, through the reaction of coupling agent with the polycondensation products, ob443

Macromolecular Mechanochemistry Table 3.68 Coupling components used for synthesis of coloured polymers [663] Coupling components Name Structure β-naphtol

pH of the coupling solution pH > 7

OH

Resorcinol

*

pH > 7 yellow (coupling either in ortho or para position with respect to – OH group) pH > 7 yellow

OH *

OH

Naphtol AS-g (diacetyl acetotoluidine)

CH 3 CH 3

CO H2C *

OC

Acid H pH > 4 *

HN 2

HO

H3OS

Colour obtaineda red

NH 2 * pH = 4 SO 3H

pH ≥ 4 the first coupling at pH = 4; the second coupling at pH = 8

violetb (after two successive couplings)

*

- Coupling position. a - The polymer was used in powder form. b – According to literature data the sulphur atom confers to the polymer ionexchanging properties.

tained by different mechanochemical methods, Figure 3.203. E. Mechanical parameters Duration of vibratory milling The kinetic characterisation of the mechanochemical polycondensation was performed correlating the amount of chemically bonded diamine, in different moments of the chemical reaction, to the most important characteristics of the primary act of mechanocracking, i.e., the number of split bonds (Z), viscosimetric molecular weight M η , and acid value (CA), determined under similar conditions but in the absence of diamines [663, 664]. The evolution of the polycondensation reaction was followed over a long period of time, from 1 to 96 h, using mixtures poly(ethylene terephthalate)-aliphatic diamines (ethyene diamine and hexamethylene diamine), which have been supposed to vibratory milling, under inert atmosphere, at T = 18±2°C, Figure 3.197. As it was already mentioned, after the removing of the unreacted agent of condensation, the final compound contains two fractions: insoluble one that decays in time and soluble fraction that increase with the prolongation of the mechanical stressing. Analogous to mechanocracking process the soluble fraction attains a constant 444

Mechanochemistry of Polymer Fracture

Figure 3.203. Enhancement of the coloration capacity of poly(ethylene terephthalate) by mechanical polycondensation [664].

value, which is not changed irrespective of process prolongation (Figure 3.198 a and b). In the case of poly(ethylene terephthalate) the limit molecular weight is attained after 48 h of vibratory milling (Figure 3.197 curves 2–4), period at which the maximum of conversion degree is reached. Therefore, in the moment when the splitting of chain fragments ceases the formation of new functional groups and their reaction with diamines is stopped, too. The above-mentioned findings have been confirmed by IR spectroscopy. Thus, the for insoluble fractions obtained at short times (6 hrs) one can observe the decay of the absorption band at 1720 cm –1 specific for ester carbonyl groups –CO–O– in the starting polymer and the apparition of numerous new bands. Thus, at 1470, 1640, 2910, and 3100 cm –1 , strong absorption maxima appear because of peptide groups, –CO–NH–. In addition, the absorption bands at 3300 and 920 cm –1 confirm the presence of primary imido and amino groups, respectively. For longer times (between 15 and 190 hrs) the product of mechanochemical polycondensation no longer exhibit in their IR spectrum the band at 1720 cm –1 but instead show a clear new absorption band at 1510 cm –1 , belonging to >C=N– groups. The authors explained the absence from IR spectra 445

Macromolecular Mechanochemistry

of the band at 1720 cm –1 by a decarboxyloation reaction that takes place at long reaction times, followed by tautomerism of peptide groups: C

NH

C

O

N

OH

Filling ratio The filling ratio η, i.e. the ratio of the quantity of materials to be processed (in this case, polymer and coupling agent) to the milling bodies, is another important parameter that was also studied. Three successive millings were done at varying durations, ranging from 1 to 24 hrs for η = 0.2%, 0.8%, and 3.2%, respectively. The results are given in Figure 3.204 [663, 664]. The correlation between the nitrogen percentage and the filling ratio leads to the conclusion that low values of the latter result in the highest nitrogen content. Influence of building material In order to demonstrate this influence, two successive milling trials, one using stainless-steel vessels and balls and the other using porcelain materials, have been performed. Working temperature was of about 28°C, and the filling ratio was 0.8%. The results are presented in Figure 3.205, which leads to conclusive differences. Nitrogen percentages obtained with metallic equipment are plotted as an ascending line in that Figure (curve 1) while porcelain equipment gives a descending line for similar milling times. Starting with the idea that there are large differences in hardness between the building materials used in the two types of milling, the authors tried to obtain a correction factor via ash determination.

Figure 3.204. Influence of filling ratio and milling time on mechanochemical polycondensation reaction: 1) η = 0.2%; 2) η = 0.8%; 3) η = 3.2% [663,664 ]. 446

Mechanochemistry of Polymer Fracture

This was possible with metallic equipment although the results were only slightly affected by applying the correction; the ash percentage was small and nearly constant with respect to time (Figure 3.205, curve 2). When the porcelain mill was used, the polycondensation products gave, on combustion, increasing amounts of residue; the increase was found to be proportional to milling duration, up to about 90% for a mechanical working time of 18 hrs (Figure 3.205 curve 3). The considerable increase in time of the residue amounts as well as the corresponding decay of the chemically bonded nitrogen proves the occurrence of a chemical reaction between inorganic powder – that is, finely ground porcelain – inevitably present as a result of the balls’ contact with the walls of equipment, and the components of the reaction system. To obtain some indications of the structure of the thermostable residue (undecomposed at 900°C) obtained in these reactions, its IR absorption was determined and compared with the corresponding IR spectrum of the control sample (pulverised porcelain). Analysing Figure 3.206, the differences between the two spectra are evident. For the first sample, the absorption maxima appear at 810 cm –1 and 1190 cm –1 (curve 1 in Figure 3.206), corresponding to ≡C– and ≡C–N= bonds. The IR spectrum of the control sample lacks these bands, testifying to the existence of a reaction having occurred either between the final polycondensation products and the active centres of the inorganic mass, or between the two compounds (polymer and diamine) and the active centres of the inorganic mass.

Figure 3.205. Influence of the nature of building material of equipment on percentage of chemically linked nitrogen: 1) percentage of nitrogen for stainlesssteel equipment; 2) percentage of residue for stainless-steel equipment; 3) percentage of residue for porcelain equipment; 4) percentage of nitrogen for porcelain equipment.

447

Macromolecular Mechanochemistry

Figure 3.206. Comparative IR spectra of: 1) porcelain; 2) mechanochemically reacted porcelain.

