Oxydative Ageing of Polymers E-Book

Jacques Verdu

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 529

Veröffentlichungsjahr: 2012

Beschreibung

This book aims to rehabilitate kinetic modeling in the domain of polymer ageing, where it has been almost abandoned by the research community. Kinetic modeling is a key step for lifetime prediction, a crucial problem in many industrial domains in which needs cannot be satisfied by the common empirical methods. The book proposes a renewed approach of lifetime prediction in polymer oxidative ageing. This approach is based on kinetic models built from relatively simple mechanistic schemes but integrating physical processes (oxygen diffusion and stabilizer transport), and use property (for instance mechanical failure) changes. An important chapter is dedicated to radiation-induced oxidation and its most important applications: radiochemical ageing at low dose rates and photo-chemical ageing under solar radiation. There is also a chapter devoted to the problem of ageing under coupled oxidation and mechanical loading.

Leseprobe

Table of Contents

Acknowledgements

General Introduction

Chapter 1. Methodological Aspects

1.1. Definitions

1.2. Empirical and semi-empirical models

1.3. Towards a non-empirical method of lifetime prediction

1.4. Arguments against kinetic modeling

1.5. Principles of model elaboration

Chapter 2. Aspects Common to all Oxidation Processes

2.1. Oxidation: a radical chain mechanism

2.2. Propagation

2.3. Termination

2.4. Initiation

2.5. Thermodynamic aspects

Chapter 3. Basic Kinetic Schemes

3.1. Simplifying hypotheses

3.2. The ASEC scheme

3.3. The ASCTL scheme

3.4. The BESC scheme

3.5. The BASC scheme

3.6. Other schemes

3.7. General problems of kinetic analysis of polymer oxidation. The outlines of a new approach

Chapter 4. Oxidation and Oxygen Diffusion

4.1. Properties of oxygen transport in polymers

4.2. The reaction/diffusion equation

Chapter 5. Stabilization

5.1. Principles of stabilization

5.2. Action on hydroperoxide decomposition

5.3. Stabilization by capture of P° radicals

5.4. Stabilization by capture of POO° radicals

5.5. Synergistic mixtures HD + CBA

5.6. Polyfunctional stabilizers

5.7. Hindered amines

5.8. Other stabilizing mechanisms

5.9. Physical aspects of stabilization by additives

Chapter 6. Molecular Mobility and Reactivity

6.1. The issue

6.2. The chemical way

6.3. The physical way

6.4. Control by diffusion of macromolecular reactive species and heterogeneity

6.5. The paradox of thermostability in glassy polymers

Chapter 7. Structural Changes Caused by Oxidation

7.1. On the molecular scale

7.2. On the macromolecular scale

7.3. On the morphological scale

Chapter 8. Effects of Oxidation on Physical and Mechanical Properties

8.1. Introduction

8.2. Weight changes

8.3. Changes in density and volume

8.4. Optical properties

8.5. Electrical properties

8.6. Glass transition and melting

8.7. Mechanical properties at low strains

8.8. Fracture properties in the case of homogeneous degradation

8.9. Fracture properties in the case of homogeneous crosslinking

Chapter 9. Couplings

9.1. Introduction

9.2. “Spontaneous” cracking

9.3. Coupling between cracking and oxidation

9.4. Lifetime under static strain and oxidation

9.5. Physical ageing and oxidation

9.6. Oxidation during processing — degradation and recycling

Chapter 10. Oxidation Under Irradiation

10.1. Definitions. General aspects

10.2. Radiochemical initiation

10.3. A perculiarity of radiochemical ageing

10.4. Photochemical initiation

10.5. Photostabilization

10.6. Ageing under natural sunlight

Bibliography

Appendix

Index

First published 2012 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Jacques Verdu to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Verdu, Jacques.

Oxydative ageing of polymers / Jacques Verdu.

p. cm.

Summary: “This book aims to rehabilitate kinetic modeling in the domain of polymer ageing, where it has been almost abandoned by the research community. Kinetic modeling is a key step for lifetime prediction, a crucial problem in many industrial domains in which needs cannot be satisfied by the common empirical methods. This book proposes a renewed approach of lifetime prediction in polymer oxidative ageing. This approach is based on kinetic models built from relatively simple mechanistic schemes but integrating physical processes (oxygen diffusion and stabilizer transport), and use property (for instance mechanical failure) changes. An important chapter is dedicated to radiation-induced oxidation and its most important applications: radiochemical ageing at low dose rates and photo-chemical ageing under solar radiation. There is also a chapter devoted to the problem of ageing under coupled oxidation and mechanical loading”-- Provided by publisher.

Includes bibliographical references and index.

ISBN 978-1-84821-336-4 (hardback)

1. Polymers--Deterioration--Mathematical models. 2. Oxidation. I. Title.

QD381.9.M3V47 2012

547′.7--dc23

2011052450

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-336-4

Acknowledgements

I have dedicated a considerable portion of my professional life to studying the ageing of polymers. This “quest” has afforded me the opportunity to collaborate on this topic with a great many people (teaching researchers, postdoctoral students, thesis candidates, engineering students, etc.) — it would be a near-impossible task to give an exhaustive list of these people here, but they figure in the list of bibliographical references. I would like to express my gratitude to them.

The team’s academic production has taken off over the last ten years, thanks to three young researchers: Xavier Colin, Bruno Fayolle and Emmanuel Richaud, whose skill and dynamism, now internationally recognized, will help to ensure continuing progress in this field of research. I am extremely grateful to them, and wish them a brilliant career.

Ludmila Audouin has been a valuable part of the team, through the trials and tribulations, for over 30 years. She played a crucial role, offering her pragmatism, her extensive knowledge of analytical chemistry, her experimental ability and her capacity to moderate my sometimes over-zealous enthusiasm. I wish to express my deep gratitude to her; long may our fruitful friendship last.

