Interaction of Polymers with Bioactive and Corrosive Media 9067641626

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New Concepts in Polymer Science Interaction of Polymers with Bioactive and Corrosive Media

New Concepts in Polymer Science Other Titles Immobilization on Polymers M. I. Shtilman Radiation Chemistry o f Polymers V.S. Ivanov Polymeric Composites R. B. Seymour Reactive Oligomers S. G. Entelis, V. V. Evreinov and A.I. Kuzaev Diffusion o f Electrolytes in Polymers G.E. Zaikov, A.L. Iordanskii and V.S. Markin Chemical Physics o f Polymer Degradation and Stabilization N. M. Emanuel and A.L. Buchachenko

O f related interest Journal o f Adhesion Science and Technology Editors: K.L. Mittal and W. J. van Ooij N ew Polymeric Materials Editor-in-Chief: F.E. Karasz Journal o f Biomaterials Science, Polymer Edition Editors: C.H. Bamford, S.L. Cooper and T. Tsuruta Composite Interfaces Editor: H. Ishida

New Concepts in Polymer Science

Interaction of Polymers with Bioactive and Corrosive Media

A.L. Iordanskii, T.E. Rudakova and G.E. Zaikov

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

First published 1994 by VSP 13V Published 2021 by CRC Press Taylor &฀ Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton. FL 33487-2742

rl,;:฀ 1994 by Taylor &฀ Francis Group, LLC CRC Press is an imprint of Taylor &฀ Francis Group, an Informa business No claim to original U.S. Government works ISBN 13: 978-90-6764- I 62-3 (hbk) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If฀any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying. microfilming, and recording, or in any information storage or retrieval system. without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center. Inc. (CCC), 222 Rosewood Drive, Danvers, MAO 1923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor &฀ Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG Iordanskii, A.L. Interaction of polymers with bioactive and corrosive media I A.L. Iordanskii, T.E. Rudakova, G.E. Zaikov. - Utrecht: VSP ISBN 90-6764-162-6 bound NUGI 841 Subject headings: polymers.

Typeset in Lithuania by TEV. Vilnius.

Contents Introduction Preface Foreword Chapter 1. Kinetic aspects of polymer interaction with components of aggressive media

xi xv xvii 1

1.1. Introduction

1

1.2. Macrokinetic correlations of the chemical degradation processes 1.2.1. Internal diffusion-kinetic zone 1.2.2. Internal kinetic zone 1.2.3. External diffusion-kinetic zone

3 4 7 7

1.3. Degradation of polymeric materials of inhomogeneous structure 1.3.1. The accessibility of chemically unstable bonds in polymeric articles 1.3.2. The reaction capability of chemically unstable bonds in polymeric articles

10

1.4. Physical model of polymeric articles degradation process

15

Chapter 2. Water diffusion in polymer systems of differenthydrophilicity

21

12 13

2.1. Introduction

21

2.2. Water sorption in hydrophobic polymers 2.2.1. The condition of Henry’s law fulfillment 2.2.2. The condition of positive deflection of the sorption isotherm from Henry’s law

25 31

2.3. Water diffusion in hydrophobic polymers 2.3.1. Diffusion with cluster formation calculation. Formulation and solution of the general problem

35

2.3.2. D iffusion in fluoroplasts. Partial im m o b ilizatio n m odel

38

32

37

2.3.3. Diffusional transport, complicated by continuous distribution of sizes of water associates 2.4. Equilibrium water sorption in hydrophilic polymers

39 42

2.5. Water diffusion in hydrophilic polymers

45

2.6. Water diffusion in moderately hydrophilic polymers

51

VI

Contents

Chapter 3. Transport processes in the system polymer-chemical (biological) medium

65

3.1. Introduction

65

3.2. Diffusion features of ionized low-molecular compounds in polymer systems 3.2.1. The Henderson-Planck approach 3.2.2. Constant field approach

69 70 70

3.3. Description of multicomponent diffusion in polymers through thermodynamics of irreversible processes

72

3.4. Theories describing the connection of diffusion coefficients of medium components with volume contents in polymers

75

3.5. Electrolyte state in polymer 3.5.1. Ions hydration 3.5.2. Electrolyte dissociation 3.5.3. Electrolyte influence on conformational behaviour of macromolecules 3.5.4. Influence of macromolecular chemicalstructure on diffusion 3.5.5. Electrolyte action on polymer morphology 3.5.6. Acid sorption causing structural transition in the crystalline phase 3.5.6.1. Version A 3.5.6.2. Version B 3.5.6.3. Version C 3.5.7. Crosslinking influence on diffusion

96 98 98 98 100

3.6. Surface phenomena complicating diffusionprocess 3.6.1. External mass transfer influence on diffusion in polymers 3.6.2. Influence of features of polymer structural organization 3.6.3. Dependence of surface concentration on time 3.6.4. Equilibrium electrolyte sorption

103 103 106 109 113

Chapter 4. The role of diffusion processes under controlled release of biologically active substances from polymer therapeutic systems 4.1. D iffusion controlled therapeutic system s

4.2. The influence of solvent diffusion on the rate of release of medicinal substance 4.3. Diffusion polymer systems of special purpose 4.3.1. Flow regulation by changing the distance between macrochains 4.3.2. Permeability regulation through liquid crystal structure formation 4.4. Erosive therapeutic systems