The insertion of peptide groups –CO–NH– in the backbone of polycondensation products along the aromatic ring of the polyester chain provides the conjugation of ring electrons with those participating in the binding of oxygen and nitrogen. This idea is supported by properties such as electrical conductivity (σ = 0.22·10 –12 to 0.55·10 –8 Ω –1 cm –1 , measured in the range of temperatures from 84 to 184°C), activation energy of conductivity (E a = 0.98 ev.), and paramagnetism. The latter was observed using ESR technique for both soluble and insoluble products. Comparative ESR spectra of soluble fractions of products synthesised by mechanochemical polycondensation for 96 hrs are given in Figure 3.207. From this spectrum, the factor g (g = 2.0029512) and the number of spins/g (N = 2.214·10 14 spin/g) were calculated. 3.8.3.2 Considerations of the mechanism of mechanochemical polycondensation The studies of the influence of the polymer’s chemical nature, of condensation agent, of radicals acceptors, of temperature proved that the mechanochemical polycondensation may dominantly proceed by both functional groups or radicalic mechanism, depending on the initial parameters of reaction and on medium polarity. Thus, in the case of poly(ε-caprolactam) processed by vibratory milling, in the presence of sebacoyl chloride, chain fragments bearing acid chloride end groups are generated, which subsequently are able to react with different amines, e.g., m- or p-phenylendiamine). The most important reactions are presented below [662]:

448

Mechanochemistry of Polymer Fracture

Figure 3.207. ESR spectrum of mechanochemical polycondensation.

a

soluble

product

synthesised

by

Mechanochemical destruction of poly( ε-caprolactam) in the presence of acid dichlorides A ) Generation of polymer's acid chloride end groups O H2N (CH2 )5

2

+

O CH2

CH2

+

2

(CH2 )8 C

C Cl

Cl

Cl

O

O

C

NH

CH2

CH2

+

2

CH2 NH

Cl O

O CH2

COOH

+

2

C

C

CH2

O (CH2 )8 C Cl

O

3

O

3

- CO2

CH2

COOH

(CH2 )8 C

C

-HCl

CH2

O

O CH2 NH2

Vibratory milling

(CH2 )8 C

C Cl

1 H2N

O

O NH (CH2 )5 COOH n

C

C

O O

(CH2 )8 C Cl

B ) Reaction between polymer's acid chloride end groups and diamine O

O 2

C

(CH2)8 C

Cl

O NH

CH2

CH2

C

+

NH2

NH2

- 2HCl

Cl

4

C

CH2

O

C

C

(CH2 )8 C

O NH

NH

NH

(CH2 )8 C

O

O

O NH CH2

Cl

5 or: O C

(CH2 )8 C

Cl

O NH

CH2

CH2

C

+

NH2

NH2

Cl O NH CH2

Cl C O

CH2

C NH

(CH2 )8 C O

CH2

C Cl

O

O

CH2

5'

449

NH 2

-HCl

Macromolecular Mechanochemistry

The reaction products containing as end groups aromatic diamino residues by diazotization and coupling with colorants assure the dyeing of polymer support in specific colours, depending on the nature of the coupling reagent chosen. If the coupling agents contain in their structure amino groups bonded to aromatic rings, the dyeing process can be continued; thus, it is theoretically possible to obtain any desired nuance (see Figure 203, for the reaction product based on polyesteric support. The involved reactions are the following: O CH 2 C

NH

NH2

NH 2 O H

O

Acid H pH = 4

CH 2

C N

NH

N

Na O3S

SO3 Na

1 )NaNO2 /HCl 2 ) Acid H/pH = 8

NaO 3 S

SO 3 Na

N

CH 2

NH 2 OH OH

N

O C NH

N

N

NaO 3 S

SO3 Na

In the case of vibratory milling, the polycondensation mainly occurs to the new-formed surfaces, by fracture of polymer support. The elementary steps occurring in the case of the radicalic chained mechanism, taking poly(ethylene terephthalate) as polymer support and different diamines are presented on the next page. Initiation (macroradicals generation under the action of mechanical energy) CH2 CH2 O C

C

O CH2 CH2 O C

O

O

O

•

Vibratory milling

C O O

•

CH2 CH2 O C

C

+ O CH2 CH2 O C

C

O

O

O

O

O

Propagation •

O C

C O CH2 CH2 O + NH2 R NH2

O

•

C

O

O

O

C O CH2 CH2 OH + NH R NH2

O

CH2 CH2 O C

CH2 CH2 O C

•

O C

O •

+ NH R NH2

O

CH2 CH2 O C

C NH R NH2

O •

O

C NH R NH2 + O CH2 CH2 O C

C

O

O

O

O

C NH R NH + HO CH2 CH2 O C

C

O

O

•

CH2 CH2 O C O CH2 CH2 O C O

O •

•

C O + NH2 R NH2 + CH2 CH2 O C

C

O

O

O

C OH + NH R NH + CH3 CH2 O C

C

O

O

•

CH2 CH2 O C O

O

O

•

O

450

O

Mechanochemistry of Polymer Fracture Recombination CH2 CH 2 O

CH2 CH2 O

CH2 CH2 O

•

C

C

O

O

C

C

O

O

C

C

O

O

C

C

O

O

C

C

O

O

CH2 CH2 O

CH2 CH2 O

•

•

•

+ NH

NH

R

NH

R

R

•

•

NH

•

CH2 CH2 O

+ O

NH

O

C

C

O

O

C

C

O

O

•

+ NH R

NH R

NH2

•

C

O

O

C

C

O

O

C

O

O

NH

R NH2

CH2 CH 2

O

NH + C

NH

O

C

CH2 CH2

O

CH2 CH2

O

R = (CH2)2 ; (CH2)6

Briefly, the most important reactions that characterising the mechanochemical polycondensation, for the discussed systems are the following: (1) C

I.

C

O

Mechanodegradation

CH2 CH2 O

(2)

O O Poly(ethylene therephtalate)

•

C

C

O

O

C

C

O

O

II.

•

C

C

O

O

C

C

O

O

•

+ O

•

O +

CH2 CH2 O

•

CH2 CH2 O

O

•

+ O

CH2 CH2 O

•

•

O +

C

Stabilisation by disproportionation

C

O

+

H

CH CH2 O

H

O

CH2 CH2 O

C

C

O

O

OH + H2C

CH

O

POLYCONDENSATION A) Through functional groups

C

C

O

O

III. O

CH2

C

H

H

NH2 R NH2

C

C

O

H CH2

O

C

O

O

C

Destruction fragments

N R NH2

C

C

O

H

O

CH2

H

O C

N R NH2

OH

C

C

O

O

C

N R N

N R

NH

C

C

O

OH

R NH2

N R NH2

C

C

O

O

C

C

O

OH

IV.

C

O

O

C

C

O

O

C

C

O

O

C

C

O

O

•

• O + H N H

+ H N

R N H H

•

HN

HN

R

R

R N H H

• N H + O H

N •

H

+

•

C

C

O

O

C

C

O

O

OH + H N •

HN

R

NH

C

C

C

C

O

O

O

N H H

C

C

C

C

O

O

O

O

C

C

O

OH

451

NH

HN

R

N •

R NH

N R

N

H

+ HO

C

C

O

O

C

C

O

O

C

C

OH

O

etc.