By way of their painstaking proofreading, Ludmila Audouin, Pierre Gilormini and Serge Verdu have helped eliminate many errors which were due to my inattention from this book. Heartfelt thanks go to all three.

General Introduction

Why oxidation?

The yellowing of a polyester-fiberglass hull, the crumbling of paint, the development of a purple coloration at the surface of a PVC extrudate for building are all manifestations of oxidative ageing of polymers. These are examples of changes in the visual aspect of the materials, which may have significant financial consequences but which do not, in themselves, pose a threat to the safe use of the system in question. The embrittlement of a carbon-polyimide part functioning at 200°C in an airplane engine, the hardening of a polybutadeine matrix rocket propeller, and the cracking of a polyethylene electrical cable sheath in a nuclear plant, are also manifestations of oxidative ageing of polymers, but here the resulting failures could have grave consequences on every level. Predicting failures is the main objective of ageing studies. What fails is a system, a structure (in the broader sense). In certain cases, this failure is related to an unforeseen change in the operating conditions (an accident, a fire, etc.). In others, it is related to an inadequate knowledge of the system’s capacity to withstand the mechanical loads to which it is subjected (creep, fatigue, etc.). These failures may also result from two incompatible materials being brought into contact, or one material coming into contact with incompatible fluids. Here, we look only at the case of a system failure resulting from the change in the properties of one of its constituent materials, and that change resulting from that material interacting with oxygen. We shall focus on deterministic approaches to the problem, i.e. cases where the system failure can be associated more-or-less accurately with a critical structural state of the material, or at the very least with a critical value of a property of the material. Why limit ourselves to the study of oxidation? For the simple reason that if we lived in a neutral atmosphere, 99% of thermal or photochemical ageing problems would disappear, with the lifespan of polymers being many times higher than it is in the presence of oxygen. However, in many cases oxidation takes place alongside other types of ageing, and there may be significant interplay between these different phenomena. For example, the performances of an antioxidant depend as much on its resistance to migration as on its chemical reactivity; it is therefore impossible to ignore the phenomena of transport of stabilizers (and of all reactive substances including, of course, oxygen), even if these phenomena exist independently of oxygen.

A brief history

As a scientific discipline, the oxidative ageing of polymers has been studied since the mid-19th Century, i.e. a little after the invention of vulcanization of rubber (Goodyear 1839). It immediately became apparent that natural rubber quickly lost its mechanical properties because of oxidation, and that discovering ways to stabilize it was a crucially important objective for research. The first patent on an antioxidant dates from the 1860s. During the earlier half of the 20th Century, the oxidation of rubber was the subject of numerous works, sometimes by very renowned authors — e.g. in France: Moureu, Dufraisse, Lebras, etc. However, they lacked the essential theoretical tools to reach a sufficient level of understanding. These tools essentially stem from macromolecular physical chemistry, established by Staudinger (Nobel Prize, 1953) between 1925-1930, and radical chain reaction kinetics, established around the same time by Semenov (Nobel Prize 1956). The modern view of oxidation kinetics developed by Semenov and his students (Emanuel, Denisov, etc.) was discovered in the western world after the Second World War by an English team from RAPRA [BOL 46a]. In normal conditions of thermo-oxidation, the kinetics are highly non-linear because the chain reaction produces its own initiator: the hydroperoxide group, the accumulation of which is responsible for the acceleration observed. Tobolsky et al. in 1950 developed an extremely pertinent model to account for this type of behavior. Unfortunately, and inexplicably, this model remained unknown to the scientific community, and apparently even to Semenov [SEM 59], for nearly half a century. Researchers came up against another hurdle: controlling the kinetics by oxygen diffusion, leading to an oxidation gradient within the thickness of the samples. Although solutions existed, they were unknown to the polymer oxidation community until the start of the 1980s. Between 1945-1980, researchers would limit themselves to studying cases where the above difficulties are avoided: constant initiation rate leading to linear kinetics, thin samples in order to minimize the gradients and oxygen excess to simplify the mechanistic schemes. Research focused, essentially, on analyzing the reaction products, determining the elementary rate constants and developing theoretical and experimental tools to look at the effects of ageing on macromolecular structure. Besides Bolland and Tobolsky, mentioned above, Mayo, Howard, Ingold, Uri, Reich, Stivala, Hawkins, Charlesby, Kamiya, Emanuel, Denisov, Kuzminskii and Shlyapnikov are among the authors most frequently cited from this period.

The earliest models of oxygen-diffusion-controlled kinetics appeared in the early 1980s in Japan [SEG 81] and Britain [CUN 82], which would later be drawn heavily upon by Gillen and Clough in the USA [GIL 85]. However, these models, based on a constant initiation rate, are not easily applicable to thermo-oxidation. 1985-2000 were essentially marked by the emergence of heterogeneous kinetic models [CEL 93a; GUG 96]. Conventional homogeneous kinetics, however, did not abandon the study of oxidative ageing. Tobolsky’s models were rediscovered (Audouin et al., [AUD 95]), then supplemented and coupled with oxygen diffusion, with a numerical resolution of the kinetic scheme (Rincon-Rubio et al. [RIN 01]). The use of the numerical tool enabled researchers to do away with almost all the simplifying hypotheses which had, up until then, greatly impaired the credibility of the models, and to reconstruct the kinetic curves, for a rigorous validation in comparison to experimental curves.

Half a century later, we can see how the discipline’s evolution is far from having been a long, calm river; we can see inexplicable delays due to missed opportunities: in the western world, Semenov’s seminal works only began being used ten years after their publication. Tobolsky’s kinetic models remained in obscurity for 45 years. The first models of oxidation-diffusion coupling appeared at the start of the 1980s, although the approach existed at least 20 years beforehand. It had been used, e.g. in the case of PET hydrolysis by Golike and Lasoski in 1961. The relative underdevelopment of the discipline is also due to the long-standing endurance of a number of collective illusions. For example: i) the idea that the ageing of polymers is a phenomenon that has its own laws to be discovered regardless of the underlying processes, the mechanisms of which are considered a black box; ii) the idea that accelerated ageing must above all be a reliable simulation of natural ageing, so that there would be a “correlation” between the two kinds of ageing; iii) the idea that ageing is too complex a phenomenon to be kinetically modeled. This view is still widely held. There will be a section of this book devoted to the issue.