77 79 82 83 85 87

125 126

129 136 136 138 139

Contents

4.4.1.1. Metabolite formation 4.4.1.2. Capsule formation 4.4.1.3. Enzyme activity influence Chapter 5. Diffusion and adsorption of plasma proteins — the processes, characterizing initial stage of polymer-blood interactions

vii

144 145 145 149

5.1. The role of primary adsorption and diffusion of proteins in the general scheme of polymer-blood interaction 5.1.1. Diffusion-convective model 5.1.2. Transmission electron micrograph 5.1.3. Haemorheological model

150 152 152 152

5.2. Thermodynamic aspect of protein adsorption

153

5.3. Surface energy of polymers and plasma protein adsorption 5.3.1. Surface topography of polymers

156 158

5.4. Structural aspect of plasmic protein adsorption

159

5.5. Medium acidity influence on protein adsorption

164

5.6. The kinetic aspect of adsorption

165

5.7. The diffusive-kinetic model of protein adsorption on polymer surface

168

Chapter 6. Polymer biodegradation: kinetics and mechanism

179

6.1. Primary reactions of the body to polymer objects

180

6.2. Medium components responsible for polymer degradation

181

6.3. Classification of resolvable polymers 6.3.1. Soluble polymers 6.3.2. Polymers decomposable via non-specific hydrolysis 6.3.3. Enzymatically decomposable polymers 6.3.3.1. General approach 6.3.3.2. Ways of controlling resolution rate of enzyme-splitable polymers 6.3.4. Dissociating polymer-polymer complexes (PPC) 6.3.5. Resolvable polymer types

182 183 184 185 185

6.4. Uses and resolvability estimates 6.4.1. Surgical sutures 6.4.2. Coats for wounds and burns 6.4.3. Osteosynthesis pins 6.4.4. Resolvable polymer compositions for filling internal canals and cavities and for use as artificial blood vessels 6.4.5. Coats for medical pills and tablets 6.4.6. Biologically active resolvable polymers 6.4.7. Medical adhesives

193 194 197 198

190 191 192

199 200 201 201

vili

Contents

6.4.8. Biodegradable materials as medicine depots 6.4.9. Drug release rate from the resolvable polymer matrix 6.4.9.1. LMS molecules in the main chain of the polymers 6.4.9.2. LMS molecules attached to side chains of dissolved polymer 6.4.9.3. Medicine encased in a resolvable polymer shell 6.4.9.4. Drug uniformly distributed in the resolvable polymer matrix in the form of a solid solution 6.5. Rough estimates of resolvability and resolution times according to model experiments

202 203 204

6.6. Kinetic regularities of drug release by biodegradablepolymers 6.6.1. Degradation in solid polymers and solutions compared 6.6.2. Solid polymer degradation 6.6.3. Degradation of drug-containing polymers in solution 6.6.4. Kinetics specialities of drug-delivery polymerdegradation

208 208 210 211 213

6.7. Conclusion

220

Chapter 7. Degradation and medico-biological estimation of polymers in biological and model chemical media 7.1. Introduction 7.2. Macrokinetic features of degradation and medico-biological estimation of fast destroyable polymers 7.2.1. Degradation of collagen materials in model media 7.2.2. Physico-chemical and medico-biological estimation of collagen haemostatics 7.3. Regularities of disintegration of long lived polymers, and their effect on a living organism 7.3.1. Polyethyleneterephthalate in model media and in the living organism 7.3.2. Carbon composite materials’ behaviour in model media and living organism Chapter 8. Mechanical reliability of polymers in physical, chemical and biological media

204 205 205 206

233 233 233 234 237 240 241 243 249

8.1. Introduction

249

8.2. The estimation of mechanical reliability of polymers in aggressive media

250

8.3. Polymers in physically active aggressive media 8.3.1. Physical-mechanical effect 8.3.2. Mechanical-physical effect

251 251 260

8.4. Polymers in chemically active media 8.4.1. Chemomechanical effect

262 262

Contents

8.4.1.1. The influence of the degradation occurring in the external diffusive-kinetic zone on the mechanical properties of polymers 8.4.1.2. Degradation of bulky polymer and mechanical properties 8.4.2. Mechanochemical effect 8.4.2.1. The influence of mechanical stress on polymer degradation occurring in external diffusive-kinetic zone 8.4.2.2. The influence of mechanical stress on reaction rate for degradation occurring in a bulky sample 8.5. Polymers in biologically active media 8.5.1. The action of biological medium on the mechanical properties of biological tissues 8.5.2. The influence of biological and model chemical media on mechanical properties of polymer substitutes of biological tissues 8.5.2.1. Kinetic changes of lavsan (PET) endoprosthesis of tendons and cords under the influence of organism internal medium and biological stresses 8.5.2.2. In vitro and ex vivo investigations of the cords from carbonic fibres 8.5.2.3. Carboplastics application in traumatology and orthopaedics Subject index