C

H2C

O

R NH C

C

O

O

N R

R N H H

O

C O

H

B) Through macroradicals C

N

H

C H

N

C

C

OH

O

Macromolecular Mechanochemistry

Interesting results were obtained by the mechanochemical polycondensation of poly(vinyl chloride) with aromatic diamines, starting from the capacity of these micromolecuar compound to bind the radical destruction fragments resulting from the polymer. Under the conditions created by vibratory milling, cryolisis, or two-roll mixing, PVC changes its molecular weight and binds chemically to the aromatic diamines or urea, a fact which entails important changes in its physico-mechanical characteristics. The most spectacular changes take place during two-roll mixing when the mechanochemical process becomes complicated by the thermooxidative one. Consequently, variable quantities of aromatic diamine (o-, m-, p-phenylene diamine or benzidine) are bound chemically to the destruction fragments of the polymer, depending on the components’ ratio in the initial mixture, temperature, and duration of the processing (Figure 3.208). The diamine concentration increase (related to the macromolecular compound) in the reaction mixture leads to even higher quantities of low molecular weight compound in the reaction products, having a reinforcing effect on the polymer that is expressed by the tensile strength increase [308, 314] From the used diamines, benzidine binds in the highest amount in the polymer. The influence of the two other parameters studied (temperature and processing duration) is evident from the data analysis in Table 3.69, in which the increase of tensile strength is considered. Once again it can be seen that the highest increases (expressed in percentage) of this property are obtained in the presence of benzidine. The reaction product vitrification temperature differs from that of the PVC, being generally higher, this fact indicating slight crosslinking of the polymer. This assumption is also sustained by the increase of the insoluble fraction of PVC in specific solvents.

Figure 3.208. The variation of chemically bonded diamine amount: 1) benzidine; 2) mphenylene diamine; 3) p-phenylene diamine; and the tensile strength variation: 4) benzidine; 5) p-phenylene di-amine; 6) mphenylene diamine, with diamine quantity from the initial mixture [308].

452

Mechanochemistry of Polymer Fracture Table 3.69. Tensile strength modification of poly(vinyl chloride) by two-roll mixing in the presence of aromatic diamines [302] Two-roll milling parameters

Duration (min) [T = 170°C, 1% diamine]

Temperature (°C) [t = ( min, 1% diamine]

Diamine concentration (%) versus PVC [T = 170°C, t = ( min]

Parameter value 5 10 15 20 30 150 160 170 180 190 1 2 3 4 5

Tensile strength increase (%) for samples with: m-Phenylene Benzidine p-Phenylene diamine diamine 1% 5% 108 112 119 118 112

145 155 152 130 -

108 117 114 106 -

104 106 116 117 -

103.5 105 108 111 108.5

105 106.5 108 107.5 105

103 103.5 104 103.5 102

108 117 125 138 145

108 112 118 123 -

104 111 116 121 -

The behaviour of the tensile static stress is also superior. The benzidine-containing product’s rheological characteristics, calculated from the creep experimental curves, have superior values as compared to the starting polymer, and show its stiffening due, especially, to crosslinking. 3.8.1.4. Mechanochemical complexation Polar polymers and mechanochemically synthesised polycondensation products proved the ability, as through electronegative atoms that they possess (oxygen, nitrogen) due to the electrons uninvolved in chemical bounds, to function as macromolecular ligands in the mechanochemically activated syntheses of polychelates. The reaction of complexation has been firstly observed as a secondary process that accompanies mechanochemical polycondensation, by the participation to this reaction of the metal from the apparatus walls (Figures 3.206 and 3.207) [660, 661, 663, 664]. Later, the processes of mechanochemical complexation were better controlled by a suitable choice of the reaction components [91, 92, 666–675]. Thus, several polymers containing electonegative atoms along their macromolecular chain or enclosure them in their structure as a result of chemical reactions, can be used in the complexing reactions of some metals such as iron, manganese, or vanadium by mechanical activation either in solid state (vibratory milling) or in solution (ultrasonic treatment). 453

Macromolecular Mechanochemistry

Other reaction systems have been studied employing natural or synthetic heterochain polymers, different metallic ions, and various activation methods, as Table 3.70 shows. The metal complexation to the macromolecular ligands determines the nitrogen percentage variation, which represents a criterion for estimating the mechanochemical complexing efficiency. The experimental data have led to the conclusion that the reaction is influenced by the chemical nature of the support polymer and by complexant center as well as by the working conditions (duration, medium, temperature, component ratio). Thus, it may be noticed, as compared to Fe 3+ , Mn 2+ has a higher capacity to complex with a ligand obtained through the mechanochemical polycondensation of poly (ethylene terephthalate) with ethylene-diamine (Figure 3.209). The nitrogen percentage in its complexes is always lower although the atomic weights of both metals are very close to each other. The amounts of complexed metal increase over time, although Figure 3.209 does not clearly point this out. Test samples obtained by the polycondensation of poly(ethylene terephtalate) with ethylenediamine, at the same duration, show a higher increase of the nitrogen percentage over time than in the presence of the complexant centers when constant values are reached only after 48 hrs of vibratory milling. It has to be mentioned that the complexation reaction, in the case of poly(ε-caprolactam), was also done in the absence of ethylenediamine as condensing agent, due to the peptidic group’s presence in the polymer structure. Furthermore, the corresponding monomer of poly(ε-caprolactam), i.e. ε-caprolactam, can play itself the role of ligand, Table 3.71. The presence of complexant centers changes essentially the structure of the initial polymer. The formed complexes may be characterised by the residue obtained by calcination (at 1000°C). One can notice the drastic decay of the amount of carbon and nitrogen accompanied by an important increase of thermostable residue. The complexes characterised by low-molecular-weight lig-ands, based on ε-caprolactam, show a particular behaviour. Under the effect of heat they do not soften but gradually decompose. The complexes with macromolecular ligands, based on poly(ε-caprolactam) show characteristic thermomechanical curves, which delimit the specific highly elastic domain depending of the nature of the complex formed. Thus, for two complexes, one of them contain-ing Mn 2+ and other one Fe 3+ as complexat center, respectively, the comparative results are presented in Figure 3.210 [671]. 454

Chemical and thermal stability Semiconductor properties • • Vibratory milling Poly(ethylene terephthalate)

• •

Some as for poly(ε-caprolactam) Some as for poly(ε-caprolactam) • Mechanodegradation products • • • Cellulose

Vibratory milling Cryolisis Ultrasonic treatment

Some as for poly(ε-caprolactam) Vibratory milling Vegetal proteins

Mechanodegradation products Polycondensation products with aliphatic and aromatic diamines