Oxidation: a multi-scale, multi-disciplinary problem

The “target” of the chemical process of oxidation is the elementary structural unit, i.e. typically, the monomeric unit or a smaller group of atoms, in other words a subnanometric structural unit. We shall call this structural scale the molecular scale. The major conceptual tool here is organic chemistry, particularly radical chemistry. The experimental tools are from organic chemistry, particularly infrared (IR) spectrophotometry and nuclear magnetic resonance (NMR). Structural changes at this scale may lead to an alteration of the electrical or optical properties, but do not, at a realistic conversion ratio, affect mechanical properties. These may, however, be hugely affected by structural changes on larger scales — particularly:

– The macromolecular scale, which relates to the size of macromolecules for linear polymers and that of the network meshes for three-dimensional (3D) polymers. The conceptual tool here is macromolecular physical chemistry, and the experimental tools are specific: e.g. viscosimetry and steric exclusion chromatography (SEC) for linear polymers; measures of modulus in the rubbery state, of swelling in solvents, of glass transition temperature (Tg) for 3D polymers.

– The supramolecular (or morphological) scale, which relates to the spatial arrangement of the chains: crystallinity, in particular the sizes of the lamellae, for linear polymers; spatial fluctuations in the crosslink density for 3D polymers; size of the separate domains in the case of immiscible mixtures, etc. Here, the investigative methods are no longer specific to polymers, they are common to all materials: light, X-rays and neutrons scattering, electron microscopy, atomic force microscopy, etc.

– The macroscopic scale, which relates essentially to the skin-core structure linked to kinetic control of oxidation by oxygen diffusion. Macroscopic inhomogeneities induced by processing may also arise, related for example to the thermal gradients in the final phase of the processing operation or to fluctuations in the temperature of the machinery. There are a great many methods in cartography and imaging that have spatial resolutions from a fraction of a micron to a fraction of a millimeter, which can be used to study structure gradients in general and the concentration of oxidation products in particular.

Certain properties of very general interest, such as the fracture properties or rheological properties, do not depend strongly on the molecular structure, but are closely linked to the larger scale structure.

Ageing analysis must therefore always take account of the effects of ageing on all these scales. Since they come from different disciplines, the study of ageing is a multidisciplinary activity, which has no doubt slowed down its development. Take for example the case of polypropylene (PP) oxidation: the main problem here is deep embrittlement, which manifests itself even before the products of oxidation have reached measurable concentrations. We can of course approach the matter using empirical methods, by postulating that there is a correlation between this concentration and that mechanical value, but knowing what slight structural change is likely to embrittle the polymer, and understanding why this change (even if only in a thin superficial layer) can catastrophically alter the impact strength, should offer a clearer view of the problem. This leads us for example to introduce concepts of fracture mechanics, a discipline which was not really developed in terms of polymers until the 1980s, long after the chemical aspects of oxidation. Initially considered to be a purely chemical problem, ageing should progressively become an issue for the material sciences.

Ageing: a problem of kinetics

Ageing can be defined as a slow and irreversible evolution in the structure (in the broadest sense of the word) of a material. By a slow evolution, we understand one which cannot be appreciated on a timescale which is compatible with economical constraints. Therefore we have to turn to accelerated ageing testing and a model capable of predicting behavior in natural ageing (in the use conditions) from the results of accelerated ageing. The term “model” still sounds dreadful to a great many practitioners, but is unavoidable. Whenever we study ageing, we use a model. Let us take the most current example, which consists of comparing lifespans in order to circumvent the problem. Samples A and B have a known lifespan and C is to be studied. Suppose that C’s lifespan in accelerated ageing is between those of A and B. We conclude from this that C’s lifespan in natural ageing will also be between those of A and B. Here, the model (implicit) is as follows: accelerating ageing does not change the hierarchy of lifespans. If authors using this approach were obliged to explicitly formulate their hypotheses, they would doubtless realize how naïve they are. However, as the tradition in this field is non-communication, aberrations such as the above example endure. We therefore propose to systematically explicitize all the hypotheses made, which would undoubtedly be helpful to the users of the models, as it would offer an evaluation of the dangers inherent in using them to predict lifespan.

Content of chapters

Chapter 1 is dedicated to methodological aspects, particularly the philosophy of our approach based on kinetic modeling, with account taken of the multi-scale nature of ageing.

Chapter 2 is devoted to aspects which are common to all oxidation processes, which have been well known for nearly half a century, and have been the subject of many books (e.g. Reich and Stivala [REI 69]; Denisov and Afanas’ev [DEN 05]).

Chapter 3 describes the three basic kinetic schemes, two of which, with constant initiation rate, have been known for a long time. The third is also old (Tobolsky et al. [TOB 50]) but had been completely forgotten by the community until it was rediscovered by our team in the 1990s. The fourth corresponds to the maximum degree of complexity beyond which analytical solutions are useless. The next section describes a number of more complex cases, studied by our team, requiring a numerical resolution. In the final section, we attempt to lay the foundations for a rational approach of kinetic analysis which is certainly not ideal, academically, but which we believe offers the highest ratio of model efficiency to cost of investigation, in view of the current lack of knowledge in the field.

Chapter 4 deals with the coupling of oxidation and oxygen diffusion. Following a brief review of the oxygen transport processes in polymers, we examine the means of introducing diffusion into a kinetic model of oxidation.

Chapter 5 looks at stabilization. The aim here is not to reiterate the detailed descriptions of the mechanisms of stabilization and the exhaustive description of the different categories of stabilizers, which have already been the subject of well-known works (e.g. Zweifel [ZWE 01]). We shall focus essentially on kinetic aspects, which are often overlooked in the existing literature. A relatively large section is dedicated to the processes of stabilizer transport in polymers, the main development being that we can now incorporate these processes into kinetic models, whereas previously, migration and chemical stabilization processes were studied separately and never brought together.