ix

262 266 270 272 274 275 275 279 281 285 287 293

Introduction During the last two decades, increased attention has been paid to problems of polymeric materials application in medicine for endoprosthesizing, in surgery, etc. Many polymeric articles are widely used in medicine: heart valves and artificial blood vessels, artificial bones and bones’ fragments, substitutes for muscular tissues, stomatological materials, contact lenses, artificial crystalline lenses, polymer eye prosthetic appliances, various surgical contrivances, apparatus and containers for blood transportation, thin films for operation field covering, dressings, adhesives for tissue glueing, surgical threads, drugs of prolonged effect, etc. Evidently, synthetic and natural polymeric materials were found the most suitable in comparison with other known non-physiological materials, both for their influence on the organism and for physico-mechanical properties, especially taking into account the lifespan of these materials in the organism. The usage of polymers in medicine makes it necessary to address two problems. First, for those polymeric articles used in endoprosthesizing it is important that the time of their reliable exploitation be sufficiently long. It is desirable that the lifespan of such polymeric articles exceed the life duration of the human being after implantation of the article as a prosthetic appliance. Second, the creation of other polymers with a relatively small and regulable time of exploitation. This second type of polymeric medical article includes stitch threads, glues and haemostatic sponges which are necessary postoperatively, but which become less necessary during the time of tissue inoculation. After that, such polymers must re-solve, and the innocuous products of their degradation must be excreted by the organism. It is particularly important, if the products are the solids, whose sizes and the configuration are of primary importance. To make them optimal there is the necessity of the X-ray-diffraction investigations, which are shortly presented in this monograph. Drugs of prolonged effect are also discussed with respect to the second type of the polymeric articles. They are attached to the polymeric chains and are received by the organism as the polymer decomposes and the drug becomes free. Thus, from the point of their exploitation for medicine, very stable (resistant to the surrounding environment) polymers, and polymers with a small and well regulated lifespan in the organism are necessary. However, there is another important task: blood proteins must not coagulate on these polymers and polymeric articles, and thrombosis must be excluded. Primarily, this concerns polymers which are to be included in the blood circulation system as endoprosthetic appliances, because clot formation on their surfaces may be lethal. One further task is the prediction of the reliable exploitation time of polymeric prosthetic appliances in the organism: a long rheological compatibility of transplantations with the organism tissue is necessary. The combined action of the biological medium and the mechanical effort on polymers should also be studied.

xii

Introduction

Investigations of this problem, concerning model chemical and biological media, are partly presented in this monograph. The prediction of re-solvable polymers’ lifespan (glues, stitch threads, haemostatic sponges, drugs of prolonged effect) does not demand much time. In this monograph we also consider kinetic and medico-biological aspects of various collagen haemostatics resolvance in detail. However, the creation of express methods of estimating reliable exploitation time of polymeric articles, which must not change their properties at all (or change them a little) during decades, is rather difficult. It is not solved yet, though ways of solving this problem are outlined. To answer all the above mentioned questions, it is necessary (though not enough) to know thermodynamic and kinetic parameters of polymers’ interaction with the organism. Kinetic and thermodynamic aspects of polymeric articles’ interaction with the media (biologically, physically and chemically active) are at present being studied intensively in many laboratories in our country and abroad. Note particularly the scientific groups, headed by Professor J. D. Andrade (USA, Utah University, Salt Lake City), by Professor J. L. Brash (Canada, McMaster University, Hamilton), by Professor H. Kus (Poland, The Sixth Department of Academy of Sciences, Chair and Clinics of Surgery, Centre of Medical Polymers in Wroclaw), by Professor J. Karlson (Canada, The National Research Centre, Ottawa), by Academician Z. Edlinsky (Poland, The Institute of Polymers PAS, Zabrze), and by Professor I. Kopechek (TCH, The Institute of Macromolecular Chemistry ChAS, Prague). In our country in this field some successful working groups should be mentioned: Academician N. A. Plate and colleagues (The Institute of Petrochemical Synthesis RAS, MSU, Moscow), Academician V. A. Kabanov and colleagues (MSU, IPCS, Moscow), Doctor of Biological Sciences G. A. Phakadze (The Institute of Organic Chemistry, UAS, Kiev), Doctor of Medical Sciences N. B. Dobrova (The Bakulev Institute of Cardio-Vascular Surgery, Moscow), Doctor of Medical Sciences A. A. Adamian (The Vishnevsky Institute of Surgery, Moscow), Doctor of Medical Sciences I. A. Movshovitch (CITO RMH, Moscow), c.t.s. N. S. Gavriushenko (CITO, RMH, Moscow), Doctors of Chemical Sciences I. V. Knets, B. A. Purinia, Doctor of Medical Sciences H. A. Yanson (The Institute of Polymer Mechanics, Latvian AS, Riga), Professor A. V. Samsonov (IHMCRAN, Saint Petersburg), Doctor of Chemical Sciences V. B. Torchilin (The Cardiologic Research Centre RAMS, Moscow), Doctor of Chemical Sciences A. B. Davydov (The Experimental Institute of Medical Techniques, Moscow), Doctor of Biological Sciences V. I. Sevastyanov, etc. Their studies are referred to in the course of this monograph. The authors of this monograph for many years have been studying both fundamental and applied aspects of the problem, together with a group of scientists from the Department of Kinetics of Chemical and Biological P rocesses of the Institute of C hem ical Physics of T he R ussian A cadem y of S ciences (Moscow), founded by Academician N. M. Emanuel. Even now it is possible to make some generalizations, which seem to us to stimulate further investigations in this human field, which stands at the intersection of chemistry, biology, medicine, mechanics and mathematics. Certainly, there are many more problems of polymer usage in medicine. For example, we paid very little attention to such important questions as biological and rheological compatibility of the polymers. We have only touched the questions of microbiological and histological investigation of such important substances as carbonic polymers. Complex consideration is necessary for such important questions as the tissue’s reactions (the organism’s in general) to the

Introduction

xiii

polymers, the allergic effects of polymers and their degradation products on the organism, their toxicity, the ways of excreting the products of polymer degradation. There is a lack of kinetic and thermodynamic data currently, but many descriptive qualitative and semiqualitative results have been obtained.