Fe3+, Mn2+, V3+

Chemical stability Chemical stability Enzyme-coupling capacity • • • Fe3+, Mn2+ Fe3+, Mn2+ Co3+

Chemical stability • Fe3+, Mn2+

New properties Chemical stability, thermal stability, semiconductor properties • Complexing center Fe3+, Mn2+ Ligand Mechanodegradation products Polycondensation product with diamines § § Activation method Vibratory milling Support polymer Poly(ε-caprolactam)

Table 3.70. Investigated systems in mechanochemical complexation studies

Mechanochemistry of Polymer Fracture

The achievement of the above-mentioned reactions was proved to be essential by both theoretical and practical point of view. Thus, the synthesis of a manganese complex with εcaprolactam contributes to the clarification of mechanochemical mechanism of ε-caprolactam polymerisation [671, 676]. The presence of the metal in the mechanochemical complexation products has as a consequence some special properties, not only in comparison with those of the initial polymer, but also in comparison with the ligand. Thus, one can note the special thermal stability which makes the polychelate compounds lose weight at over 200°C: the higher metal content, the lower percentage of weight loss. It may also be noticed that, at 900°C the calcination residue is superior to the content of the complexed metal, in fact, which led to the conclusion that it still contains an organic phase linked with the metal in very stable thermal structures. Due to the metallic atoms, the synthesised polychelate have paramagnetic properties, with an ESR signal that has a characteristic hyperfine structure (Figure 3.213 a) and is, as a rule, an asymmetric one. The Mössbauer spectrum confirms the Fe complexation at oxygen and nitrogen atoms existing in the macromolecular ligand chain 455

Macromolecular Mechanochemistry

Fig. 3.209. The influence of duration on nitrogen content and on the activation energy of the electrical (E a ) for some mechanochemical synthesised complexes: 1) poly(ethylene terephthalate) + ethylene diamine + Fe 3+ (% N); 2) same as 1 (E a ); 3) poly(ethylene terephthalate) + ethylene diamine + Mn 2+ (% N); 4) same as 3 (E a ) [305]. Table 3.71 Results of the elementary analysis of some complexes with Fe3+ and Mn2+, obtained by vibratory milling and using ε-caprolactam and poly(εcaprolactam) as ligands Sample

Poly(ε-caprolactam) Poly(ε-caprolactam) Complex poly(ε-caprolactam)-MnCl2, 10:5 (w/w), soluble Thermostable residue after calcination Complex poly(ε-caprolactam)-FeCl3.6H20, 10:5 (w/w) Complex poly(ε-caprolactam)-MnCl2.4H2O, 10:5 (w/w), insoluble Complex (ε-caprolactam)MnCl2.4H2O, 10:1 (w/w) Complex (ε-caprolactam)MnCl2.4H2O, 10:1 (w/w) Complex (ε-caprolactam)MnCl2.4H2O, 10:1 (w/w)

Duration (h)

Elementary analysis N Cl (%) (%)

C (%)

H (%)

0 24 96

61.52 60.66 44.13

9.42 8.65 5.66

11.76 9.55 5.41

96

0.1

-

1

36

52.81

7.87

10.13

2.37

-

50

16.34

2.90

1.75

3.09

67.43

24

30.43

5.6

1.84

0.77

27.6

50

36.5

5.44

2.73

2.38

38.4

24

31.67

5.56

3.72

0.61

23.95

2.75

Residue (%) 29.9

99.82

(Figure 3.213 b). The semiconductor properties of the soluble fractions belonging to such compounds can be explained on the same basis. It has been found that there is a direct dependence between the amount of 456

Mechanochemistry of Polymer Fracture

Figure 3.210. Thermo-mechanical curves for: 1) complex obtained from 10 g poly(ε-caprolactam) and 0.1 g MnCl 2 . 4H 2 O; 2) complex obtained by 10 g poly (ε-caprolactam) and 0.1 g FeCl 3 . 6H 2 O [671]. Table 3.72. Variation of electrical conductivity of some complexes with parameters of mechanochemical synthesis [668, 671] Parameter of mechanochemical synthesis Amount of Duration EDA (g) (h)

Support polymer

Polychelate based on Fe3+ [Poly(ε-caprolactam) + FeCl3] Polychelate based on Fe3+ : [Poly(ε-caprolactam) + EDA + FeCl3] Support polymer

Electrical conductivity (Ω.cm-1)

Activation energy (eVb))

4 36

-

(8.79.10-12)112° – (9.74.10-14)63°C (18.79.10-12)112° – (1.27.10-14)60°C

2.77 1.35

1 36

5 5

(4.3.10-12)112° – (3.6.10-134)99°C (7.15.10-10)116° – (1.61.10-11)50°C

3.2 1.25

0.25

5

(1.03.10-9)106° – (2.06.10-13)30°C

-

15 96 72 72

5 5 15 30

(5.60.10-7)108° – (2.24.10-20)30°C (1.6.10-6)106° – (3.85.10-10)30°C (2.60.10-7)121° – (1.59.10-10)30°C (5.60.10-7)108° – (2.24.10-10)30°C

-

96

5

(5.41.10-8)96° – (1.15.10-10)12°C

-

96

5

(1.50.10-10)110° – (1.15.10-14)31°C

-

3+

Polychelate based on Fe : [PET + EDA + FeCl3]

Polychelate based on Mn2+ : [PET + EDA + Mn(OCOCH3)2 PET + Mn(OCOCH3)2

complexed metal and the electric conductivity activation energy (see Figure 3.209). Milling time increases result in ever greater amounts of complexed Fe or Mn (curve 2 and 4, respectively, in Figure 3.209) and, consequently, in the decrease of electric conductivity 457

Macromolecular Mechanochemistry Table 3.73 Values of electrical conductivity and activation energy a) of polymeric metal complexes synthesised mechanochemically [662] Sample

Type of action

Complex from: PET + EDA + VCl3+ c)

– E from

b)

Electrical conductivity (Ω.cm-1)

Activation energy (eVb)) 1.3

Ultrasonic

5

3.71.10-9 at 146°C 2.27.10-11 at 43°C

Vibratory milling

96

7.8.10-8 at 155.3°C 3.12.10-10 at 62.9°C

1.51

144

4.10-7 at 154.2°C 3.68.10-9 at 63.9°C

-

Complex from: PA + MnCl2.4H2O a)

Duration of action (h)

σ T = σ à exp(− E / RT ) ;

– 1 eV + 1.602095.10-19 J; c) – PET, poly(ethylene therephtalate); EDA, ethylenediamine; d) – PA, poly(ε-caprolactam).