Chapter 7 looks into structural changes caused by oxidation, distinguishing the molecular, macromolecular and morphological scales. The existing literature is very rich in terms of these aspects. Our focus here shall also be on the possible connections between the values which characterize the structure on these three scales and a kinetic model.

Chapter 8 examines the effects of oxidation on physical and mechanical properties. Our goal here is to establish a link — quantitative if possible — between the chemistry of oxidative ageing and material science, to achieve a rational use of the properties in the study of ageing, but above all to approach lifetime prediction with end-of-life criteria which are pertinent from the user’s point of view.

Chapter 9 focuses on couplings, and attempts to partially answer the following questions: oxidation generates a state of stress in thick samples. What is the mechanism for this? What are the consequences? When a crack develops, what is the effect of oxidation on its propagation rate? Can a state of stress influence the kinetics of oxidation? Can oxidation influence the kinetics of fracture of a sample under stress? The fourth section is dedicated to the study of the combination of oxidation and physical ageing by structural relaxation. It seemed important to include a passage in this book about oxidation in processing conditions and its potential impact on recycling. This is the subject of the final section, although here, it must be recognized that the “coupling” aspect is not crucial.

Chapter 10 is a brief overview of oxidation problems caused by irradiation, whether for photochemical or radiochemical processes. Each of these processes merits an entire book in itself, but our approach, as in the previous chapters, is to focus on kinetic aspects. The reader is referred to the abundant literature on the subjects for detailed information about such-and-such a case. The aim here is only to show the extent of the possibilities of kinetic modeling in these areas, particularly photochemistry, where it has been almost completely overlooked. “Natural” ageing, which is very important on the practical level, is the subject of the final section. We do not claim to provide the definitive solution to this complex problem, but rather to indicate the promising paths and those to be avoided.

Chapter 1

Methodological Aspects

1.1. Definitions

Physical ageing: ageing that does not involve a change in chemical structure — for example ageing by structural relaxation in a glassy state, ageing resulting from the migration of plasticizers or the absorption of solvents, etc.

Chemical ageing: ageing involving a change in the chemical structure of the macromolecules. Oxidation is a type of chemical ageing, which may coexist with other types — physical or chemical.

Natural ageing: ageing in operating conditions.

Accelerated ageing: ageing carried out in such conditions as to make the change of the properties faster than in natural ageing so that definitive information can be obtained within acceptable timescales.

Lifetime: the material belongs to a structure, a system. Ideally, the lifetime is that of the system; it can be defined as that age of the system beyond which the probability of failure exceeds a threshold, conventionally defined, based on technological or economical criteria specific to the application. When the change in the probability of failure is linked to the change in a material which is part of the system, and we can establish a link between that probability and a value of a property of that material, it is possible to define an end-of-life criterion for that property and label the age of the material at which that criterion has reached its “lifetime”. It is important to note that the lifetime is a characteristic which is specific to a property, an environment and an application, not an inherent characteristic of the material.

Embrittlement: change expressed as an increase in the probability of fracturing under a given mechanical load. Embrittlement is a particularly important phenomenon for the following reasons: whatever the functions of the material, it is usually not acceptable for it to lose its geometric integrity by cracking or fracture. Moreover, it is very commonplace for its fracture properties to evolve more quickly than other properties. Finally, embrittlement is often a catastrophic phenomenon in the case of plastics — i.e. the behavior changes suddenly from a ductile-tough regime to a brittle regime, with the characteristic values changing sometimes by more than an entire order of magnitude. This sudden change corresponds to a sharp increase in the probability of failure in a great many applications, which reaffirms the interest of this type of criterion.

Deterministic approach, probabilistic approach: this book is dedicated to a deterministic approach to lifetime prediction. This involves establishing a kinetic model of ageing, constructed based on a hypothesis of mechanism, expressing the evolution of a given property depending on the relevant environmental parameters (temperature, light intensity, pressure of oxygen, etc.). However, these parameters, which may be set and controlled during accelerated ageing tests, vary over time and according to the site of exposure in the case of natural ageing, without these variations necessarily being known to the user. In these circumstances, the deterministic model may gain by being associated with a probabilistic model. On the other hand, to our knowledge there is no probabilistic approach which, on its own, could yield a reliable prediction of lifetime using the results of accelerated ageing testing.

Durability: this term may have two different meanings. Firstly, it may be taken as a synonym of longevity, i.e. likelihood to endure. It is also used to denote the discipline of the study of ageing in the broader sense.

Stabilization: change (usually minor) in structure (internal stabilization) or composition (external stabilization by incorporation of additives or fillers) leading to an increased lifetime.

Synergy, antagonism: these terms will only be used if they have a quantitative counterpart. If a cause C1 has an effect E1 and a cause C2 has an effect E2 in similar conditions, e.g. if C1 and C2 are different stabilizers (with equal mass fractions), E1 and E2 being the corresponding lifetimes, and if the mix (with the same mass fraction) has effect E, we would say that there is synergy if and there is antagonism if . For instance, it makes no sense to speak of temperature/radiation synergy because the two factors can neither be separated nor combined. It makes no sense to carry out an irradiation test without temperature. Note in passing the particular status of the temperature parameter. It is not, as is frequently stated, a cause of ageing. The cause is always the instability of the material; the temperature is merely (one of) the parameter(s) that influences the kinetics. The concept of synergy/antagonism only makes sense if it is quantifiable, which is only possible if the two causes can be represented by extensive values, in the same system of units.