Preface In everyday life we see the entry of polymeric materials in different spheres of human activities. It is difficult to identify any branch of industry, agriculture or science where it is possible to manage without plastics, caoutchoucs, composition materials, glues, thin films and filaments. For polymeric materials used in biomedical practice as prosthetic appliances in vitally important organs and tissues, stability (their lifespan must exceed a human being’s) is one of the most important characteristics. Another group of polymers (stitch materials, drugs depots, coverings and bindings for wounds), on the contrary, must function only for a definite, strictly given time. After which these materials must degrade or dissolve in biologically active medium. Many natural polymers are highly reliable when used in medical practice. They are natural proteins and carbohydrates (cellulose, starch, alginates, polysaccharide derivatives), natural caoutchouc, etc. However, today chemists not only reproduce well known natural polymers, they also synthesize the new, unknown ones, which have principally new characteristics of exploitation, permitting their usage in vital organisms. The authors of the monograph consider the problem of polymers application in medicine from the point of the stability of their physical and chemical structure both to chemical and to biological media. This book differs from many others in its physicochemical (kinetic) approach to the problem of polymeric materials (articles) and aggressive media interaction. From that point of view the monograph is unique. It has no analogues in our country or abroad. Certainly, we do not present all the polymers of medical appointment, and information about them is uneven; this is connected with the absence of kinetic results in the world literature. The authors should press on when the necessary data are published. I hope that the book will bring great benefit to everybody working in the fields of the physics and chemistry of polymers, and to those interested in applications of polymers in medicine and biology. Editor-in-Chief N. S. Enikolopov

Foreword Medical development is tightly bound to achievements of chemistry as a whole and its individual branches. As early as in the sixteenth century iatrochemistry became significant, with its main idea of alliance with 'great matter’ — i.e. medicine. Paracelsus, the founder of this trend, stated that “the real aim of chemistry is preparing not gold, but medicines”. “Chemistry should march forward hand in hand with medicine” — it was a slogan of iatrochemists, who were the precursors and founders of pharmaceutical chemistry. Medical people began to use polymers for curing patients as early as the outset of civilization. As a rule they were natural polymers, such as amber, propolis, resins from different plants, wool, etc. But polymer prosthesis was not widely spread. According to ancient legends and dicta, a human being created no 'spares’ to change the worked out organs and tissues. Modem progress of science and technology allows to fill this gap. A number of organism 'details’ can be made on the basis of non-physiological artificial materials, destined for the imitation of functioning of external and internal human organs (heart, kidneys, lungs, liver, vascular prosthesis, etc.). Achievements in this branch are well known. For instance, remember Barney Clark, the first patient, who lived for a long time thanks to an artificial heart. The first detailed description of a stitch and fibres used for it was given in a vast medical work Aeurveda — The Life Knowledge, dated as 1100-1400 B.C. Linen and silk fibres were mentioned as stitching materials in cases of amputation, laparotomy, stone sectioning, etc. [LSE, 1959]. Galen (130-210 A.D.) has described silk and 'string’ (intestinal) threads for putting in the stitches. The Greek surgeon Antil (200 A.D.) used these material while operating on aorta aneurysm. Recent active development of polymer chemistry made possible the use of synthetic polymeric articles simultaneously with natural ones. It should be underlined that as long ago as the beginning of the 60s, high-molecular chemistry has ignored medical necessities. Not a single polymer material was specially synthesized for biomedical aims. Now the situation has changed greatly. Positive results of polymer implantation into the organism depend not only on the surgeon’s skill, m odem apparatus, m ethods o f control and diagnostics used, b ut also

on the physico-chemical and special characteristics of the polymer. The main demands made of medical polymers are the following: (i) They should be biologically compatible with tissues, not initiate oncogenesis or allergic reactions, not induce blood cell and tissue trauma, not be toxic, etc. (ii) They should remain stable for a long time or dissociate in accordance with their mission in the organism.

xviii

Foreword

(iii) Their diffusional characteristics should be as close as possible to those of natural transport processes in the organism. (iv) They should be Theologically compatible with tissues and organism fluids. In other words, the biomechanical properties of the transplantant should be close to those of biological medium. Rheological incompatibility leads to strong strains on the border of the polymer and the biological tissue. (v) They should have a complex of necessary physico-mechanical characteristics, such as durability, elasticity, etc. This book is in the main devoted to kinetic and structural aspects of the realization of these demands. A large number of monographs appearing in our country and abroad during the last decades form the basis of a new, actively developing branch of science — biomedical macromolecular chemistry. Here we have made an attempt to examine in detail the processes of diffusion, chemical and biological disintegration, changes in various structural levels induced by chemical and biological media, and the problems of simultaneous influence of these media and mechanical strains upon the polymers used in medicine. Chapters 1 and 6* are written by Professor G. E. Zaikov, Chapters 2-5* by A. L. Iordanskii DSc (chemistry), and Chapters 7 and 8 by T. E. Rudakova PhD (chemistry). G. E. Zaikov A. L. Iordanskii T. E. Rudakova

* Chapter 5 was written in collaboration with PhD (chemistry) A. Ya. Polishchuk. Chapter 6 was written in collaboration with PhD (chemistry) V. S. Livshitz and DSc (chemistry) E. F. Vainshtein who are thanked by the authors.