Table 3.74. Composition of some samples obtained by ultrasonic action in methanol and by vibratory milling [669] Type of action

Duration of action (h)

Composition H (%) 4.81

N (%) -

Residue

-

-

C (%) 63.2

Polyesterpolyamideb)

Ultrasonic

5

60.2

5.59

5.9

-

Metal complexc)

Ultrasonic

10

60.5

4.93

1.02

6

PAa)

-

-

60.66

8.65

11.94

-

Metal complexd)

Vibratory milling

96 144

44.13 43.94

5.66 6.47

5.41 5.34

29.9 27.8

1.44 2.15 Residue after calcinatione) a) – PET, Poly(ethylene terephthalate); PA, poly(ε-caprolactam); b) – From 10 g of PET and 20 g of ethylenediamine, EDA; c) – From 10 g of PET, 20 g of ethylenediamine, EDA, and 1.6 g of VCl3; d) – From 10 g of PET and 5 g of MnCl2.4H2O; e) – From the metal complex obtained after 144 h; calcination at 1000°C.

<1

-

Sample PET

a)

(%) -

activation energy. Generally, the semiconductor character is enhanced with an increase of mechanochemical complexation reaction efficiency. The polymers with paramagnetic properties can also be obtained by mechanochemical homo- or copolymerisation of some vinyl, acrylic, or unusual monomers. In this case, the metallic surfaces strongly activated due to the electronic emission determined by the intense shock friction forces developed in the vibratory milling conditions, have an important role in the reaction initiation. The role of highly activated metal surfaces in the polymerisation reaction’s 458

Mechanochemistry of Polymer Fracture

Figure 3.213. The ESR spectrum (a) and Mössbauer one (b) of a complex synthesised by vibratory milling of the system poly(ethylene terephthalate) + ethylenediamine + FeCl 3 (10/30/6.5), milling time being 96 h.

initiation was already discussed (see Section 3.8.1.1.3). The analysis of the electric and magnetic properties of the mechanochemically synthesised polymers, by vibratory milling, proved that the complexation reaction accompanies all the mechanochemical reactions (Table 3.75). Especially those complexation reactions carried out with the reactants in liquid state along with a support polymer supposed to mechanodegradation are favoured. The liquid reactants, adsorbed to the activated surfaces of the reaction equipment and of milling bodies, penetrate into the already initiated microcracks of the metallic lattice rallying very fine metal particles. These colloidal particles furnishes the centers of complexation, especially Fe 3+, to the organic phase, which, in turn, offers the ligands required for complexation (Table 3.75). Thus, firstly for the insoluble fractions but sometimes even for the soluble ones (obtained by both mechanochemical polycondensation and homo- or copolymerisation of certain monomers, chemical bonding, by co-ordination) of the metal from equipment walls could be demonstrated by chemical analysis and spectral methods (ESR and Mössbauer) [573, 676–682]. Figure 3.214 presents the Fe content variation for three products with milling time. From this Figure, it is clear that the amount of complexed Fe depends on the milling duration. The existence of the metallic atoms as well as of the double bonds in a conjugated system in polyacrilonitrile or in the products of mechanical polymerisation, i.e. benzene, pyridine, aliphatic or aromatic nitriles) has suggested the possibility that the latter ones might possess semiconductor properties. As is seen in Table 3.76, the values of E a for the above-mentioned polymers, ranging from 1.12 to 2.5 eV, pointed out semiconductor properties, especially in the case of polyacrilonitrile synthesised at high milling durations and in the case of polyacetonitrile. 459

Macromolecular Mechanochemistry Table 3.75. Mechanochemical compounds synthesised by vibratory milling [573] Polymer

Initial materials

Polychelate based on poly(ethylene terephthalate) (PET)

PET + ethylenediamine + FeCl3

Polystyrene Polyacrylonitrile Poly(acrylonitrile-co-styrene) Poly(acrylonitrile-co-vinyl acetate-co-αmethyl styrene) Polyacetonitrile Polyacetylene

Styrene Acrylonitrile Acrylonitrile + styrene Acrylonitrile + vinyl acetate + -αmethyl styrene Acetonitrile Benzene or pyridine

Method of synthesis Polycondensationmechanochemical complexation Polymerisation Polymerisation Copolymerisation Copolymerisation Polymerisation Ring-opening polymerisation

The metal (Fe) is also present in the reaction products synthesised by the vibratory milling of benzene or pyridine. In the pyridine case, the Mössbauer spectrum consists of four subnetworks, two of them presenting magnetic order. The other two (the non magnetic ones, can be attributed to Fe 3+ ions in a noncubic vicinity (Figure 3.215, curve 1). The Fe 3+ ions present two nonequivalent positions, so there are two possibilities for bonding in the system. A similar shape – allowing the same interpretation – was found in the Mössbauer spectrum of benzene milling product (Figure 3.215, curve 2). The presence of bonded Fe in the structure of the two reaction products has also been confirmed by the ESR spectrum (see Figure 3.193, Section 3.8.1.1.3) The polychelate feature of the mechanochemically synthesised polymers has suggest the possibility of their employment as initiators in some vinyl monomer polymerisation, especially of methyl methacrylate [679]. The reaction, carried out in vacuum glass ampules (~10 –4 at), has led to the synthesis of a product that pre-

Figure 3.214. Variation of the Fe content with milling duration: 1) acrylonitrile; 2) acrylonitrile + vinyl acetate; 3) acrylonitrile, insoluble fraction [573].

460

Mechanochemistry of Polymer Fracture Table 3.76. Activation energy values of the electrical conductivity for some mechanochemically synthesised polymers [313] Sample

Polyacrylonitrile Polyacrylonitrile Polyacrylonitrile Polyacrylonitrile Copolymer of acrylonitrile (90%) with vinyl acetate (5%) and α-methyl styrene (5%) Polyacetonitrile

Synthesis conditions Filling ratio Milling duration (h) (%)

Fraction

Activation energy, Ea (eV)

48 96 120 192

1.0 0.5 0.5 0.5

Unseparated Soluble Soluble Soluble

3.52 2.46 1.87 1.44

96 48

0.5 0.5

Soluble Soluble

3.74 1.12

sented a soluble fraction in toluene, poly(methyl methacrylate) and another one in DMF, and which proved to be a block or a graft copolymer of poly(methyl methacrylate) with the polymer used as macroinitiator. The reaction was carried out efficiently both in DMF and water. As Figure 3.216 shows, it is influenced by certain factors among which the most important are the macroinitiator concentration, duration, and the copolymer ratio from the substrate submitted to copolymerisation for obtaining a macroinitiator representing an acrylonitrile copolymer. From the analysis of the results presented, it may be seen that the decisive factor in the initiation of the methyl methacrylate polymerisation is the quantity of chemically bound Fe. This increases along with the initiator concentration as well as with its synthesis duration, i.e. with the respective acrylonitrile quantity in the polymer. This fact assures an ever-greater number

Figure 3.215. The Mössbauer spectrum of a milling product of pyridine (1) and (2) benzene. (96 h; T = 20±2°C; soluble fraction) [573].