Induction period: in many instances of oxidation, the kinetic curves reveal strongly non-linear behavior. The oxidation rate is so slow in the initial period of exposure that no change is detectable, possibly for a very long time. After a certain amount of time, however, the reaction speeds up and its effects become measurable. This period is called the induction time/period. The existence of a phenomenon of induction may have a number of causes:

– the measured value only changes beyond a certain conversion ratio of the reaction. As we shall see, this is often the case with fracture properties;

– the material contains a stabilizer which is consumed by the reaction, but which protects the polymer as long as its concentration remains above a certain threshold. If an induction phenomenon exists for the non-stabilized polymer, the presence of a stabilizer will result in a longer induction period.

These three causes may be combined.

Kinetic model: a mathematical tool which ranges from a simple proportionality relation to a set of over 20 coupled non-linear differential equations, the aim of which is to describe the evolution over time of one or more properties of the material for given values of the influencing environmental parameters, which must vary over a fairly wide range to cover accelerated ageing and natural ageing. Beyond a certain degree of complexity, often exceeded in the context of oxidative ageing of polymers, the usual parlance is incapable of describing the interactions at stake and the multiple relations of cause-to-effect in play. Thus, a mathematical model is an irreplaceable tool, both for interpreting behaviors and for discussing the mechanisms. A model does not claim to be an exact representation of reality; it tries to get as close as possible to it, but its main purpose is to serve as the basis for discussion and a starting point for creating a better model, which, in time, will replace it. In that respect, an “open” model, i.e. extendable and modifiable depending on the hypotheses made, is preferable to a “closed”, unchangeable model.

1.2. Empirical and semi-empirical models

1.2.1. The Arrhenius model

Since the 19th Century, we have had Arrhenius’ law at our disposal, which expresses the rate v of an elementary process as a function of the temperature:

where v0 (pre-exponential coefficient) and H (activation energy) are characteristic of the process. In the 1940s, the idea emerged that this law could be extended to complex processes such as ageing, in which numerous elementary processes are at work [DAK 48]. One of the hypotheses upon which this idea is founded is that, generally, the overall kinetics will be governed by an elementary process which “dictates” the rate of change. If the rate obeys Arrhenius’ law, then the lifetime tf must also obey this law:

NOTE.– The reasoning which leads us to reject the Arrhenian model remains valid for any law of time-temperature superimposition, e.g. the WLF law, or the unformulated law represented by a master curve.

1.2.2. The isodose model

Let us consider the case of ageing by irradiation (photo or radiochemical). It may be remarked that the literature on radiochemical ageing often gives tables of lethal doses, which only makes sense if we assume that the kinetics are independent of, or only slightly dependent on, the dose rate — in other words, that the end of life is an isodosic characteristic. As we shall see, the reality is entirely different. Certain authors have attempted to resolve the problem by seeking empirical laws, e.g. linking the lethal dose to the dose rate by power laws [WIL 87], but the limits of the validity of these laws are difficult to appreciate, and we shall see that in reality, the exponent of these laws diminishes constantly and tends towards zero as the dose rate decreases. In the case of photochemical ageing, the norms are ambiguous [VER 07], but in practice, we note that for a long time accelerated ageing systems were unable to vary the light intensity. This only makes sense if we assume, here as well, that the lifetime is an isodosic value, which again is far from true. The remark made about empirical power laws linking the lifetime or lethal dose to the dose rate, is also valid in the field of photo-oxidation.

1.2.3. The pseudo-kinetic model

The Arrhenian and isodose models ignore the path taken by the material to reach the end of its life. The overall kinetic model is based on the hypothesis that this path obeys the elementary laws of chemical kinetics, i.e. that the property P in question varies over time, according to:

where K and n are algebraic parameters.

1.2.4. The correlation method

This method is very widely used, but the principles upon which it is founded have never been explicitized, which makes it difficult to criticize. We shall therefore present our version of these principles, in the knowledge that it is not an “official” version. According to the first principle, accelerated ageing must be a good simulation of natural ageing. To our knowledge, there is no international standard which gives a quantitative criterion enabling us to appreciate the quality of a simulation. For our part, we attempted to do so [VER 07]. A good test of accelerated ageing would be one in which the various reaction products would be formed in the same proportions as in natural ageing. In other words, there would be no “deformation” of the ageing mechanisms. Kinetic analysis of the phenomenon however shows that a perfect simulation is impossible to obtain, especially because oxidation results from a branched chain mechanism controlled by oxygen diffusion. Let us suppose, however, that the approach can cope with an imperfect simulation. The second principle stipulates that there is a “correlation” between accelerated ageing and natural ageing. Here again, the definition of the term “correlation” is unsaid. In the crudest version, the definition could be as follows: there is correlation if, for a number of different materials, the hierarchy of lifetimes is the same in accelerated and natural ageing [FIS 00]. The validity of such approaches has been discussed [AMI 95; BRO 95b; SIM 87]. The idea that the correlation is valid for all polymeric materials is indefensible. However, it can be said that it is valid for a finite category of materials. That being the case, how is one to know if a new material belongs to that category? One way is if we have good evidence that it does, but that implies already having enough information about the material at our disposal to forego an experimental study. Another is to decide to include the material in the category in question based on intuition, and run a risk which is difficult to evaluate. In other words, the correlation method, while it may be well-founded, does not enable us to make predictions: at the very most it enables us to verify results we have already obtained.

1.2.5. Various mathematical “laws”

The basic idea here is that ageing obeys its own laws, which generally have the advantage of being expressed by mathematical functions in the repertoire of a decent final-year student: power laws, exponential sums, stretched exponentials, simple functions of the logarithm of time, etc. There is a wide range of functions which could lend themselves to the results of accelerated ageing, but what is the physical meaning of their parameters? How do they vary with the conditions of exposure? There is no scientific response to these questions — their use in the context of lifetime prediction is therefore problematic.

1.2.6. Conclusion

The approaches mentioned above are either totally empirical or are abusive generalizations of physical laws, which thus lose the status of laws and become empirical relations. However the latter, which may be effective in interpolation, are inappropriate for extrapolation.