CHAPTER 1 Kinetic aspects of polymer interaction with components of aggressive media

1.1. INTROD U CTIO N

The degradation of polymeric materials in liquid aggressive media is a complex physicochemical process, which includes adsorption, diffusion and chemical reactions themselves [1,2]. In contrast to low-molecular substances, degradation processes for macromolecules have a number of essential peculiarities. They depend on the specificity of polymeric state of condensed systems and that of ionic, radicalandmolecular reactions proceeding at an interphase border or in a polymer volume. The process of polymer interaction with components of an aggressive medium may be achieved by a series of consecutive and parallel stages, among which, in the first place, the following should be provided: — diffusional and convective transport of aggressive components to the surface of a polymeric sample; — adsorption of the aggressive medium on this surface; — diffusion of the aggressive medium components (water, ions, molecules of the undissociated electrolyte) in the polymer volume; — physico-chemical interactions of diffusing components with the functional groups of the polymer (protonization, ionization, complex formation, redistribution of hydrogen bonds, etc.); — reactions of aggressive components with chemically unstable polymer bonds; — diffusional removal of degradation products from the reaction zone in the polymer volume; — desorption of degradation products from the polymeric sample’s surface to the interface with the layer of liquid; — diffusional and convective transport of the reaction products from the interface layer of the liquid to its volume. Each o f the stages is described by proper diffusional and k in etic equations. H ow ever, it is very difficult to carry out jo in t analysis o f the w h o le k in etic schem e, even if a highly effective com puter is used.

In reality, investigators usually install some reasonable suggestions, thus simplifying the problem. For example, intensive convective transfer (mixing) in the external solution makes it possible to ignore the speeds of release of the components from the volume to the polymer surface and the removal of reaction products from the polymer surface

2

Chapter 1

back to the liquid volume. Adsorption processes for highly elastic polymer samples proceed very rapidly in comparison with diffusional transport in the polymer volume. The physico-chemical interaction between electrolyte solution components and the reactive groups of the polymer usually precedes a chemical reaction itself and is often considered as the beginning of the chemical interaction as a whole, but not as an independent stage. The speed correlation of diffusion and chemical reaction defines the macrokinetic degradation field [3]. The most typical for investigated polymer-electrolyte solution systems are (i) the internal kinetic field (the rate of the diffusional stage exceeds that of the chemical reaction); (ii) external diffusion-kinetic field (the rate of chemical reaction exceeds that of the diffusion in polymer volume, but is compared with that of the transport in an interfacial zone of the sample); (iii) internal diffusion-kinetic field (the diffusion and chemical reaction rates in polymer volume are comparable) [4]. Reaction zones with changing physico-chemical and mechanical properties present in these cases correspondingly (i) the whole polymer volume, saturated with diffusional medium; (ii) a thin interfacial layer — the sample’s size decreases, as if it is melting; (iii) a layer of variable thickness, the size of which increases with time and in principle may reach the whole sample size. The polymeric article and the aggressive medium are different phases (solid-liquid). The chemical reaction between the aggressive medium and chemically unstable bonds of a polymer may occur both on the phase interface and in the polymer phase volume (polymer-dissolved aggressive medium components take part in the reaction). The rate of chemical reaction u>can be expressed via the number of desintegrated bonds n at time t in the volume V: w = dn/Vdt. The degradation process goes on only at the surface of polymeric article (the rate of chemical reaction greatly exceeding that of the aggressive media diffusion into the polymeric article), and the reaction rate is proportional to the surface S. For disintegration going on in the polymer volume, the dependance is expected to be more complicated. If the mass action law is realized [5], the polymer volume does not effectively change during the degradation process, and the polymer is isotropic (according to its properties) [6], then the rate of chemically unstable bonds disintegration may be written as (l.i) where is the starting concentration in the polymer, Cn is the disintegrated bonds concentration, Ccat is the catalyst concentration in the polymer, C7Wis the solvent (reagent) concentration, and k n is the rate constant of the chemically unstable bonds disintegration. The catalyst concentration can be found from ( 1. 2)

where V is the Laplace operator, C, is the concentration of polymer functional groups, able to run the reaction of complexation or substitution, is the rate of the complexation or substitution of the catalyst by the polymer functional groups, and Dcat is the catalyst diffusional coefficient within the polymer.