461

Macromolecular Mechanochemistry

of nitrogen atoms able to complex the metal. As a consequence, a mechanism for the reaction initiation of the following type has been suggested, implying a complex formation with the participation of the polychelate, activator (water or DMF) and monomer: The monomer radical as well as the one from DMF propagates the polymerisation reaction, the graft product being obtained as a result of some chain transfer reactions between the increasing radicals and the macroinitiator chain. CH2 CH

OCH3 C

C

CH

CH3

Fe

CH2 CH

O

CN

CH2

O

CH

O

CN

C

•

C

CH3

Fe

CH2

CH2 CN

OCH3

CH3 CN

O

H CH2

C N

CH2

CH3

C N

CH3

or

•

CH3

or

H

•

O

O

H

CH3

H

Macromolecular compounds able to render enzymes insoluble by coupling reactions have been obtained by microcrystalline cellulose ultrasonic treatment in the presence of Co 3+ ion or by their vibratory milling with transition metal salts (Ni, Fe, Mn, Cu, Co, Ti). The metal content of the cellulose-based complexes that are obtained depends on the morphological characteristics of the initial material (particle size, crystallinity, specific surface area, porosity) Figure 3.216. The influence of some factors on methyl methacrylate polymerisation with mechanochemically synthesised macro-initiators: 1) concentration (poly-acrylonitrile, 108 h milling, 2 ml DMF, 5 ml water); 2) duration; 3) amount of chemically bound metal (Fe, %); 4) synthesis duration of acrylonitrile + α-methylstyrene copolymer; 5) ratio of comonomers in the initial mixture for ternary copolymer synthesis [acrylonitrile/acrylonitrile + vinyl acetate + α -methylstyrene (g/g)], [313].

462

Mechanochemistry of Polymer Fracture Table 3.77. Influence of metal nature on invertase immobilisation capacity in complexes formation by vibratory milling [673] Cellulose type Cellulose II Cellulose III Cellulose IV Cellulose II Cellulose III Cellulose IV Cellulose IV Cellulose IV Cellulose IV Cellulose IV

Metal

Complexed metal content (%)

Coupled enzyme yield (%)

Co Co Co Fe Fe Fe Mn Ni Cu Ti

0.94 1.20 1.64 1.80 2.46 3.34 1.12 3.07 1.48 0.85

97.80 90.12 98.29 85.03 89.39 89.78 80.54 72.40 68.39 98.68

Table 3.78. Influence of some parameters on the invertase coupling on products obtained by ultrasonic treatment of micronized cellulose in the presence of Co 3+ ion [674] Concentration of Co3+ ion (mol/l)

Temperature (°C)

Duration (h)

Co in complexes (%)

Coupling yield of invertase (%)

0.1 0.2 0.3 0.2 0.2 0.2 0.2

50 50 50 30 40 50 50

24 24 24 24 24 12 36

1.27 1.48 1.76 1.28 1.59 1.29 2.21

43.20 50.40 63.15 41.15 56.80 47.15 69.67

as well as on the mechanical regime parameters. The efficiency of enzyme coupling (invertase) to synthesised complexes was found to be influenced by the complexed metal content, and therefore on the previously mentioned factors. Examining the Table 3.77, it can be seen that Fe and Ni have again been found to a great extent in the resulting products, but the best results were obtained with polychelates based on Co and Ti. The activity determination of the immobilised invertase has revealed that the enzymatic activity of the coupled invertase of the complexes based on Co (which gave the best results) is even higher as compared to the activity of the free enzyme, thus proving the role of metal as an initiator. The investigation was extended by studying the reaction of Co complexation on cellulose II, working with water suspension and reaction, activation was performed by ultrasonic treatment. The results are shown in Table 3.78. It can be noticed that some high Co content products having higher coupling efficiency are obtained if the reaction is carried out 463

Macromolecular Mechanochemistry

in the presence of higher Co 3+ ion concentrations, at a high temperature and longer stressing time. Thus synthesised complexes are usually coloured substances, in accordance to the chemical nature of the complexing center they contain, Figure 3.217 [661, 667–671]. Based on the results obtained in this field, the most important steps of the reaction mechanism, on the poly(ethylene terephtalate) + ethylenediamine + Fe 3+ , have been established and are presented below. CH 2 CH 2 O

C

C

O

O

NH

R

NH

C

C

O

O

O

n+

CH2 CH 2 O

C

C

O

O

NH

R

NH

C

C

O

O

O

Me O CH 2 CH 2 O

C

C

O NH

R

NH

C

O

C

O

O

n+

CH 2 CH 2 O

C

C

O

HO

N

R

N

C

C

OH

O

O

Me HO CH2 CH 2 O

C

C

OH N

O Me = Fe

3+

, Mn

2+

,V

R

N

C

C

O

O

3+

It can be noticed that complexation reaction may occur intercatenary, when crosslinked products are obtained. These compounds are insoluble an infusible, with a high thermal and chemical stability, being characterised by valuable electric and magnetic properties. In turn, intracatenary reaction leads to soluble products, able to function as macroinitiators [675]. Particularly, the compounds mechanochemically synthesised by vibratory milling, ultrasonic treatment, and even thermally activated, using as support 464

Mechanochemistry of Polymer Fracture

Figure 3.217. Influence of the metallic ion nature on the colour of the mechanochemically synthesised (by vibratory milling) polychelates based on poly(ethylene terephthalate) and ethylene diamine).

micronized cellulose, represent cheap supports for enzymes’ immobilisation, offering final products with high biological activity. In addition, the mechanochemically activated syntheses by polycondensation and complexation, using the most varied forms of mechanical energy, such as: vibratory milling, ultrasonic treatment, cryolisis, etc., can be achieved on the same principle as by other destructive thermal methods [682] or under the action of high energy radiations [660, 661]. 3.8.1.5. Mechanochemical reactions on the surface of polyfunctional acceptors Black carbon was the first product whose activity has been investigated in its interaction with the rubber, under the conditions its mechanical processing on two-roll mixers or kneaders. Thus, it was followed the behaviour of a system composed from natural rubber and butadiene in the presence of black carbon, by could mastication. Characterisation of the reaction products led to the idea that black carbon behaves as a polyfunctional acceptor, fixing on the new generated surfaces, during the mechanical processing, both the natural rubber ’s chains and polybutadiene ones, which were synthesised by mechanochemical polymerisation [684]. Using labelled atoms, in was established that black carbon contains to its freshly-generated surfaces carbon atoms having free valences that are able to interact with the macromolecules by chain 465