1.3. Towards a non-empirical method of lifetime prediction

1.3.1. Principles

Since the key stage in the process of lifetime prediction is an extrapolation, what is the safest way to go about this? It is clearly that path which offers the most guarantees in scientific terms, and which includes the following stages:

– deconstructing the phenomenon into its constituent processes to which one must apply simple laws of dependence in conditions of exposure — e.g. Arrhenius’ law for temperature, proportionality of rate to intensity for irradiation, etc. Such a decomposition requires a mechanistic scheme. The information needed to establish such a scheme is generally abundant in the literature — sometimes too abundant, and contradictory, which means choices must be made, or else we must seek experimental data ourselves to justify the choice. To a certain extent, it is the success of the kinetic model which will validate that choice;

– determining the values of all the necessary parameters using accelerated ageing testing or taking them from the literature;

– extrapolating the values of all these parameters in the conditions of use, separately;

– “recreating” the overall phenomenon using the kinetic model and calculating the lifetime by applying a relevant end-of-life criterion. This approach must have been obvious to the pioneers of the discipline in the 1950s; however, with the exception of a few sporadic and unpursued attempts, it was not carried out in its entirety until the 2000s. It is important to note that, while this is the best available approach, it does not offer an absolute guarantee because, in the words of Sidney Benson: “A mechanism may be disproven but never proven”. In other words, the fact that a model gives a good simulation does not mean that there is not a better model out there. The only certainty is that the proposed approach is the best available in view of current knowledge.

1.3.2. The multiscale model

This is a question of predicting the evolution over time of a property which takes the value P0 before ageing and P after ageing. In the case of oxidation, we know that chemical reactions take place on a molecular scale and we have chemical kinetic tools at our disposal to describe the evolution of the structure on this scale. However, in order to predict the evolution of the property in question, we need to know the structural modifications on larger scales. These will depend on the property, but in general we cannot ignore the macroscopic scale (skin-core structure) and, in the case of mechanical properties, the macromolecular scale. The lifetime prediction approach could then be represented by the diagram in Figure 1.2.

According to this approach, in the absence of couplings, it is only on the molecular and macroscopic scales that the effect of time manifests itself. The only theoretical tools we have are those of chemical kinetics, which only describe modifications on the molecular scale, and the diffusion laws to describe the effects of the oxygen diffusion on the macroscopic scale. It is not beyond the realms of possibility, however, for certain kinetic parameters to depend on other timescales, e.g. the laws governing viscoelastic behavior in the case of oxidations under stress. In Figure 1.2, the elementary stages of the approach are represented by vectors corresponding to the following disciplines: chemical kinetics (a); relation between mechanism and scission/crosslinking statistics (b); relation between molecular mass and morphology (c); direct relation between molecular mass and properties (d); relation between morphology and properties (e); reaction-diffusion coupling (f); effect of structure gradient on the properties (g). The evolution of the property P can be predicted if each of the relations involved can be expressed in a quantitative form deduced from physical reasoning.

In the case of oxidation, the mechanistic scheme includes a certain number of elementary reactions — at least 6. While ageing leads to modifications on the macromolecular scale, it is by way of cutting and/or welding of chains. To go from the molecular scale to the macromolecular scale, we need to: i) determine the elementary reaction in which the cutting or welding takes place, ii) determine the efficiency of the process, i.e. the number of acts of cutting or welding per “elementary” reaction, iii) calculate the molecular mass or the crosslinking density, based on the number of cuts or welds and the initial characteristics of the polymer. To go from the chemical structure to the local use properties (in an elementary layer forming part of the thickness), we have recourse to the structure-property relations offered by polymer physics.

Figure 1.2.Diagrammatic representation of the lifetime prediction approach

To predict the evolution of the structure on the macroscopic scale, we must return to the molecular scale to establish an expression of the local rate of oxygen consumption. We then solve the reaction-diffusion equation, which necessitates the introduction of a new variable: the depth of the elementary layer in the thickness.

Knowing the conversion profile of oxidation in the thickness will firstly enable us to calculate the overall quantities by integration of local quantities into the thickness. It will also help to model certain behaviors, e.g. the propagation of cracks, thanks to fracture mechanics concepts.

Such a model may reach a high degree of complexity, but it offers a range of possibilities for experimental validation commensurate with its complexity.

1.3.3. A new philosophy of ageing

In the conventional approach, the first stage in the process of lifetime prediction is to seek exposure conditions which provide a good simulation of natural ageing. The natural ageing-accelerated ageing transfer function is specific to the conditions in question and does not apply to other conditions. The choice of methods for characterizing the polymer is arbitrary. In the new approach, the first stage is to construct the model. Accelerated ageing tests only serve to identify the parameters of the model — they are not supposed to simulate natural ageing, which may lead to testing configurations which are more diverse but also cheaper.

The characterization methods are chosen depending on the model: the property in question must be able to be quantitatively related to a value predicted by the model, and the advantage of using one property over another would be judged according to the number of adjustable parameters needed to link that property to the model.

While in the conventional approach, certain stages of reasoning are more or less opaque, the modeling approach is completely transparent, all its stages are testable, which is proper in a scientific approach.

While the traditional approach may content itself with a few fairly sophisticated tests (particularly in the field of photo-oxidation), the kinetic modeling method may call for a larger number of relatively simple tests. In the short term, kinetic modeling requires more effort of adaptation on the part of practitioners, and leads to a higher experimental cost. In the long term, however, it may prove to be cheaper because it produces capitalizable information, which is not so for the conventional method.

1.4. Arguments against kinetic modeling

Approaching lifetime prediction by kinetic modeling generally raises two types of criticism relating to a supposed overcomplexity of the ageing mechanism or a supposed heterogeneity, on the small scale, of the oxidation phenomenon. These criticisms give rise to the following remarks.

1.4.1. Overcomplexity

The argument is linked to the fact that the analytical methods, such as IR spectrophotometry, show the formation of a wide variety — sometimes dozens — of reaction products. The interpretation which springs to mind is that oxidation is strongly heterogeneous and that the local degree of conversion reaches such high values that a great many secondary reactions become possible. However, let us consider a part of the oxidation mechanism: for example, the decomposition of hydroperoxides.