Kinetic aspects o f polymer interaction

3

The last term in Eq. (1.2) takes into account the possibility of reactions with the catalyst — protonation, interaction with hydroxyl ions, etc. Some solvent (reagent) may be expended during the disintegration of chemically unstable bonds in the polymer, for example water expense in hydrolysis reactions. The concentration of the solvent is given by ^

= DwV C l - kn{C°n - CnJCctCW

(1.3)

It is possible to use this equation if some assumptions are valid. (1) The polymer-aggressive medium system is, as a rule, greatly diluted in comparison with the aggressive medium. Thus the diffusion coefficientsof thecatalyst Dcat and the solvent Dw can be assumed not to depend on the concentration of the proper polymer components. If the aggressive medium is dissolved in the polymer in sufficient degree, than it is necessary to use the equation, taking into account the connection of the diffusion coefficient with the diffusant concentration. (2) The rate constant value must be invariable. The dissolvation degree of aggressive media in the polymer being low, this suggestion is true. In general the influence of aggressive media upon the rate constant value can be reduced in the first approximation to the influence of the solvent on the chemical reaction rate, which is predicted on the basis of existing theories [7]. (3) The reaction of chemically unstable bonds disintegration should be irreversible. This condition is fulfilled if the degradation proceeds to a small degree of transformation in a certain reaction zone. For hydrolysis, the transformation degree must be less than 0.05. In this case the concentration of chemically unstable bonds is changing insignificantly and it is possible to consider C„ — Cn « C„. The combined solving of Eqs (1.1)—(1.3) will permit the determination of the rate of chemically unstable bonds disintegration under the aggressive media action in the polymer. Having determined the rate, it may be linked with the changes of certain parameters of the polymeric article of interest to us, for example with time variation of mechanical properties. Most medical polymeric articles could be approximated by simple geometric figures: parallelepiped being the model for polymeric layers and covers; cylinder for thread, etc. In the next part we will show the solutions of Eqs (1.1)— (1.3) for the parallelepiped and cylinder. 1.2. M A CR O K IN ETIC CORRELATIONS O F T H E C H EM ICA L DEGRADATION PROCESSES A s w e have already noted, the process o f polym eric articles’ degradation in aggressive

media could occur in different fields depending upon correlations between the rates of diffusion and chemical reaction. (1) The rate of the aggressive medium diffusion being commensurable with that of the chemical reaction, the degradation takes place in a certain reactional zone. Its size will grow with time and will reach the polymeric article’s sizes in the limit, i.e. the reaction will occur in the internal diffusion-kinetic zone [1, 7].

Chapter 1

4

(2) The rate of the aggressive medium diffusion being much greater than that of the chemical reaction, as soon as the solvent (reagent) is saturated, the degradation will take place in the whole polymer volume, i.e. the reaction occurs in the internal kinetic zone. (3) The rate of the aggressive medium diffusion being much smaller than that of the chemical reaction, the degradation will go on only in a thin reactional interface layer or, in the limit, only on the polymeric article’s surface, i.e. in the external diffusion-kinetic zone. Let us consider the three cases of the degradation process [8, 9]. 1.2.1. Internal diffusion-kinetic zone Even taking into account certain assumptions and simplifications mentioned above, the joint solving of Eqs (1.1)— (1.3) seems a rather difficult mathematical problem. The practical consideration of aggressive media diffusion into polymers helped to ascertain that the catalyst and solvent diffusion could occur with equal rates and a common front, or the solvent diffusion could have a much greater rate than that of the catalyst. The case when the catalyst diffused quicker than the dissolvent in practice seems unrealizable [10]. The first case (equal rates) occurs, as a rule, when the aggressive media diffuse in hydrophylic polymers, and with the diffusion of, for example, acids and bases with high vapour pressure in hydrophobic polymers [1]. The second case (solvent moves quicker than catalyst) takes place when acids and bases with low vapour pressure diffuse in hydrophobic polymers. Taking into account these correlations simplifies the solution of the problem as a whole. In the first case the catalyst and solvent diffusion could be characterized by one and the same coefficient = A v In the second case Dw > Dcat and it can, after a certain time interval, be considered that the solvent concentration in the reaction zone of the polymeric article become constant and equal to its dissolvation C®, i.e. ^

=0

for

Cw = C°

In this case the problem is simplified and can be reduced to the solution of Eqs (1.1) and (1.2). Taking into account — C « Cj), Eq. (1.1) becomes ^

= fceffCca.

(1-4)

where fceff = knC„C®. In Eq. (1.2), we restrict to a single item for simplification and assume C = C{. Depending whether the catalyst links to the polymer functional groups, it is possible to derive two equations describing changes in the number of macromolecule ruptures during the degradation. Case 1. Functional groups available in the polymer and those generated during the degradation process react with catalyst irreversibly, i.e. the equilibrium constant of this process kp —►oo. Such reactions (complex formation, donor-acceptor interaction,

5

Kinetic aspects o f polymer interaction

formation of hydrogen bonds, protonizing, etc.), as a rule occur much faster than the degradation. In this case, Eq. (1.2) transforms to

^

= .DcatV^ca, - ¿effCca,

(1.5)

The solution of Eq. (1.5) was for the first time given in [11], on the basis of the analogous problem of heat conductivity [12] for a parallelepiped. One of the dimensions of that parallelepiped / is much smaller than the two others under the limit conditions Ccîit = ¿cLt> x ^ Ô and x ^ l for t —►0, and starting condition Coat = 0 for t = 0 and 0 ^ x ^ /. In this case, the expression for the catalyst concentration becomes 1

Coat = C2

4 ^ sin bmx “ *m \ =U (2m + l)(&m£>cat + 1)

( 1. 6)