Macromolecular Mechanochemistry INITIATION CH2 CH2 O

CH2 CH2 O

C

C

O

O

O

CH2 CH2 O

C

C

O

O

CH2 CH2 O

C

CO2H +

•

C

C

O

O

•

O +

CH2 CH2 O

C O

O

CH2 CH

C

C

O

O

O

O + NH2 R

NH2

Mechanocracking

O

C

Disproportionation

O

O

POLYCONDENSATION

CH2 CH2 O

C

C

O

O

C

C

O

O

NH

R

NH

C

C

O

O

C

C

O

O

C

C

O

O

C

C

O

O

O

O

COMPLEXATION CH2 CH2 O

NH

R

NH

O

+

O

Fe3+ + CH2 CH2 O

C

C

O

O

C

C

O

O

NH

R

NH

O

O

3+

CH2 CH2 O

NH -

R

NH -

O

O

Fe O CH2 CH2 O

C

C

O NH

NH

R

O

C

C

O

O

O

transfer reactions. W.F. Watson, using an elastomer labelled with tritium, proposed the following mechanism: T •

+ R

C

CH2

CH2

CH

CH

CH2

R' •

Black Carbon

T

+

R

•

C

CH2

R' •

T

R

C R'

CH2

CH2

CH

CH

CH2

T = labelled hydrogen

466

CH2

CH

CH

CH2

Mechanochemistry of Polymer Fracture

In this way, the chemical fixation of an elastomer to the black carbon surface occurring by hydrogen transfer was proved. It seems that the black carbon functions containing oxygen atom are not implied in this reaction. The amount of chemically bonded elastomer increases with the increasing of mastication period. The net result of this reaction is the improvement of the physico-mechanical characteristics; effect that was defined as reinforcing - term rapidly assimilated at industrial scale. The reactive hydrogen atoms are located superficially, at the periphery of the condensed aromatic structures of black carbon, in certain preferential positions, for instance in the structural faults. The hydrogen transfer, from the surface of black carbon to elastomer, is achieved by the reaction with the mechanochemically generated macroradicals during the mastication of these compounds. It was established a direct relation between the amount of black carbon “peripherical hydrogen” and the number of irreversible rubber-black carbon bonds. Similarly results are obtained by using aluminium oxide as reinforcing agent [315, 640, 643]. This compound introduced during the mastication of a mixture of polyethylene and poli(vinyl acetate) leads to some crosslinked fractions. Aluminium isopropoxide also acts as reinforcing agent in the presence of natural and synthetic rubbers. It was found that the aluminium atoms are intercalated between the polymer’s chains, determining their crosslinking. In a similar manner, the reactions that occur between the mechanochemically processed polymers and unpolymerisable monomers might be interpreted. The mastication of a mixture consisting from two polymers, in the presence of a functional acceptor, determines the formation of grafted structures. This kind of reaction occur in the systems composed by natural rubber and polyethylene in the presence of acetophenone, or in the case of natural rubber mixed with maleic anhydride, when the following structures are generated: CH2

H3C CH2 HC C O

C

CH

CH

HC

O

CH

C

C O O

HC

C O

CH3

CH2

C O O (I)

467

C

CH

CH

HC

O O

CH2

CH

C

C O

CH2

C O

O

Macromolecular Mechanochemistry

The study of the influence of processing conditions revealed o series of particularities, namely: 1) reaction is mechanically activated, by mixing; but also 2) thermally, by heating above of 150°C, in inert atmosphere or air; 3) in the presence of radicalic acceptors the process is retarded or even stopped, and elastomer ’s unsaturation does not vary after comonomer fixation. Based on these observations, it may be supposed that maleic anhydride preferentially reacts with the mechanoradicals.

H3C HC C

CH2

CH2

C

CH

CH

HC

O

O

CH2

C

CH

CH

C

C

CH2

H3C

C O

O O

O

( II ) CH3 CH2

CH3 CH

C

CH

C

CH

CH2

CH

HC C

C O

O

CH2

O ( III )

CH3 CH2

C

CH

CH2

CH

HC C O

C O

O

( IV )

The formation of cross-linked structures, through a similar mechanism, was also mentioned in the case of poly(methyl methacylate), poly(vinyl acetate), polyethylene, polymers masticated in the presence of some aluminium alcoxides [643]. The gel effect has also been observed in the case of natural rub468

Mechanochemistry of Polymer Fracture

ber mastication with phenolic resins. The complete dispersion of resin, evidenced by electron microscopy, confirms the fact that its interaction with the elastomer matrix is of chemical nature. In order as the reticulation to occur the ingredient’s functionality must be equal to 3. A very interesting reinforcing effect was evidenced in the case of poly(vinyl chloride) processing by two-roll mixing in the presence of aromatic diamines (o-, m-, p-phenylenediamine, benzidine) [311– 314, 571–576]. As Figure 3.218 shows, the increase the amount of diamine determines a continuous increase of polymer tensile strength. The reaction mechanochemically occurs through a radicalic mechanism that implies some crosslinking reactions: CH2

CH

CH2

CH

Cl CH

CH2

Cl

CH2

Cl

•

CH

CH2 + H2N

R

NH2

CH

Cl

Cl

•

CH2

CH

•

CH + CH2

CH

Cl

Cl CH

CH2

CH2

CH Cl

•

CH3 +

HN

R

NH2

Cl

Cl

This mechanism leads to: 1) long linear chains (1) CH

•

CH2

+

CH2

CH

Cl

(2)

Cl

CH

CH3

+

CH2

Cl CH

CH3

+

CH

•

•

C Cl CH

Cl CH2

CH

CH2

CH2

•

CH + H2N

NH

R

CH

CH2

+ H2N

R

CH2

NH

CH

CH2

HN

R

CH Cl

Cl •

NH2

Cl

Cl

CH2

Cl

•

Cl

Cl CH

•

CH

CH2

CH

HN

R

NH

Cl

Cl

CH2

CH Cl

or 2) crosslinked structures CH

CH

CH

NH

Cl

Cl

NH

Cl

Cl

CH

CH

CH2

R

CH2 469

CH

HN

R

NH2

Macromolecular Mechanochemistry

Figure 3.218. The influence of diamine concentration on polymer tensile strength: 1) benzidine; 2) p-phenylenediamine; m-phenylenediamine [310].