(k1u)

(k11)

(k12)

(k13)

We can see that an act of decomposition gives rise to two P° radicals and at least three stable reaction products: an alcohol (POH), a carbonyl (P=O) (various modes of rearranging the PO°s which produce different carbonyls may coexist) and water (H2O). We can therefore take into account at least four elementary chemical acts. However, it happens that the first reaction is considerably slower than the three others, the ratio of rates being greater than 103, or 106. It is therefore licit to reduce the system to a single balance reaction:

(k13)

where g is a yield value linked to competition between the two reactions involving a PO° radical. We can see therefore that a small number of reactions may “set the pace for the overall process”. It is these reactions which will be taken into account in the kinetic model; the others will be incorporated into the balance reactions. Of course, we do not deny the existence of hypercomplex cases, particularly in co-oxidation, where the oxidations of several substrates interfere, but in many cases a simple scheme can account for a great many products without weakening the analytical rigor. On the other hand, using numerical methods means we can envisage dealing with relatively complex schemes with dozens of reactions. In conclusion, the argument of overcomplexity should not be advanced a priori — rather it is the possible failure of modeling attempts which should decide its validity. A model will be judged acceptable if it fulfills the following two conditions: i) it simulates experimental behavior, and from this point of view proves to be better than previous models, either in terms of the accuracy of its predictions or by its ability to predict a greater variety of results without major discrepancies, ii) the parameters used, particularly the rate constants, take physically realistic values.

1.4.2. Heterogeneity

Kinetic modeling requires knowledge of the concentrations of the reactive species, but experimentation only gives us access to the values of these concentrations averaged over a macroscopic volume. Modeling only makes sense if the measured values reflect real local values, which is not necessarily the case if the oxidation is heterogeneous.

We are aware, schematically, of three types of heterogeneity at three or four scales of different dimension:

a) Macroscopic heterogeneity relating to controlling the kinetics by oxygen diffusion. This heterogeneity can be modeled using diffusion-reaction coupling; it is therefore not an obstacle.

b) Morphological heterogeneity in semi-crystalline polymers. Since the crystalline phase is impermeable to oxygen, oxidation only takes place in the amorphous phase, which leads us to envisage two scales of heterogeneity: the lamellar scale (a few nm to a few dozens nm) and the spherulitic scale (a few hundreds nm to a few fractions of a mm). On the lamellar scale, certain authors have suggested that the chain folds at the surface of the lamellae could be particularly reactive because of the local tensions in the chain. The existence of these tensions was later contested. Also, if chain folds were oxidized particularly quickly, analyzing the molar mass distributions would reveal the early development of a portion with low molar mass, corresponding to chains whose length is equal to the thickness of the lamellae or has a small multiple of this thickness [FAY 02]. In reality, to our knowledge, in all cases where the molar mass distribution was analyzed, it showed that such species appear only when the amorphous phase is almost completely destroyed — that is, long after the embrittlement of the material. It seems therefore that the chain folds on the surface of the lamellae do not constitute particularly weak points. If there were no difference between the amorphous interlamellar and interspherulitic areas, kinetic modeling would pose no problem, it would suffice to express the local concentrations (c in the amorphous phase) depending on the apparent overall concentrations (C, measured):

where Xc is the ratio of crystallinity of the polymer.

Crystals here play the role of an inert filler. The problem becomes more complicated if the amorphous interspherulitic phase has a different reactivity, as certain authors envisaged, e.g. [MUC 80]. Since the interspherulitic areas are separate from the rest of the amorphous phase, we can assume that they are oxidized independently and the overall conversion ratio is the sum of the conversion ratios in the two areas, weighted by the volumic fractions of the two areas, that of the interspherulitic area in principle being far smaller than that of the interlamellar area. We can therefore imagine the following examples:

– the interspherulitic area is more stable than the interlamellar area, then the heterogeneity on the spherulitic scale has practically no effect on the overall kinetics for durations shorter than the lifetime;

– the interspherulitic area is more reactive than the interlamellar area, then we should observe the destruction of the interspherulitic “cement”, with an embrittlement relating to a decohesion mechanism (“uprooting” of the spherulites) with no noticeable change in the average molecular mass.

If the volume fraction of the interspherulitic area is great enough, the kinetic oxidation curves should include two distinct phases. These characteristics may have been observed in samples presenting extreme characteristics (large spherulites), generally undesirable from a practical point of view because the samples are highly brittle, but they have never been observed (to our knowledge) in samples representative of the industrial methods of processing. To conclude, there are certainly morphological heterogeneities, but they should pose no problem to kinetic modeling. We shall see later on how to quantify potential heterogeneities.

c) Heterogeneity on a nanometric scale, relating to the local propagation of the reactions. The basic idea is that in a “solid” polymer, the radicals have low mobility. A chain reaction would therefore propagate locally around the initiation site, leading to the formation of highly oxidized micro-volumes, growing in an unadulterated or only slightly oxidized matrix. Celina and George [CEL 93a; CEL 93b] compare this process to an epidemic propagating from infection centers and put forward a model in which the growing degraded area is made up of a “dead” volume where the polymer is completely oxidized, an active area at the boundary between the dead volume i.e. the non-oxidized matrix (like the burning area in a forest fire) and the as-yet undamaged part to the detriment of which oxidation spreads. This type of behavior can be observed in certain samples of stabilized polypropylene after the end of the induction period [RIC 70] and the “infectious” model developed by Celina et al. [CEL 93a; CEL 93b; CEL 95a] gives a good account of this as long as the origin of the time is set at the end of the induction period [FAY 02a]. However, all evidence points to the lack of any significant heterogeneity during the induction period, i.e. during the time interval when the polymer is subject to degradation, playing a major role in its embrittlement [FAY 02b]. In the (most commonplace) cases where oxidation leads to random chain scission, analyzing the evolution of the molar mass distribution should allow us to determine whether the process is heterogeneous and the degree of heterogeneity. Indeed, when the distribution is initially unimodal, it should stay that way, and the polydispersity index should tend towards 2 if the degradation is homogeneous. On the other hand, it should become bimodal with the growth of a species of small molar mass with an “infectious” propagation (Figure 1.3). In the case of oxidation of polyolefins at oxygen pressure equal to or greater than atmospheric pressure, we do indeed see a decrease in the average molar mass and in the polydispersity index, with no apparition of a bimodal distribution (e.g. [IRI 76], cited in [FAY 08b]).