[fceff + -Dcat&m e x p ( - 6 ^ D c a t -

fceff)
A;eff, it is possible to truncate to the first term of a row. The detailed consideration of this case will be given below. The solution of Eq. (1.5) for a cylinder with the radius r, much smaller than the length /, under the limit condition Ccat = C when x = r for t > 0, and under the starting condition Coat = 0 for t = 0 and x < r, is rather complicated Coat = C\

2~—2 exp ^(DcatH2r 2 - fceff)*]Io(xr fceff + Dcat^r

2„ r

(Dcat/i2r - 2 + fcefr)/l(/L£Xr“ 1)

n=l

( 1. 8)

where Jo and Ji are Bessel functions of the first sort of zero and first degree one, respectively, and p represents routes of Bessel functions. Expression for Cn could be derived from Eqs (1.4) and (1.8) after integration from 0 to t and from 0 to r Cn = keSC ^t J 2

■Dcat f _ 1 - exp(zi) i

(1.9)

where z = D ^ / r 2 + For the starting period of degradation, if exp(—zt) > 0.9, it is possible to use for calculations an approximate equation Cn « fceffC«,

8

D ll??12

3 ^ 1/2

r

Dca\t2 2r2

2Dlit

(Pc*

157r!/2r V r2

( 1. 10)

Chapter 1

6

If exp(- z t) < 0.1, Eq. (1.9) transforms to ( l.n ) n=l

If Z)cat^2/ r 2 > then, as in the case considered before, it is possible to truncate to the first term of the row, thus simplifying Eqs (1.9) and (1.11). Case 2. Functional groups in polymers do not react with catalysts in large degree, i.e. the equilibrium constant of this process keq —> 0. In this case, Eq. (1.2) transforms to Fick’s diffusional equation, the solution of which for a layer (parallelepiped) and a thread (cylinder) is shown in a number of monographs devoted to the general questions of diffusion. Having introduced the solution of the Fick’s equation for parallelepipeds into Eq. (1.4) and integrating using the same limits as for Eq. (1.9), we obtain [2, 3] [i - exp(2m + 1fy ]

tf {1 - J ? ë

(1.12)

where y = 7r2Dc^it/l2. For y < 1 this case shows the starting period of degradation for layers of any thickness c„ = where V’(y) = ë

m=0

(1-13)

7T

exp [ —y(2m + l)2 —1 + y(2m + 1)] y (2m + l)4

By computer calculations [1], a simple expression was found x^(y) = 0.589y1/2, i.e. Cn =

(1.14)

This equation may be transformed to n = ^ j ï keSC°calD l£ s t 3/2

(1.15)

It can be seen that from Eq. (1.15), in the starting period of degradation the number of disintegrated bonds (n) depends on the rate constant of the chemical reaction, the diffusion coefficient, the catalyst solubility (S), the polymeric article surface (layer) state and the time*. For cylindrical polymeric articles, after a number of analogous operations, we obtain c„ =

|

- g - [! - exp ( -

}

(1.16)

*In practice: is most important to characterize exactly the starting period of polymer degradation, because of great deterioration of mechanical and other properties of a polymer even at a small degree of transformation.

7

Kinetic aspects o f polymer interaction

In many practical cases for solving this equation it is possible to truncate to the first term of the row. For the starting period of degradation process, when exp(—Dc^xp^t/r2) < 0.1, it is possible to use the simplified equation C n « * e ffC £ ,

'

n 1/2

8

-

37r1/2

2

•Pcat^ 2r2

157T1/ 2

n 3/2 2_cat_^5/2 r3

(1.17)

If exp(-jDcat/i2V r2) ^ 0.9, it is possible to derive from Eq. (1.16) a simple linear relationship 4r2 \ (1.18)

('

In this case, from a bend angle of the straight line k ^ C ^ can be found, and from the segment on the time coordinate 4r2 (1.19) at In [13] an approximated solution of Eq. (1.2) was found for chemically reversible reaction, i.e. when the equilibrium constant k eq does not tend to infinity. 7.2.2. Internal kinetic zone In this case [2, 3] the kinetic equation for a parallelepiped can be derived from Eq. (1.12), if y » 1, and for a cylinder from Eq. (1.16), if exP ( -

^ l* )

1

Note that in both cases we derive one and the same equation C n = k d tC & jt

( 1 .2 0 )

Thus, the concentration of disintegrated bonds in the initial steps of transformation is proportional to the catalyst concentration provided the polymeric article is saturated by the aggressive medium. 7.2.3. External diffusion-kinetic zone In this case the process of degradation takes place in a rather thin reactional interface layer, sizes of which can hardly be defined as the values of ke& and Dcat are unknown. As a rule, this layer is assumed to be infinitely thin, and the degradation is assumed to proceed practically on the surface of a polymeric article*. In this case the degradation process rate may be described by dn

— &surf

n(surf) Ccat(surf) ^w(surf) S

( 1. 21)

*As a rule, the reaction is considered [14], to proceed in the first molecular layer or to touch several layers of macromolecules.