These structures confer to the final material new properties, such as: a higher molecular weight, improved dying capacity (due to free amino groups), good thermostability. The last property is stimulated on one side by the radicalic acceptor character of diamine and on the other side by the diamine reaction with hydrochloric acid released by thermal degradation. In this way, the diamine’s presence allows the reduction of the amount of thermal stabiliser (tin-based salts) from 3% to 1%, respectively. Another reinforcing effect has been evidenced in the two-roll mixing or extrusion processing of polyethylene with epoxy oligomers [685]. To the concentration of 2% with respect to the epoxy polymers determines a significant increase of tensile strength as well as the improvement of deformation capacity. Once again the both effects are a direct consequence of the mechanochemical reaction. The use of higher amounts of epoxy resin diminishes the tensile strength with the corresponding increase of the flow index, which constitute an argument in the favour of the plasticizing effect exerted by the oligomer. The reactions of the mechanically stressed polymers with radicalic acceptors also favour the stability to mechanodegradation, under exploitation conditions. Thus, the introduction of phenyl-βnaphtyl amine or of 2,4-diamino-diphenyl amine in elastomer’s composition determines their resistance to fatigue [686, 687]. The galvynoxil radicals, introduced into natural rubber, decrease their concentration during mechanical stressing to stretching, concomitantly with the increase of polymer’s mechanical resistance [688]. 470

Mechanochemistry of Polymer Fracture

In the case of poly(vinyl chloride) a reinforcing effect was obtained in the presence of small amounts of o-toluidine or bisphenol A [690]. Concluding, we have to admit that polymer reinforcing and their stabilisation under exploitation conditions is achieved both by mechanochemical reactions, as those already mentioned, and stimulating new types of physical interactions in the presence of chemical agents used. Thus, the important increase of the tensile strength of poly(vinyl chloride), in the presence of diamines, must be ascribed to chemical reactions, especially to crosslinking reactions, but also to the intercatenary physical interactions, for instance, hydrogen bonds which form between diamine and support polymer. These reactions are particularly important ones, allowing the control and fine tuning of the properties of mechanically stressed polymers, by an adequate selection of acceptors and their rigorous dosing, from the quantitative point of view.

471

Macromolecular Mechanochemistry

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472

Mechanochemistry of Polymer Fracture

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491

Macromolecular Mechanochemistry

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492

Mechanochemistry of Polymer Fracture

Index A

D

α-keratin 152 acid value 444 acrylamide 393 acrylonitrile 316 acryonitrile 407 activation energy of the viscous flow 47 Andrews’s theory 182 Araldine-502 386

DEFO hardness 259, 375 degradation index 231 degree of reticulation 261 density of reticulation 138 deoxyribonucleic acid 338 destructibility state 13 destruction degree 246 destruction limit 215 Diamond–450 360 dicumyl peroxide 158 disordered zone 15 DPPH reaction 114

B β-keratin 152 Baramboin’s relation 288 Benzidine-modified PVC 105 Berry-Watson equation 120, 121 block copolymerisation 422 bond dissociation energy 183 Brabender masticator 423 Bueche–Halpin theory 182 Bueche’s theory 343 Burgers model 103 butadiene–styrene rubber 183

E ε-caprolactam 400 elastomer mastication 248 electronic transition 187 elementary volume of fracture 47 enthalpy of relaxation 30 EPDM rubber 235 ESR kinetics of mechanoradical formation 307 Estane 316 Estane 5707 112 ethylene–propylene rubber 183 Euler’s angle 42

C C-heteroatom bonds 87 cellulose triacetate 100 chains conformation 266 Charlesby equation 135 chemorheology 142 chemorheology of linear polymers 154 cold mastication 224 collagen fibres 12 constant of chain elasticity 24 constant of molecular collision frequency 180 critical stress 61 cross-linking degree 117 crossing zones 14 crystallinity index 110

F fibril 18 filling ratio 446 Flory–Rehner equation 75 fractoemission 385 fracture activation energy 71 friction coefficient of the monomer unit 30 G glass transition temperature 22 grafting 422

493

Macromolecular Mechanochemistry grafting degree 429 Griffith’s criterion 19 Griffith’s theory 171

mechanodispersion 35 mechanoinitiators 392 mechanoactivation 7 mechanochemical complexation 453 mechanochemical destruction 201 mechanochemical polycondensation 439 mechanochemical polymerisation 397 mechanocracking 7, 9 mechanocracking activation energy 95 mechanocracking kinetic law 94 mechanocracking rate constant 83 mechanodegradation rate 232 mechanodispersion 275 mechanoexcitation 7 mechanopolymerisation 405 mechanoradical 197 methacrylamide 395 methyl methacrylate 407 microcrazing 11 microfibrils 19 mirror’ zone 58 Money viscosity 298 monodisperse polystyrene 157 Monte-Carlo simulation 341 Morse potential curve 71 MWD curve 346

H heterocatenary polymers 330 heterolytical mechanism 226 high density polyethylene 86 homolytic cleavage 31 Hooke’s law 22 Horiks equation 134 hot mastication 225 hydrogalvinoxyl 79 I initial molecular weight 262 initiated destruction 213 inter-spherulitic fracture 52 intercatenary dehydrocyanuration 327 interchange reaction rate 130 intermolecular interaction forces 46 intermolecular mechanism 170 intermolecular sliding 10 intrinsic binding energy 185 intrinsic viscosity 248 isobutylene rubber 124 isoprene 316

N

J

neoprene 124 nylon 6 19

Jurkov’s equation 66, 84, 88, 95

O K Kjeldahl method 317

OLTVIL–10 360 OLTVIT–70 361 oxidase 335

L

P

Lewis acid 402 linear polymers 154 Loschmitd’s number 250 low density polyethylene 86

p-phenylenediamine 309 packing density 268 penny-shaped crack 96 PMAAm 308 PMMA 308 poly(ε-caprolactam) 56 poly(ethylene terephthalate) 217 poly(vinyl chloride 103 polyamide-6 17, 31, 100 polyamides 215 polycarbonate 64 polychloroprene rubber 77 polyelectrolytes 330

M macromolecular chain splitting 201 mastication 232 mastication agents 303 mastication constant 303, 376 Maxwell–Boltzmann function 71 mechanical regime 320 mechanoactivated hydrolysis 216

494

Mechanochemistry Index of Polymer Fracture polyethylene 17 polyisoprene rubber 77 polymer polydispersity 245 polymer rigidity 258 polymerization degree 244 polyoxoamide 74 polypropylene 17 polysulphone 64 polyurethane 85 polyurethane elastomer 113 protein degradation 337 PVC-S 359 PVC-S model 359

surface work 177 swelling degree 75 T tensile compliance 61 tensorial series 42 tetramethyl thiuram disulphide 135 thermal degradation rate constant 95 thermal-oxidative destruction 282 Thomas–Rivlin’s model 19 TMM method 138 Tobolski equation 121 torsional braid analysis 146 two-roll processing 352

R rate of growth of the magistral crack 33 rate of scission of a bond 32 reticulation degree 148 rubbery flow region 155, 159

V vibration frequency of chemical bonds 32 vibratory milling 237 Vincent’s relation 184 viscosimetric molecular weight 444 vitreous polymers 63 vitreous temperature 86 vitreous transition temperature 152 Voight’s generalised model 103 vulcanisation 129

S Schultz–Zimm distribution 341 stick-slip mechanism 388 strain tensor 41 stress concentration coefficient 48 stress intensity factor 177 stress tensor 40 stretching ratio 178 supra-contraction 151 surface energy 61

Y Yu equation 121

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