Figure 1.3.Diagrammatic representation of the distribution of molar masses before and after degradation by chain breakage. Left: homogeneous degradation. Right: heterogeneous degradation. Dotted line: initial distribution; solid line: distribution after degradation

How can we explain the homogeneity of propagation in a “solid” polymer? Note the use of inverted commas. In fact, in a polymer such as polypropylene, which is generally taken as an example, the amorphous phase is rubbery, and that mobility makes it more like a liquid than a solid. If we associate heterogeneity and mobility, we must contrast the timescale of the mobility with that of the chemical processes. The slower the latter, the more likely the reactive species are to be redistributed in the whole volume of the sample to tend towards homogeneity. However, with ageing, the oxidation processes are slow — very slow. We shall return to this question later after learning about the mechanisms at work. Note also that oxidation does not only produce macroradicals, it also produces small radicals, e.g. the hydroxy radical, which have far greater diffusivity than macroradicals do and thus eventually propagate oxidation far from the initiation sites, in the same way as pine cones burning in a forest fire. Reactive species and thus initiation sites for new oxidation chains may spread over long distances into the atmosphere if the aerothermal conditions are favorable [CEL 06].

Another argument in favor of homogeneity is the relative suddenness of auto acceleration at the end of the induction period (in the case of PP). Suddenness means relative synchronism of the kinetics in all the volume elements of the sample, as shown by a numerical simulation [AUD 00], and synchronism means homogeneity.

To conclude this section, while it is undeniable that very small heterogeneities exist, which may therefore evade characterization methods such as the molar mass distribution measurements, the heterogeneous process would coexist with a homogeneous process, responsible for the changes observed in the molar mass and, as we shall see later, for embrittlement.

1.4.3. Conclusion

The above points could be discussed in greater depth, we will come back to them later. We can however conclude from the above that nothing stands in the way, a priori, of the use of kinetic models based on concepts of conventional chemical kinetics, the first validity condition of which is for the notion of concentration to make sense. In any case, the most pragmatic approach here is to judge the model on its predictive qualities. If by chance two different models prove comparable, only then can the arguments a priori be decisive.

1.5. Principles of model elaboration

Non-empirical – the kinetic scheme must be derived from a mechanistic scheme, all stages of which must be testable.

Hypotheses – all the hypotheses, even the most obvious, must be explicitized. The number of hypotheses should be kept to a minimum.

Simplicity – as certain parameters are likely to be determined by inverse method, the model should be as simple as possible. Complications must not be introduced unless absolutely necessary.

Physical validity – the values of the parameters must be physically reasonable.

Capitalizable – the choice of values and kinetic parameters should favor the capitalization of knowledge. The closer the model is to the fundamental mechanisms, the more applicable it will be, with a minimum of modifications, to a wide variety of cases.

Consistency – contradictions between the model’s predictions and experimental results are unacceptable. If they exist, either the model or the experiments must be re-examined. A good model should simulate: the kinetic curves on thin samples; the profiles of oxidation in the thickness of thick samples, or at the very least the effect of the thickness on the overall kinetics if profiles are not available, and the effect of oxygen pressure on the kinetics.

Chapter 2

Aspects Common to all Oxidation Processes

2.1. Oxidation: a radical chain mechanism

2.1.1. Radical nature [PRY 69; WAL 57]

Dioxygen, which we shall call oxygen hereafter, has the particularity of being, in its ground state, a biradical:

This particularity lends it a high reactivity with most free radicals, to which it adds:

Oxygen is also capable of abstracting hydrogen from molecules containing them:

This reaction, which is important in the gaseous phase at high temperatures, is generally negligible at the normal temperatures for use of polymers [RIC 08] except at high oxygen pressure, for molecules containing labile hydrogen atoms (antioxidants, [COQ 08]).

There is also an excited form of oxygen (in singlet state), which is capable of reacting with unsaturated substrates, particularly in a photochemical context:

This type of reaction aroused a great deal of interest in the 1960s-70s (e.g. [KAP 70; TRO 68]), but interest seems to have fallen back again since.

Finally, we can mention the existence of very reactive species derived from oxygen, but either in low concentration in our environment (ozone) or present only in the vicinity of intense energy sources (electrical arcs, electrical coronas, sources of short-wave ultra-violet, etc.) or in the stratosphere (atomic oxygen).

At low temperatures, ozone selectively attacks double bonds by an ionic mechanism (see e.g. [DEV70a; DEV 70b; LEW 86; POP 83; RAZ 71]). However, the reaction products are unstable, and lead to chain cleavage and rapid cracking, even in low load conditions. Also, they are likely to initiate radical processes [CAT 92], especially above ambient temperature [DEV 70a; DEV 70b]. It may be said that atmospheric ozone has no significant effect on the ageing of saturated polymers. Atomic oxygen is extremely reactive and therefore not very selective (see e.g. [GOL 88b]). Because of its high reactivity, it is hardly penetrative at all (see Chapter 5), hence it is of interest for superficial modifications by oxidation (treatments by flaming, plasma, etc.).

2.1.2. Chain reaction [BOL 46a; BOL 46b; BOL 49; SEM 35; SEM 59]

A radical chain reaction always involves three types of reactions:

(ri)

(kp)

(kt)

where Qi, Qp and Qt are non-radical reaction products, kp and kt