8

Chapter 1

Here the index surf shows that the concentration refers to the polymeric-aggressive medium interface. To solve the equation, the polymer is assumed to be oriented with the macromolecules arranged in parallel to the interface (to the film surface for the film; to the lateral surface of the cylinder for the thread). Concentration of active centres on the surface Cn{surf) in this case depends on the type of macromolecule disintegration, their packing, cohesion energy and solubility of the disintegration products (fragments of molecules — oligomers and monomers) in the surrounding aggressive medium. In this case, on the surface of the polymeric article the stationary concentration of active centres C ^sur^ 2r_1 is established in the initial moments of the process (z is a constant depending on the above mentioned factors). In particular, if macromolecular disintegration proceeds as depolymerization (separation of end groups) and generated monomers dissolve immediately in the surrounding aggressive medium, then r

_ 2Cn(suri)

where P nQ is a mean polymerization degree. In this case fcSUIf is the rate constant of polymerization. But if the macromolecular disintegration proceeds by a chance law followed by fast one-act depolymerization (as is often observed for polymers [1]), and degradation products dissolve easily, then C„(SUrf) ~ ^n(surf) anc*&surf is the rate constant of disintegration by a chance law. It is important to know the characteristics of linear sizes and mass changes of the polymeric articles of various geometric forms with time. It is connected with the fact that, in the case of polymer biodegradation, the disintegration of such type will prevail, especially when the process is catalyzed by enzymes which are too large to penetrate inside the polymeric matrix and, as a rule, catalyze the degradation process from the surface to the polymer [15]. The transformation degree in the degradation process can be expressed via the number n of disintegrated chemically unstable bonds, in relation to the maximal possible number of breaks n n rioo

( 1. 22)

The value of n ^ can be defined from n0o

m oA

(1.23)

M

where M is the monomeric chain molecular mass. For rather large P n in Eq. (1.23), it is possible to truncate to the first multiplicant. The degradation products being soluble in the environment, a can be expressed via the polymer mass o: = 1 — —

(1.24)

da _ 1 dn _ 1 dm dt n oo dt mo dt

(1.25)

m0

In this case

Kinetic aspects o f polymer interaction

9

Introducing Eq. (1.21) into Eq. (1.25), we obtain dm _ M , ~

Ksut^

^n(surf) o r i n z *^'-'cat(surf)*-/w(surf)

(1.26)

For a film of thickness l we obtain m = ISg. The sample thickness changes accordingly to l —Iq

&surf ~~7~ ^n(surf) A

*^^cat(surf)^w(surf)^

ZQ

(1.27)

The time of the whole disintegration of the polymer r is given by r

_____________ loQ_____________

&surf “f ^n(surf) z ^cat(surf) ^w(surf)

(1.28)

where g is the polymeric density. If the process proceeds in the external diffusion-kinetic zone, the surface size of the polymeric article remains practically constant up to large degrees of transformation. Then from Eq. (1.28) we can easily obtain M „„

m —mo —&surf ~~T ^n(surf)

1

^^cat(surf)Cw(surf)^

(1.29)

Eqs (1.27) and (1.28) can be expressed in zero dimension parameters m m0 f

w + ipp + X¥>p = 0 where X

XH

_ F W( 6 l - 6 j ) r t

(2.6)

Here x is the non-dimensional Flory-Huggins parameter (its enthalpic part), and ipi, 6{ are the volume fraction and solubility parameters of water (w) and polymer (p) in the system. From Eq. (2.5), it is seen that the (In + ^ p) dependence on the square of the solubility parameters difference multiplied by p is linear. However, the analysis of solubility of 32 polym ers of different hydrophilicity (see Table 2.1) show s that the dependence is non-linear and may be approximated by two branches in accordance with the value of the product (SJ - S*)tp* < 600 J cm“ 3 for one type of hydrophilic polymers and > 800 Jem -3 for hydrophobic ones [15]. The values corresponding to the point of intersection of the branches characterize moderately hydrophobic polymers (Fig. 2.1). The transition from hydrophobic polymers to hydrophilic ones reflects the appearance of the entropy non-combinatorial term of the

24

Chapter 2

Table 2.1.

Water solubility in polymers and calculated value of solubility parameter at 25 °C [15] Polymer

Hydroxyethylmetacrylate

Water solubility,

h ,

g per 100 g

J0-5 c m - 1-5

52

27.3

Polyoximethylene

2.5

20.1

PVC

0.9

19.7

PVA

80

33.5

Bisphenol A

0.36

19.5

Hydrine 100

6.0

19.86

PVAcet.

3.0

20.23

PMMA

7.5

18.7

Polyethylmetacrylate

1.5

18.3

TAC

8.0

20.47

PAN

10.0

27.2

PETF

2.0

21.23

Polymethylacrylate

2.5

20.23

Poly(propylene oxide)

3.1

18.6

Cellulose

60

33.44

Copolymer PVA-PE (0.7:0.3)

15

29.1

PE Cellulose acetate

0.09

15.95

22.0

27.17

Cellulose acetate (43.8% acetate groups)

7.4

25.27

Ethylcellulose (48.7% ethyl groups)

7.5

23.55

PS

0.09

18.4

Nylon-6

16.5

27.98

Nylon-610

5.8

25.73

Nylon-12

2.0

23.13

Nylon-13

1.5

22.7

PU-10

5.0

20.34 20.95

N , N '-D iiso h ex a m eth y len eseb a cy n a m id e

3.8

A^-Isobutylhexamethylenesebacylamide

6.4

21.95

iV-Methylated PA-10.10 (55% methylated groups)

3.1

21.86

Phenylone S-4

15.1

30.8

Notech

17.0

30.8

6.0

22.65

Vitur T0533

Water diffusion in polym er systems o f different hydrophilicity

25

(£p -